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USING ANODIC ALUMINUM OXIDE AS THE TEMPLATE:

EXPERIMENTAL STUDIES OF LOW-TEMPERATURE ANODIZATION, E L E C ~ R O D E P O S ~ O N AND

BAND GAP MEASUREMENT OF CdS NANO.WIRES USING RESONANCE RAMAN S P E ~ O S C O P Y

by

Jimmy Chan

A thesis submitted in conformiity with the requirements

for the degree of Masters of Science

Graduate Department of Chemistry

University of Toronto

0 Copyright by Jimmy Chan 1997

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Nano-wire Fabrication Using Anodic Aluminum Oxide as the Template:

Experimental Studies of Low-Temperature Anodization and Electrodeposition and

Band gap Measurement of CdS using Resonance Raman Spectroscopy

Master of Science, 1997

Jimmy W. Chan

Graduate Department of Chemistry

University of Toronto

Abstract

Anodization of aluminum in methanol solutions of &SO4 at sub-zero

temperatures (0 OC to -80 O C ) has been studied for the first time. The resulting anodic

aluminum oxide (AAO) films have uniform and regular pores whose diameters are

significantly smaller than those found in AAO films anodized at room-to-zero-

temperature. The sub-zero temperature was successfully achieved using a novel

electrolytic apparatus that utilizes temperature-controlled nitrogen cooling and 1.2 M

H2S04 in 3 : 1 (by volume) mixture of methanol and water as the electrolyte. At a constant

anodization temperature of -40 "C, for example, the pores of the resulting AAO template

were as small as 3.6 nm. Nonaqueous a.c. electrodeposition was then used to fabricate

CdS nano-wires (of a mean diameter of 5 MI) by filling the pores of these AAO nano-

templates with the semiconductor. Polarized Resonance Raman spectroscopy (RRS) was

subsequently used to study these CdS nano-wire arrays.

Acknowledgments

I would like to thank my supervisor Professor Martin Moskovits for his exceptional

patience, continuous encouragement and ingenious advice during my two years of

Master's residence. My deep thanks also go to Dr. Drnitri Roukevitch, who has worked

closely with me and taught me with great passion. Finally, I would like to thank the rest

of the research group, especially Dr. Tom Haslett, for their useful advice and countless

instances o f support during the course of my study.

iii

To my Lord, my parents, and my fiends,

for their love and support

Contents

Abstract

Contents

List of Tables

List of Figures

List of Appendices

Introduction

1. Low-Temperature Anodization

1.1 Introduction

1.2 Theory

1 -3 Experimental

1.4 Results and Discussion

1.5 Conclusion

1.6 References

2. Electrodeposition

2.1 Introduction

2.2 Cadmium sulfide

2.2 1 Introduction

vii

. . . Vll l

2-22 Experimental

2.23 Results

2.3 Nickei

2.2 1 Introduction

2.22 Experimental

2.23 Results and Discussion

2 -4 References

3. Band gap Measurement Using Resonance Raman Spectroscopy

3.1 Introduction

3.2 Theory

3.3 Experimental

3.4 Results

3.5 Discussion

3.6 Conclusion

3 -7 References

4. Conclusions

5. Appendix I

6. Appendix I1

List of Tables

Table 1. Composition of electrolytes used in this project and their melting points. 8

Table 2. Anodization conditions and resulting AAO f i h parameters. 13

Table 3. Linear relationship of d, or D, vs. T, at LI, = 15 V. 22

Table 4. Activation energies and pre-exponentid factors for various electrolytes. 24

Table 5. Deposition conditions for porous anodic alllminum oxide (AAO) supports

for Raman studies.

Table 6. Results of pioneer studies of non-aqueous nickel deposition.

Table 7. Results of band gap determination of CdS nano-wires.

vii

List of Figures

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Structure of Porous Anodic Aluminum Oxide (AAO).

Schematic diagram of the kinetics of porous oxide growth

on aluminum in (a) galvanostatic and (b) potentiostatic regimes.

Experimental set-up for low-temperature anodization.

SEM micrographs of the cleaved sections of the AAO films

obtained at different anodization voltages.

SEM micrographs of the cleaved sections of the AAO films

obtained at -20 "C and 15 V d.c.

AAO film parameters as a function of anodization temperature.

Natural logarithm of current density as a function of

inverse anodization temperature.

Experimental set-up for nonaqueous electrodeposition.

An SEM micrograph of the cross-section of AAOKdS nanowire array,

with a mean pore diameter of 13 m.

SEM micrographs of nickel nano-wire arrays in anodic alumina matrix.

Figure 1 1. Experimental set-up for polarized resonance Raman spectroscopy.

Figure 12. Resonance Raman spectra of CdS nano-wires of different diameters

excited with an s-polarized 458 nm laser.

\J iii

Figure 13. Experimental and calculated band area ratio as a function of

excitation wavelength (A: ss-polarization).

Figure 14. Experimental and calculated band area ratio as a function of

excitation wavelength @: pp-polarization).

Figure 15. Excitation energy as a function of particle size.

Figure 16. Polynomial fits of experimental data (dashed curve) and

recalculated data using parameters fiom the "Band Gap Fit" program

(solid curve) for 10 nm wires and ss-polarization. 143

Figure 17. Polynomial fits of experimental data (dashed curve) and

recalculated data using parameters fkom the "Band Gap Fit" program

(solid curve) for 8 nm wires and ss-polarization.

Figure 18. Polynomial fits of experimental data (dashed curve) and

recalculated data using parameters from the "Band Gap Fit" program

(solid curve) for 5.5 nm wires and ss-polarization.

Figure 19. Polynomial fits of experimental (dashed curve) and recalculated data

(solid curve) for 10 nm wires and pp-polarization.

Figure 20. Polynomial fits of experimental (dashed curve) and recalculated data

(solid curve) for 8 nm wires and pp-polarization. 147

Figure 2 1. Polynomial fits of experimental data (dashed curve) and recalculated data

(solid curve) for 5.5 nrn wires and pp-polarization. 148

List of Appendices

Appendix I. Input and Output of the "Baud Gap Fit" program.

Appendix II. Figures of band area ratio as a function of excitation wavelength:

Polynomial fits of experimental data (dashed curve) and

recalculated data using parameters fiom the "Band Gap Fit" program

(solid curve).

Introduction

Doing great science in small dimensions is no Longer a privilege of the

microbiologists and genetic engineers. With the combined efforts of the physical

scientists and engineers, the scientific arena is no longer ULlfdar with the field of

nanotechnolgy, which has attracted many research efforts around the world since 1974,

when Esaki and changl reported resonant tunneling across potential barriers in

nanostructures grown by molecular beam epitaxy W E ) , and ~ i n ~ l e ~ reported optical

verification of quantum confinement in semiconductor quantum well. Inspired by these

pioneer discoveries, nanotechnologists began to focus themselves on both demonstrating

quantum size effects of the nanostructures made through various methods and nano-

engineering of materials and devices. There are two approaches in nanomaterial

fabri~ation.~ The "top-down" approach utilizes lithographic technologies with resolution

limits of approximately 80-100 nm. An alternative "bottom-up" approach creates nano-

structure fi-om atoms ("the bottom") making use of their self-organization phenomena.

The essence of this kind of chemical synthesis of materials with nano-dimensional .

structure narrows down to being able to restrict the growth of the new phase to required

geometry and size. This problem, in turn, can be approached fiom two directions. One is

to control non-confined nucleation and growth, as in the case of arrested growth by

surface inhibition4 or in carefully controlled electrochemical nucleation.' The other is to

restrict growth spatially inside the cavities of the inert matrix. Non-lithographic

electrochemical deposition into the uniform pores of the anodic aluminum oxide (AAO)~

or nuclear-track membrane filters7 has been shown to be inexpensive and straightforward

method of producing nanostructures.

Anodic aluminum oxide (AAO) is known to have relatively uniform parallel pores

when produced acidic electrolytes.* A self-organized h e shucture with a nanohole

array, porous AAO has been used as a host material for many applications. For instance,

AAO films provides convenient planar packaging media with excellent isolating and

optical properties.g When loaded electrochemically with metal particles, these films have

been used as corrosion resistant and decorative coatings.' In addition, magnetic materials

based on the highly anisotropic coercivity of ferromagnetic metal wires deposited in

A40 were fabricated since mid-seventies.1° Nevertheless, a full recognition of the

potential of AAO a template for nano-fabrication only developed in the last few years.

While other porous materials such as polymer nuclear track membranes" and zeolites'

are also actively used for nano-ternplating, AAO templates, with their natural highly

uniform parallel pores, offer unique opportunities for the nanostructure fabrication.

Figure 1 depicts the structure of anodic aluminum oxide (AAO). The pores of

AAO are uniform, parallel, and open only at the oxide-electrolyte (OR) interface. The

barrier layer (BL) is a dense scallop-shaped insulating oxide layer that exists at the pore

base and separates the porous oxide from the substrate aluminum metal. The distance

between the pores (which is equivalent to the cell diameter D,) is approximately twice the

barrier layer thickness (&), which in turn is proportional to the forming voltage (U,) at a

ratio of approximately 1.0 nmN:

porous a lumi te l a y e r

pme ta l - aluminum l a y e r

i e r l a y e r

Figure I: me cross sectional view of the pore srructure of a porous aluminium oxide film

supponed by bulk aluminium. 7Re bnm'er layer and the hexugonally close packed pore

arrays in rhe y-Al,O, can be seen.

0,s 2 ob (1)

4 (nm) n(I.0 nm/V) Ua(volt) (2)

The pore density p,, , expressed in number of pores per nm2, is a simple function of the

anodizing voltage of the formL2

where a is a constant approximately equal to 1.1 5; d, is the pore diameter, whose value

depends greatly on the acid medium used, the anodizing temperature, pH and voltage. P

is the unit wall thickness (in nmN) which is also dependent on the acid medium and

temperature. For example, the value of p for 15% (by weight) of sulfuric acid at 10 OC is

1.6 nmN.13 From geometry, the cell diameter D, is related to dp, P, and U, by the

following expression:

D,=d,+P v, (4)

From Equation (3) and (4), the pore density is inversely proportional to the square of the

cell diameter.

There are recent advances in producing U O templates with highly symmetrical

hexagonally close packed pores14 and in electrodepositing arrays of semiconductor micro-

and nano-wired6 Nonetheless, while major factors determining the structural

parameters of the AAO have been thoroughly investigated (starting fiom fundamentai

work of Woods and 0'~ullliva.n~~) and the mechanism of the porous structure nucleation

and development suggestedYt8 the potential of AAO as a template for nanofabrication has

not been m y exploited and no systematic andysis has been made on how the

anodization parameters affect pore uniformity, long-range order of pore packing, degree

of branching, merging, and lateral pore movement during the growth. ALI these qualities,

referred to as "template integrity" effects must be critically controlled if the template is to

be a host of an array of nanostructures. Device-suitable nano-arrays require a high Level

of template integrity and dimensional uniformity, as well as control over the structure and

composition of the nano-wires. There are two main gods to this project. One is to

modify the existing AAO technology to produce templates with pore diameters below 10

nm while maintaining a high template quality with a narrow pore size distribution.

Another is to provide a general analysis of the potential and limitations of the AAO-based

approach as a tool for nano-technology.

Low-Temperature Anodization

1.1 Introduction

The main question remained open is what the smallest diameter (dTin) achievable

for a regular array of pores in AAO. Commercially fabricated anodic alumina membrane

filters are available with nominal pore diameters of 20 nm." Their mean diameter is

often larger by 20 - 50 %.20 It has been reported that AAO with pores as small as 14 nm

can be obtained in H2C204 at 2 . 5 ~ . ' ~ The pore diameter d', cell diameter D, and barrier

layer (BL) thickness have long been known to be almost linear function of anodization

voltage Ua. Empirical coefficients of these functions were reviewed by Paterson and

~ a r d i l o v i c h : ~ ~

D,(nm> = 2.8 U,(V> (for any electrolyte) ( 5 )

d, = D, /a (6)

where a = 4.88 for H2SO4 based e l e ~ t r o l ~ t e s , ~ 3.01 for H2C2O4 based e l e ~ t r o l ~ t e s ~ ~ and

1 .7425 or 1 .7120 for &PO4 based electrolytes. These dependences deviate fiom linearity

when Ua < SV." The minimal Ua at which porous AAO can still be formed is not

known.

7

The cell diameter depends only on U, but not on the type of electrolyte. W e

the linear dependence of the ratio of d$Q on Ua might suggest that pores of very small

diameters could be obtained at low anodization voltages, the degradation of the porous

structure at low voltage renders this method ineffective in making small pores. That is, at

lower voltage the template integrity is severely sacrificed.

Alternatively the pore diameter d, can be achieved by lowering the anodization

temperature T,. It has been claimed that the pore diameter varies linearly with

anodization temperature; however, the precise dependence of the pore diameter and

structure on temperature is still unclear. ~bihara*' found no difference in porekell

diameter or pore density for AAO prepared in oxalic or sulphuric acid in the range 10 - 40

OC though the rate of film growth was affected significantly. On the other hand, a pore

diameter of 9 nm was achieved by Roukevitch et a1,I6 who anodized at 0 OC and found a

consistent decrease of d' with Ta. However, no one has attempted to anodize at a

temperature below 0 "C (sub-zero anodization), which should reduce the pore diameter

M e r if there is pore-diameter decrease with decreasing temperature. Therefore, a

strong motivation for this project comes from the possibility of pressing towards smaller

pore diameters and thus smaller nanostructures.

In this regard, purely aqueous electrolyte cannot be used for sub-zero anodization,

because of severe reduction of ionic mobility once the electrolyte fieezes. A reasonable

solution is to partially substitute the water in the electrolyte with methanol (MeOH), as

methanol-water mixtures can have very low melting points (Table I)? In this project,

the following electrolyte compositions (solutions A to D), with various melting points,

were used:

Table 1. Composition of electrolytes used in this project and their melting points

Electrolyte: 1.2 M H2S04 with

A. 100 % H20 and 0% MeOH

B. 75% H,O and 25% MeOH

C. 50% H20 and 50% MeOH

The resulting anodic oxide templates produced did, indeed, possess much

narrower pores and far better template integrity. These results will be presented below

followed by a discussion on the influence of anodization voltage U, and temperature T,

and electrolyte composition on the structural integrity of the porous AAO and its

suitability for nano- ternplating purposes.

Melting Point ("C)

0

-25

-50

D. 25% H20 and 75% MeOH -98

1.2 Theory

The formation of aluTninulll oxide (or alumina) at the anode occurs due to the

reaction:

2 A l + 3 Hfl +A1203 + 3 (7)

This reaction occurs spontaneously until the compact barrier layer is formed. Two

interfaces exist: the aluminum oxide (AVO) and the oxide/electrolyte (OLE). The two

underlying processes at these interfaces are, respectively,

Anodization (AVO): 2 A1 + ( 3 0 ~ - + N203 + 6e-

Chemical Dissolution (OIE): A1203 + 6 ~ + + 2 A l ~ ' + 3 H,O

At the cathode, hydrogen formation occurs:

H+ + e- + 1/2 H, (1 0)

Electrical potential differences are built up at both interfaces due to the transfer of an

excess of aluminum ions and oxygen ions, respectively, across the two interfaces, which

compensates for the further tendency for the formation of the oxide."

As ~arkhutik" puts it, a lot of empirical data have been accumulated relating to

both barrier and porous alumina growth. However, the nature of porous oxide growth is

far fiom being fully understood. Several models have been proposed for the growth

mechanism. For example, as early as 1961 Murphy and ~ i c h e l s o d ~ formulated a

colloid-precipitation model of pore formation. Various local dissolution models that

involve thermal heating, electric field and mechanical stress effects have also been

proposed.29 Most of these models, while attractive, lack theoretical substantiation.

Parthuik's model will be discussed briefly here.

Figure 2 shows the current versus time kinetics of porous oxide growth on

aluminum in (a) the galvanostatic (constant current) and (b) the potentiostatic (constant

voltage) regimes. The latter regime produces more uniform porosity and pore size (other

conditions being equal) and thus is the one chosen for this project. Pore stages can be

identified in these kinetic curves. In Stage I a barrier oxide layer starts to grow and, due

to its insulating properties, causes the current to drop drastically. Then, fine current

pathways begin to form in the barrier oxide surface in Stage II, followed by their

enlargement and "head expansion" in Stage III, which causes the current to rise again as

ions start moving through the oxide more freely. Finally in Stage IV a steady state is

achieved in which the current is constant and the pore structure consists of closely packed

hexagonal cells, each containing a central pore and separated from the aluminum

substrate by the hemispherical barrier oxide layer.

The elementary processes involved in the porous structure formation include

oxide growth at the O/E boundary due to the outward migration of A13+ ions and their

reaction with oxygen-containing species (e.g. SO:- ions for H2S0, based electrolyte).

Simultaneously the O/E interface is also dissolving as a result of electric-field stimulated

interaction of electrolyte species (especially H+ ions) with the oxide surface. Meanwhile

aluminum at the AVO interface also dissolves into the oxide due to the reaction of

moving oxygen species with aluminum. In short, the propagation in the direction n o d

Figure2. Schematic diagram of the kinetics of porous oxide growth on aluminium in (a) galvanostatic and (6) wtentiostatic regimes. The stages of porous structure development are also shown.

12

to the plane of the aiufninum substrate is determined by the dynamic equilibrium between

the oxidation of aluminum (at both AVO and O/E interfaces) and dissolution of alumina

at the OE interface, which is both field and current-assisted; As the O/E interface is

dissolved by the H+ assisted electric field enhanced mechanism, the electric field at the

pore bottom becomes stronger due to the reduction of film thickness at that fiont which

stimulates the field assisted migration of oxygen-containing species to the AVO fkont and

causing oxide formation. Then negative feedback sets in because when film growth

occurs the distance between the two fronts increases and thus the electric field decreases

until a constant thickness of cell wall is achieved. Parkhutik's model correctly predicts a

linear dependence of the cell diameter D, with anodic voltage U,, which is the product of

electric field and the distance along the normal between the AVO and O/E interfaces. So

the electric field is highest at the pore bottom for a given anodic voltage, and thus the

pores propagate vertically into the aluminum, eventually forming a cell with diameter D,.

1.3 Experimental

Aluminum strips were anodized at 1.2 M sulfUric acid, made in 0%, 25%, 50%

and 75% (by volume) methanovwater solutiom. In order to maintain a constant AAO

film thickness, anodization was carried out until a certain charge density Q was reached.

Initially Q was set to 3 c/cm2 for the 50% methanol electrolyte, and to 2 c/cm2 for the

75% methanol electrolyte. Because the time required to reach these charge densities were

so long, anodization at -40 OC and -60 "C has been carried out only to 0.6 c/crnL and 0.1

c/cmZ respectively (where steady sate growth rate might not yet have been attained.)

Anodization below -60 O C , though experimentally feasible, was not carried out due to the

enormous length of time (of the order of weeks) required to produce a usable AAO film.

The experimental parameters used are presented in Table 2.

Table 2. Experimental conditions and resulting AAO film parameters.

--

Anodization

temperature

Steady state

current density

Anodization

time ra (min)

Charge

density Q

AAO f i h

thickness

14

Materials and Sample Preparation. Anodic oxide films were grown on 0.05 mm thick

99.5% aluminum foil (Alcan). Samples were degreased with ethanol, dipped into solution

of 25 gA Na,CO, at 90 O C for 5-10 seconds to remove the native oxide layer, then

anodized in 1.2 M H2S04 or 0.85 M H3P04 with graphite counter-electrodes. Low-

temperature anodization was achieved with the solvent water of H2S04 was partially

substituted with methanol (up to 75% by volume). The feasible anodization temperature

ranges from -4 OC (for aqueous 1 -2 M &SO4) to -90 OC (H,O / 75 % MeOH).

Figure 3 shows the experimental set-up designed to provide a constant electrolyte

temperature in the range from 20 to -80 OC. The temperature of the electrolyte was

maintained to within 0.1 OC using cold nitrogen (N3 gas flow through cooling coils

controlled by a CN76000 temperature controller and a solid state relay (Omega

Technologies). A platinum resistance temperature detector (RTD) was used for the

temperature measurements. A 400 mL beaker ("the inner cell"') was used to contain the

electrolyte; it was coiled with copper tubing (which transfers the cooling N2) and

immersed in methanol which is contained in a 1000 mL beaker which served as an outer

cell. The outer cell was insulated by a Styrofoam box which helps to minimize

temperature fluctuation due to heat loss to the surroundings. The flow of N2 was

produced by evaporating of liquid N2 contained in a dewar, in which a resistive heater

was immersed and connected to the temperature controller. When more than one dewar

of liquid N2 was required during long anodization runs, two dewars were switched

through a Teflon 4-way cross-over valve. The temperature fluctuations were no more

F J GURE 3. EXPERIMENTAL SETUP FOR LOW-TEMPERATURE ANODlZATlON

to variac

temperature, voltage, current

to data aquisition I

board

temperature 0

controller i 0

0

? ?

thermally insulated anodization cell dewar with liquid N2

16

than 0.5 OC in amplitude and were damped quickly. The set of temperature control

parameters used in this study was: (Proportional Band = 12 OC, Reset time = 30.4 min,

Rate = 4.86 min).

Instrumentation and characterization. Scanning electron microscopy (SEM), was

carried out on a Hitachi S-4500 (Field Emission) instrument operated at 2-20 kV and 2-5

mm working distance. Samples of the anodized aluminum were bent against a razor blade

to provide a cleaved edge of the AAO film. The cleaved section as well as the top surface

of the samples were imaged without requiring additional conductive coatings.

The diameters of at least ten pores were measured for each mean value reported.

Additional measurements were made along the length of the pores to gauge the

uniformity of the pores. The standard deviation of the pore diameter was never higher

than 10% of the mean diameter.

Pore widening was performed in 0.1 M phosphoric acid (&PO,) at 35 OC

followed by immediate washing in triply distilled water. Pore widening is a convenient

method to open up the pores to the desired diameters, as the relationship between pore

diameter and pore widening time r,, can be found in the literature. Such pore size tuning

in essential in subsequent deposition of material into these pores. In this project, r, is

usually taken to be 1 minute.

1.4 Results and Discussion

It is important to investigate the effects of the various anodization parameters on

the structural parameters @ore diameter, cell diameter, film thickness and pore density)

of anodic aluminum oxide (AAO), as thesc factors determine the size and distribution of

the nano-wire subsequently formed.

It is well established that the pore diameter a', depends on the anodization voltage

Ua, the anodization temperature Ta, the electrolyte concentration, and the nature of

electrolyte. It was previously contirmed by Roukevitch et all2 that the mean pore

diameter decreases in the order of phosphoric, oxalic and sulphuric acids. In contrast, the

cell diameter D, remains more or less constant for different electrolytes and depends only

on U, The results obtained in this project add to the knowledge of the existing data to

the sub-zero temperature regime.

The structure of AAO obtained at various values of U, in sulphuric acid (1.2 M

H2S04) and phosphoric acid (0.9 M &Po4) electrolytes was analyzed by SEM. It was

observed that the template integrity degrades with decreasing anodization voltage (Figure

4). As the voltage decreases, the pores become less straight and more branched. At 5 V

the pore diameter in sulphuric acid anodized films was around 5 run, but the template

quality is unsatisfactory for device applications. The observation is best explained in

terms of a generally accepted pore growth mechanism. The integrity of the porous

network is determined by the ratio of the lateral and normal propagation rates of reaction

at the metdoxide interface. Propagation in the normal direction is determined by the

room temp.

Ua = I O V

dynamic equilibrium between aluminum oxidation and field-assisted dissolution of

alumina, which depend on the electric field strength at the interface. The lateral growth,

on the other hand, is governed by the homogeneous and inhomogeneous disturbance of

the hemispherical reaction interface, which is determined by the concentration of crystal

structure defects of the aluminum substrate and is more or less independent of the electric

field.

Anodization at -10 OC in 1.2 M H2S04 (50% MeOH) was carried out to confirm

the well-established linear reIationship of pore diameter and anodization voltage. Indeed

it was found that dp varies linearly with Ua in the form:

d, = 0.386 Ua + 3.23 (R' = 0.9724); (1 1)

Equation (1 1) is valid for Ua t 5 V and Ta = -1 0 OC.

The pore diameter decreases with decreasing temperature. From scanning

electron micrographs such as those in Figure 5, it is observed that the template integrity

remains intact for the low-temperature anodized films at Ua = 15 V. Reaching the lowest

pore diameters (below 4 nm) does not result in the degradation of the structural integrity

of the templates as with low anodization voltage. The AAO film parameters as a h c t i o n

of the temperature are presented in Figure 6. The observed trend in cell diameter as a

function of temperature conflicts with the aforementioned published theories while the

decrease in pore diameter with decreasing temperature is correctly predicted. Table 3

shows the linear equations of dp as a function of Ta for 50% MeOH (Equation 12) and

75% MeOH (Equation 13) electrolytes, and the linear h c t i o n of the cell diameter D,

versus T, (Equation 14), where IZ2 is the dimensionless linear correlation coefficient:

Figure 6. AAO porelcell diameter as a function of anodization

temperature in H,SO, based electrolytes

anodization temperature T, , 'C

-

low temperature and high voltage anodization provides low pore diameter and sufficient template integrity

H,O 50% MeOH

A 7 5 % MeOH

Our result challenges recent theories of pore formation during anodic oxidation.

Table 3. Linear relationship of d, or D, vs. Ta at U, = 15 V

The failure of the prediction regarding the temperature dependence of the cell diameter

Electrolyte

1.2 M &SO4, 50% MeOH

1.2 M H2S04, 75% MeOH

1.2 M H2S04, 50% MeOH

might be due to the simplified assumption regarding the potential distribution across the

aluminum/oxide (AVO) and oxiddelectrolyte (OLE) interface used in that model?

Equation

d, = 0.1 l Ta + 9.9 (p = 0.9938) (1 2)

d, = 0.1 165 Ta + 7.682 ( R ~ = 0.9539) ( 1 3 )

D, = -0.2046 Ta + 39.721 (RL = 0.9468) (14)

Moreover, the plot of h(J) (where J is the current density) versus l/Ta gives a

straight line (Figure 7). This implies that the pore formation, which is assisted by the

current, is an activated process in the form:

J= A exp (&,I RT,)

where E,,, is the activation energy for films produced between 20 and -80 "C. Table 4

below summarizes parameters in the linear form of i n Q versus inverse temperature

obtained with various electrolyte compositions:

Figure 7. Ln (Current density) vs. Inverse Anodization Temperature

Table 4. Activation energies and pre-exponential factors for various electrolytes

Percentage

MeOH

0%

25%

y: Ln (J) vs x: (1IT' (kT/mol ion)

A = exp (intercept)

Since the activation energy for all four electrolytes is of the same order, the

limiting step of the pore growth mechanism is likely to be the same over the whole

experimental temperature range. The dependence of current density on temperature

(Equation 15) is the functional form suggested by Christov and ~ k o n o ~ i s o v ~ ~ who

propose that the rate determining step involves the ionic transport fiom the pore bottom

(OE interface) through the barrier layer to the N O interface. In other words, the oxide

growth in the internal oxide (AVO) interface, among the various elementary processes of

pore development, is likely to be the limiting step. The kinetics model of Equation (6)

further implies that the activation energy Eact is a b c t i o n of the electric field strength E,

which is usually taken to be the linear form E,,, = E, - aqE, where a is the activation

distance and q is the charge on the moving ion, which is predominantly the oxygen-

containing species.

From Equation (4), the unit wall thickness P is given by:

P = (D,- d J / U ,

25

Substituting the D, and d, dependences on Ta fiom Table (3) (Equations 12 & 14) into the

above equation, one finds that, for an electrolyte of 1.2 M H2S04 (50% MeOH):

p (in nmN) = -0.02 T, (OC) + 2 (1 7)

Hence the wall thickness is temperature dependent resulting in an opposite trend for the

dependence of a', vs Ta and Dc vs T,. From Equation (17), it is clear that when the

anodization temperature reaches the sub-zero regime, the yield of wall thickness per unit

voltage (the physical interpretation of P) is increased. As the wall of anodic alumina cells

consists mainly of anion-contaminated alumina, the increase of P may signify an

increased amount of anion incorporation in the outer layer of the unit cell. This may

happen as a result of the reluctance of the anions to dissolve out of the oxide layer.

Substituting Equation (I 1) into Equation (4), the cell diameter at T, = -10 OC and

U, = 15 V, is given by:

D, = (0.386 Ua + 3.23) + 2.2 (1,

= 2.6 Ua + 3.23

= 42.2 nm (1 8)

which gives a unit cell diameter D, of 2.8 nmN, which is in perfect agreement with the

value given by the literature,' where the general assumption is that for different

electrolytes D, is constant and determined mainly be the forming voltage. The latter

supposition needs to be modified, as this study shows that the cell diameter is a

temperature dependent. The magnitudes of the opposing effects of anodization

temperature on a', and p determine the overall dependence of Dc on Ta. However, it is

still correct to say that the anodization voltage is a larger determinant of the cell diameter

than is the anodization temperature, because while both the pore diameter and wall

thickness are directly proportional to U,, the wall thickness is only weakly dependent on

temperature (through P). In addition, it is observed that the ratio Did, increases as the

anodization temperature decreases. The effect of temperature works in two ways; to

decrease the pore diameter possibly by retarding the ionic transport in the oxide and thus

decreasing the rate of oxidation and dissolution. On the other hand, the lower the

temperature, the lower is the rate of formation of defect sites ("pits") in the first place.

Less unit cells are developed around these centres for a given area. The cell diameter is

thus increased and the pore density is decreased.

Table (4) also shows the effect of methanol substitution of the electrolyte-solvent.

The film making process possesses a higher activation energy in the 0% and 25% MeOH

elect~olytes than in the 50% and 75% methanol electrolytes. The ionic mobilities of H*

and O K ions in methanol are lower than those in water, because of a Grotthuss type of

conductivity by proton transfer, superimposed on the normal bansport process.31

Methanol molecules, on the other hand, are less efficient in offering the proton transfer

transport mechanism, because 0 atom in the CH3-0- group is less electronegative than

the 0 atom in the H-0- group, making the dissociation of H+ relatively more difficult.

Therefore it is the water in the electrolyte that plays the important role of anodic oxidant

for the aluminum.

Another important structural parameter of an kAO film is its thickness DAAO,

which determines the length of the nano-wires made in these templates. The fiIm

thickness Duo is determined

passed to the anode. At the

27

by the current-time integral, or the total ionic charge Q

potentiostatic mode, the thickness of the A1203 film is L

increased mainly in the constant current density stage. The steady-state current density is

related to a steady growth of the porous oxide, and is responsible for maintaining a

constant pore density and a constant pore diameter. It is observed that the lower the

anodization temperature, the longer it takes for the current density to reach its steady

state. Again, this is consistent with the supposition that the low temperature slows down

the ionic transport processes which determines the rate of oxidation and chemical

dissolution. For a given anodization voltage, the steady state current density decreases

with decreasing temperature.

In addition, the pore formation process can be viewed in from the physical

standpoint. There are actually three interfaces in the AYAAO system: the Allbarrier layer

(BL), BL/porous AAO and porous AAO/acid interfaces. The porous layer can be

considered an ionic conductor and the BL a compact dielectric film. The potential drop

occurs mainly in the barrier oxide layer. It is known that at a certain anodic potential, the

BL breaks down and allows electrons to pass through without much resistacce. This

"dielectric breakdown" effect was observed in this study. The critical voltage U* at

which this occurs is approximately 26.5 V, with the 1.2 M H$04 (50% MeOH) as

electrolyte at T, = -10 OC and U, = 15 V. This result is compared to the empirical

relationship for the dependence of the dielectric breakdown voltage on hydrogen ion

concentration suggested by Palibroda for various concentrations of sulfuric acid at T, = -

8.4 "C:

28

U* = 20.5 + 4.2/w] (19)

From Equation (19) it is predicted that for pC] = 1.2 M, U* = 24 V. This value is not

very different from the value found in this study (26.5 V), extending the validity of the

equation over the broader temperature range. The slightly higher breakdown voltage than

predicted might be due to the presence of methanol in the electrolyte. The lowering of

the temperature may have reduced ionic migration and micro-defect formation in the

barrier layer, both of which are considered important factors in dielectric breakdown.

The substitution of water with methanol may have weakened the effectiveness of

hydrogen bonding of the electrolyte system since the H20 molecules have a stronger

bonding than the MeOH molecules. This in turn leads to a higher aaiodproton ratio

which determines the increase of (I*. From Palibroda's correlation,32 a U* of 26.5 V

found in this study corresponds to an ionization energy E, of the barrier layer of 2-76 eV,

which is close to the bond energy of Al-0 (2.27-2.87 eV). This suggests that the

chemical dissolution step of Equation (9) may be composed of the formation of the weak

(AL-OH) bonds upon arrival of the H+ ions at the OIE interface caused by the imposed

electric field, followed by the breakage of these bonds with O H being released due to Al-

0 bond polarization. The last step is the aluminum ionization to form A13+ ions.

1.5 Conclusions

Low temperature anodization is a novel technique extended greatly in this project

in order to produce anodic aluminum oxide with very narrow and uniform pores. Such an

advance not only allow the fabrication of nano-wires that could exhibit strong quantum

confinement effects, but also facilitate the development of devices based on nano-wire

arrays.

1.6 References

(1) Esaki, L.; Chang, L. L. Phys. Rev. Lett. 1974,33,495.

(2) Dingle, R.; Wiegmann, W.; Henry, C . H.; Phys. Rev. Len. 1974,33,827.

(3) (a) Ozin, G. A. Adv. Mater., 1992,4,612;

(b) Brus, L. Eigler, D. Nature 1994,369,273.

(4) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Science 1995,270, 1335.

(5) Hsiao, G. S.; Anderson, M. G.; Gorer, S.; Harris, D.; Penner, R. M J. Am. Chem.

Soc. 1996, preprint.

(6) Al-Mawlawi, D.; Liu, C. 2.; Moskovits, M. J. Muter. Res. 1994,9(4), 1014.

(7) Martin, C. R. Science 1994,266, 1 96 1.

(8) Wernick S.; Pinner, R.; Sheasby, P. G. The Surface Treatment and Finishing of

Aluminum and its Alloys; Finishing Publishing: Teddington, 1987; Vol. 1.

(9) Preston, C. K.; Moskovits, M. J. Phys. Chem. 1993,97,8495.

(1 0) (a) Kawai, S. In Proceedings of the Symposium on Elecirochernical Techniques in

Electronics; Romankiw, L. T. , Osaka, T., Eds.; Electrochem. Society:

Pennington, NJ, 1987; PV 88-23, p 389.

(b) AMawIawi, D.; Coombs N.; Moskovits, M. J. Appl. Phys., 1991, 70,4421.

(c) Dunlop, D. 5.; Xu, S.; Ordernir, 0.; AlMawlawi D.; Moskovits, M. Phys.

Earth Planet. Inter. 1993, 76, 1 1 3.

(1 1) (a) Martin, C. R. Science 1994,266, 196 1.

@) Whitney, T. M.; Jiang, J. S.; Searson, P.C.; Chien, C. L. Science 1993,261,

1316.

(12) AiMawlawi, D.; Coombs, N.; Moskovits, M. .l Appl. Phys. 1991, 70(8), 4421.

(1 3) Diggle, J. W.; Downie, T. C.; Godding, C. W. Chern. Rev. 1969,69,3 65; Keller,

F.; Hunter, M. S.; Robinson, D. L. J. Electrochem. Soc. 1953,i00,411.

(14) Masuda, H.; Fukuda, K. Science 1995,268, 1466.

(15) Klein, J. D.; Hemck, R D., 11; Palmer, D.; Sailor, M. J.; Bnunlik, C. J.; Martin,

C. R. Chem. Mater. 1993,5,902.

(26) Routkevitch, D.; Bigioni, T.; Moskovits, M.; Xu, J. M. J. Phys. Chem. 1996,10,

1403 7.

(27) (a) O'Sullivan, J. P.; Wood, G. C. Proc. R. Soc. London, A 1970,317, 51 1.

(b) Wood, G. C. in Oxide and Oxide Films, vol2, Diggie, J. W.; Ed,; Dekker:

New York, 1973; p 167-280.

(18) Parkhutik, V. P.; Shershulsky, V. I. J Phys. D: Appl. Phys. 1992,25, 1258.

(1 9) Whatman Catalog; Whatman Inc.: Clifton, NJ, 1997; p 67.

(20) Chlebny, I.; Doudin, B.; Ansennet, J.-Ph. Nanocryst. Muter. 1993,2,637.

(21) Ebihara, K; Takahashi, H.; Nagayama, M. J. Met Fin. Soc. Jap. 1982, 33,4.

(22) Randon, J.; Mardilovich, P. P.; Govyadinov, A. N.; Paterson, R. J. Colloid

Interface Sci 1995,169,335.

(23) Pavlovic, T.; Ignatiev, A. T h i ~ SoZidFiIms 1986,138, 97.

(24) Sokol, V. A. Dokl. Akad. Nauk. BSSR 1986,30,243.

(25) Konno, M.; Shindo, M.; Sugawara ,S.; Saito, S. J. Membr. Sci. 1988,3 7, 193.

(26) Wolf, A. V.; Brown, M. G.; Prentiss, P. G. CRC Hun&ook of Chemistry and

Physics 73rd; CRC Press: Boca Raton, FL, 1972; D237.

(27) Parkhutik, V. P. In Modern Elechochemistry; Bockris, J. OyM.; Reddy, K. N., Eds;

Plenum: New York, 1994; Vol. 2.

(28) Murphy, J. F.; Michelson, C. E.; Proc. Con$ Anodiz. Aluminium; Alumin.

Federation: Nottingham, 196 1 ; p 1 14.

(29) Despic, A. R.; Parkhutik, V. P. in Modern Aspects of Elecirochernistry; Bockris, J.

O'M.; et al. Eds: Plenum: New York, 1989; Vol. 20; p 397.

(30) Christov, S. G.; Ikonopisov, S. J. Electrochem. Soc. 1969, 116(1) ,56.

(3 1) Moore, W. J.; Physical Chernisby; Prentice Hall: London, l972,43 5.

(32) Fumwawc, R. C.; Rigby, W. R.; Davidson, A. P. US Patent No. 468755I, 1987.

Electrodeposition

2.1 Introduction

Pre-anodized aluminum is placed in a suitable electrolyte containing ions of the

metal that is to be deposited into the pores. The main constraint in using porous alumina

films directly after anodization is the insulating dense barrier layer which precludes the

use of d.c. electrodeposition to fill the pores. However, the inherent rectifying properties

of the barrier layer allow the pores to be filled d o r m i y by a.c. electrolysis without

simultaneously depositing material on the surface or into macroscopic defects of the film,

which occurs in d.c. electrodeposition. Alternating current (a.c.) is imposed between the

aluminum and a suitable counter-electrode. Since anodic aluminum oxide (AAO)

conducts preferentially in only the cathodic direction, it is called a "valve metal oxide."

Metal ions are reduced to zero-dent metal within the pores during the cathodic half-

cycles of the ac signal, but are not re-oxidized in the anodic half-cycles. In addition, the

electric fields are greatest near the bottom of the pores due to the geometry. Hence the

metal growth begins there and the pores fill fiom the bottom up.

In some aqueous eiectrolytes, though, the dumindanodic alumina (AVO)

substrate is prone to a number of side reactions that affect the template's morphology and

compete with the desired electrodeposition process. Among these are re-anodization,

AVAAO pit corrosion (especially in chloride-containing electrolytes), barrier layer

breakdown, and water electrolysis. High deposition voltages, often required to deposit

certain materials, promote side reactions due to their high limiting current density,

resulting in the formation of nano-wires of non-uniform lengths and the development of

defects in the film. It is difficult to fill pores of diameter smaller than 10 nm using high-

voltage deposition. Non-aqueous solvents, with their increased range of solvent stability

and low corrosivity, are good candidates for avoiding these problems. Solvents such as

ethylene glycol (EG), prop ylene glycol (PG), dimethy lf- (DMF) and

dimethy lsulphoxide (DMSO), which are compatible with AVAAO, lower the deposition

voltage and expand the range of materials for deposition. Thus, CdS nano-wires have

been successfidIy electrodeposited fiom DMSO, while aqueous electrolytes, developed

for the deposition of CdS fihs, have failed. In general, one obtains better uniformity of

pore filling and deposition into the smallest pores with non-aqueous electrolysis.

In this chapter, two types of nano-wire fabrication processes will be introduced.

In Section 2.2 the synthesis of CdS nano-wires with various diameters are described.

Some of these CdS wire arrays are characterized subsequently by SEM and resonance

Raman spectroscopy (RRS). Section 2.3 describes briefly the attempt to deposit nickel

into AAO templates in a nonaqueous electrolyte.

2.2 Cadmium Sulphide

2.21 Introduction

The 11-VI semiconductor CdS was electrodeposited into the porous anodic

allrminum oxide (AAO) template by alternating current (ax.) electrochemical deposition

from an electrolyte containing cd2+ and elemental S in DMSO at 120 OC.

There are two consecutive steps involved in the CdS deposition process; the fist

one is the electrochemical reduction of solvated cd2+ ions to form zero-dent Cd:

cd2+ + 2e' (from cathodic cycle) + cd0 [Electrochemical]

Then follows the sulphidation of Cd by dissolved sulphur:

cd0 + s -t C ~ S [chemical]

The three samples used for resonance Raman spectroscopic studies were annealed at 500

OC under a flow of oxygen-fkee N2 for 60 minutes. The effect of annealing were

previously studied by Routkevitch et al,' who has shown that the annealing of similar

samples under oxygen-£kee N2 at 500 OC for 1 hour provided a drastic increase in both

signal-to-noise ratio and the number of observable overtones in the resonance Raman

(RR) spectra. As a result, only previously annealed samples were used for Raman studies

of CdS nanowires presented below.

2.22 Experimental

The AAO film and the graphite rod counter-electrode were immersed in the non-

aqueous electrolyte as shown in Figure 8. A J type thermocouple was inserted into the

electrolyte and connected to a temperature controller (OMEGA CN8500) which controls

the heating rate by comparing the temperature measured by the thermocouple and the pre-

set temperature (usually 120 'C for CdS array fabrication.) The power supply was set to

the ax. mode and a sinusoidal waveform was chosen. The deposition voltage Ub was set

at 35 Va.c. The deposition temperature Td and time rd were set to 120 OC and 20 min

respectively. The frequency was fixed at 200 Hz with a zero offset. When the desired

deposition time was reached, the sample was removed carefblly from the electrolyte, and

rinsed first with methanol, then for 10 minutes in tap water, and finally in triply distilled

water for 30 seconds. The rinsed sample was then allowed to dry in air.

Table 5. Deposition conditions for porous anodic dluninum oxide (AAO) supports for

Raman studies

Comment

annealed, non-widened

Mean pore diameter

(nm>

Anodization Temperature

("C, in 1.2 M H2S0,)

8

10

5 -5 -20

-10

0

annealed, non-widened

annealed, non-widened

2.23 Results

CdS wires were successfully deposited into the pores of AAO i5hs pre-anodized

at sub-zero temperatures down to -20 "C. M O films produced in this way were

measured to have mean diameter of 5.5 m. Figure 9 shows an SEM micrograph of

AAO template loaded with CdS nano-wires, where the mean pore diameter is 10 nm.

Macroscopically, the deposited films appear golden yellow in colour.

Figure 9. SEM of the cross-section of AAO\CdS nanowire array, mean pore diameter 13 nm.

2.3 Nickel

2.3.1 Introduction

Nickel nano-wires that result from depositing nickel into the AAO pores possess

magnetic properties that make them good candidates for storage devices. Additionally,

the nickel nano-wires have a very high resistivity that would enable the observation of

the Coulomb Blockade effects in devices fabricated fkom them. These and many other

potential applications such as flat panel display make the study of nickel deposition a

worthwhile goal. Nickel has been previously deposited with good results, however only

for pores with diameters above 15 nm.

2.32 Experimental

The experimental set-up was the same as that for CdS deposition, except that the

electrolyte used was 0.05 M nickel@) chloride hexahydrate (NiCI2*6H20) dissolved in

dimethylsdphoxide (DMSO). The deposition parameters used are listed together with

summary observations in Table 6.

2.33 Results and Discussion

Table 6. Results of pioneer studies of non-aqueous nickel deposition

Sample

#

1

2

3

4

5

6

7

8

9

10

1 1

12

13*"

14*

15*

16*

Ax. Visual

Frequency v Observation I Deposition

voltage Ud

(Va.c.)

Pore

Widening

Time

T V (mid

100 I no deposition

Deposition

Temperature

TJ (OC)

100 no deposition

100 no deposition

100 no deposition

200 no deposition

300

200

no deposition

bIack, corrosion (left)'

200 black, corrosion (right)

200 no deposition

200

I slight black (top)

black, corrosion (bottom)

200

t

200 I black, corrosion (right)

corrosion on all 4 sides (gray spots) ,

200 no deposition

200 no deposition, slight black.(right)

200 same as above

200 no deposition, black (bottom and

no deposition, black at all 3 edges

corrosion (right), black (top)

top 113 golden, bottom 2/3 black,

wavy interface between them

top Z 3 golden, bottom 1/3 black,

wavy interface between them

non-uniform black with some golden

mixed with it

very non-uniform deposition (V-

shaped interface)

black, I ' is best, 5' and 10'

indistinguishably non-uniformiv

black, 1 ' is best,

5' and 10' non-uniform

black + golden, wavy interface

same as above

same as above

same as above

no deposition, slight black at 5'

non-uniform deposition for all

black on left for all, corrosion (white

specks at right and bottom)

grayish black for l', black at 5' and

corrosion at some right of l', more

of 5' and all of 10'

black + golden, wavy interface

black + much golden, V-shaped

interface I

(bottom), straight interface

golden (top) and golden black

no deposition at ail

L

-- -

golden gray 1 golden

some slight golden patches

golden + 1 black strip

two black strips

black, slight curved top interface

dull black

dull grayish black

dull grayish black

metallic, uniform deposition I no deposition, slight black on left

no deposition, slight black-I-yellow

same as above

same as above I golden metaltic,

uniform deposition I golden metallic, some black at the bottom I

I

Lej refers to the le

70 16 10 200 golden rneta.Uk

I I

: edge of sample, ditto for subsequent descri

1 bottom

200 golden metalIic, some black at the

I and non-uniform deposition

200 golden metallic, but largely blzck

I (bottom), straight inarfase

f

200

I

200 black

golden metallic (top) and black

200 black, non-uniform deposition

I

200 I black

200 black

1

200 black, uniform deposition,

200

I except at 1 '

yellow patches (17,5'), black at 10'

I

tions of right, top, battom

200

ii The symbol * denotes the use of stepwise voltage reduction (a metbod established by Fumeaux, R C. et

a?) was used at the anodizaton stage: (15V for the prescribed time of anodization, at the end: 10V for

5 min, then 5V for 5 min)

" "1,5,10" refers to the deposition time of I min, 5 min, 10 min on the same sample by withdrawing the

sample at the approximate time

The apostrophe denotes "minute".

black, uniform deposition,

46

The electrolyte used in this study contains 6 H20 for each M2+. The

concentration of water at this level can cause side reactions that can compete with the

reduction of M2+. By adding water in concentration of 1%, 3%, and 5%, the deposition

was shown to vary with water concentration. Good deposition resulted when the

concentration reached 3%, while no significant deposition was observed at 1% or 5%.

Figure 10 shows two nickel nano-tip arrays formed in anodic alumina matrix.

The quality of the porous anodic aluminum is speculated to have an effect on

nickel deposition. In this preliminary study we used templates that are two to three

weeks old. The aging of these AAO template may have caused the inconsistent results

obtained. This speculation was confirmed by Cornu et a13 who showed that fiesh

templates that were prepared within one or two days before deposition produced more

consistent results.

Additionally, exposed d e u m on the cut-side of the samples seems to react

with the electrolyte by forming a redox couple with nickel(II), thus competing with the

nickel reduction in the pores. This was also confirmed by Comu's results which shows

that aluminum reacts with the electrolyte at the deposition voltage used. Comu carried

out a systematic study of the influence of water concentration, deposition temperature and

voltage on the deposition of nickel into AAO pores. He showed that the concentration of

water dramatically affected the electrodeposition of nickel and for subsequent deposition

he used anhydrous nickel@) chloride, which he synthesized by the following rea~tion:~

Figure 10.

Ni nano-tip arrays formed in anodic alumina matrix

A. Side view, matrix dissolved almost completely, 60 nm diam. B. Top view, only top of the tips exposed, 12 nm diam..

The temperature and voltage at which deposition is carried out are important

parameters which need to be carefully selected and controlled. If the deposition

temperature is too high, the rate of diffusion of material into the pores will be too rapid

and the deposition will be n o n - d o r m and a great deal of the deposition will take place

on the surface of the AAO film as opposed to the interior of the pores. A high

temperature also promotes aluminum corrosion and other undesired side reactions. If the

temperature is low, on the other hand, slow diffusion results which handicaps the nickel

deposition into the pores and the subsequent sulphidation of the Cd that make CdS nano-

wires. Likewise high voltage deposition tends to result in surface deposition and non-

uniform pore filling, since the voltage directly affects the rate of reduction of the metal

cation to its zero valent state. A low voltage tends to reduce the rate of metal reduction

and hence might hamper the metal fiom filling of pores. Each type of deposition of

metal or semiconductor deposition has its own set of electrochemical mdor chemical

reactions involved and thus has its unique set of optimum conditions for deposition. The

temperature and voltage are only two of the many factors that affect the quality of nano-

wire arrays obtained.

Before going on to the band gap measurement of some CdS samples, the key

processing steps in the fabrication of the nano-wire arrays will be discussed briefly. The

ability to make electrical contact or to attain and optical access to the nano-wires is a

desirable goal after depositing nano-arrays of the desired quality and dimensions. The

structure of AAO is inhomogeneous; the inner walls of the pores are composed of

amorphous (anion-contaminated) alumina which is, in turn, surrounded by polycrystalline

49

(relatively pure) alumina.5 In fact, it is known that the rate of dissolution of AAO in

acids is dependent on the concentration of the impurities in the alumina and is lower for

relatively pure alumina! As a result the pore wall does not etch uniformly. Wire length

uniformity is achieved by polishing the surface with 50 nrn alumina powder, thus

removing the exposed ends of the wires while leaving the AAO intact. The anodic oxide

layer can be removed in a mixture of phosphoric acid (6 wt% H3PO4) and chromic acid

(1.8 wt% H2Cr0,), or 0.1 M NaOH at 40°C. Occasionally, one may want to make direct

contact to the end of the nano-wires at the bottom of the pores, which requires

consecutive removal of the aluminum substrate and the barrier layer. While common

etching solutions such as CH30W5%Br2 and HgC12(sat)/H20 would do the job, the best

results, in terms of the rate of etching, selectivity, defect formation and ease of handling,

are obtained with 0.1 M CuCl2/2O%HC1. Using this solution a 1 p m thickness of

aluminum can be etched in less than 30 seconds without undercutting the masked area

and without any noticeable dissolution of the barrier layer. The barrier layer can then be

gradually etched in 0.5 M H3P04 at 50 OC. The process can be easily monitored by

imposing a small potential (5 mV) aod measuring the polarization resistance. Free-

standing AAO films filled with nano-wires can be prepared using this method.

2.4 References

(1) Routkevitch, D.; Bigioni, T.; Moskovits, M.; Xu, J. M. J. Phys. Chem. 1996,10,

14037.

(2) Furnwaux, R.C.; Rigby, W. R.; Davidson, A. P. US Patent No. 4687551, 1987.

(3) Roukevitch, D.; Comu, C; Davydov, D.; Moskovits, M. Unpublished results.

(4) Pray, A. R. In Inorganic Synthesis; Moeller, T., Ed.; 1957; Vol. 5, p 153.

(5) (a) Thompson, G. E.; Fumeaw, R. C.; Wood, G. C. Corros. Sci. 1978,18,481.

@) Thompson, G. E.; Wood, G. C. Nature 1981,290,230.

(c) Ono, S.; Ichinose, H.; Mausuko, N. Corros. Sci. 1992,33(6), 841.

(6) Takahashi, H.; Fujinrnoto, K.; Nagayama, M . .I Electrochem. Soc. 1988,135, 1348.

Band gap Measurement

Using Resonance Raman Spectroscopy

3.1 Introduction

The band gap energy (or the exciton energy) of a semiconductor is defined as the

energy difference between the highest energy point in the valence band (HOMO) and the

lowest energy point in the conduction band (LUMO). Therefore, the exciton energy is

the minimum energy required to excite an electron fiom the valence band to the

conduction band. The exciton energy corresponds to the band-gap in particles for which

there is quantum confinement.

A direct band-gap semiconductor is a material in which the highest point in the

valence band occurs at the same electronic momentum as the lowest point in the

conduction band.' In other words, transitions between the two allowed bands can occur

with no change in crystal momentum. This 'direct' nature has a significant effect on the

optical properties of the materiaL2 CdS, GaAs and InP are examples of direct

semiconductors, which are ideally suited for used in semiconductor lasers and other

optical devices.

52

The importance of band gap measurement stems fiom the fact that the band

structure of a material determines its electronic, thermal and optical properties. For

example, the width of the band gap determines the energy at which light is emitted fiom

the exited material. Recent studies show that it is possible to control the exciton energy

of a semiconductor by producing particles with sizes smaller than or approximately equal

to the excitonic Bohr diameter? The band gap energy can be determined by absorption

spectroscopy (or its complement reflection spectroscopy) and conductivity measurement.

However, these techniques are relatively difficult to perform. Resonance Raman

spectroscopy, on the other hand, is a convenient technique fiom which one can extract the

band-gap energy of anisotropic nanostructures.

The motivation for carrying out polarized RR measurement comes from the

theoretical speculation of observable quantum confinement in these kinds of quasi-one-

dimensional system. The CdS nano-wires is basically anisotropic, that is, their properties

depend on orientation. Therefore, it is interesting to probe the CdS nano-wires with both

s- and p-polarized light in order to study their optoelectronic response in the radial and

axial directions. The electric field of s-polarized light lies in the radial direction and that

of the p-polarized light is approximately aligned along the axial direction. The

anisotropy of CdS nano-wires arises fiom two causes. First the aspect ratio of the wire is

very great. Second, CdS has hexagonal crystalline symmetry and it was found4 that the c-

axis of the CdS nano-wires lies along the axis of the pore.

3.2 Theory

In 1928, K. S. Krisnan and C. V. ama an' first observed the phenomenon in which a

photon is scattered with a frequency displaced by a fixed quitntity fiom that of the

incident radiation hv. This type of inelastic light scattering is then called Raman

scattering in recognition of its discoverer. The fiequency displacement corresponds to

the energy difference between two molecular ground electronic states n and m. The

positive (+) and negative displacement (-) are referred to as the anti-Stokes and Stokes

scattered radiation, respectively. Ln other words, when the molecule undergoes a

transition to a higher energy level and thus the photon loses energy, the detected light is

at a lower energy (lower fiequency) and Stokes lines are obtained. If, on the other hand,

the molecule loses energy and drops to a lower energy state, the photon is scattered at a

higher fkequency resulting in the anti-Stokes lines.

The resonance Raman of many compound semiconductors with band gaps in or

near the visible are often dominated by an intense progression of an series of optical

phonons, usually the longitudinal optical (LO) phonons, that are excited through a

distortion of the ionic lattice that can be expressed in terms of crystalhe normal modes.

The most prominent normal mode of excitation forms the RR progression. In CdS, the

lowest electronic excited state (the exciton) is most strongly coupled with long

wavelength optical phonons via Frohlich interaction: where the radial electric field that

accompanies the displacement of the partially ionic nuclei (cd2+ ad s2] couples with the

exciton in a Coulombic fashion. The process was discussed in great detail by ~rolich'

3.2 Theory

In 1928, K. S. Krisnan and C . V. ama an' first observed the phenomenon in which a

photon is scattered with a fiequency displaced by a fixed quantity from that of the

incident radiation hv. This type of inelastic light scattering is then called Raman

scattering in recognition of its discoverer. The fiequency displacement corresponds to

the energy difference between two molecular ground electronic states n and m. The

positive (i) and negative displacement (-) are referred to as the anti-Stokes and Stokes

scattered radiation, respectively. In other words, when the molecule undergoes a

transition to a higher energy level arid thus the photon loses energy, the detected light is

at a lower energy (lower fiequency) and Stokes lines are obtained. If, on the other hand,

the molecule Loses energy and drops to a lower energy state, the photon is scattered at a

higher fiequency resulting in the anti-Stokes lines.

The resonance Raman of many compound serniconductors with band gaps in or

near the visible are often dominated by an intense progression of an series of optical

phonons, usually the longitudinal optical (LO) phonons, that are excited through a

distortion of the ionic Iattice that can be expressed in terms of crystalline normal modes.

The most prominent normal mode of excitation forms the RR progression. In CdS, the

lowest electronic excited state (the exciton) is most strongly coupIed with long

wavelength optical phonons via Friihlich interactioq6 where the radial electric field that

accompanies the displacement of the partially ionic nuclei (cd2+ ad s2-) couples with the

exciton in a Coulombic fashion. The process was discussed in great detail by ~ r ~ l i c h '

where p is the electronic transition dipole moment, E* is the excited electronic state

energy, is the laser fkequency, and r is the homogeneous electronic linewidth. The

Franck-Condon overlap integrals in the numerator are summed over intermediate m

vibrational levels and n is the final phonon state in the Raman process. For the purpose

of describing the intensities of the LO Raman bands, one needs only to consider the

Raman A term because strongly allowed transitions are symmetric. In the above

equation, the Raman cross section of the A-term depends parametrically on the exciton

energy (E*) and the homogeneous electronic linewidth m. By taking the ratio of peak

intensities of two RR overtones, one can determine these two parameters; That is:

where n = j and k are the two LO modes in the same RR spectrum, and Bjk is the ratio of

the jth to the kth Frank-Condon factor, that is,

3.3 Experimental

Arrays of aligned highly anisotropic semiconductor nano-wires with diameters in the

range 5.5 - 10 nrn and lengths of 1 pm were fabricated by electrodepositing CdS into the

pores of anodic alumitlum oxide (AAO). This work continues a previous study by Terry

Bigioni and later by Lori an.'' The band gap, or exciton energy, of the wires were

determined as a hc t ion of wire diameter fkom the excitation wavelength dependence of

the polarized resonance Raman spectra in the vicinity of the CdS absorption edge.

The excitation source used in this research project was a Spectra Physics 171

Argon Ion laser. The power of the incident laser was maintained at ( 9 0 s ) m W and

(5Ok5) mW for p- and s-polarization respectively. (The variation in laser powers affects

the absolute band areas but not their ratio.) The wavelengths of the excitation radiation

used in this study were 514.5, 501.7, 496.5, 488.0, 476.5 and 457.9 nm. These

wavelengths span the band gap of bulk CdS, with the longest of the wavelengths

corresponding to the exciton gap nearly exactly, producing an excitation just into the

bottom of the conduction band.

Figure 1 1 shows the experimental set-up for the Raman experiment. The sample

(#dl6, d3 1 or d51) was a CdS nano-wire array on an AAO substrate, taped on a glass

slide and mounted on an A1 sample stub. The laser light was filtered to remove emission

lines, polarized and focused onto the film at an incident angle of about 85". The scattered

light was collected at normal incidence to minimize the collection of elastically scattered

light. The light scattered fiom the sample was passed through a polarizer, collected with

SIZE EFFECTS IN CdS NANOWIRE ARRAYS i

Experimental setup for RRS

*--_ .- . . . . . filter

double beam mnochromtor

after twlo mirrors polarization vector

is at 45O

spectra consist of LO fundamental and overtone bands

number of overtones as well as overtone to fundamental band area ratio depends on CdS nano-wires diameter and on the excitation wavelength

size effect is more pronounced for spectra collected with ss- configuration due to broad and uncertain crystallite size distribution along the wire

58

an f7l achrornat lens, and focused on the entrance slit of a SPEX triplemate with an fl7

lens. After dispersion, the light was detected by a CCD camera (EEG 1024x256 liquid

N2 cooled) and the data acquisition was carried out using the EEG OMA 4000 software

run on a personal computer. The spectra of five randomly chosen spots were taken for

each sample at each wavelength and for each of ss- and pp-polarization. (There are thus

altogether 180 resonance Raman spectra fit.) In ss-polarization, for example, the incident

radiation &om the laser was polarized in the s-direction, which is perpendicular to the

scattering plane, and the s-polarized component of the scattered light was collected.

Therefore, the s-polarized light impinged on the sample with the electric field pointing

across the nano-wire in the radial direction. The p-polarized light, on the other hand, is

parallel to the scattering plane and impinged on the sample with the electric field pointing

almost along the nano-wire in the axial direction. A subsequent experiment involves

measuring only two spots per sample per wavelength per polarization. A neon lamp was

used as a standard to determine accurately the band frequency. Thus there were 72 RR

spectra in the second set.

The spectral region from 150 to 1050 cm-' of Raman shift was fit using

GRAM1386 software. While all Raman bands are fit with Lorentzians, only the first set

of data is baseline corrected before the fit. The second set of data was directly fit with

Lorentzians and a quadratic baseline.

Data sets with the ratios of the band areas (r2 = az/al and r3=a3/a,), the frequencies

of the LO modes £iom the spectral fits (in cm-') and the laser excitation energy (also in

cm-') were constructed for each of the six experimental conditions (3 samples and 2

polarizations). The data was inputted to a program that fit the experimental data to

Equation (26). The output of the program contains values for the band gap, the electronic

linewidth, and the ratio of the Franck-Condon overlap integrals of LO2 to LO1 (B2,), and

LO3 to LO1 (B3*). The fitting program utilizes the VA05 fitting subroutine which

minimizes a sum of squares of M b c t i o n s of N variables, without partial derivatives,

using a combination of Newton-Raphson, steepest descent and Marquardt algorithms.

Each data set was fit with ten sets of initial values. The errors in the parameters

were detennined based on the steps outlined in Wentworth7s artide,I2 which determined

the standard deviation of the parameters on the basis of the dependence of the sum of the

residuals on the change in each of the parameters.

3.4 Results

Table 7. Results of band gap determination of CdS nano-wires.'

ss-polarization I pp-polarization

0 the "Band Gap Fit" program is given in Appendix I; Errors given represent the

standard deviations generated by the program

3.5 Discussion

n e resonance Raman spectra consists of a progression based on a single

f'undamental band at approximately 304 cm-' and its overtones, as has been previously

observed8 for bulk CdS and assigned to the longitudinal optical (LO) phonon.

The number and the relative intensities of the RR overtones increases with

increasing particle size and with increasing excitation energy (Figure 12). However, fiom

Table 7, it is noted that polarization seemed to have little effect on the RR spectra and the

band gap values. The lack of an observable difference between ss- and pp-polarized

spectra might be due to the imperfect anisotropy of the CdS excitons. The wavefimctions

of the excitons produced by both axially and radially polarized exciton may be close to

spherically symmetric; The two excitons might have experienced the same environment.

XRD studies can be done to check this speculation.

The exciton energies E, determined with RRS polarized across (ss-) and dong

@p-) the nano-wires are around 2.48 eV. All reported values are significantly higher than

2.376 eV, the bulk band-gap energy determined fiom previous RRS experiments, or 2.42

eV, the same value determined from optical absorption.8 As the diameter of the CdS

nano-wires approach the bulk exciton, the delocalization is limited by the nano-wire

boundaries. This decreases the overlap between electron and hole and thus decreases the

electron-phonon (Frohlich) coupling which induces the LO modes. The size dependence

of the overtone intensity ratio is not as pronounced as predicted.

Additionally, the exciton energy seems to be independent of wire diameter in the

range of d' studied. There are at least two reasons for this observation. First, the

I I i 1

300 400 500 600 700 800 900 Raman Shift (cm-1)

Figure 12. Resonance Raman spectra of CdS nano-wires of different diameters

excited w i i h an s-polarized 458 nm laser

63

relatively large scatters in the LO band areas ratios, which may be due to imprecise

adjustment filter position in the first set of experiment, constitute the wide error bars in E,

for all the three wire diameters. The true band gaps can Lie anywhere in this range and so

unless the LO band area ratios happen to cluster around the correct value, the reported

results may have preclude the observation of a realistic h c t i o n d dependence on wire

diameter. More importantly, the constancy of E, versus $ might not be inaccurate at all;

It should not be surprising to see that E, does not totally agree with Kayunma's

variational calculation (Equation 27, 28) because the latter theory is proposed for

spherical particles while the shape of the CdS nano-wires is likely not to be purely

symmetrical.

The ratio of Frank-Condon overlap integrals (B2, and B,,) decreases as the nano-

wire diameter decreases. From Equation (26), this means that the Franck-Condon factor

for the first vibrational (bdamental) mode increases with respect to that of the second

mode (B,3 increases. This is another evidence of quantum confinement; when the

exciton are in a quantum size regime, the electron-hole overlap increases for decreasing

particle size and the excited state vibrational wavefunctions become very close to the

ground state. This trend resembles the result of Shiang et alYf3 who reported that the ratio

of the intensity of the fundamental to those of the overtones in an RRS spectrum

increases with decreasing cluster size due to an increase in electron-hole overlap.

For both polarizations, the electronic linewidth at d, = 5.5 run is considerably

larger than that at d, = 10 nm and d, = 8.0 nm. It is known that the electronic linewidth is

64

the inverse lifetime of the excited state. Thus the excited state Lifetime is approximately

20 fs. This is the same order sf the electronic excited state lifetime of 50 fs for a 7 nm

CdS cluster,'' while the lifetime of an excited state in bulk material is on the order of

nanoseconds. The discrepancy between the bulk and cluster lifetimes has been attributed

to the trapping of electronic state by lattice defects that can reduce the excited state

lifetime. Despite the difference, the small linewidth and its sharp increase for smaller

diameters demonstrate the quantum confinement phenomenon.

As far as the LO mode fiequency is concerned, there is no significant LO phonon

frequency differences were found in the ss- and pp-spectra though it has been reported

that in hexagonal CdS the LO phonon eequency is crystaIlographically anisotropic with

LO 1 = 306 cm' in the z-direction and 302 ern-' in the x-dire~tion.'~ Neither is there any

noticeable dependence of LO phonon fiequency with wire diameter or excitation

wavelength.

Errors in E, were estimated fiom two sources. First, the statistical errors fiorn the

band gap fits were calculated in the normal fashion, giving the standard deviations for

each of the parameters. The other sources of errors are fiom the band area ratios that are

input to the fitting program. Band area ratios fiom the first and second set of data were

combined and any outliers were rejected using standard statistical techniques.15 For each

sample, the standard deviation of the band area ratio of any particular excitation

wavelength and polarization is within iO.l nm, which is equivalent to a 12% change in

band areas. Since this statistical deviation is about 10 times larger than that of the band

gap fit (Table 7), it is legitimate to assume that the overall error estimate for the band-gap

fits come mainly from the errors in the band area ratios. From Ref. [a], a 10% change in

peak area ratios give an error bar of AE, = k0.015 eV for the E, values, so in this study a

12% change in peak area ratio should give an upper bound for hE, = M.02 eV. This

value is taken to be the overall error in the calcdated band gaps. Moreover, the goodness

of the band-gap fits may also be gauged from Figure 13 and 14, which compare the

measured and the recalculated L02/L0 1 (solid curve) and L031LO 1 (dashed curve) band

area ratios as a function of excitation wavelength for ss- and pp-polarization respectively.

The recalculated values were obtained using Equation (26) and the frnal fit parameters. .

(The interested reader is also referred to the figures in Appendix I1 for more details.) The

position of the maximum of these plots is determined by the exciton energy due to the

resonance condition. From the plot it is obvious that this maximum shifts towards lower

wavelength as the particle size decreases. This "blue shift' signifies the onset of quantum

confinement. The lack of observable size dependence of exciton energy may then be

caused also by some limitations of the fitting program, especially those in the aIgorithm

used for calculations for the four parameters in Table 7. Further analysis should be done

in order to debug or improve the program.

Furthermore, the shift in the exciton energy as a h c t i o n of the nano-wire

diameter can be compared with the results of the semi-empirical theory of Kayunama for

spherical CdS particles16 and the results of Lori Ryan et a2.l' The important reduced

parameter in Kaparna's analysis is the ratio of the radius of a particle, R, to the Bohr

radius of the buk exciton a,* which is equal to 2.1 nm for CdS. Hence for the nano-

, d16s I w d31s I 1 A d51s I

0 d16s(2) I 0 d31s(2)

& d51s(2) ,- Poly. ( d ? 6 ~ )

1- Poly. (d3ls) I - Poly. (d5ls)

1 - -PoIy. (d1&(2))

I - - Poly. (d3l s(2)) i - -- Poly. (d5l s(2))

480 490

Wavelength (nm)

Figure 14. Area Ratio (LONLO1 8 L031L01) vs. Wavelength: B. p p-polarization

1- Poly. (d51p) - - Poly. (d 1 6p(2)) - - Poly. (d31p(2)) - 1 - Poly. (d5l p(2))

Wavelength (nm)

wires in this study, this ratio ranges fkom 2.6 to 4.8. These values fail in a transition

region between two size regimes which can be described by approximations for which

analytical expressions relating the exciton energy to the particle radius can be obtained.

For Rl a,' 5 2, the excitation is described by a strongly confined electron and a strongly

contined hole, with an accompanying Coulombic interaction. The appropriate expression

relating exciton energy to size in the case is:13

where hE is the energy of the exciton relative to the bulk band-gap, rn, is the reduced

mass of the effective masses of the electron and hole, K is the dielectric constant, and

E,,' r rn, e4 1 2 K~ h2 is the effective Rydberg energy of the bulk exciton. The effective

masses of the electron and hole are taken to be 0.18 and 0.51 me respectively and K is

taken as 5.3, yielding a value for Em of 64.4 meV. On the other hand, when R/aB* 2 4,

the confinement of the electron and hole wavehctions is weak, and the expression

relating the exciton energy to particle size becomes:

where M is the sum of the electron and hole effective masses. In the bulk limit, Equation

(28) approaches -E~,,* as predicted. There is no analytical expression for particles whose

dimensions fall in the range 2 ~ a , * S 4. However, Kayunama has performed a fidl

variational calculation for particles spanning a very broad range of sizes encompassing

the strong, intermediate and weak confinement regions. The results of that calculation

Fig LS . Exciton energy as a function of CdS nanowire diameter

, - - - - - S trConf-Y

WkConf-2 1- Variation Cafcn

10 15 20

Wire diameter (nm)

provide a basis for estimating the excitonic energy in the intermediate confinement size

range. Figure 15 shows the three experimental data points, as well as the curves

calculated based on Equations (27) and (28) and the solid curve that describes the

intermediate confinement regime pertinent to the range of nano-wires in this study. For

both polarizations, the solid curve fits well the experimental data for d, = 5.5 nrn and 8.0

nm, but not that for d, = 10.0 nm. The latter observation is expected since the 10 nm

nano-wire is at weak confinement region where ~/a,* 2 4. Kayunarna's theory, proposed

for spherical particles, should have failed for the smallest nano-wires which have the

highest aspect ratio; the good agreement for the smaller-diameter wire, while gratifying,

might imply that the RR spectra is reporting the properties of low aspect ratio

microcrystallites that constitutes the nano-wire instead of the larger structure of the nano-

wire which has a higher aspect ratio. The Raman spectra of BN microcrystallites and S i

microcrystallites have shown to be sensitive to the microscopic The

author echoes the comment made by Lori et a2" that the presence of CdS rnicrostmchrre

could have obscured any observable anisotropy in the ss- and pp-spectra.

3.6 Conclusions

Polarized resonance Raman spectra of CdS nano-wires with mean diameters of 5.5,

8.0 and 10.0 nm were collected at six different excitation frequencies. The exciton

energy was determined by fitting the ratios of resonance Raman overtones as a kct ion

of excitation energy to a fitting program. The exciton energy was found to be almost

independent of wire diameter and polarization, at a value of - 2.48 eV that is much higher

than the bulk band-gap energy of CdS. It is possible that the nano-wires are comprised of

microcrystallites with low aspect ratios, which may have contribute to the lack of

polarization dependence. As a small blue shift is observed for the nano-wire with the

lowest diameter, the lack of size dependence is likely to be caused by limitations of the

fitting program.

3.7 References

(1) Kittel, C . lnhoduction to Solid State Physics; Wiley : New York 1 996; p 2 12.

(2) Nearnen, D. A. Semiconductor Physics and Devices; Irwin: Homewood, 1992; p 86.

(3) Brus, L. E . J. Chem. Phys. 1984,80,4403.

(4) Routkevitch, D.; Bigioni, T.; Moskovits, M.; Xu, J. M . J. Phys. Chem. 1996, 10,

14037.

(5) Jarrold, M. F. Science 1991,252, 1085.

(6) Nivisatos, A. P.; Harris, T. D.; Carroll, P. J.; Steigerwald, M. L. J. Chem. Phys.

1989,90,3463.

(7) Frolich, H.; Proc. Roy. Soc. London A 1937,160,230.

(8) Loudon, R.; Proc. Roy. Soc. Loudon A 1963,275,218.

(9) Merlin, R.; Giintherodt, G.; Humphreys, R.; Cardona, M.; Suryanarayanan, R.;

Holtzberg, F. Phys. Rev. B 1978,17,4951.

(10) Rossetti, R.; Ellison, J. L.; Gibson, J. M.; Brus, L. E. J: Chem. Phys, 1984,80,4464.

( 1 1) Roukevitch, D; Haslett, T. L.; Ryan, L.; Bigioni, T.; Douketis, C.; Moskovits, M.

Chem. Phys. 1996,210,343-352.

(1 2) Wentworth, W. E. J Chem. Ed. 1965, #Z(Z), 96.

(13) Shiang, J. J.; Goldstein, A. N.; Alivisatos, A. P. J. Chem. Phys. 1990,92,3232.

(14) Scott, J. F.; Leite, R. C. C.; Damen, T . C . Phys. Rev. Lett. 1969,22,780.

(1 5 ) Moore, D. S.; McCabe, G. P. Introduction to the Practice of Statistics; Freeman:

New York, 1993.

(1 6) Kayanuma, Y. Phys. Rev. B 1988,38,9797.

(17) (a) Iqbal, 2.; S.; Veprek, A. P.; Capemto, P. SoZidState Commun. 1981,37,993.

@) Richter, H.; Wang, 2. P.; Ley, L. Solid State Commun. 1981,39,625.

(18) Nemaaich, R. J.; Solin, S. A.; Martin, R. M.; Phys. Rev- B 1981,23,6348.

Conclusions

Templated electrochemical deposition into the pores of the anodic aluminum

oxide (AAO) film was shown to be a convenient route for the fabrication of metal and

semi-conductor nano-wire arrays. A novel low-temperature anodization method (T,

&om 0 O C to -80 "C) was developed for this purpose. Templates with very small pore

diameters (< 4 nm) and high structural integrity and uniformity was successfdly made.

Polarized resonance Raman spectroscopy (RRS) is usefid for band gap

determination. Effects due to anisotropy and quantum confinement have been observed

with these nano-wires. The band gap Eg of semiconductor nano-wires (e.g. CdS) can be

tuned through its dependence on wire diameter d,. (Eg increases as d, diminishes.) In

addition, both semiconductor (e.g. CdS) and metal (e-g . Ni) nano-wires have properties

(optical, electronic, magnetic, etc.) that open up opportunities for device applications.

This project has meant to provide a fundamental analysis of the factors involved

in each step in this fabrication process with an aim at producing device-quality metal and

semiconductor nano-arrays. Further analyses of this sort should be made in order to

study more thoroughly the electrochemical factors that affect nano-template production

and electrodeposition, and the properties of the nano-wires (such as crystallinity and

anisotropy) that makes them suitable for the various potential device applications.

5

Appendix I

BAND GAP FIT VAO5MP SUM OF SQUARES OPTIMIZATION BAND2ER3 . IN (VER: JAN 8, 1979) band2er3 o 4 variables, 78 terms in sum of squares, maxit = 500, print modulus = 0 Oacc= 1.0000000D-15, dstap = 5.300000D-05, dmax= 2.000000D+00

,829345 -317767 299.626500 603.104300 909.266500 21838.83 .894596 -198746 303.694900 606.226600 909.828700 21838.83 -753094 -467790 305.963900 608-457300 910.827500 21838.83 -605262 ,303288 308.393600 610.493600 911.617800 21838.83

1,097418 ,520443 302.746300 606.459400 909.285700 20986.36 ,979928 -390939 302.590600 605.859300 908.661000 20986.36 -916927 .317679 302.809100 606.137100 908.032900 20986.36 -923119 .466564 302.825700 606.175100 908.244800 20986.36

1.026850 -522871 302-966800 606.448600 909.638800 20986.36 -893777 -583760 305,261500 607.801800 908.377100 20986.36 ,975474 ,682592 305.663100 608-368100 908,176900 20986.36 -694098 ,053787 300.568800 602.395200 907.032800 20491.80 ,855249 -016263 300.418000 601-484700 897.125300 20491.80 ,690997 .052173 298.854300 601.291700 909.983000 20491.80 ,655256 .OOOOOO 302.140000 604.802100 .OOOOOO 20491.80 .844805 .OOOOOO 301.172100 604.179500 .OOOOOO 20491.80 .725248 -190427 304.910000 607.618800 909.699800 20491.80 ,672984 -172692 304.252500 607.158900 909.815600 20491.80 .502406 .OOOOOO 311.378300 615.087600 .OOOOOO 20140.99 .461584 .OOOOOO 312.548500 615.612000 .OOOOOO 20140.99 .438205 .OOOOOO 312.740000 616-008200 .OOOOOO 20140.99 -506756 .OOOOOO 312.526900 615.525800 ,000000 20140.99 .549087 .OOOOOO 311.626500 615.111600 ,000000 20140.99 .420406 -088494 306.237400 609.042200 909.960500 20140.99 -509037 -237800 307.279800 610.047700 901.796200 20140.99 -393579 .OOOOOO 316.067900 619.630400 .OOOOOO 19932.23 -334598 .OOOOOO 315.963800 619.055700 .OOOOOO 19932.23 -252483 .OOOOOO 316.501700 618.028300 .OOOOOO 19932.23 -357369 .OOOOOO 315.658300 619.564200 .OOOOOO 19932.23 -272091 .OOOOOO 315.803400 619.556100 .OOOOOO 19932.23 -501530 -188458 305.822000 608.483900 902.999800 19932.23 -423473 .OOOOOO 304.909300 607.450700 .OOOOOO 19932.23 -356767 .OOOOOO 314.721600 618.228400 .OOOOOO 19436.35 .230213 .OOOOOO 314.299400 615.960500 .OOOOOO 19436.35 -291642 .OOOOOO 314.247100 616.607000 .OOOOOO 19436.35 .290200 .OOOOOO 314.596700 618.985300 ,000000 19436.35 -293863 .OOOOOO 314.470400 619.075000 .OOOOOO 19436.35 .325343 ,000000 314.330500 617-791700 .OOOOOO 19436.35 ,305177 .OOOOOO 305.645300 608.612300 .OOOOOO 19436.35

ZFILE = j dl6s .prn dl6s dl6s (2) wlol wl02 wlo3

INITIAL CO-ORDINATES 1 2 -3770 2 -0040 3 -1010 4 .0610

OSUM OF SQUARES = 4.97390713Dt00 I*** F(X) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 67, 72 FVNCTION EVALUATIONS OSUM OF SQUARES = 6.67794877D-01

fit data ydif f -75206 -82935 -. 07729 .32520 -31777 .00743 .75193 .a9460 -. 14266 -32456 -19875 .I2581 -75214 -75309 -. 00096 -32441 -46779 -. 14338 -75216 .60526 ,14690 -32417 .30329 -02088

-80275 .80302 -80270 .80370 .80291 -63605 .63797 -63057 -63084 .32625 -32614 .32642 -32625 -32623 -32708 -33815 -33884 -33836 .33848 -33918 .33896 -33735 .33740 .39801 -39925 .39910 -39995 -39820 -39991

total spec .80142?400509504 variance, sd of parameters

x ( 1 ) bandgap 2.47566634 . 00001737 .00416770 x (2 ) linewidthA2 -00137329 .00000014 .00037315 x(3) ~ 2 1 ~ 2 -27887456 -00023841 .00036506 -01544040 -01910653 x(4) ~ 3 1 ~ 2 -02946876 .00003778 .00014239 -00614627 .01193269 va12 -.00000004 va13 -.00000427 va14 -.00000022 va23 .00000009 va24 .00000130 va34 -,00000112 vext -01635566 INITIAL CO-ORDINATES

1 2 -4700 2 .0020 3 -4000 4 -0610

OSUM OF SQUARES = 1.40313331Dt00 I*** F (XI NO LONGER D E C W E S . . . OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 68, 73 FUNCTION EVALUATIONS OSUM OF SQUARES = 8.01425418D-01

fit data ydif f .64818 -68965 - -04147 -27152 .28879 - - 01727 -64775 .74107 - -09332 .27084 .29293 - -02209 -64784 .68912 -. 04128 .27099 .34646 - -07547 ,64755 -82558 - .I7803 -27035 -35268 - -08233 .64865 .64804 -00062 .27136 .32819 - -05683 -64887 ,56122 .08765 -27142 -26122 .01020 .80264 -75466 -04798 .41760 .24337 .I7423 -80269 -73810 .06459 -41677 -29759 .I1918

-80296 -80264 -80364 .a0285 -63 674 -63866 -63126 -63 153 -32635 .32624 -32652 -32635 -32633 .32718 -33815 -33884 -33836 .33848 -33 917 -33896 -33735 .33740 - 19802 -39926 -39911 .39996 -39822 .39992

t o t a l s p e c .8014254177050023 variance, sd of parameters

x ( 1) bandgap 2 -47561524 .00001735 x(2) l i n e w i d t h A 2 -00137369 .00000014 x ( 3 ) ~ 2 1 ~ 2 ,27893953 .00023840 .01910642 x(4) ~ 3 1 ~ 2 -02939213 .00003762 -01190806 va12 -.00000005 va13 -.00000422 va14 -. 00000021 va2 3 .00000009 va2 4 .00000130 va3 4 - - 00000109 vext -01635562

INITIAL CO -0RD INATES 1 -8000 2 .0400 3 . so00 4 -9000

OSUM O F SQUARES = 1.33704038D+01 I*** MAXIMUM NUMBER O F ITERATIONS EXCEEDED OWSULTS AT ITERATION 500, 5 0 5 E'UNCTION EVALUATIONS OSUM O F SQUARES = 1.70257039D+00

f i t data ydif f .59955 .68965 - -09010 -32370 -28879 -03491 -59927 .74107 - . I 4180 -32324 .29293 .03031 -59932 -68912 - -08980 .32333 -34646 - -02313 .59915 -82558 - -22643 -32291 .35268 - -02976 -59960 .64804 - -04844 -32327 -32819 -. 00492 -59974 -56122 .03852 -32331 .26122 .06209 -59517 -75466 -. 15949 .29741 -24337 .05404 -59519 -73810 - -14292 .29735 .29759 -. 00024 -59522 -88523 - - 2 9 0 0 1 -29735 -27432 -02302 .59514 , 88515 -. 29001 -29732 .38302 - -08571 -59489 . 92771 - .33282 .27390 .56923 - -29533

.59482 ,52892 -52914 -52828 -52831 ,47182 .47188 -47189 -47182 -47183 -47265 -45184 .45226 -45185 -45183 -45221 -45202 -45276 -45270 .43881 -43 972 -43964 -44021 -43897 -44074

total spec 1.7025703868349 variance, sd of parameters x ( 1 ) bandgap 2.47585644 .00105599 x (2) linewidthA2 ,01338447 .00007128 x(3) 321A2 -26690251 .00077068 .03435254 x(4) ~ 3 1 ~ 2 .05651803 .00030286 -03378678 va12 .00008087 va13 .00000611 va14 -.00023696 va2 3 -.00040255 va2 4 .00003235 va34 .00001288 vext .03474633

INITIAL CO-ORDINATES 1 -6000 2 -0300 3 -0400 4 .I200

OSUM OF SQUARES = 5.87817042D+00 l*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 1.86737126D+00

fit data ydif f .58210 -68965 -. 10755 -31920 .58186 -74107 -. 15921 -31881 -58189 -68912 -. 10722 -31888 -58175 -82558 -. 24383 -31853 -58208 .64804 - -06596 .31875 -58220 -56122 -02099 .31879 ,56800 -75466 -. 18667 -28703 -56801 -73810 - .I7010 -28699 .56803 -88523 -. 31721 -28698 .56796 .a8515 -. 31718 -28696 .56772 .92771 - .35999 .27075 .56769 1.03464 - -46695 -28658 .51474 ,59746 -. 08272 .23083 .51490 -70368 -.I8878 -23096

total spec .186737D+01 14 .63178 1.86737125741574 variance, sd of parameters

x ( 1 ) bandgap 2.47845650 -00223649 x ( 2 ) l i n e w i d t h A 2 .01795417 . 00018190 x ( 3 ) ~ 2 1 ~ 2 .25847854 .00089486 -03701701 x ( 4 ) 831A2 -05873915 .00040286 -03896762 va12 .00018760 va13 -00012867 va14 - -00073310 v a 2 3 - .00066244 v a 2 4 .00005432 va34 .00007306 vext -03810962 INITIAL CO-ORDINATES

1 -6700 2 -3000 3 . I 500 4 -4500

OSUM OF SQUARJ3S = 6.12017699D+00 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 417, 422 mTNCTION EVALUATIONS OSUM OF SQUARES = 2 . 1 0 3 5 9 5 0 5 ~ t 0 0

fit -56630 .56612 .56614 .56603 ,56620 .56630 -54659 .54660 .54661 -54657 -54638 -54637 .51149 ,51158 .51120 .51122 -48426

d a t a ydif f

-48429 -47887 -00542 .OOOOO -48429 .37817 -10613 .OOOOO -48426 .39945 .08481 .OOOOO -48426 -40554 -07872 .OOOOO -48471 .36466 .I2005 -22527 -47205 -29800 ,17404 .OOOOO -47230 -36333 ,10897 -00000 -47205 -33184 .I4021 .OOOOO -47203 -22747 .24455 -00000 -47225 -24156 -23069 .OOOOO .47213 -27948 -19265 .OOOOO ,47267 -27364 -19903 .OOOOO -47263 -30033 -17231 .OOOOO .45651 ,19022 -26629 .OOOOO -45716 -15040 -30676 .OOOOO .45712 .07912 -37800 .OOOOO -45751 -06655 -39096 .OOOOO .45663 .22490 -23 172 -00000 -45804 -33095 -12709 .OOOOO

total spec .210360D+01 16.48271 2.10359505145384 variance, sd of parameters x (1) bandgap 2.47840018 -00730441 x (2 ) linewidthA2 .02919879 .00076214 x(3) ~ 2 1 ~ 2 .25759742 .00118595 -04261431 x(4 ) ~ 3 1 ~ 2 .06518488 -00067482 -05043369 va12 .00059219 va13 .00103096 va14 -.00466347 va23 -.00037899 va24 .00013288 va34 ,00031691 vext .04293051 INITIAL CO-ORDINATES 1 -6000 2 -9000 3 -2000 4 -1000

OSUM OF SQUARES = 2.86621679D4-00 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 117, 122 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.69629713D+OO

fit -50152 -50152 -50152 .50151 -50148 -50148 .49677 -49677 -49677 -49677 -49675 -49676 -49408 .49408 -49408 .49408 -49225 -49225 -49226 .49225

data ydif f

-49225 -40554 -08671 .OOOOO .OOOOO .OOOOO -49229 ,36466 - 12764 -27137 .I2549 .I4589 -49124 .29800 -19324 .OOOOO .OOOOO .OOOOO .49129 ,36333 -12796 .OOOOO .OOOOO .OOOOO -49124 -33184 .I5941 -00000 .OOOOO -00000 .49124 -22747 .26377 .OOOOO .OOOOO -00000 .49128 -24156 -24972 .OOOOO .OOOOO .OOOOO -49126 .27948 -21178 .OOOOO .OOOOO .OOOOO .49131 -27364 -21767 .OOOOO .OOOOO .OOOOO .49131 -30033 -19098 .OOOOO .OOOOO - 00000 .48905 -19022 ,29883 ,00000 . 00000 -00000 .48917 -15040 -33877 .OOOOO .OOOOO -00000 -48916 ,07912 -41005 .OOOOO .OOOOO .OOOOO -48924 -06655 .42269 .OOOOO .OOOOO .OOOOO .48907 ,22490 -26417 -00000 .OOOOO .OOOOO -48935 -33095 .I5840 .OOOOO .OOOOO .00000

total spec .269630D+Ol 21.12682 2.696297133 10724 variance, sd of parameters x ( 1) bandgap 2.57678280 53.79885856 7.33477052 x (2) linewidthA2 ,41188889 21.68709695 4.65694073 x(3) B21A2 -24817295 -09671377 -14809297 .31098838 .38482849 x(4) B31A2 -07763281 -04555128 .I7169329 .21342746 -41435889 va12 -25.08659508 va13 2.23987844 va24 ************ va2 3 ************ va2 4 -.79134551 va3 4 -06592228 vext .05502647 INITIAL CO-ORDINATES 1 -1000 2 -1000 3 .go00 4 -0900

OSUM OF SQUARES = 1.08038067D+01 I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 1.35519656D+00

fit data ydif f

-42546 -36333 -06214 -00000 - 00000 . O O O O O .42496 -33184 .09312 . O O O O O . O O O O O -00000 -42496 -22747 -19748 . O O O O O . 00000 . O O O O O -42547 -24156 -18391 . O O O O O . O O O O O . O O O O O -42523 .27948 . I 4575 . O O O O O . O O O O O -00000 - 4 2 5 7 1 -27364 -15207 . O O O O O . O O O O O . O O O O O -42565 -30033 -12533 . O O O O O ,00000 . O O O O O ,42723 . I 9022 .23701 . O O O O O . O O O O O -00000 -42828 . I5040 .27788 . O O O O O -00000 ,00000 -42818 -07912 -34906 . O O O O O . O O O O O . O O O O O ,42886 -06655 -36231 . O O O O O . O O O O O . O O O O O - 4 2 7 4 1 .22490 .20250 . O O O O O . O O O O O . O O O O O -42925 -33095 -09830 . O O O O O . O O O O O . O O O O O

total spec .135520D+01 10.61864 1.3SSl9655749407 v a r i a n c e , sd of parameters

x ( 1 ) bandgap 2 -47990385 .00033049 .01817926 x ( 2 ) l i n e w i d t h A 2 -00727829 .00001004 .00316856 x ( 3 ) ~ 2 1 ~ 2 ,27515090 -00049713 -00076123 -02229636 -02759033 x ( 4 ) ~ 3 1 ~ 2 -05176752 .00018946 .00071411 -01376435 -02672280 va12 .00001860 va13 -.00006713 va14 -.00002342 va2 3 -.00008188 va2 4 .00000914 va3 4 - . 00003210 v e x t -02765707 INITIAL CO-ORDINATES 1 .4000 2 -5000 3 -6000 4 -6000

OSUM OF SQUARES = 1.05809247D+01 I*** F ( X ) NO LONGER DECREASES . . . OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AN13 ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 474, 479 FUNCTION EVALUATIONS OSUM OF SQUARES = 8.01435418D-01

fit data ydif f .64855 .68965 - . 04110 - 2 7 2 2 1 .28879 - -01659 - 6 4 8 1 1 .74107 - . 09296 .27152 -29293 -. 02141 -64820 -68912 - .04092 .27168 -34646 -. 07478 . 64791 .82558 - . I 7767 -27103 .35268 -. 08165 .64902 -64804 ,00098 -27205 .32819 -. 05614 -64923 .56122 .08802 . 27211 .26122 -01089 -80322 -75466 -04856 . 41871 -24337 . I7534 ,80327 -73810 .06517 -41788 .29759 -12 02 9 -80354 .88523 -. 08169 . 41801 .27432 -14369 -80322 -88515 -. 08193 -41790 .38302 .03488 .80422 -92771 -. 12349 -26212 .56923 -. 30710 .80344 1 .03464 -. 23120 -41546 .58902 -. 17356 -63658 .59746 -03912 . I 3 2 0 4 -03847 -09358 -63850 -70368 - -06517 -13257 -03944 ,09313 -63110 -63951 -. 00841 -13050 . I2088 .00963 -63137 -65413 -. 02276 -13059 -12585 -00474 -32641 .34945 -. 02304 . O O O O O . O O O O O . O O O O O .32630 -47887 -. 15257 . O O O O O . O O O O O . O O O O O ,32658 -37817 -. 05159 . O O O O O . O O O O O . O O O O O - 32641 .39945 -. 07304 . O O O O O . O O O O O .00000 .32639 .40554 -. 07914 . O O O O O . O O O O O . O O O O O .32724 .36466 -. 03742 -07098 . I2549 - , 05451 -33833 .29800 .04033 . O O O O O . O O O O O . O O O O O -33902 -36333 -. 02430 . O O O O O . O O O O O . O O O O O

-33854 - 33184 . 0 0 6 7 1 . O O O O O -00000 . O O O O O , 3 3 8 6 6 - 2 2 7 4 7 . I 1 1 1 8 . O O O O O . O O O O O , 0 0 0 0 0 - 3 3 9 3 6 - 24156 .09779 . O O O O O . O O O O O . O O O O O , 33914 - 2 7 9 4 8 .05966 - 0 0 0 0 0 -00000 , 0 0 0 0 0 - 3 3 7 5 3 -27364 ,06389 . O O O O O . O O O O O . O O O O O - 3 3 7 5 8 - 3 0 0 3 3 .03726 . O O O O O -00000 . O O O O O - 3 9 8 2 4 -19022 -20802 . O O O O O . O O O O O . O O O O O - 3 9 9 4 9 -15040 .24909 ,00000 -00000 . O O O O O - 3 9 9 3 4 .07912 ,32022 . O O O O O . O O O O O . O O O O O - 4 0 0 1 9 - 0 6 6 5 5 .33364 . 00000 . 00000 . O O O O O -39844 -22490 -17354 . O O O O O . O O O O O . O O O O O . 40015 - 3 3 0 9 5 -06920 . O O O O O . O O O O O . O O O O O

total spec .801435D+00 6 .27964 .8014354183526788 variance, sd of parameters

x ( 1 ) b a n d g a p 2.47565927 .00001729 -00415872 x ( 2 ) l i n e w i d t h A 2 .00137255 .00000014 .00037228 x ( 3 ) B21A2 ,27921988 .00023840 .00036506 - 0 1 5 4 4 0 3 6 - 0 1 9 1 0 6 4 7 x ( 4 ) B31A2 .02953290 .00003777 .00014238 - 0 0 6 1 4 6 1 3 - 0 1 1 9 3 2 4 1 v a 1 2 - .00000004 v a 1 3 - -00000425 v a 1 4 - .00000021 v a 2 3 .00000009 v a 2 4 .00000130 v a 3 4 -. 00000111 vext -01635582

INITIAL CO-ORDINATES 1 . s o 0 0 2 - 2 0 0 0 3 1 . 0 0 0 0 4 3 . 0 0 0 0

OSUM OF SQUARFS = 5.18848155D+Ol l*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 5 00 , 5 0 5 FJNCTION EVALUATIONS OSUM OF SQUARES = 8 -01466658D-01

fit - 6 4 7 1 3 .64670 - 6 4 6 7 9 .64650 - 6 4 7 6 0 .64782 - 8 0 0 6 9 - 8 0 0 7 5 . 8 0 1 0 1 .80069 - 8 0 1 6 8 .80090 , 6 3 5 8 3 - 6 3 7 7 3 .63039 - 6 3 0 6 6 - 3 2 6 5 4 - 3 2 6 4 3 , 3 2 6 7 1 - 3 2 6 5 4 .32653 .32739 - 3 3 7 9 1 .33860 - 3 3 8 1 2 .33823 - 3 3 8 9 3

d a t a ydiff

.92870 ,92800 . 9 2 8 1 6 - 9 2 8 2 0 .92844 .92788 - 9 2 8 2 6 .73382 , 7 3 4 5 1 .73640 . 7 3 064 - 7 3 2 1 0 - 7 2 5 8 6 .72687 - 3 8 3 4 8 - 3 8 3 7 2 - 3 8 3 5 8 - 3 8 3 7 6 - 3 8 3 5 8 - 3 8 4 6 5 - 3 8 4 5 4 - 3 9 5 4 0 - 3 9 5 6 2 - 3 9 6 4 7 .39517 ,39527 - 3 9 4 4 0 .39433 - 4 6 3 5 5 .46420 - 4 6 3 9 3 - 4 6 3 2 1 . 4 6 3 1 1 .46353 . 4 6 2 7 7

t o t a l spec .6677948774508796 variance, sd of parameters

x ( 1) bandgap 2 .47563391 .00000584 x ( 2 ) linewidthA2 .00145034 .00000006 x ( 3 ) ~ 2 1 ~ 2 -37547079 -00044498 .02620187 x ( 4 ) ~ 3 1 ~ 2 -04204343 - 0 0 0 0 2 5 6 9 .00961605

v a 1 2 .00000012 v a 1 3 .00001299 va14 .00000007 v a 2 3 .00000179 v a 2 4 .00000035 va3 4 .00002007 vext .01236657 INITIAL CO-ORDINATES

1 2.4700 2 -0020 3 -4000 4 -0610

OSUM OF SQUARES = 7.62136305D-01 l*** F ( X ) NO LONGER DECREASES . - . OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 8 1 , 86 FUNCTION EVALUATIONS OSUM OF SQUARES = 6.67792053D-01

f i t data ydif f . 75237 -82935 -. 07697 - 3 2 5 1 2 .31777 , 0 0 7 3 6 .75225 -89460 - . I 4 2 3 5 - 3 2 4 4 8 -19875 - 1 2 5 7 4

-75245 ,75247 ,92898 -92829 -92845 -92848 -92873 -92817 -92855 .73393 -73462 - 7 3 6 5 1 -73075 - 7 3 2 2 1 ,72598 -72699 -38376 .38400 -38386 -38404 .38386 ,38494 -38482 -39564 -39585 .39671 - 3 9 5 4 1 -39550 .39464 . 3 9457 .46377 .46442 -46415 .46342 .46333 -46374 -46299

total spec -6677920528320915 variance, sd of parameters

x ( 1) bandgap 2.47563879 -00000585 x ( 2 ) linewidthA2 .00145219 .00000006 x ( 3 ) ~ 2 1 ~ 2 .37578819 -00044497 -02620168 x ( 4 ) ~ 3 1 ~ 2 -04202578 .00002569 .00961743 va12 .00000012 va13 .00001298 va14 .00000007 va2 3 .00000179 va24 ,00000034 va3 4 .00002003 vext .01236652 INITIAL CO -ORDINATES

1 -8000 2 -0400 3 . SO00 4 -9000

OSUM O F SQUARES = 1.28727148D+01 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 196, 2 0 1 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.91712726D+00

fit data ydiff -62188 .a2935 -. 20746 -33494 -31777 .01718 .62175 -89460 -. 27285 -33473 -19875 . I 3598

-62173 -62 166 -60883 -60881 -60881 -60881 ,60881 -60872 -60872 -59701 -59700 -59706 .S9697 .59700 .S9690 -59692 -58755 -58753 ,58752 -58753 -58755 ,58770 -58767 ,58212 .58214 -58219 -58211 -58212 -58241 -58243 -57118 -57132 ,57127 .57112 -57111 -57119 -57139

total spec 2,91712725733031 variance, sd of parameters x ( 1) bandgap 2 -45364281 -36400899 x ( 2 ) linewidthA2 -10444218 -05430158 x ( 3 ) ~ 2 1 ~ 2 -34869399 -01587674 .15651050 x(4) 831A2 .09214178 -00618864 -14926191 va12 ,05696123 va13 .07247577 va14 -6.08331081 va2 3 5.51408935 va24 .00811061 va3 4 -00934819 vext -05402088 INITIAL CO-ORDINATES

1 -6000 2 -0300 3 -0400 4 .I200

OSUM OF SQUARES = 9.12039823D+00 l*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 202, 207 mTNCTION EVALUATIONS OSUM OF SQUARES = 2.98774038D+00

fit data ydif f -61854 ,82935 -. 21081 . 3 1766 -31777 - .00010 .GI843 .89460 -.27617 .31749 .I9875 -11875

.61841 -75309 - -13469 - 3 1742 -61835 -60526 -01309 .31734 -60817 1 - 09742 - .48925 -30580 -60815 -97993 - -37178 ,30579 -60815 -91693 --30878 .30578 -60815 .92312 - -31497 -30578 .60816 1 .02685 - .41869 .30580 -60808 .89378 - -28570 .30571 -60808 -97547 -. 36740 -30570 -59942 -69410 - -09468 .29672 -59941 -85525 - -25584 .29675 .59946 -69100 -. 09154 -29673 -59940 -65526 - -05586 . O O O O O .59942 . 84481 - -2453 8 .00000 -59935 -72525 - 12590 -29664 -59936 .67298 - -07362 -29665 -59241 - 5 0 2 4 1 .09000 .00000 -59239 -46158 ,13081 .00000 -59239 - 4 3 8 2 1 -15418 . O O O O O -59240 -50676 -08564 . O O O O O -59241 -54909 .04332 . O O O O O .59252 . 42041 -17211 ,28993 -59250 -50904 .08346 -29005 -58828 .39358 -19470 .00000 ,58829 -33460 .25369 . O O O O O .58832 -25248 .33583 . O O O O O -58828 -35737 -23091 -00000 .58828 .27209 -31619 .00000 .58849 .SO153 -08696 -28624 -58851 .42347 -16504 . O O O O O -57947 . 3 5677 -22270 . O O O O O .57957 - 2 3 0 2 1 .34936 .00000 -57953 - 2 9164 -28789 . O O O O O -57942 . 2 9020 -28922 . O O O O O .57942 - 2 9386 -28555 . O O O O O -57948 -32534 -25413 . O O O O O -57964 . 3 0518 ,27446 . O O O O O

t o t a l spec .298774D+01 16.07016 2.98774037656902 v a r i a n c e , sd of p a r a m e t e r s

x (1 ) bandgap 2.44155806 1.11625324 x (2 ) l i n e w i d t h A 2 -14094017 .19083910 x ( 3 ) ~ 2 1 ~ 2 .35130781 .03010430 -21551480 x ( 4 ) ~ 3 1 ~ 2 -08583221 .00929015 -03344456 .09638545 .I8287853 va12 -22475346 va13 -17926097 va14 -27.98923924 va2 3 26.78405957 va2 4 -02267656 va3 4 -01620252 vext -05532853 INITIAL CO -ORDINATES

1 -6700 2 .3000 3 -1500 4 -4500

OSUM O F SQUARES = 7.65171248D+00 l*** SUM O F SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 99, 104 FUNCTION EVALUATIONS OSUM OF SQU-S = 3.10469639D+00

f i t data y d i f f -60312 -82935 - .22623 -31232 -31777 - -00545 .60306 -89460 - .29154 ,31224 . I9875 . I1349

.60304 -75309 - -15005 -31220 ,46779 - -15559

.60301 -60526 - -00225 -31216 -30329 -00887 ,59664 1.09742 - -50078 -30534 -52044 - -21511 .59663 -97993 - -38329 -30534 -39094 -. 08560 -59663 -91693 -. 32029 -30533 .31768 - -01235 -59663 .92312 - -32649 -30533 .46656 - .I6123 -59663 1.02685 -. 43022 -30533 ,52287 - -21754 -59660 .89378 - -29718 -30531 -58376 - -27845 -59660 .97547 - -37887 -30530 .68259 - -37729 -59238 ,69410 - -10172 -30096 -05379 -24717

-59238 .85525 - -26287 .30101 .01626 -28474 -59239 .69100 - -09860 -30095 -05217 -24878 -59237 -65526 -. 06289 .OOOOO .OOOOO .00000 -59237 .84481 - -25243 .OOOOO .OOOOO .00000 -59234 -72525 - -13291 -30093 -19043 .11050 .59235 -67298 - -08064 -30093 .I7269 -12824 .58921 ,50241 -08680 .OOOOO .OOOOO .00000 -58920 -46158 -12762 .OOOOO ,00000 .00000 -58920 -43821 .15100 .OOOOO .OOOOO .00000 -58921 -50676 -08245 .OOOOO .00000 .00000 -58921 -54909 -04012 .OOOOO ,00000 .00000

-58926 ,42041 -16886 -29785 -08849 -20936 -58925 -50904 -08022 -29793 -23780 .06013 -58738 -39358 -19380 - 00000 .OOOOO .00000 .58739 ,33460 -25279 .OOOOO .OOOOO .00000 -58741 .25248 .33492 .OOOOO .OOOOO .00000 -58737 .35737 .23000 .OOOOO .OOOOO .00000

-58738 -27209 -31528 .OOOOO .OOOOO .OOOOO ,58748 -50153 -08595 -29617 .I8846 .I0772 -58749 - 42347 .I6402 .OOOOO .OOOOO .00000 .58339 -35677 .22662 .OOOOO .OOOOO .00000 -58344 ,23021 -35323 .OOOOO ,00000 .00000 .58342 -29164 -29178 .OOOOO .OOOOO .00000 .58336 -29020 -29316 .OOOOO .OOOOO .00000 -58335 -29386 -28949 .OOOOO .OOOOO .00000 ,58339 -32534 -25805 .OOOOO .OOOOO .00000 ,58347 -30518 -27829 .OOOOO ,00000 .00000

total spec .310470D+01 16.69923 3.10469639113787 variance, sd of parameters x ( 1 ) bandgap 2.47000089 23.10251514 4.80650758 x (2 ) linewidthA2 .31345983 2.92884400 1.71138657 x ( 3 ) ~ 2 1 ~ 2 .34969570 .I3599711 -20982411 .36877786 .45806562 x(4) ~ 3 1 ~ 2 .09076176 -04197694 -15111698 -20488274 .38873767 va12 2.33188456 va13 1.76118873 va14 ************ va23 ************ va24 ,09815789 va34 -07504651 vext ,05749438 INITIAL CO-ORDINATES

1 .6000 2 .go00 3 -2000 4 -1000

OSUM OF SQUARES = 3.95602283D+00 I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 1.73134609D+00

fit data ydif f -71349 .82935 -. 11586 .37390 -31777 .05613 -71327 .a9460 -. 18132 .37328 -19875 ,17453

- 7 1 3 3 4 - 7 1 3 2 7 .71740 . 7 1 7 2 7 - 7 1 7 2 7 . 7 1 7 2 8 . 7 1 7 3 1 . 7 1 6 8 2 .71684 - 6 3 1 7 3 - 6 3 1 8 0 - 6 3 2 1 1 - 6 3 1 3 0 - 6 3 1 5 1 - 6 3 0 6 2 , 6 3 0 7 7 , 5 5 2 7 0 .55267 - 5 5 2 5 9 - 5 5 2 6 9 - 5 5 2 7 1 - 5 5 3 7 8 - 5 5 3 6 2 - 5 2 6 2 9 - 5 2 6 4 4 - 5 2 6 8 5 - 5 2 6 2 3 - 5 2 6 2 6 - 5 2 7 4 4 - 5 2 7 5 6 . 5 1 3 2 6 - 5 1 3 7 8 - 5 1 3 5 8 - 5 1 3 0 0 - 5 1 2 9 4 - 5 1 3 2 7 - 5 1 3 3 2

t o t a l spec 1 .7313460912842 variance, sd of p a r a m e t e r s

x ( 1 ) b a n d g a p 2 .47388576 .00050083 x ( 2 ) l i n e w i d t h A 2 .01142061 .00002834 x ( 3 ) ~ 2 1 ~ 2 .37303431 .00130156 - 0 4 4 8 1 2 0 2 x ( 4 ) ~ 3 1 ~ 2 .07276925 .00031818 . 0 3 3 8 4 4 7 1 v a 1 2 .00003451 v a 1 3 .00028350 v a 1 4 - .00038005 v a 2 3 - .00044206 v a 2 4 .00001610 v a 3 4 .00024180 vext .03206196 INITIAL CO-ORDINATES

1 . I 0 0 0 2 . I 0 0 0 3 .go00 4 -0900

OSUM O F SQUARES = 8.63825083D+OO I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500 , 5 0 5 FUNCTION EVALUATIONS OSUM O F SQUARES = 6 . 7 3 3 3 5 7 9 7 ~ - 0 1

fit d a t a ydif f . 7 4 9 0 7 .82935 -. 08027 -32558 .31777 - 0 0 7 8 1 .74894 .89460 -. 14566 .32495 . I9875 . I 2 6 2 0

-74914 -75309 -. 00396 -32480 -46779 - -14299 -74915 .60526 -14389 -32456 -30329 -02127 -91395 1.09742 -.I8347 -48056 -52044 - -03988 -91329 -97993 -. 06663 -48033 .39094 .08939 .91344 .91693 -. 00348 -47988 -31768 -16220 - 91348 -92312 -. 00964 ,47998 -46656 -01342 ,91370 1.02685 -. 11315 -48062 .52287 - .04225 -913 15 -89378 .01937 ,47871 .58376 - .lo505 .91350 -97547 -. 06197 -47839 .68259 - .20420 .75334 -69410 -05924 -17105 .05379 -11726 .75389 -85525 - .lo136 -17374 .01626 -15747 .75574 - 69100 ,06475 -17071 -05217 .I1854 ,75052 -65526 .09527 .OOOOO . 00000 .OOOOO .75188 -84481 - .09292 .OOOOO .OOOOO .OOOOO .74616 -72525 .02091 -16925 ,19043 - ,02118 -74710 -67298 .07412 -16938 -17269 -.00331 .39446 -50241 -. 10795 .OOOOO .OOOOO .OOOOO -3 9462 -46158 - .06696 .OOOOO - 00000 .00000 .3 9447 -43821 - .04374 ,00000 .OOOOO .OOOOO .39467 -50676 -. 11209 ,00000 .OOOOO .00000 .39455 -54909 -. 15454 .OOOOO .OOOOO .00000 .39600 .42041 - ,02440 .08959 -08849 .00110 ,39582 -50904 - -11322 -09054 .23780 -. 14726 .39716 .39358 .00358 .OOOOO .OOOOO .OOOOO -39738 -33460 -06279 .OOOOO . 00000 .OOOOO -39823 -25248 .I4575 ,00000 .OOOOO .00000 ,39694 -35737 -03957 .OOOOO .OOOOO .O O O O O -39704 -27209 .I2495 .OOOOO .OOOOO .OOOOO -39639 -50153 - .lo514 .09670 -18846 -. 09176 -39635 -42347 - .02713 .OOOOO .OOOOO .OOOOO -46227 -35677 .lo550 .OOOOO .OOOOO .OOOOO .46292 -23021 .23271 .OOOOO .OOOOO .OOOOO ,46265 -29164 .I7101 .OOOOO .OOO O O .OOOOO -46192 -29020 .I7172 .OOOOO .OOOOO .OOOOO ,46183 .29386 -16796 .OOOOO 100000 .OOOOO -46224 .32534 .I3690 .OOOOO .OOOOO .OOOOO .46149 -30518 .I5632 .OOOOO .OOOOO .OOOOO

total spec .673336D+00 3.62167 -6733357966525934 variance, sd of parameters x ( 1) bandgap 2 -47336569 .00000616 .00248196 x (2) linewidthA2 .00158007 .00000007 .00026223 x(3) ~ 2 1 ~ 2 .37487618 .00045054 .00069511 -02122583 ,02636499 x(4) ~ 3 1 ~ 2 -04285195 ,00002600 .00009361 .00509937 .00967537 va12 .00000010 va13 .00001404 va14 .00000004 va2 3 -00000239 va24 .00000028 va34 -00002182 vext -01246918 INITIAL CO-ORDINATES I -4000 2 ,5000 3 .6000 4 .6000

OSUM OF SQUARES = 9.397943230+00 I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 6.67795505D-01

fit data ydif f .75277 .82935 - . 07657 .32513 -31777 -00736 .75264 -89460 -. 14195 .32449 .I9875 .I2574

. 7 5 2 8 5 - 7 5 2 8 7 - 9 2 9 4 3 .92873 .92889 - 9 2 8 9 3 .92917 - 9 2 8 6 1 - 9 2 8 9 9 - 7 3 4 0 6 - 7 3 4 7 5 - 7 3 6 6 4 - 7 3 0 8 9 -73234 - 7 2 6 1 1 - 7 2 7 1 2 - 3 8 4 0 3 - 3 8 4 2 7 - 3 8 4 1 3 - 3 8 4 3 1 - 3 8 4 1 3 -38520 - 3 8 5 0 9 - 3 9 5 9 0 - 3 9 6 1 2 - 3 9697 - 3 9 5 6 7 - 3 9 5 7 7 - 3 9 4 9 0 - 3 9 4 8 3 .46403 - 4 6 4 6 8 . 4 6 4 4 1 - 4 6 3 6 9 - 4 6 3 5 9 - 4 6 4 0 1 - 4 6 3 2 5

total s p e c -6677955051442646 v a r i a n c e , sd of p a r a m e t e r s

x ( 1 ) bandgap 2.47565102 .00000585 x ( 2 ) l i n e w i d t h A 2 -00145337 .00000006 x ( 3 ) ~ 2 1 ~ 2 - 3 7 6 1 8 2 1 1 -00044496 -02620125 x(4) ~ 3 1 ~ 2 -04202592 .00002570 -00961940 v a 1 2 .00000012 v a 1 3 .00001297 v a 1 4 .00000007 v a 2 3 .00000179 v a 2 4 .00000034 v a 3 4 .00002000 v e x t .01236658 INITIAL CO -ORDINATES

1 -5000 2 -2000 3 1 - 0000 4 3 .0000

OSUM O F SQUARES = 5.25793378D+01 I*** SUM O F SQUARF,S CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 8 3 , 88 FUNCTION EVALUATIONS OSUM OF SQUARES = 3.15487065D+00

f i t d a t a y d i f f - 5 9 9 6 6 -82935 - - 2 2 9 6 9 .31014 -31777 -. 00763 .59963 -89460 - .29497 .31012 -19875 - 1 1 1 3 7

-59962 ,75309 - . I5348 -59960 -6052 6 - .00566 .59538 1.09742 -.SO204 -59538 - 97993 - -38455 -59538 -91693 - -32155 .59538 -92312 - ,32774 -59538 1 - 0 2 6 8 5 - -43147 -59537 -89378 - -29840 -59537 - 97547 - -38010 .59301 -69410 - -10109 - 59302 -85525 - -26222 -59301 ,69100 - .09799 .59299 - 65526 - -06226 -59299 .84481 - -25181 -59298 -72525 - -13227 .59298 -67298 - .08001 -59132 .50241 -08892 ,59133 -46158 -12975 -59133 -43821 -15312 -59133 -50676 -08458 .59133 -54909 .04224 -59137 -42041 . I7096 -59136 -50904 -08233 -59040 -39358 .I9682 -59041 -33460 -25582 -59045 -25248 -33797 -59040 ,35737 -23303 ,59040 -27209 -31831 .59047 .SO153 -08894 -59047 -42347 -16700 .58844 -35677 .23168 -58850 -23021 -35829 .58848 -29164 -29684 -58842 .29020 -29822 .58841 -29386 -29455 -58845 -32534 .26310 -58849 -30518 -28332

total spec .315487D+01 1 6 3.15487064683172 variance, sd of parameters x ( 1 ) bandgap 2.58677431186.63434266 13.66141803 x (2 ) l i n e w i d t h A 2 -55385401 83.35866819 9.13009683 ~ ( 3 ) ~ 2 1 ~ 2 -35645824 -42441514 -65481192 -65147152 -80920450 x ( 4 ) ~ 3 1 ~ 2 -09499872 -12984218 -46743183 -36033620 -68368986 va12 ************ va13 8.83476745 va14 ************ va2 3 ************ va24 -2.80798321 va3 4 -23425092 vext .05842353 INITIAL CO -ORDINATES

1 1.0400 2 -0040 3 -3000 4 -4000

OSUM OF SQUARES = 5.75099054D+OO l f * * MAXIMUM NUMBER O F ITERATIONS EXCEEDED ORESULTS AT ITERATION 5 0 0 , 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 1.94039742D+00

f i t d a t a ydif f .70861 .82935 -. 12073 -36393 -31777 .04616 -70839 .89460 -. 18621 -36337 -19875 -16462

-70843 -75309 - -04466 -36318 .46779 - -10461 -70836 -60526 -10310 .36293 .30329 -05964 ,70440 1.09742 -.39301 .33869 -52044 - -18175 -70429 -97993 - -27563 -33868 ,39094 -.05226 -70429 -91693 - -21263 -33861 .31768 -02093 - 70430 -92312 - .21882 .33 862 ,46656 - -12794 .70433 1.02685 - -32252 -33867 -52287 -. 18420 .70391 .a9378 - -18987 -33822 -58376 - -24554 -70392 -97547 - - 27155 -33815 .68259 - - 34444 -63814 -69410 -. 05595 .26724 -05379 -21345 .63818 .85525 -. 21707 -26804 -01626 -25178 -63845 -69100 - .05255 -26712 ,05217 -21495 -63784 -65526 - -01741 .OOOOO ,00000 .OOOOO -63801 -84481 - -20679 -00000 .OOOOO -00000 - 63733 ,72525 - -08792 -26672 -19043 .07630 -63745 -67298 - -03553 .26676 .I7269 -09407 -57470 -50241 -07229 .OOOOO .OOOOO -00000 -57465 ,46158 -11307 -00000 .OOOOO - 00000 .57458 -43821 -13638 . 00000 .OOOOO .OOOOO -57467 -50676 -06791 -00000 .OOOOO .OOOOO -57473 -54909 .02562 .OOOOO .OOOOO .OOOOO -57563 -42041 -15523 -22417 -08849 .I3568 .57549 .SO904 -06645 -22505 -23780 - -01275 -54908 -39358 .I5551 -00000 .OOOOO -00000 -54921 -33460 -21461 .OOOOO .OOOOO -00000 -54954 -25248 .29706 -00000 .OOOOO .OOOOO -54904 -35737 .I9167 .OOOOO .OOOOO .OOOOO 54906 .27209 -27697 -00000 .OOOOO -00000 -55027 .SO153 -04874 -21085 .I8846 .02240 -55038 -42347 -12691 .OOOOO .OOOOO .OOOOO -52831 -35677 .I7155 .OOOOO .OOOOO .OOOOO -52881 -23021 -29859 -00000 .OOOOO -00000 .52862 .29164 -23698 -00000 .OOOOO .OOOOO -52808 -29020 ,23788 .OOOOO .OOOOO -00000 -52802 -29386 .23416 .OOOOO .OOOOO -00000 -52833 .32534 -20299 -00000 .OOOOO .OOOOO .52851 ,30518 -22333 . 00000 .OOOOO .OOOOO

total spec .19404OD+Ol 10.43681 1.94039742272317 variance, sd of parameters x ( 1 1 bandgap 2.46909700 .00096417 .03105106 x (2) linewidthA2 -01514774 .00007022 -00837946 x(3) ~ 2 1 ~ 2 .37827511 .00163726 .00252605 -04046304 -05025987 x(4) ~ 3 1 ~ 2 .07364274 .00040477 -00145719 .02011899 ,03817310 va12 .00006195 va13 -00059666 va14 -.00094918 va23 -. 00095415 va2 4 .00003413 va3 4 .00038083 vext -03593329

*** NORMAL TERMINATION

BAND GAP FIT VAO5MP SUM OF SQUARES OPTIMIZATION BAND2ER3 . IN (VER: JAN 8, 1979) band2er3

o 4 variables, 66 terms in sum of squares, rnaxit = 500, print modulus = 0 Oacc= 1~0000000D-15, dstep = 5.300000D-05, dmax= 2,000000Dt00

-775046 -432692 308.389500 610.471600 912.423100 21838.83 .805266 .471777 308.621700 610.812600 911.949400 21838.83 -947686 -484944 302.237800 605.868500 909.132300 20986.36

1.127080 -467992 302.426400 606.136700 908.841400 20986.36 -859308 .S66282 304.611200 606.518700 903.897000 20986.36 -893414 -615626 304.613600 606.437100 902.838700 20986.36 -818183 .033160 301.096400 604.059600 909.653600 20491.80 -647119 -073130 297.890100 601.453300 904.518700 20491.80 -716274 -038607 298.649500 601.575700 906.801900 20491-80 -803867 -024787 298.757500 601.712700 903-938100 20491.80 -784382 .030562 298.365200 601.421300 905.713700 20491-80 -755118 -188320 305,581700 607.835000 908.762700 20491-80 .756609 -186097 305.427300 608.008300 908.970700 20491-80 -551545 .OOOOOO 311.280000 615.143600 .OOOOOO 20140.99 ,467637 -006261 312.596800 615.548900 917.531500 20140.99 -455766 -016491 312.703100 616.077100 917.354800 20140.99 .398772 .019795 312.966900 616.155000 917.854200 20140.99 -383406 .OOOOOO 313.303700 616.087000 .OOOOOO 20140.99 -646965 -182107 306.184600 609.123700 903.115800 20140.99 -589599 .I12240 305.911800 608.738000 906.469700 20140.99 -263433 .OOOOOO 316.451200 620.136800 .OOOOOO 19932.23 .298716 -027637 315.440900 620.026800 911.810000 19932.23 -247258 ,000000 316 .548100 616.983600 -000000 19932.23 .378479 .OOOOOO 316.177400 620.148100 -000000 19932.23 -330641 .OOOOOO 314.736700 614,769300 .OOOOOO 19932.23 .430677 .OOOOOO 305.478200 608.384700 -000000 19932.23 -372389 .OOOOOO 314 -456100 618.169200 .OOOOOO 19436.35 -275899 .OOOOOO 314.398000 616.935900 -000000 19436.35 .334096 .OOOOOO 314.372200 616.091000 .OOOOOO 19436.35 -239657 .OOOOOO 314.529300 619.855600 -000000 19436.35 ,280586 .OOOOOO 314 -324300 617.181400 .OOOOOO 19436.35 -288810 .OOOOOO 304.168400 606.386400 .OOOOOO 19436.35 ,339912 .OOOOOO 303.974600 604.225300 -000000 19436.35

ZFILE = jdl6p .prn dl 6p dl6p (2) wlol wl02 wl03

INITIAL CO-ORDINATES 1 2 -3770 2 -0040 3 .I010 4 -0610

OSUM OF SQUARES = 4.41818258D+00 I*** F ( X ) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 129, 134 FUNCTION EVALUATIONS OSUM OF SQU-S = 6.23399329D-01

fit data ydif f -73956 .77505 -. 03549 .33513 -43269 -. 09756 .73964 .80527 - -06563 -33494 .47178 - .I3684 -91462 -94769 -. 03306 .51700 -48494 -03206 .91481 1.12708 -.21227 -51671 .46799 -04872 -91300 -85931 .05369 .51243 -56628 - -05385 -912 8 8 -89341 .01947 -51178 - 61563 - -10384 .74298 .81818 - . 07520 -16736 .03316 .I3420 -74828 .64712 .lo116 .I6964 -07313 -09651 .74729 -71627 .03102 -16880 -03861 -13020 + 74708 -80387 - . 05678 -16956 .02479 .I4478

.74772 -78438 -.03666 -16918 -03056 ,13862 -73551 -75512 - -01961 -16639 - 18832 - -02193 -73559 -75661 - -02102 .I6638 - 18610 -. 01972 .37367 -55154 - .I7787 ,00000 .OOOOO .OOOOO -37403 -46764 -.09360 -08732 -00626 -08106 -37377 -45577 - -08199 .08735 -01649 -07085 .37385 .39877 -.02492 ,08732 -01980 -06753 ,37404 -38341 - -00936 .OOOOO -00000 .OOOOO -37493 -64697 - -27204 -08813 - 18211 -. 09398 ,37503 -58960 -.21456 -08775 - 11224 - -02449 -3 8522 -26343 -12179 .OOOOO .OOOOO ,00000 -38463 ,29872 -08592 ,09791 -02764 ,07027 .3 8684 .24726 .I3958 .OOOOO .OOOOO .OOOOO -38504 -37848 -00656 .ooooo .ooooo . ooocia -3 8677 .33064 .05613 .O O O O O .OOOOO .00000 .38402 -43068 -. 04666 .OOOOO .OOOOO .OOOOO -45445 -37239 -08207 .O O O O O . 00000 .OOOOO -45489 ,27590 -17899 ,00000 .OOOOO .OOOOO -45519 ,33410 .I2109 .OOOOO .OOOOO .OOOOO -45386 -23966 -21421 .OOOOO . 00000 .OOOOO -45476 -28059 -17417 .OOOOO .OOOOO .OOOOO .45389 -28881 .I6508 .OOOOO .OOOOO .OOOOO -45461 -33991 -11470 .OOOOO -00000 .OOOOO

total spec .623399D+00 4 -52652 -6233993285879519 variance, sd of parameters x ( 1) bandgap 2.47442196 .00000563 -00237303 x (2) linewidthA2 -00137933 .00000005 -00022721 x(3) ~ 2 1 ~ 2 -36361286 .00056587 .00093661 .02378805 .03060416 x(4) 831A2 -04503406 .00002910 .00009312 -00539444 -00964986 va12 -.00000013 va13 -00001348 va14 -.00000052 va2 3 .00000167 va2 4 -.00000052 va3 4 .00001243 vext .01298749 INITIAL CO-ORDINATES

1 2.4700 2 -0020 3 -4000 4 -0610

OSUM OF SQUARES = 7.13810259D-01 I*** F ( X ) NO LONGER DECREASES . . . OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 82, 8 7 FUNCTION EVALUATIONS OSUM OF SQUARES = 6.23399228D-01

fit data ydiff -73950 .77505 -. 03554 .33517 -43269 -. 09752 . 73959 -80527 -. 06568 -33497 -47178 -. 13681 -91452 -94769 -. 03317 -51695 -48494 ,03201 .91470 1.12708 -.21238 -51667 -46799 -04867 -91290 -85931 -05359 -5123 8 .56628 -. 05390 -91278 .89341 -01936 .51174 -61563 - -10389 -74284 -81818 - .07534 -1673 8 .03316 -13422 -74813 .64712 .lo101 -16966 .07313 .09653 .74715 .71627 ,03087 .I6883 -03861 -13022 -74694 -80387 - .05693 -16959 .02479 -14480 .74757 .78438 - .03681 .I6920 .03056 -13 8 64 .73537 -75512 - ,01975 -16641 .I8832 -. 02191 -73545 -75661 -. 02116 -16640 ,18610 -. 01970 -37370 .55154 -. 17784 .OOOOO .OOOOO ,00000

total spec .623399D+00 4 - 5 2 6 5 2 -6233992276497621 variance, sd of parameters

x ( 1 ) bandgap -

2 , 4 7 4 4 2 3 5 5 .00000564 .00237400 x ( 2 ) linewidthA2 . 00138012 .00000005 -00022735 x(3) ~ 2 1 ~ 2 - 3 6 3 5 6 4 1 7 .00056584 .00093657 -02378748 .03060343 x ( 4 ) ~ 3 1 ~ 2 .04504392 .00002911 . 00009317 -00539583 -00965236

v a 1 2 - .00000013 v a 1 3 .00001348 v a 1 4 - .00000052 v a 2 3 .00000167 v a 2 4 - . 0 0 0 0 0 0 5 2 v a 3 4 .00001244 vext - 0 1 2 9 8 7 4 8 INITIAL CO-ORDINATES

1 .8000 2 -0400 3 -5000 4 -9000

OSUM OF SQUARES = 1 . 5 4 1 9 2 5 4 3 D t 0 1 I f * * MAXIMUM NlTMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500 , 5 0 5 FUNCTION EVALUATIONS OSUM OF SQUARES = 1 .44522221Dt00

fit data ydif f

-48722 -26343 -22378 . 00000 .48704 .29872 -18832 .I4889 .48822 ,24726 -24096 - 00000 -48716 -37848 .I0868 -00000 -48854 -33064 -15789 . 00000 -48862 ,43068 -05794 .OOOOO -47427 -37239 .lo188 -00000 -47461 ,27590 .I9871 . 00000 .47486 -33410 -14076 .OOOOO .47379 .23966 -23413 .OOOOO -47452 -28059 .I9393 -00000 -47452 -28881 .I8571 -00000 .47510 .33991 -13519 .OOOOO

total spec .144522Dc01 10 -49380 1.44522220671089 variance, sd of parameters x ( 1 ) bandgap 2.46639931 - 00050216 -02240895 x (2 1 linewidthA2 -00873208 -00000978 -00312765 x(3) ~ 2 1 ~ 2 -33337202 -00195913 -00324269 -04426201 -05694463 x(4) B31A2 -04574717 -00021644 -00069262 . 01471204 .02631770 va12 -.00004577 va13 .00066560 va14 -.00034336 va2 3 - .00007036 va24 -.00003735 va3 4 -00044973 vext .03010880 INITIAL CO-ORDINATES

1 -6000 2 -0300 3 .0400 4 .I200

OSUM OF SQUARES = 7.29776948D+00 I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.06013982D+00

fit data ydif f -64105 -77505 -. 13399 .26630 ,43269 -. 16639

.SO415 -37239 . I3176 . O O O O O . O O O O O -00000 ,50439 .27590 -22849 . O O O O O . O O O O O . O O O O O .SO455 .33410 -17046 -00000 . O O O O O . O O O O O .SO382 -23966 .26416 . O O O O O ,00000 . O O O O O .SO432 -28059 .22374 . O O O O O . O O O O O . O O O O O ,50461 .28881 -21580 . O O O O O . O O O O O . O O O O O .SO502 .33991 -16510 . O O O O O . O O O O O -00000

t o t a l spec .206014D+01 14.95874 2.06013981647018 v a r i a n c e , sd of parameters

x (1) bandgap 2.47173788 .00780106 .08832362 x (2) l i n e w i d t h A 2 -02329729 -00035468 .C1883299 x ( 3 ) ~ 2 1 ~ 2 -32263135 -00552228 .00914033 -07431205 -09560506 x ( 4 ) ~ 3 1 ~ 2 .04363125 . 00056451 .00180644 -02375947 -04250223 va12 -. 00103605 va13 -00556383 va14 -.01998475 va2 3 .00550966 va24 -.00035225 va34 .00155414 v e x t -04291958 INITIAL CO-ORDINATES

1 -6700 2 -3000 3 -1500 4 -4500

OSUM OF SQUARES = 8.18267876D+00 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 127, 132 F'UNCTION EVALUATIONS OSUM OF SQUARES = 2.78273982D+OO -

f i t data ydif f .56136 .77505 - -21369 -21361 -43269 - -21908

-55078 .33991 -21087 .OOOOO .OOOOO .00000 total spec .278274D+01 20.20556 2.78273981632635 variance, sd of parameters x ( 1 ) bandgap 2.50882953454.06105475 21.30870843 x (2) linewidthA2 .56073699109.43036166 10.46089679 x(3) ~ 2 1 ~ 2 ,30941690 -78016288 1.29130408 .88326830 1.13635561 x(4) ~ 3 1 ~ 2 .04419605 -06589076 -21085045 .25669197 -45918455 va12 ************ va13 18.78426336 va14 ************ va23 ************ va24 -2.26683510 va34 ,22652930 vext .05797375 INITIAL CO-ORDINATES 1 -6000 2 -9000 3 -2000 4 .lo00

OSUM OF SQUARES = 3 -4l862345DtOO I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 1.87551874D+00

fit data ydif f -66642 -77505 - -10863 -27847 -43269 - .I5423 .66645 ,80527 -. 13881 -27838 -47178 -. 19340 .65951 -94769 - .28817 -25873 .48494 - .22622 -65952 1.12708 -.46756 -25869 -46799 - .20930 -65895 -85931 - .20035 .25824 -56628 - -30804 -65893 .89341 -. 23448 -25820 .61563 -. 35742 -60253 -81818 - -21566 ,20875 -03316 -17559 -60301 -64712 - -04411 .20920 .07313 .I3607 -60290 .71627 - -11337 .20903 -03861 -17043 -60289 .80387 - -20098 -20919 .02479 .I8440 - 60294 .78438 -. 18144 .20911 -03056 -17855 -60184 .75512 -. 15327 -20858 .I8832 .02026 -60186 .75661 - .I5475 .20858 -18610 -02248 -54871 .55154 - .00284 .OOOOO .00000 .00000 -54869 .46764 .08105 .I7748 -00626 -17121 -54861 .45577 .09284 -17749 .01649 .I6100 -54860 -39877 -14983 -17746 -01980 -15766 -54863 .38341 .I6522 .OOOOO ,00000 ,00000 .54952 .64697 -. 09745 .I7851 -18211 - .00360 - 54957 -58960 - .04003 -17824 -11224 .06600 -52577 .26343 .26233 .OOOOO .OOOOO .00000 - 52566 -29872 -22694 -16744 .02764 .I3980 .52645 -24726 .27919 ,00000 .00000 .00000 -52573 -37848 -14725 .OOOOO .OOOOO .00000 .52669 -33064 ,19605 .OOOOO .00000 .00000 -52688 .43068 -09620 .OOOOO ,00000 .00000 -50471 .37239 .I3232 .OOOOO .00000 .00000 -50499 -27590 -22909 .OOOOO .00000 .00000 .SO518 -33410 .I7109 .OOOOO .00000 .00000 -50432 .23966 -26466 .OOOOO .OOOOO .O O O O O - 50491 -28059 .22433 - 00000 .00000 .00000 -50517 ,28881 -21636 .OOOOO .OOOOO .OOOOO .SO564 -33991 .I6573 .OOOOO .00000 .00000

total spec .187552D+01 13.61820 1.87551873609261 variance, sd of parameters x ( 1 ) bandgap 2.46809266 00302771 .05502461 x (2) linewidthA2 -01707734 .00009908 .00995380

x(3) B21A2 ,33865814 .00393696 -00651635 -06274520 - 08072390 x ( 4 ) B31A2 .04450239 .00039217 -00125495 - 01980334 ,03542529 va12 - . 00033464 va13 .00278521 v a l 4 - .00501065 v a 2 3 -00051670 va24 - . 00015339 va34 -00103931 vext .03907331 INITIAL CO -ORDINATES

1 . l o 0 0 2 -1000 3 -9000 4 -0900

OSUM O F SQUARES = 8.58341873D+00 I*** SUM O F SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 215, 2 2 0 FUNCTION EVALUATIONS OSTJM OF SQUARES = 2.53630668D+00

fit d a t a ydiff - 59461 -77505 -. 18044 -24805 -43269 -. 18464 -59462 .a0527 -. 21065 -24802 .47178 - .22376 -58073 .94769 - .36696 .23450 -48494 - -25044 .58073 1 .12708 -. 54635 -23449 -46799 - .23350 .5805? , 85931 -. 27874 -23436 .56628 - .33193 -58056 . a9341 -. 31285 .23434 .61563 - -38128 -56640 -81818 - -25178 -22243 -03316 -18927 , 56651 -64712 -. 08061 -22253 -07313 -14940 .56648 -71627 -. 14980 -22250 .03861 -18389 -56647 .80387 -. 23739 .22253 .02479 -19774 -56649 -78438 -. 21789 - 2 2 2 5 1 .03056 . I 9195 ,56625 -75512 -. 18887 -22237 . I 8832 ,03405 .56626 - 75661 - -19035 -22237 ,18610 .03628 -55476 -55154 .00322 . O O O O O . O O O O O .00000 -55475 -46764 -08711 ,21358 .00626 .20732 -55473 .45577 -09897 -21358 ,01649 . I 9709 -55473 .39877 . I 5596 -21357 .01980 . I9378 -55473 -38341 . I 7133 . O O O O O . O O O O O .00000 ,55495 -64697 - -09201 - 2 1 3 9 1 -18211 .03180 .55496 .58960 -. 03463 -21383 -11224 -10159 -54817 -26343 .28474 . O O O O O . O O O O O ,00000 -54815 -29872 -24944 -20925 -02764 -18152 .54833 -24726 .30107 . O O O O O . O O O O O -00000 -54816 ,37848 ,16968 . O O O O O . O O O O O .00000 -54840 .33064 .21776 . O O O O O . O O O O O .00000 .54853 .43068 -11786 ,00000 . O O O O O .00000 .S3556 -37239 -16317 . O O O O O . O O O O O -00000 -53566 ,27590 .25976 . O O O O O . O O O O O .00000 -53573 -33410 .20163 . O O O O O . O O O O O ,00000 -53542 -23966 -29576 . O O O O O . O O O O O .00000 -53563 -28059 -25505 . O O O O O . O O O O O .00000 ,53590 ,28881 -24709 . O O O O O . 00000 . O O O O O -53607 .33991 . I9616 . O O O O O . O O O O O .00000

total s p e c .253631D+01 1 8 -41620 2,53630667780443 variance, sd of pa r ame te r s

x(1) bandgap 2 -45635464 -42379460 -65099509 x ( 2 ) l i n e w i d t h A 2 .08021767 -01688318 . I2993531 x ( 3 ) ~ 2 1 ~ 2 .31259024 .02854899 -04725349 -16896445

v a 1 4 -7.65485673 v a 2 3 6.59704385 v a 2 4 - .00347837 v a 3 4 .00951744 vext .05283972

I N I T I A L CO-ORDINATES I -4000 2 . so00 3 ,6000 4 .6000

OSUM OF SQUARES = 1.12739422Dt01 l*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, 5 0 S FUNCTION EXALUATIONS OSUM O F SQUARES = 2.06486926D+OO -

f i t data y d i f f -64480 -77505 -. 13024 -27614 .43269 - - 1 5 6 5 5 .64483 -80527 -. 16043 -27606 - 6 3 1 9 1 .94769 - . 3 1578 -25514 - 6 3 1 9 1 1.12708 - .49517 .25512 .63148 -85931 -. 22783 - 2 5 4 7 6 . 6 3 1 4 6 -89341 -. 26195 -25472 .58956 .81818 -. 22863 -21754 .58990 -64712 -. 05721 -21788 .58982 -71627 -. 12645 .21776 - 5 8 9 8 1 -80387 -. 21406 -21787 ,58985 -78438 -. 19453 .21781 .58907 -75512 - . I 6 6 0 5 -21740 -58909 .75661 - . I 6 7 5 2 -21740 -55083 -55154 -. 00072 .00000 - 5 5 0 8 1 -46764 -08317 ,19229 - 5 5 0 7 5 -45577 -09498 ,19230 -55074 -39877 . I 5 1 9 7 -19227 - 5 5 0 7 6 .38341 . I 6 7 3 5 . O O O O O -55143 -64697 -. 09553 -19316 - 5 5 1 4 7 -58960 -. 03812 -19295 - 5 3 2 3 5 -26343 -26892 . O O O O O -53228 -29872 -23357 -18278 -53287 -24726 - 2 8 5 6 1 . O O O O O .53233 -37848 . I 5 3 8 5 ,00000 -53307 .33064 -20243 . O O O O O -53330 -43068 . l o 2 6 2 . O O O O O -51010 .37239 -13772 . O O O O O -51034 -27590 -23444 . O O O O O . 51051 -33410 - 1 7 6 4 1 . O O O O O -50978 -23966 -27012 . O O O O O -51028 -28059 -22969 .00000 .51062 -28881 .22181 . O O O O O -51102 .33991 .17111 . O O O O O

t o t a l spec .206487D+01 1 4 . 9 9 3 0 8 2 .06486925668566 variance, sd of parameters

x ( 1 ) bandgap 2.46519985 .00829495 .09107661 x ( 2 ) l i n e w i d t h A 2 .02393819 .00027263 .01651149 x ( 3 ) ~ 2 1 ~ 2 .32776408 .00554943 .00918526 -07449447 -09583975 x ( 4 ) ~ 3 1 ~ 2 .04723603 .00063830 .00204257 -02526466 -04519480 va12 - .00089609 v a 1 3 -00586670 v a 1 4 - .02159795 v a 2 3 -00660697 v a 2 4 - .00030436 va34 -00166516 vext .04301811

I N I T I A L CO-ORDINATES

1 - 5 0 0 0 2 .2000 3 1 . 0 0 0 0 4 3 .0000

OSUM O F SQUARES = 5.77884901D+01 I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 5 0 0 , 5 0 5 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.02277263Dt00

f i t ,65084 - 6 5 0 8 7 - 6 3 9 5 8 - 6 3 9 5 9 - 6 3 9 1 2 - 6 3 9 1 0 , 5 9 4 4 9 ,59487 - 59478 , 5 9 4 7 6 - 5 9 4 8 2 - 5 9 3 9 6 - 5 9 3 9 8 - 5 5 2 3 7 , 5 5 2 3 4 - 5 5 2 2 8 . 5 5 2 2 8 - 5 5 2 2 9 - 5 5 3 0 2 .55307 - 5 3 2 5 6 .53248 - 5 3 3 1 1 - 5 3 2 5 3 - 5 3 3 3 2 - 5 3 3 5 6 .SO978 .51003 .51020 - 5 0 9 4 4 - 5 0 9 9 6 - 5 1 0 2 9 - 5 1 0 7 1

to ta l spec

data ydif f

2 .02277262972514 variance, sd of parameters

x ( 1 ) bandgap 2.46488110 - 0 0 6 6 2 6 4 1 x ( 2 ) l i n e w i d t h A 2 .02207409 -00021166 x ( 3 ) ~ 2 1 ~ 2 .33133864 .00517779 -09257503 x ( 4 ) ~ 3 1 ~ 2 - 0 4 4 8 9 3 0 1 ,00053387 .04133270

v a 1 2 -. 00068831 v a 1 3 .00500646 v a 1 4 -. 01502845 v a 2 3 - 0 0 3 8 6 4 4 1 v a 2 4 - .00024325 v a 3 4 .00145692 vext ,04214110 INITIAL CO-ORDINATES I 1 .0400 2 -0040 3 -3000 4 .4000

OSUM O F SQUARES = 6.81924635D+00 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY

to3

ORESULTS AT ITERATION 84, 89 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.83066601D+00

fit data ydif f -55353 -77505 -. 22152 -20944 .43269 - -22325 .55353 .a0527 - -25174 -20944 -47178 - -26233 -55350 -94769 - .39419 .20942 -48494 -. 27552 -55350 1.12708 - . 57358 -20942 -46799 - -25857 -55349 ,85931 - -30582 -20940 -56628 -. 35688 -55349 -89341 - -33993 .20940 ,61563 - -40623 -55347 -81818 - -26471 -20941 -03316 .I7625 -55347 -64712 - -09365 .20940 .07313 -13627 -55347 -71627 -.I6280 .20940 .03861 - 17080 -55347 ,80387 - -25040 -20940 -02479 -18461 -55347 -78438 - -23091 .20940 ,03056 -17884 -55346 -75512 - .20165 -20939 .I8832 -02107 .55347 -75661 - -20314 -20939 -18610 -02330 -55346 -55154 -00191 .OOOOO ,00000 .OOOOO -55345 -46764 -08581 -20938 -00626 ,20312 .55345 -45577 -09769 -20938 ,01649 -19289 -55345 -39877 -15468 .20938 .01980 -18959 -55345 .38341 ,17004 -00000 .OOOOO .OOOOO -55345 .64697 - -09351 -20936 -18211 ,02725 -55345 -58960 - -03615 .20937 .I1224 -09713 -55344 .26343 .29001 .OOOOO .OOOOO ,00000 -55345 -29872 -25473 -20935 .02764 - 18171 -55342 -24726 .30616 .OOOOO .OOOOO .OOOOO .55345 -37848 -17497 .OOOOO .OOOOO .OOOOO -55342 -33064 -22278 .OOOOO .OOOOO -00000 -55344 -43068 .I2276 .OOOOO .OOOOO - 00000 .55342 -37239 -18103 .OOOOO .OOOOO ,00000 - 55341 -27590 -27751 .OOOOO .OOOOO -00000 -55340 -33410 ,21931 .OOOOO .OOOOO .OOOOO -55343 -23966 -31377 .OOOOO .OOOOO .OOOOO -55341 -28059 -27282 .OOOOO 00000 .OOOOO -55341 .28881 -26460 .OOOOO .OOOOO .OOOOO -55339 -33991 -21348 .OOOOO .OOOOO .OOOOO

total spec .283067D+Ol 20 -55355 2.83066601183036 variance, sd of parameters x ( 1 ) bandgap 0 0 0 0 2 3 0 6 * * * * * * * * * * f * * * * * * * * * * * * * ~ ( 2 ) linewidthA2 18.70008983************************ x ( 3 ) ~ 2 1 ~ 2 .30403873 8.41387378 13.92641177 2.90066782 3.73181079 x(4) ~ 3 1 ~ 2 -04319723 ,67633674 2.16427757 -82239695 1.47114838 va12 ************ va13 ************ va14 ************ va2 3 ************ va24 ***t***t**++

va34 2.38530867 vext -05897221

*** NORMAL TERMINATION

BAND GAP FIT VAOSMP SUM OF SQUARES OPTIMIZATION BAND2ER3 . IN (VER: JAN 8, 1979) band2er3 o 4 variables, 76 terms in sum of squares, m a x i t = modulus = o 0acc= 1.0000000~-15, dstep = 5.300000D-05, dmax= 2.

-812761 .I59833 303.871700 605.831800 903.762900 -949523 .319874 300.027300 601.638500 902.173400 -870974 -335791 298.309800 601.162200 900.800100 -913205 .542197 297.772500 599.768200 900.262400 -885519 -490374 302.810300 604.175000 906.706300 -893319 .424724 308-987300 611.065900 909.612800 -769023 .375021 302.373800 604.810500 908.091500 -816420 ,330083 302.391700 604.939000 907.201000 -972084 .314484 302.573400 605.285600 906.878300 -835578 .482928 302.397300 604.840300 906.340000 -942447 .709354 305.261300 604.432400 904.866000

1.004092 .807075 305.551500 607-759800 905.148900 -607239 -074152 300.665100 603.974300 903.365700 -719543 .026712 300.680800 603-520000 907.287400 -670295 -083501 300.350100 603,475200 907.683900 -603132 .068841 301.013200 603.703100 905.767000 -654192 -064782 300.829300 603.872100 906.587600 -619645 -117198 304.329100 606.745900 909.248800 -750851 -150720 304.751100 606.751400 908.765500 -318763 .OOOOOO 311.569600 611.342900 .OOOOOO -479370 -027259 311.594300 614.684600 920.061000 -381255 .OOOOOO 312.683600 615.158600 .OOOOOO .366530 .OOOOOO 312.765900 615.110900 .OOOOOO -333881 .OOOOOO 312.629500 615.310400 .OOOOOO -473160 ,000000 305.445100 608.716400 .OOOOOO -523810 .OOOOOO 305.580800 607.713700 .OOOOOO -264519 . 000000 314.996200 617.544200 . 000000 -236712 .OOOOOO 315.520100 618.051700 .OOOOOO -291035 .OOOOOO 314.506500 617.432600 .OOOOOO -268754 .OOOOOO 315.762200 618.361900 .OOOOOO -272536 . 000000 315 -784200 618.183400 .000000 -368885 .OOOOOO 305.656400 607.623100 .OOOOOO -328483 .OOOOOO 305.057300 607.608100 .OOOOOO -246537 .OOOOOO 314.160000 618.122700 .OOOOOO -250896 .OOOOOO 314.663000 617.487600 ,000000 -298412 .OOOOOO 314.005700 616.748700 .OOOOOO .289208 .OOOOOO 314.321800 618.762500 . O O O O O O .397312 .OOOOOO 314.084200 616-325500 .OOOOOO

500, print

ZFILE = j d3 lp . prn d3 1p d3 1p (2 ) wlol wl02 wlo3

I N I T I A L CO-ORDINATES 1 2.3770 2 -0040 3 ,1010 4 -0610

OSUM OF SQUARES = 5.26158094D+00 If** F(X) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 84, 89 FUNCTION EVALUATIONS OSUM OF SQUARES = 8.55304375D-01

fit data ydif f ,73634 .81276 - -07642 .33479 -15983 -17496 .73575 .94952 - -21378 -33508 -31987 -01521 -73627 -87097 -. 13470 -33500 .33579 -. 00080 -73573 .91321 -. 17747 -33493 .54220 -. 20726 -73589 -88552 -. 14963 -33598 .49037 -.I5439

- 73693 -92375 - 92393 .92425 -92377 -91988 -92460 -65819 - 65852 .65889 -65805 -65810 .65239 .65197 -36597 -36412 .36445 -36453 -36434 -36413 .36476 -38706 .38715 -38680 -38716 -38726 -38586 -38549 ,45418 -45464 .45460 -45402 -45479

total spec -8553043754966793 variance, sd of parameters x ( 1 ) bandgap 2 -48007625 .00000847 x (2) linewidthA2 .00133245 .00000007 x(3) ~ 2 1 ~ 2 -35629837 .00052675 -02892402 x(4) ~ 3 1 ~ 2 -04397953 .00004220 -01193475 va12 .00000010 va13 -00001387 va14 .00000013 va2 3 .00000101 va24 -00000084 va3 4 .00002088 vext -01583597 INITIAL CO-ORDINATES 1 2.4700 2 -0020 3 -4000 4 .0610

OSUM OF SQUARES = 1.10379215D+00 l*** F ( X ) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE: VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 74, 7 9 FUNCTION EVALUATIONS OSUM OF SQUARES = 8.55304527D-01

f i t data ydif f -73625 .81276 - -07651 -33479 -15983 .I7496 -73566 .94952 - .21387 -33508 -31987 -01521 -73618 -87097 - -13479 -33499 -33579 - .00080 -73564 .91321 - -17756 -33493 -54220 -. 20726

. 73580 -88552 -. 14972 - 3 3 5 9 8 - 4 9 0 3 7 - . I 5 4 3 9 - 7 3 6 8 4 -89332 -. 15648 - 3 3 5 6 3 .42472 - . 08910 - 9 2 3 6 5 -76902 . I 5 4 6 3 .51180 .37502 , 1 3 6 7 8 - 9 2 3 8 2 -81642 -10740 .51142 - 3 3 0 0 8 - 1 8 1 3 4 - 9 2 4 1 4 .97208 -. 04794 .51117 - 3 1 4 4 8 , 1 9 6 6 9 - 9 2 3 6 7 -83558 -08809 . 5 1 1 0 6 - 4 8 2 9 3 - 0 2 8 1 3 - 9 1 9 7 7 -94245 -. 02267 ,50862 - 7 0 9 3 5 - - 2 0 0 7 3 - 9 2 4 5 0 1 .00409 - .07959 , 5 0 8 5 6 - 8 0 7 0 8 - - 2 9 8 5 2 - 6 5 8 0 9 ,60724 .05085 - 1 4 3 7 1 - 0 7 4 1 5 - 0 6 9 5 6 - 6 5 8 4 2 -71954 -. 06112 , 1 4 2 8 1 - 0 2 6 7 1 - 1 1 6 1 0 - 6 5 8 7 9 ,67030 -. 0 1 1 5 1 - 1 4 2 7 9 - 0 8 3 5 0 - 0 5 9 2 9 - 6 5 7 9 4 - 6 0 3 1 3 .05481 , 1 4 3 0 9 - 0 6 8 8 4 - 0 7 4 2 5 - 6 5 8 0 0 .65419 - 0 0 3 8 1 - 1 4 2 9 4 .06478 - 0 7 8 1 6 - 6 5 2 2 9 -61965 -03264 - 1 4 1 5 7 - 1 1 7 2 0 .02437 , 6 5 1 8 7 -75085 -. 09899 . I 4 1 5 9 . I 5 0 7 2 -. 00913 - 3 6 5 9 1 - 31876 - 0 4 7 1 5 . O O O O O ,00000 . O O O O O . 36407 -47937 -. 11530 - 0 8 5 8 0 - 0 2 7 2 6 - 0 5 8 5 4 ,36440 -38126 -. 01685 . O O O O O -00000 . O O O O O - 3 6 4 4 8 .36653 -. 00205 . O O O O O . O O O O O ~ 0 0 0 0 0 - 3 6 4 2 9 -33388 - 0 3 0 4 1 , 00000 . O O O O O . 00000 , 3 6 4 0 7 ,47316 -. 10909 . O O O O O . O O O O O . 00000 - 3 6 4 7 1 - 52381 -. 15910 . O O O O O . O O O O O . O O O O O - 3 8 7 0 1 .26452 . I 2 2 4 9 . O O O O O . O O O O O . 00000 - 3 8 7 1 0 - 2 3 6 7 1 - 1 5 0 3 9 . O O O O O . O O O O O . 00000 - 3 8 6 7 6 .29104 ,09572 , 0 0 0 0 0 . O O O O O . O O O O O - 3 8 7 1 1 .26875 . I 1 8 3 6 . O O O O O . O O O O O . 00000 , 3 8 7 2 1 -27254 . I 1 4 6 7 . O O O O O . O O O O O . O O O O O - 3 8 5 8 1 -36889 -01693 . O O O O O . O O O O O . O O O O O , 3 8 5 4 4 -32848 - 0 5 6 9 6 . O O O O O . O O O O O . O O O O O - 4 5 4 1 2 -24654 - 2 0 7 5 8 . O O O O O . 00000 , 0 0 0 0 0 - 4 5 4 5 8 -25090 - 2 0 3 6 9 . O O O O O . O O O O O . O O O O O - 4 5 4 5 5 - 2 9 8 4 1 . I 5 6 1 3 . O O O O O . O O O O O . 00000 - 4 5 3 9 6 - 2 8 9 2 1 - 1 6 4 7 6 ,00000 . O O O O O . O O O O O - 4 5 4 7 3 .39731 -05742 . O O O O O . O O O O O . 00000

t o t a l spec .855305D+00 4 . 8 4 9 5 0 .8553045268395259 variance, sd o f p a r a m e t e r s

x ( 1 ) b a n d g a p 2 .48007786 .00000847 .00291088 x ( 2 ) linewidth62 -00133238 .00000007 .00026275 x ( 3 ) ~ 2 1 ~ 2 .35620932 -00052674 -00083659 . 0 2 2 9 5 0 8 1 - 0 2 8 9 2 3 8 1 x ( 4 ) ~ 3 1 ~ 2 -04397881 . 0 0 0 0 4 2 2 1 -00014246 -00649700 .01193575 v a 1 2 .00000010 v a 1 3 .00001388 v a 1 4 .00000013 v a 2 3 .00000101 v a 2 4 .00000085 v a 3 4 .00002089 vext -01583897 INITIAL CO-ORDINATES

1 .8000 2 .0400 3 .5000 4 - 9 0 0 0

OSUM OF SQUARES = 1.40873488Di-01 I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500 , 5 0 5 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.28490023D+00

f i t data ydif f - 6 8 4 3 9 -81276 -. 12837 .36388 - 1 5 9 8 3 - 2 0 4 0 4 - 6 8 4 2 3 .94952 - . 26529 . 3 6424 - 3 1 9 8 7 - 0 4 4 3 6 .68460 .87097 -. 18637 - 3 6 4 2 9 .33579 - 0 2 8 4 9 .68432 - 9 1 3 2 1 - .22888 - 3 6 4 2 8 .54220 - . I 7 7 9 1 .68419 -88552 - .20133 - 3 6 4 5 3 .49037 -. 1 2 5 8 4

-68450 -65929 - 6 5 9 3 1 -65932 -65929 -65847 -65893 -59127 -5913 1 .59134 -59128 .59127 .59080 -59078 -54589 - 5 4 5 2 1 -54523 -54525 ,54519 -54576 -54598 - 5 2 9 5 1 .S2949 -52945 ,52946 . 52951 -53017 .53007 .51823 .51850 .51852 . 51811 -51864

total spec 2.28490022707043 variance, sd of parameters

x ( 1 ) bandgap 2 -48878093 . 00160103 x (2 ) linewidthA2 -01780455 .00008981 x ( 3 ) ~ 2 1 ~ 2 -35585676 -00175666 -05282032 x ( 4 ) ~ 3 1 ~ 2 -07639257 .00037567 -03560748 va12 .00008924 v a 1 3 .00076490 va14 - - 00082781 va2 3 - .00019045 va24 - .00001943 v a 3 4 .00042748 vext -04231297 INITIAL CO-ORDINATES 1 -6000 2 -0300 3 .0400 4 . I 200

OSUM OF SQUARES = 8.71966496D+OO I*** SUM O F SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 242 , 247 FUNCTION EVALUATIONS OSUM O F SQUARES = 3.26745144D+00

fit data ydi ff .59870 .81276 - - 21406 .31734 -15983 . I 5 7 5 1 .59872 -94952 - .35080 .31745 -31987 - .00242 -59882 .87097 - - 27215 .31748 -33579 - - 0 1 8 3 1 -59877 .91321 - - 31443 -31749 -54220 - . 2 2 4 7 1 -59868 .88552 - -28684 -31746 -49037 - . I 7 2 9 1 -59865 -89332 -. 29467 -31729 -42472 - . l o 7 4 3

-58627 -58627 -58627 .58627 -58616 .58621 -57726 -57727 -57727 -57726 -57726 -57720 .57720 -57080 .57069 -57069 .57070 -57069 .57080 -57083 -56712 -56711 -56711 .56711 -56711 .56730 -56728 .55989 -55996 .55997 -55986 ,56000

total spec 3.26745144335169 variance, sd of parameters x ( 1 ) bandgap

- 2.48724385 1.22025680 1.10465234

x (2 ) linewidthA2 -14448479 .I1331827 .33662779 x(3) B21A2 -33370570 -02741163 -04353612 .I6556459 -20865312 x(4) B31A2 .08845211 -00928027 .03132091 .09633416 -17697715 va12 .03133459 va13 -17732726 va14 -15.71506132 va2 3 14.57274070 va24 .00051801 va34 -01551813 vext .06050836 INITIAL CO-ORDINATES 1 .6700 2 -3000 3 ,1500 4 .4500

OSUM OF SQUARES = 7.92360060D+OO I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITEFtATION 99, 104 FUNCTION EVALUATIONS OSUM OF SQUARES = 3.26597269D+00

fit data ydif f .59578 -81276 - .21698 -30716 .I5983 -14732 -59582 -94952 - .35370 .30725 .31987 -. 01262 .59590 .87097 - .27507 -30729 .33579 - .02850 -59587 .91321 - -31733 .30730 -54220 - .23490 .59577 -88552 - -28975 -30723 -49037 - .I8314 ,59570 .a9332 - -29762 .30708 -42472 - .I1764 .58039 .76902 - - 18863 -29110 -37502 -. 08392

-58039 -58039 -5803 9 -58037 -58034 -57110 -57112 -57112 .57112 - 57111 -57107 -57108 .56534 .56515 -56517 -56517 -56516 -56523 .56529 - 562 19 .56218 -56217 -56218 -56219 -56235 -56232 -55670 .55679 .55680 -55666 .55684

total spec 3.26597269289168 variance, sd of parameters x (1) bandgap 2 -54334443 1.15099231 x (2 ) linewidthA2 -13881765 .I7164586 x ( 3 ) 821A2 -33643929 .02843401 -21250858 x(4) ~ 3 1 ~ 2 -08624519 .00915195 -17574935 va12 -. 23721836 va13 -17161554 va14 -11.88007287 va2 3 10.38483631 va24 -.02690279 va3 4 -01569284 vext -06048098 INITIAL CO-ORDINATES

1 -6000 2 -9000 3 -2000 4 .lo00

OSUM OF SQUARES = 4.06165775D+OO l*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.22873680D+OO

fit data ydif f .68700 -81276 - .I2576 .36996 -15983 -21013 .68682 .94952 - -26270 .37034 -31987 -05046 -68721 .87097 - -18377 -37039 ,33579 -03460 -68691 .91321 -. 22629 .37039 -54220 - .I7181 -68678 .88552 - -19874 -37066 -49037 - .I1972 - 68712 .89332 - -20620 -37011 -42472 -. 05461 -65916 .76902 - -10986 .31796 .37502 -. 05706 -65918 .81642 -.I5724 -31796 -33008 -. 01212

,65918 -97208 -. 31290 .31794 -65916 .83558 -. 17642 ,31797 -65832 -94245 - .28413 -31761 -65876 1.00409 -.34533 .31757 - 58428 -60724 - -02296 -24 8 96 -58433 .71954 - -13521 -24858 -58435 -67030 - -08595 -24855 -58429 -60313 -. 01884 .24872 -58428 -65419 - .06991 .24864 -58379 -61965 - - 03585 -24832 .58378 .75085 -. 16708 -24836 .53816 -31876 -21940 .OOOOO .53742 .47937 .05805 -21829 -53746 -38126 -15621 .OOOOO -53748 -36653 .I7095 .OOOOO -53742 -33388 ,20354 ,00000 -53795 -47316 -06479 .OOOOO .53819 .52381 -01438 .OOOOO -52291 -26452 -25839 .OOOOO -52289 -23671 .2 8617 ,00000 -52284 -29104 .23180 .OOOOO -52286 -26875 .25410 .OOOOO - 52291 .27254 -25037 .OOOOO .52351 -36889 -15462 .OOOOO -52339 -32848 -19491 .OOOOO -51464 -24654 .26811 .OOOOO -51492 -25090 .26403 .OOOOO -51494 .29841 -21653 .OOOOO -51453 -28921 -22532 .OOOOO .51506 .39731 -11775 .OOOOO

total spec .222874D+01 12.63675 2.22873679800565 variance, sd of parameters

x ( 1 ) bandgap 2.49307559 ,00136548 .03695239 x (2) linewidthA2 -01639225 .00006902 .00830770 x(3) B21A2 .35473493 .00163189 -00259183 -04039668 .05091000 x(4) B31A2 -07722019 -00034423 .00116177 -01855336 -03408470 va12 .00008065 va13 .00058371 va14 -.00057965 va2 3 - .00017502 va2 4 -.00002078 va3 4 -00035997 vext -04127290 INITIAL CO-ORDINATES

1 -1000 2 -1000 3 -9000 4 -0900

OSUM OF SQUARES = 9.40820324Dt00 If** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 19, 24 FUNCTION EVALUATIONS OSUM OF SQUARES = 3.52372110D+00

fit data ydiff

-57055 -83558 - -26503 ,29529 -48293 - -18764 .57052 .94245 -. 37192 -29527 -70935 - .41408 .57055 1.00409 -.43354 .29527 -80708 - -51181 -57053 .60724 -. 03671 -29525 .07415 .22110 .57052 -71954 - ,14902 ,29527 -02671 -26855 -57052 -67030 -. 09977 -29527 -08350 .2 1177 .57052 -60313 -. 03261 -29526 -06884 - 22642 .57052 -65419 - -08367 ,29526 -06478 .23048 -57052 -61965 - ,04913 -29526 -11720 -17806 .57052 -75085 -. 18034 .29525 -15072 -14453 -57047 -31876 -25171 .OOOOO .OOOOO .OOOOO -57050 .47937 - 09113 .29525 -02726 -26799 -57049 -38126 ,18924 .OOOOO .OOOOO .OOOOO -57049 .3 6653 -20396 .OOOOO .OOOOO .OOOOO ,57050 -33388 -23661 .OOOOO .OOOOO .OOOOO .57050 -47316 -09734 .OOOOO -00000 . 00000 -57049 -52381 -04668 .OOOOO .OOOOO .OOOOO -57048 .26452 -30596 ,00000 -00000 . 00000 .57048 -23671 .33377 .OOOOO .OOOOO .OOOOO -57048 .29104 ,27945 ,00000 - 00000 . 00000 -57048 -26875 .30173 .OOOOO ,00000 ,00000 -57048 -27254 -29794 .OOOOO - 00000 -00000 -57048 -36889 .20159 .OOOOO .OOOOO .OOOOO -57048 -32848 -24200 .OOOOO .OOOOO .OOOOO ,57045 -24654 .32392 .OOOOO .OOOOO .OOOOO -57045 .25090 -33955 .OOOOO .OOOOO .OOOOO .57045 .29841 -27203 .OOOOO .OOOOO .OOOOO -57046 -28921 -28125 .OOOOO .OOOOO .OOOOO .57044 -39731 .I73 13 .OOOOO .OOOOO .OOOOO

t o t a l spec .352372Dt01 19.97920 3.52372110445411 variance, sd of parameters x ( 1 ) bandgap .26056341************866.70013925 ~ ( 2 ) linewidthA2 14 .65012343* * * * * * * * * * * * * * * * * * * * * * * * x (3 ) 321A2 .32273332 41.32270384 65.63017668 6.42827378 8.10124538 x(4) ~ 3 1 ~ 2 -08571209 11.77640712 39.74537403 3.43167701 6.30439323 va12 ************ va13 ************ va14 ************ va2 3 ************ va24 **t*********

va34 22.05935386 vext .06525409 INITIAL CO-ODINATES I .4000 2 .so00 3 ,6000 4 -6000

OSUM OF SQUARES = 1.04065452D+Ol I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESWLTS AT ITERATION 500, 5 0 5 FUNCTION EVALUATIONS OSUM OF SQUARES = 8.55304369D-01

fit data ydif f -73633 -81276 - -07643 -33480 -15983 -17497 .73574 -94952 -. 21378 -33509 -31987 - 01522 -73626 -87097 -. 13471 .33501 -33579 - -00078 ,73573 -91321 -. 17748 -33494 .54220 - -20725 -73588 .88552 -. 14964 -33599 -49037 - -15438 -73692 -89332 - -15639 -33564 -42472 -. 08908 -92374 .76902 .I5472 -51179 -37502 -13677 ,92392 -81642 .lo750 .5 1141 .33008 -18133 -92424 .97208 -. 04785 -51116 -31448 -19668 .92376 -83558 ,08818 -51105 .48293 -02812

-91987 -94245 - .02258 -50861 ,70935 - ,20074 -92459 1.00409 -,07950 -50855 -80708 - -29853 -65812 -60724 ,05089 .I4372 ,07415 ,06956 .65845 .71954 -.06109 .I4281 -02671 -11610 .65882 .67030 - -01147 -14280 -08350 ,05929 -65798 .GO313 -05485 .I4309 -06884 -07425 .65804 -65419 ,00384 .I4294 -06478 ,07816 .65233 .61965 -03268 .I4157 -11720 ,02438 -65190 .75085 - -09895 -14159 -15072 - ,00913 -36596 .3 1876 -04720 .OOOOO .OOOOO .OOOOO -36412 .47937 - .I1525 -08581 .02726 ,05855 .36445 .38126 -. 01680 .OOOOO .OOOOO ,00000 -36453 -36653 - - 00200 -00000 .OOOOO .OOOOO -36434 .33388 .03046 .OOOOO .OOOOO .OOOOO -3 64 12 -47316 -. 10904 -00000 .OOOOO ,00000 -36475 .52381 -,15906 .OOOOO .OOOOO ,00000 -38706 -26452 -12254 -00000 .OOOOO - 00000 -38715 -23671 -15044 .OOOOO .OOOOO ,00000 -38681 -29104 -09577 .OOOOO .OOOOO ,00000 -38716 -26875 ,11841 .OOOOO .OOOOO .OOOOO -38726 -27254 .I1472 .OOOOO .OOOOO .OOOOO .38586 .36889 -01698 .OOOOO .OOOOO .OOOOO -38549 -32848 .05701 .OOOOO - 00000 .OOOOO -45417 .24654 -20764 .OOOOO ,00000 - 00000 -45464 -25090 -20374 .OOOOO .OOOOO .OOOOO -45460 ,29841 -15619 .OOOOO .OOOOO .OOOOO -45402 .28921 -16481 ,00000 .OOOOO ,00000 .45479 .39731 -05747 .OOOOO .OOOOO .OOOOO

total spec .855304D+00 4,84950 -8553043691554959 variance, sd of parameters

x ( 1 ) bandgap 2.48007993 .00000847 .00291083 x (2 linewidthA2 -00133254 .00000007 -00026276 x(3) ~ 2 1 ~ 2 -35628664 .00052674 .00083659 .02295080 -02892379 x(4) 831A2 -04398169 .00004221 .00014247 -00649716 -01193604 va12 . O O O O O O ~ O va13 .00001387 va14 .00000013 va23 .00000101 va2 4 .00000085 va34 .00002088 vext -01583897 INITIAL CO-ORDINATES

1 .so00 2 ,2000 3 1.0000 4 3.0000

OSUM OF SQUARES = 5.60943345D+Ol 1""" SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 30, 3 5 FUNCTION EVALUATIONS OSUM OF SQUARES = 3.51112036D+OO

fit data ydif f -57099 -81276 -.24177 ,29425 .I5983 -13442 .57099 .94952 -. 37853 .29426 -31987 - ,02562 -57100 -87097 - - 29998 .29426 .33579 - -04153 .57100 ,91321 - -34221 -29426 -54220 - .24794 -57099 .88552 - -31453 -29425 .49037 - -19612 .57099 .89332 - -32233 -29425 -42472 - -13 048 -57025 .76902 - .I9878 -29349 .37502 - -08153 -57025 .81642 - -24617 .2 9349 .33008 - -03660 -57025 .97208 - .40184 -29349 .31448 - -02100 .57025 .83558 - -26533 .2 9349 .48293 - -18944 -57025 .94245 - -37220 -29349 ,70935 - -41586

,57025 1.00409 -.43385 ,29349 ,80708 - -51358 -56982 -60724 - .03742 ,29306 -07415 .21890 -56982 -71954 - .I4972 -29305 -02671 .26634 -56982 -67030 -. 10048 -29305 .08350 -20955 -56982 -60313 - .03331 -29305 -06884 -22421 -56982 -65419 - -08437 -29305 ,06478 -22827 .56982 -61965 - .04983 .29305 -11720 -17585 -56982 -75085 - -18193 -29305 -15072 -14233 .56952 .31876 -25076 ,00000 .OOOOO -00000 -56951 -47937 -09014 -29273 -02726 -26547 -56951 -38126 .I8826 .OOOOO .OOOOO -00000 -56951 -36653 -20298 .OOOOO .OOOOO .OOOOO ,56951 -33388 .23563 .OOOOO .OOOOO -00000 - 56951 -47316 .09635 . 00000 .OOOOO .OOOOO -56952 -52381 .04571 .OOOOO .OOOOO -00000 .56933 .26452 -30481 .OOOOO .OOOOO -00000 -56933 -23671 .33262 .OOOOO .OOOOO .OOOOO -56933 -29104 -27830 .OOOOO -00000 .OOOOO -56933 -26875 -30058 - 00000 ,00000 .OOOOO -56933 -27254 .29680 .OOOOO ,00000 -00000 -56934 -36889 .20046 .OOOOO .OOOOO -00000 -56934 -32848 -24086 .OOOOO .OOOOO .OOOOO .56891 .24654 -32238 .OOOOO .OOOOO .OOOOO -56892 -25090 -31802 -00000 .OOOOO .OOOOO -56892 -29841 -27051 .OOOOO .OOOOO -00000 .56891 ,28921 -27970 .OOOOO ,00000 .OOOOO -56892 -39731 .I7161 .OOOOO .OOOOO .OOOOO

total spec .351112Dt01 19.90775 3.5Ill203578797 variance, sd of parameters x ( 1 ) bandgap 2 .60608454* * * * * * * * * * * *406 .31244510 x (2 ) linewidthA2 3 .03798015* * * * * * * * * * * *265 .84566623 x ( 3 ) B21A2 -32566735 10.60352458 16-84089198 3.25630536 4.10376559 x(4) ~ 3 1 ~ 2 -08647155 3.04919664 10.29103867 1.74619490 3.20796488 va12 *******+**t*

va13 ************ va14 ******+***** va2 3 ************ va24 ************ va34 5.68573207 vext .06502075 INITIAL CO-ORDINATES 1 1.0400 2 .0040 3 -3000 4 -4000

OSUM OF SQUARES = 6.28701920D+00 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT' ITERATION 202, 207 FUNCTION EVALUATIONS OSUM OF SQUARES = 3.13558664D+00

fit data ydif f -60494 -81276 - -20782 - 31713 -15983 .I5730 .GO497 .94952 -. 34456 ,31729 .31987 -. 00259 .60511 -87097 -. 26587 -31733 -33579 - .01846 .60503 ,91321 -. 30817 -31734 -54220 - .22486 .GO490 .88552 -. 28062 .31730 .49037 -. 17307 ,60488 .89332 -. 28844 -31'707 -42472 - .I0766 -58637 .76902 - -18265 -29617 -37502 -.07885 .58637 -8i642 -. 23005 .29617 ,33008 - . 03391 -58637 -97208 -. 38571 .29617 .31448 -.01831 .58637 -83558 - .24921 .29618 -48293 -. 18675 -58621 .94245 - .35623 .29611 ,70935 - -41325 .58628 1.00409 -. 41781 -29610 -80706 - -51098

-57193 -60724 - - 03534 -28184 -07415 -20768 -57191 ,71954 - -14763 -28174 -02671 -25502 -57191 .67030 - - 09838 -28173 .08350 .I9823 -57190 .GO313 - - 03123 -28177 .06884 -21293 ,57190 -65419 - - 08229 .28175 -06478 -21697 -57181 ,61965 -. 04783 ,28168 -11720 -16448 ,57181 -75085 - -17904 -28169 -15072 -13097 ,56197 -31876 .24320 .OOOOO .OOOOO .OOOOO -56178 -47937 -08241 -27238 -02726 -24512 -56179 -38126 -18053 - 00000 .OOOOO .OOOOO -56179 .3 6653 -19526 -00000 .OOOOO .00000 -56178 ,33388 -22790 .OOOOO .OOOOO .OOOOO .56193 -47316 ,08877 .OOOOO .OOOOO .OOOOO -56199 -52381 -03818 .OOOOO .OOOOO .00000 -55663 -26452 -29211 .OOOOO .OOOOO .00000 -55662 ,23671 -31991 .OOOOO , 00000 .OOOOO -55662 .29104 -26558 .OOOOO .OOOOO .00000 -55661 -26875 -28786 .OOOOO .OOOOO -00000 -55662 .27254 -28409 .OOOOO ,00000 -00000 ,55689 ,36889 - 18800 - 00000 .OOOOO -00000 .55686 ,32848 -22837 . GO000 .OOOOO .OOOOO -54734 .24654 .30081 ,00000 .OOOOO .00000 -54744 -25090 -29655 -00000 .OOOOO .OOOOO .54746 -29841 -24905 .OOOOO .OOOOO .OOOOO -54729 -28921 -25809 .OOOOO .OOOOO .OOOOO -54751 -39731 -15020 .OOOOO .OOOOO .00000

total spec .313559D+01 17 -77851 3 .I3558663909375 variance, sd of parameters x (1) bandgap 2.49780475 .23950629 -48939380 x (2 ) linewidthA2 .08965536 -02109310 .I4523464 x(3) ~ 2 1 ~ 2 .33071940 .01200197 .01906195 .I0955349 -13806501 ~ ( 4 ) ~ 3 1 ~ 2 -08365014 -00393492 -01328034 -06272892 -11524038 va12 -.00090069 va13 -04945738 va14 -1.25029868 va2 3 1.02742661 va24 - -00135332 va34 -00643925 vext .05806642

*** NORMAL TERMINATION

BAND GAP FIT VA05MP SUM OF SQUAReS OPTIMIZATION BAND2ER3 . IN (VER: JAN 8, 1979) band2er3 o 4 variables, 72 terms in sumof squares, rnaxit = 500, print modulus = 0 Oacc= 1.0000000D-15, dstep = 5.300000D-05, dmax= 2.000000D+00

.689650 -288791 300.785500 603.359300 907.010800 21838.83

.741071 ,292930 300.747500 602.427700 904.332200 21838.83 -689116 .346460 301.194200 602.985300 905.222700 21838.83 -825576 -352677 300.680300 601.959200 902.367300 21838.83 .648036 -328188 308.965200 611.053400 911.714900 21838.83 ,561215 -261220 308,812000 611.366700 911.840900 21838.83 -754661 .243371 302.095900 604.314900 908.071200 20986.36 -738103 ,297586 302.064700 604.335000 906.208400 20986.36 ,885232 -274321 302.191400 604.636800 906.635700 20986-36 .885147 ,383024 302.372200 604.522700 906.598900 20986-36 -927709 -569225 305.685300 607,786900 609.158700 20986.36

1.034638 .589015 305-095300 606.732800 904.217400 20986.36 -597460 .038466 300.657800 604,046000 905.862900 20491.80 -703676 -039442 299-250300 603.149900 904.798500 20491.80 ,639510 -120875 304.627300 606,750400 909.171400 20491-80 ,654126 -125853 304.489600 606,507800 908.912900 20491.80 -349446 .OOOOOO 312.253000 615.161400 .OOOOOO 20140.99 -478868 .OOOOOO 310.994000 614.342000 -000000 20140.99 ,378169 -00G000 312.205600 614.779000 .OOOOOO 20140.99 .399446 -000000 312.245600 615.153800 .OOO O O O 20140.99 -405537 .OOOOOO 312.067700 615.036900 .OOOOOO 20140.99 -364655 -125487 306.196200 608.608400 906.648100 20140.99 .298003 .OOOOOO 313.739700 617.359800 ,000000 19932 - 23 .363325 -000000 313.362200 615.262400 .OOOOOO 19932.23 ,331838 .OOOOOO 314.481300 617.835000 .OOOOOO 19932.23 -227473 .OOOOOO 315.097300 618.372700 .OOOOOO 19932.23 -241562 .OOOOOO 315.047500 616.677600 -000000 19932.23 .279484 .OOOOOO 315.622200 617.924400 .OOOOOO 19932.23 .273641 -000000 303.986500 606.538500 .OOOOOO 19932.23 .300325 .OOOOOO 304.654500 607.279300 .OOOOOO 19932.23 .I90220 .OOOOOO 314.668200 621.204800 -000000 19436.35 -150399 .OOOOOO 314.348900 616.953100 .OOOOOO 19436. 35 -079119 -000000 313.856600 616.774400 .OOOOOO 19436.35 -066552 -000000 314.425900 614.898000 .OOOOOO 19436. 35 -224904 .OOOOOO 314.441300 620.296700 .OOOOOO 19436.35 -330948 .OOOOOO 305.392200 603.408300 .OOOOOO 19436.35

ZFILE = jd3ls . p m d3 1s d31s(2) wlol wl02 wlo3

INITIAL CO -ORDINATES 1 2.3770 2 .0040 3 .I010 4 -0610

OSUM OF SQUARES = 3.35784446Dt00 l*** F ( X ) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 74, 79 FUNCTION EVALUATIONS OSUM OF SQUARES = 8.01427401D-01

fit data ydif £ ,64815 .68965 -. 04150 .27191 -28879 -.01688 -64771 .74107 -. 09336 .27123 -29293 - -02170 -64780 .68912 -. 04131 -27138 .34646 -. 07508 .64751 -82558 -. 17807 .27074 .35268 -. 08194 .64862 -64804 .00058 .27175 ,32819 -. 05643 .64883 .56122 -08762 .27181 .26122 -01059 -80270 -75466 .04804 .41817 -24337 .I7480

.33872 .27948 .05923 .OOOOO -33712 -27364 ,06348 . 00000 -33717 -30033 -03685 .OOOOO -39745 -19022 -20723 .OOOOO -39870 -15040 -24830 .OOOOO -39855 -07912 -31943 .OOOOO -39940 -06655 -33285 .OOOOO -39765 .22490 -17275 .OOOOO .39936 ,33095 .06841 .OOOOO

total spec .801467D+00 6 -27989 -8014666575347037 variance, sd of parameters x ( 1) bandgap 2.47555503 .00001754 x (2) linewidthA2 .00138427 .00000014 x(3) ~ 2 1 ~ 2 .27811060 ,00023844 ,01910796 x(4) ~ 3 1 ~ 2 .02955165 .00003775 ,01192913 va12 - . 00000004 va13 - .00000425 va14 -.00000022 va2 3 .oooooooa va24 .00000130 va3 4 - . 00000125 vext .01635646 INITIAL CO-ORDINATES

1 1.0400 2 .0040 3 -3000 4 .4000

OSUM OF SQUARES = 5.54010725D+00 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 280, 2 8 5 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.27513936~+00

fit -55585 .55571 -55572 .55565 -55571 -55579 .53587 .53587 -53588 -53585 -53571 .53571 .51165 .51171 -51146 -51147 -49335 -49338 -49338 -49336 -49336 -49367 .48445 .48463 .48445 -48443 -48460 .48451 .48492 .48489

data ydif f

-47065 .I9022 -28043 .OOOOO ,47117 -15040 -32077 .OOOOO -47113 ,07912 -39202 .OOOOO -47144 -06655 -40489 .OOOOO -47074 - 22490 -24584 .OOOOO .47191 -33095 -14096 .OOOOO

total spec -227514Dt01 17.82684 2.27513936339689 variance, sd of parameters x (1) bandgap 2.47975088 -02413700 x (2) linewidthA2 -04454456 -00273675 x ( 3 ) ~ 2 1 ~ 2 .25971419 -00178564 -05229012 x(4) ~ 3 1 ~ 2 .06833989 .00110989 -06467945 va12 .00159118 va13 .00396611 va14 -.02584655 va2 3 .00969812 va24 .00024930 va3 4 -00084236 vext .04643142

*** NORMAL TERMINATION

BAND GAP FIT VAOSMP SUM OF SQUARES OPTIMIZATION BAND2ER3 . IN (VER: JAN 8, 1979) band2er3 o 4 variables, 80 terns in sum of squares, maxit = 500, print modulus = 0 Oacc= 1.OOOOOOOD-15, dstep = 5.300000D-05, dmax= 2~000000D+00

-803930 .390875 302.274400 604.969800 903.987000 21838.83 -824368 -330240 301.958800 603.096800 900.860100 21838.83 .821748 -516602 301.826700 603.181000 907.903500 21838.83 -722401 .390875 308.931100 611.025200 908.596800 21838.83 -624933 .327117 308.492800 610.898500 911.858800 21838.83 .776926 -295185 302.983500 605.202800 906.490500 20986.36 .877515 -327810 303.089900 605.984100 908.759800 20986.36 -874826 .471606 303.215400 606.165500 908.139800 20986.36 -838720 -437628 303.094000 605.952000 907.881500 20986.36 -782574 .363785 302.971300 605-512400 908.521000 20986.36 -906727 .576531 305-264400 607.355700 905.330300 20986.36 .833778 -439897 304.313800 606.151500 905.353600 20986.36 -517626 .031803 301.137400 604.529900 907.594500 20491.80 -616351 .OOOOOO 301.916500 604.868500 .OOOOOO 20491.80 ,430599 -052539 301.340400 604.458200 904.896300 20491.80 -539108 .005678 301.114800 604.681500 905.840800 20491.80 -616119 ,100543 301.228200 604.848000 906.864700 20491.80 -722186 ,171153 305.309900 607.514700 907.245200 20491.80 ,707827 -181038 305.363100 607.589400 907.310300 20491.80 .276903 .OOOOOO 313.326300 615.408000 .OOOOOO 20140.99 -313470 .OOOOOO 312.988200 616.025400 .OOOOOO 20140.99 -319108 -000000 313.139000 615.945000 .OOOOOO 20140.99 -396694 .OOOOOO 313.187100 615.893600 .OOOOOO 20140.99 -412976 .OOOOOO 312.954900 616.278800 .OOOOOO 20140.99 -575852 ,000000 306.350700 609.308400 .OOOOOO 20140.99 .548283 .OOOOOO 305.088300 607.709500 .OOOOOO 20140.99 .I85419 .OOOOOO 316.100900 618.357400 .OOOOOO 19932.23 -345028 . O O O O O O 315.455300 618.379100 .OOOOOO 19932.23 -461349 .OOOOOO 315.211900 618.652800 .OOOOOO 19932.23 -246214 .OOOOOO 315-919200 618.650800 .OOOOOO 19932.23 -376719 .OOOOOO 314.180000 617.090400 .OOOOOO 19932.23 -446372 .OOOOOO 303.357800 606.129300 .OOOOOO 19932.23 -422102 .OOOOOO 304,881300 606.835300 .OOOOOO 19932.23 -204455 -000000 314.202800 616.994600 .OOOOOO 19436.35 -267532 .OOOOOO 314.499000 618.714800 ,000000 19436.35 -259404 .OOOOOO 314.513800 617.485700 .OOOOOO 19436.35 -226606 -000000 314.632200 618.112200 .OOOOOO 19436.35 .223103 .O O O O O O 314.022600 619.504000 .OOOOOO 19436.35 -272993 .OOOOOO 303.845900 605.672600 .OOOOOO 19436.35 -413829 .OOOOOO 304.334000 606.239100 .OOOOOO 19436.35

ZFILE = jd5lp . p m d5 1p dSlp(2) wlol wl02 wlo3

INITIAL CO-ORDINATES 1 2 -3770 2 -0040 3 .I010 4 .0610

OSUM OF SQUARES = 3.59760174D+00 I*** F(X) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN JACOBIAN ORESULTS AT ITERATION 77, 82 FUNCTION EVALUATIONS OSUM OF SQUARES = 6.61184550D-01

fit data ydif f .68127 -80393 -.I2266 -32543 -39087 -. 06545 .68044 -82437 -. 14393 -32452 -33024 - .00572 -68053 ,82175 -. 14121 .32674 -51660 -. 18986

.68157 -68169 .82596 -82670 -82688 .82674 -82634 .82629 -82579 ,57933 -57863 .57924 ,57927 -57910 .57494 -57486 -36353 ,36307 -36318 -36323 -36293 -36350 -36375 -37404 .37369 -37344 .37382 -37356 .37249 -37300 ,42574 -42529 -42570 ,42555 .42484 -42516 ,42518

total spec .66118%5495201567 variance, sd of parameters x ( 1 ) bandgap 2.48170315 -00001336 x (2) linewidthA2 .00185311 .00000009 x(3) B21A2 .30590057 -00032223 ,02198519 x(4) B31A2 ,04197633 .00003045 .01083804 va12 .00000054 va13 .00001454 va14 -.00000175 va2 3 .00000475 va24 .00000031 va3 4 .00001671 vext -01224416 INITIAL CO-ORDINATES 1 2.4700 2 .0020 3 -4000 4 .0610

OSUM OF SQUARES = 1.23190147D+00 I*** F ( X ) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO IN THE JACOBIAN ORESULTS AT ITERATION 77, 82 FUNCTION EVALUATIONS

LOSS OF RANK

OSUM OF SQUARES = 6.61184053D-01 fit data ydif f

-68136 .68052 .68062 .68166 .68178 .a2605 .82687 .82696 -82683 ,82643 -82638 -82588 -57964 -57893 -57954 -57957 -57940 -57524 -57516 -36359 .36314 -36325 -36329 -36300 -36357 -36382 -37408 -37373 -37348 .37386 -37360 .37253 .37304 .42579 -42535 -42575 -42560 -42489 -42521 -42523

total spec .6611840525494048 variance, sd of parameters x ( 1) bandgap 2.48168153 .00001333 x (2) linewidthA2 .00185315 .00000009 x ( 3 ) ~ 2 1 ~ 2 -30599555 -00032225 -02198588 x(4) ~ 3 1 ~ 2 .04194303 .00003039 .01082646 va12 .00000054 va13 .00001455 va14 -.00000175 va2 3 .00000475 va24 .00000031 va3 4 .00001672 vext .01224415 INITIAL CO-ORDINATES

1 -8000 2 .0400 3 -5000 4 .so00

OSUM OF SQUARES = 1.26958173D+01 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 34, 3 9 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.51731707D+OO

fit -52993 -52991 -52991 .52990 .52991 -52680 -52680 -52680 -52680 -52680 -52679 .52679 -52489 -52489 -52489 -52489 -52489 -52488 -52488 -52350 .52349 - 52349 -52349 -52349 -52352 -52352 .52270 .52269 -52269 -52269 .52270 -52274 ,52274 .52089 -52087 .52088 -52088 -52085 -52094 -52094

total spec

data ydif f

2.51731706846045 variance, sd of parameters x (1) bandgap

- 2.48941807353-86233632 18.81122900

x (2) linewidthA2 .62956545 43.90427600 6.62603018 x(3) ~ 2 1 ~ 2 .27567417 -34780617 .52170926 -58975094 -72229444 x(4) ~ 3 1 ~ 2 .08950134 -15919086 .61402190 -39898730 .78359549 va12 1.88065696 va13 11.07276167 va14 ************ va23 * * * k t * * * * * * *

va24 .00532806 va3 4 .23496249 vext ,04661698 INITIAL CO-ORDINATES

1 -6000 2 -0300 3 -0400 4 -1200

OSUM OF SQUARES = 6.77817176D+00 I*** MAXIMUM NUMBER OF ITERATIOKS EXCEEDED ORESULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS

OSUM OF SQUARES = 6.61185215D-01 fit -68129 -68046 .68056 .68159 ,68171 .82590 ,82673 .82682 .82669 .82628 -82624 -82573 -57923 -57853 .57913 -57916 .57900 -57484 -57476 -36360 -36315 -36326 -36330 -36301 -36358 -36383 -37410 ,37375 -37350 .37388 -3 73 62 ,37255 ,37306 -42577 .42532 -42573 .42558 ,42487 .42519 .42521

total spec

data ydiff

.6611832152765251 variance, sd of parameters

x(1) bandgap 2.48171362 .00001338 x (2) linewidthA2 .00185477 .00000009 x ( 3 ) ~ 2 1 " ~ .30591935 -00032223 ,02198516 x(4) ~ 3 1 ~ 2 -04201228 -00003052 .01084940 va12 .00000054 va13 .00001454 va14 -.00000175 va2 3 -00000475 va24 .00000031 va34 .00001672 vext -02224417 INITIAL CO-ORDINATES

1 -6700 2 -3000 3 -1500 4 -4500

OSUM OF SQUARES = 6.07784356D+OO I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED

ORESULTS AT ITERATION 500 , 5 0 5 E'UNCTION EVALUATIONS OSUM O F SQUARES = 1.28270085D+00

f i t data ydif f - 6 5 5 6 5 . 8 0 3 9 3 -. 14828 - 3 7 6 6 5 .39087 - -01422 - 6 5 5 0 4 - 8 2 4 3 7 - . I 6 9 3 3 - 3 7 5 9 9 - 33024 . 04575 .65512 - 8 2 1 7 5 - . I 6 6 6 3 - 3 7 7 6 6 - 5 1 6 6 0 - -13894 - 6 5 5 6 7 . 7 2 2 4 0 - - 0 6 6 7 4 - 3 7 6 4 1 , 3 9 0 8 7 - -01447 - 6 5 5 7 7 - 6 2 4 9 3 -03084 - 3 7 7 2 6 - 3 2 7 1 2 - 05014 ,64673 - 7 7 6 9 3 - -13020 -32924 , 2 9 5 1 8 -03406 - 6 4 6 8 8 . 8 7 7 5 2 - - 23063 - 3 2 9 2 0 , 3 2 7 8 1 .00139 ,64688 - 8 7 4 8 3 - .22794 .32918 - 4 7 1 6 1 - - 14242 - 6 4 6 8 7 - 8 3 8 7 2 - -19185 . 3 2 9 2 1 - 4 3 7 6 3 - -10842 - 6 4 6 8 1 - 7 8 2 5 7 - - 13576 ,32923 .36379 - - 03456 - 6 4 6 4 0 - 9 0 6 7 3 - .26033 .32880 - 5 7 6 5 3 - -24773 .64646 - 8 3 3 7 8 -. 18732 .32899 - 4 3 9 9 0 - - 1 1 0 9 1 - 5 4 0 7 7 , 5 1 7 6 3 -02314 ,22619 .03180 -19439 - 5 4 0 6 5 - 6 1 6 3 5 - .07570 ,00000 .00000 * 00000 ,54076 - 4 3 0 6 0 - 11017 ,22653 - 0 5 2 5 4 . 17399 - 5 4 0 7 5 ,539'11 - 00164 - 2 2 6 4 2 - 0 0 5 6 8 -22074 , 5 4 0 7 1 - 6 1 6 1 2 -. 07541 - 2 2 6 2 8 - 1 0 0 5 4 -12574 - 5 3 9 9 6 - 7 2 2 1 9 - - 18223 - 2 2 6 1 0 - 1 7 1 1 5 .05495 - 5 3 9 9 4 . 7 0 7 8 3 - -16789 - 2 2 6 0 9 . I 8 1 0 4 -04505 - 4 7 6 8 4 - 2 7 6 9 0 - 19994 - 0 0 0 0 0 . O O O O O -00000 . 4 7 6 6 1 - 3 1 3 4 7 . I 6 3 1 4 . O O O O O . O O O O O . O O O O O - 4 7 6 6 6 . 3 1 9 1 1 -15755 . O O O O O . ooooo -00000 ,47668 . 3 9 6 6 9 . 07999 -00000 . O O O O O - 00000 ,47653 - 4 1 2 9 8 .06356 . O O O O O . 00000 .00000 - 4 7 7 3 3 , 5 7 5 8 5 - -09853 . O O O O O . O O O O O - 00000 - 4 7 7 5 5 . 5 4 8 2 8 -. 07073 . O O O O O .00000 -00000 - 4 6 2 7 1 - 1 8 5 4 2 .27729 . O O O O O . O O O O O -00000 .46254 - 3 4 5 0 3 . I 1 7 5 1 . O O O O O . O O O O O . O O O O O - 4 6 2 4 0 . 4 6 1 3 5 .00105 . O O O O O . O O O O O . 00000 - 4 6 2 5 8 - 2 4 6 2 1 .21636 . O O O O O . O O O O O . O O O O O . 46259 - 3 7 6 7 2 -08587 . O O O O O . O O O O O -00000 - 4 6 3 0 3 . 4 4 6 3 7 -01666 . O O O O O . O O O O O -00000 - 4 6 3 2 0 - 4 2 2 1 0 .04110 . O O O O O .00000 .00000 .46368 - 2 0 4 4 6 -25922 . O O O O O . O O O O O . 00000 - 4 6 3 3 1 - 2 6 7 5 3 -19578 . O O O O O . O O O O O -00000 - 4 6 3 6 4 - 2 5 9 4 0 .20423 ,00000 . O O O O O . O O O O O - 4 6 3 5 1 - 2 2 6 6 1 .23690 . O O O O O . O O O O O . O O O O O .46297 - 2 2 3 1 0 .23987 . O O O O O . O O O O O . O O O O O - 4 6 3 6 9 . 2 7 2 9 9 -19070 . O O O O O . O O O O O . 00000 - 4 6 3 6 8 . 4 1 3 8 3 .04986 . 00000 .00000 .00000

total spec - 1 2 8 2 7 0 D t 0 1 8 .40909 1 .28270085459844 variance, sd of parameters

x ( 1 ) b a n d g a p 2 .49105639 . 00047016 - 0 2 1 6 8 3 1 9 x ( 2 ) l i n e w i d t h A 2 -00997230 .00001429 - 0 0 3 7 8 0 5 5 x ( 3 ) ~ 2 1 ~ 2 -30683268 .00069289 .00103934 .02632286 -03223879 x ( 4 ) 3 3 1 A 2 -07048289 .00026751 .00103184 -01635582 .03212219

v a 1 2 .00002912 v a 1 3 .00015126 v a 1 4 - . 00149564 v a 2 3 - .00053181 v a 2 4 - .00000310 v a 3 4 .00016994 vext -02375372 INITIAL CO-ORDINATES

1 - 6 0 0 0 2 - 9 0 0 0 3 - 2 0 0 0 4 . I 0 0 0

OSUM OF SQUARES = 2.78782007D+00

I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESVLTS AT ITERATION 209, 2 1 4 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.19352186D+00

f i t .56727 ,56710 -56712 .56712 .56716 -54820 -54822 .54822 -54822 ,54821 -54812 .54814 -53112 -53110 -53112 -53111 .53111 -53099 -53099 .51882 .51877 ,51878 -51879 ,51876 -51899 -51905 -51259 -51256 -51253 .51256 -51260 -51290 -51292 -50203 .50188 -50201 ,50195 -50175 -50229 .SO227

to ta l spec

d a t a ydif f -31729 -31715 -31753 - 31707 ,31727 -29341 -29340 -29340 -29340 -29341 -29332 -29336 -27514 - 00000 -27522 -27519 -27516 -27512 -27512 .00000 -00000 .00000 - 00000 .00000 .00000 - 00000 .00000 .00000 .00000 .00000 *00000 *00000 *00000 .00000 .00000 .00000 .00000 .00000 .00000 t O O O O O

2.19352186057656 v a r i a n c e , sd o f p a r a m e t e r s x ( 1) bandgap 2.48787709 . I0408547 x ( 2 ) l i n e w i d t h A 2 -06893629 .01120150 x ( 3 ) ~ 2 1 ~ 2 .28314277 .00550498 -09087062 x ( 4 ) ~ 3 1 ~ 2 .07936191 -00281379 . lo417865 va12 -00442029 va13 .02114591 va14 -6.14679200 va2 3 4.85189766 va24 -00015223 v a 3 4 .00358206 vext -04062078 INITIAL CO-ORDINATES

1 . I 0 0 0 2 -1000 3 .go00

OSUM OF SQUARES = 1.02437647D+01 l*** F ( X ) NO LONGER DECREASES -.. OPTIMIZATION TERMINATED

THIS MAY BE DUE TO VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN JACOBIAN ORESULTS AT ITERATION 391, 396 FUNCTION EVALUATIONS OSUM OF SQUARES = 6.61184064D-01

fit data ydif f -68134 ,80393 -. 12259 -32530 -39087 -. 06557 - 6 8 0 5 1 -82437 - -14386 -32440 .33024 - .00584 -68060 - 8 2 1 7 5 - . I 4114 -32661 .51660 - -18999 .68164 -72240 - .04076 -32538 .39087 -. 06550 -68176 -62493 -05683 .32649 -32712 - .00063 -82603 .77693 -04910 -43613 -29518 -14094 -82686 ,87752 - -05066 -43657 -32781 -10876 ,82695 -87483 -. 04788 .43637 .47161 - .03524 .82681 -83872 -. 01191 -43637 ,43763 - -00125 - 8 2 6 4 1 ,78257 -04384 -43658 -36379 ,07279 -82636 ,90673 - -08036 -43470 -57653 - -14183 .82586 -83378 - - 00792 -43519 ,43990 - . 00471 , 57941 -51763 .a6179 - 14332 .03180 -11152 - 5 7 8 7 1 -61635 -. 03764 -00000 . O O O O O . O O O O O -57932 -43060 -14872 -14383 -05254 ,09129 -57935 - 5 3 9 1 1 .04024 -14368 .00568 -13800 .57918 -61612 - -03694 -14345 ,10054 -04291 -57502 -72219 - -14717 . I4271 -17115 - .02844 -57494 ,70783 -. 13289 -14269 -18104 - .03835 -36357 -27690 -08667 -00000 . O O O O O . O O O O O .36312 ,31347 .04965 . O O O O O . O O O O O -00000 .36323 - 3 1 9 1 1 -04412 . O O O O O . O O O O O -00000 -36327 ,39669 -. 03342 -00000 . O O O O O . O O O O O ,36298 -41298 - .04999 . O O O O O . O O O O O . O O O O O .36355 -57585 - .21230 . O O O O O . O O O O O -00000 .36380 -54828 -. 18448 -00000 . O O O O O ,00000 -37408 ,18542 -18866 -00000 . O O O O O . O O O O O -37373 -34503 .02870 -00000 -00000 . O O O O O -37348 -46135 -. 08787 . O O O O O ,00000 -00000 .37386 - 2 4 6 2 1 -12765 -00000 . O O O O O . 00000 .37360 -37672 -. 00312 - 00000 . O O O O O -00000 -37254 -44637 - -07384 -00000 . O O O O O . O O O O O -37304 ,42210 -. 04906 - 00000 ,00000 . O O O O O -42578 -20446 .22133 -00000 . O O O O O . O O O O O .42534 -26753 -15781 . O O O O O . O O O O O . O O O O O -42575 .25940 -16634 -00000 . O O O O O . O O O O O -42559 . 22661 -19899 -00000 . O O O O O . O O O O O -42488 -22310 .20178 -00000 ,00000 .00000 .42521 -27299 . I 5 2 2 1 . O O O O O . O O O O O .00000 -42522 -41383 -01139 . O O O O O . O O O O O . 00000

t o t a l spec .661184D+00 4.33457 .661184063690445 variance, sd of parameters

x ( 1 ) bandgap 2 -48170123 ,00001335 -00365426 x ( 2 ) l i n e w i d t h A 2 -00185330 .00000009 -00029197 x ( 3 ) ~ 2 1 ~ 2 -30596565 -00032224 -00048336 .01795102 -02198542 x ( 4 ) ~ 3 1 ~ 2 ,04194560 .00003042 .00011733 -00551543 .01083209 va12 .00000054 va13 .00001454 va14 - .00000175 va2 3 .00000475 va2 4 .00000031 va34 .00001670 vext .01224415 INITIAL CO-ORDINATES

1 .4000

2 -5000 3 .6000 4 -6000

OSUM OF SQUARES = 9.79103195Dt00 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 314, 3 1 9 FUNCTION NALUATIONS OSUM OF SQUARES = 1.93125490D+00

fit -59358 -59328 -59332 -59344 .59350 .57128 -57134 .57133 -57133 -57131 .57115 -57118 .53864 -53860 -53863 .53864 - 53863 -53837 .53837 -51411 .51403 .51405 .51405 .51401 .51444 -51455 .SO288 -50283 -50277 .SO283 -50289 .50341 -50344 -48804 -48781 -48801 .48792 -48761 .48836 -48834

total spec

data ydif f

1.931254904985 variance, sd of parameters

x (1) bandgap 2 -48096072 .01064711 x ( 2 ) l i n e w i d t h A 2 -03419902 . 00102194 x ( 3 ) 321A2 .28794922 .00196828 .05433623 x ( 4 ) ~ 3 1 ~ 2 .07947878 .00108958 -06482811 va12 -00086812 va13 .00320256 va14 - .25248965 va2 3 . I1366323 va2 4 -00014325 va3 4 .00109609 vext .03576398

INITIAL CO-ORDINATES

1 -5000 2 -2000 3 1.0000 4 3.0000

OSUM OF SQUARES = 5.24270593D+01 I*** F (X) NO LONGER DECRESSES . . . OPTIMIZATION 'I%RMINATED

THIS MAY BE DUE TO TRE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THJ3 JACOBIAN ORESULTS AT ITERATION 497, 5 02 FUNCTION EVALUATIONS OSTJM OF SQUARES = 6.61184189D-01 -

fit -68128 -68045 -68055 -68158 -68170 - 82596 -82678 -82688 -82674 -82634 -82629 -82579 -57941 .57870 -57931 ,57934 .57917 -57501 -57494 -36355 -36309 -36320 -36325 -36295 .36353 .36378 .37405 -37370 -37345 -37383 -37357 .37250 -37301 -42574 .42530 ,42571 .42556 .42485 ,42517 .42519

total spec

data ydif f

.661184D+00 4.33457 .6611841894932051 variance, sd of parameters x (1) bandgap 2.48169718 .00001335 x (2) linewidthA2 -00185329 .00000009 x(3) 1321A2 - 30591750 .00032224 -02198551 x(4) 331A2 .04193902 ,00003041 -01083119 va12 .00000054 va13 .00001455 va14 -. 00000175 va2 3 .00000475 va2 4 .00000031

va34 .00001670 vext .01224415

INITIAL CO-ORDINATES 1 1.0400 2 -0040 3 ,3000 4 ,4000

OSUM O F SQUAFSS = 5.03001851D+OO I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500 , 5 0 5 E'UNCTION EVALUATIONS OSUM O F SQUARES = 6.64282928D-01

f i t .68241 .68157 -68167 ,68272 ,68285 - 83631 -83718 -83728 -83713 -83671 -83669 -83615 .56892 .56819 -56883 ,56885 -56867 -56432 -56424 -35671 -35624 .35635 .35640 .35610 .35647 -35668 -37149 -37113 -37088 -37127 -37099 -36979 .37032 -42541 .42497 -42538 -42523 -42452 -42483 -42485

total spec

data ydiff

.6642829275869403 variance, sd of parameters x (I) bandgap 2.48284791 .00001292 x (2 ) linewidthA2 .00171075 .00000007 x(3) B21A2 -30554425 -00032166 .02196576 x(4) B31A2 -04203134 . 00003025 .01080234 va12 .00000050 va13 .00001318 va14 - -00000109 va2 3 .00000361

va24 .00000033 va3 4 ,00001498 v e x t .01230154

*** NORMAL TERMINATION

BAND GAP FIT VAOSMP SUM OF SQUARES OPTIMIZATION BAND2ER3 . IN (VBR: JAN 8 , 1979) band2 er3

o 4 variables, 74 terms i n s u m of squares, maxit = 5 0 0 , print modulus = 0 Oacc= 1.0000000D-15, ds tep = 5.300000D-05, dmax= 2.000000D+00

-283715 302 .610700 604.977700 8 9 9 . 5 8 4 1 0 0 2 1 8 3 8 . 8 3

ZFILE = j d 5 l s . pm d51s dSls(2) wlol w102 wl03

INITIAL CO-ORDINATES 1 2 . 3 7 7 0 2 -0040 3 -1010 4 -0610

OSUM OF SQUARES = 2.87125037D+00 I*** F (X) NO LONGER DECREASES . . . OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO IN THE JACOBIAN ORESULTS AT ITERATION 194, 199 FUNCTION EVALUATIONS OSUM OF SQUARES = 7 .30679754D-01

fit data ydif f

LOSS OF RANK

,77724 - 77743 - 77628 - 77627 -63093 -63132 - 63108 ,63079 ,62718 -62783 -39645 -39674 -39664 -39659 - 39667 -39822 -39819 -38246 ,38234 - 38269 -38223 -38262 - 38257 - 38229 -42132 -42185 -42231 -42157 -42138 .42205 -42015

total spec .7306797538871061 variance, sd of parameters x (1) bandgap 2.47329737 .00002621 x (2) linewidthA2 .00255077 .00000039 x(3) B21A2 ,30126444 .00034835 .02297387 x(4 ) B31A2 ,03723157 .00005059 -01394896 va12 -.00000004 va13 .00001870 va14 -.00000004 va2 3 .00000099 va2 4 .00000145 va34 .00001482 vext -01461360 INITIAL CO-ORDINATES 1 2 -4700 2 -0020 3 -4000 4 .0610

OSUM OF SQUARES = 1.28512807D+00 I*** F ( X ) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

'THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 61, 66 FUNCTION EVALUATIONS OSUM OF SQUARES = 7.30678652D-01

fit data ydiff .66780 .77372 - - 10592 -29536 .28372 .01164 .66827 -53103 .I3724 .29676 .I9666 .lo010 .66817 ,61569 .05248 .29722 -33470 -. 03748 .77874 ,89714 - -11840 .37989 .39540 -. 01551 -77863 .71246 .06616 .37981 .35204 .02778 -77853 -89729 -. 11875 .37983 .34170 -03813

-77856 .77874 ,77759 ,77758 .63036 -63 075 - 6 3 051 - 6 3 022 -62658 -62724 -39558 -39587 -39577 .39572 -39580 -39734 -39730 .38221 ,38210 .38244 -38199 -38237 -38230 ,38202 -42150 -42203 -42249 -42175 -42156 .42223 -42033

total spec -7306786520673203 variance, sd of parameters

x(1) bandgap 2.47349401 .00002595 x (2) linewidthA2 .00253047 .00000039 x(3) ~ 2 1 ~ 2 .3015 3461 -00034845 -02297724 x ( 4 ) ~ 3 1 ~ 2 .03718729 . 00005059 -01394961 va12 -.00000004 va13 .00001847 va14 -.00000004 va23 .00000100 va24 .00000146 va34 .00001473 vext .01461357

I N I T I A L CO-ORDINATES 1 .8000 2 -0400 3 ,5000 4 ,9000

OSUM OF SQUARES = 1-23543601D+Ol I*** MAXIMUM NUMBER O F ITERATIONS EXCEEDED OFZSULTS AT ITERATION 500, 505 FUNCTION EVALUATIONS OSUM OF SQUAREIS = 7.30681106D-01

fit data ydif f -66821 -77372 -. 10551 .29544 ,28372 -01173

, 7 7 7 5 1 -77750 - 6 3 1 1 1 .63150 - 6 3 1 2 6 -63097 -62735 .62801 .39664 .39692 -39682 .39678 . 39685 -39840 .39837 ,38287 ,38276 -38310 .38265 -38303 -38297 .38269 .42188 - 4 2 2 4 1 .42288 .42214 .42195 -42262 . 4 2 0 7 1

total s p e c -7306811064429031 variance, sd of parameters

x ( l ) bandgap 2 -47339593 . 00002611 x ( 2 ) linewidthA2 - 0 0 2 5 4 6 8 1 . 00000039 x ( 3 ) ~ 2 1 ~ 2 .30201910 .00034838 -02297488 x ( 4 ) ~ 3 1 ~ 2 -03724554 .00005064 ,01395531 va12 - . 0 0 0 0 0 0 0 4 va13 .00001860 va14 - .00000005 va23 .00000098 va24 .00000146 va3 4 .00001474 vext -014613 62 INITIAL CO-ORDINATES

1 -6000 2 .0300 3 .0400 4 -1200

OSUM O F SQUARES = 6.00165016D+00 I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 500, OSUM OF SQUARES = 7.30691134D

fit data .66685 .77372 -. 10688 . 6 6 7 3 1 -53103 .I3628 .66722 .GI569 . 0 5 1 5 3 .77679 .89714 -. 12035 .77668 .71246 . 0 6 4 2 1 .77658 .89729 -. 12070 . 7 7 6 6 1 -86958 - . 0 9 2 9 7 ,37679 .96426 - . I 8 7 4 7 .77565 -85439 - - 0 7 8 7 5 .77563 .go065 - . I 2 5 0 2

50 5 FUNCTION EVALUATIONS -01 ydiff

- 2 9 5 3 6 .28372 -01165 .29677 . I 9 6 6 6 . I 0 0 1 1 .29722 .33470 -. 03748 .37930 .39540 - .O1610 .37923 -35204 -02719 .37925 .34170 .03754 . 3 7 8 9 1 .30960 .06931 .37928 ,36293 .01636 .37797 .44156 - -0635 9 .37763 .49877 - . I 2 1 1 5

-63069 .63108 ,63084 ,63056 - 62695 .62760 -39637 .39666 -39656 -39651 .39659 .39814 -39811 .38228 .38217 .38251 .38206 .38244 -38239 -38211 -42105 -42158 .42205 .42131 .42112 .42179 -41989

t o t a l spec -7306911340247328 variance, sd of parameters

x ( 1) bandgap 2.47326348 .00002628 .00512661 x (2 ) linewidthA2 .00255386 .00000039 ,00062650 x(3) ~ 2 1 ~ 2 .30088806 -00034833 .00052777 -01866361 -02297331 x(4) ~ 3 1 ~ 2 .03725593 .00005062 ,00019471 . 00711512 .01395389 va12 -.00000004 va13 .00001875 va14 - .00000004 va2 3 .00000099 va24 .00000146 va3 4 .00001485 vext -01461382 INITIAL CO-ORDINATES 1 -6700 2 .3000 3 .I500 4 ,4500

OSUM OF SQI3ARES = 5.75762487D+OO l*** F ( X ) NO LONGER DECREASES ... OPTIMIZATION TERMINATED

THIS MAY BE DUE TO THE VALUES OF DSTEP AND ACC, OR TO LOSS OF RANK IN THE JACOBIAN ORESULTS AT ITERATION 454, 459 FUNCTION EVALUATIONS OSUM OF SQUARES = 7.30679748~-01

fit data ydif f -66804 .77372 - .lo569 ,29574 .66850 .53103 -13747 -29715 .66841 .61569 ,05272 -29760 -77828 .a9714 -. 11886 .37955 .77816 .71246 -06569 .37948 .77807 .a9729 - -11922 .37950 -77809 .86958 - -09149 -37916 -77827 .96426 - .I8598 -37953 -77712 ,85439 - .07727 .37822 -77711 .go065 -. 12354 -37788

,63066 .63104 .63081 .63052 ,62690 ,62756 .39672 .39700 -39690 .3 9685 ,39693 -39848 ,39844 .38292 .38281 -38315 -38270 ,38308 ,38303 -38275 .42183 -42236 -42283 -42208 -42189 -42257 - 4 2 066

total spec -7306797478635649 variance, ad of parameters

x ( 1 ) bandgap 2 ,47341314 .00002622 x (2 ) l inewid thA2 -00255279 . 00000039 x ( 3 ) B21A2 -30187325 .00034834 .02297376 x ( 4 ) B31A2 -03732538 .00005080 - 01397773 va12 - .00000004 va13 .00001862 va14 - .00000005 va2 3 - 00000098 va2 4 .00000146 va3 4 .00001474 vext -01461359

INITIAL CO-ORDINATES 1 -6000 2 .go00 3 -2000 4 -1000

OSUM OF SQUARES = 2.36308965D+OO I*** MAXIMUM NUMBER O F ITERATIONS EXCEEDED ORESULtTS AT ITERATION 500 , 505 FUNCTION EVALUATIONS OSUM OF SQUPFRES = 7.30686948D-01

f i t d a t a ydif f .66806 .77372 - . l o 5 6 6 .29577 . 28372 .01206 -66853 -53103 . I3750 -29718 - 1 9 6 6 6 -10052 -66843 .61569 .05275 .29764 . 33470 - .03706 .77924 .a9714 -. 11790 -38044 -39540 - -01496 .77912 -71246 .06665 .38036 . 35204 -02832 .77902 .89729 - . I 1826 .38038 , 34170 -03868 .77905 .86958 - .09053 .38005 . 30960 .07045 .77923 .96426 - . I 8502 .38042 -36293 -01749 .77808 -85439 - - 07631 -37910 - 4 4 1 5 6 - -06246 -77807 .go065 - , 12259 .37876 , 49877 - - 12001 .62993 .64636 - ,01643 . I 6 6 2 1 . 0 7 0 8 2 .09539 .63032 .54274 .08758 -16801 . I 9 9 9 4 -. 03193

.63008

.62979 -62614 -62680 .39537 .3 9565 -39555 ,39551 .39558 - 3 9711 -39708 -38224 .38213 .3 8247 -38202 .38241 .38232 -38204 -42165 -42218 .42265 .42190 -42171 -42238 .42048

total spec .7306869482814491 variance, sd of parameters

x(1) bandgap 2 -47359203 . 00002588 x (2 1 l i newid thA2 .00252608 .00000038 x ( 3 ) B21A2 .30170117 -00034847 -02297789 x ( 4 ) ~ 3 1 ~ 2 -03727085 .00005074 -01396930 va12 -.00000003 va13 .00001838 va14 -.00000004 va23 .00000100 va24 .00000147 va3 4 .00001471 vext -01461374 INITIAL CO -ORDINATES

I -1000 2 . I000 3 .go00 4 -0900

OSUM OF SQUARES = 9.41255872Di-00 I f * * SUM OF SQUARES CONVERGED TO DESIRED AC-a ORJISULTS AT ITERATION 51, 56 FUNCTION EVALUATIONS OSUM O F SQUARES = 2.06844356D+00

fit data ydiff -53732 .77372 - -23640 .2 8404 .53729 .53103 -00626 -28405 .53728 -61569 -. 07841 . 2 8407 -53069 -89714 - -36645 .27690 .53069 .71246 -. 18178 -27689 -53069 .a9729 -.36660 .27689 -53069 .86558 -. 33889 .27689 .53069 ,96426 - -43357 .27689 .53066 -85439 - -32373 .27688 -53066 .go065 - .36999 ,27688 .52635 .64636 -. 12001 .27237 -52635 .54274 - -01639 .27243 .52635 .GO884 -. 08249 .27235 -52634 .46515 .06119 .27237

.52631 , 6 5 5 0 0 -. 12869 .27234 -52632 , 6 2 5 7 7 - -09945 -27234 -52316 - 4 8 3 6 7 -03949 . O O O O O -52316 - 5 1 2 4 8 .01068 . O O O O O .52316 , 5 1 3 6 6 -00950 . O O O O O -52316 , 4 6 4 7 4 .05842 . O O O O O -52316 , 5 2 9 5 7 - - 00641 . O O O O O -52322 , 5 6 1 3 7 - -03815 . O O O O O .52322 , 5 2 0 5 9 - 00262 ,26934 -5213 8 , 3 9 7 9 0 ,12348 . O O O O O -52138 - 4 4 1 2 2 - 08015 . O O O O O -52138 - 2 9 6 5 5 -22484 . O O O O O -52137 - 3 5 5 6 8 . I 6 5 6 8 . O O O O O -52138 - 3 8 7 5 3 -13385 . O O O O O -52148 - 3 6 1 1 5 . I6034 . O O O O O -52147 - 3 9 5 1 8 - 12629 . O O O O O - 5 1 7 5 1 , 3 2 3 1 6 . I 9 4 3 6 . O O O O O -51756 - 1 8 7 0 0 -33056 . O O O O O - 5 1 7 6 1 - 2 2 1 8 4 -29576 ,00000 -51754 - 1 8 5 5 5 -33199 . O O O O O -51752 - 1 1 3 8 1 - 4 0 3 7 1 ,00000 .51772 , 2 7 4 7 0 -24302 . O O O O O .51754 - 2 0 4 4 2 - 3 1 3 12 . O O O O O

t o t a l spec .206844D+01 15.32162 2 .0684435609072 v a r i a n c e , sd of parameters

x ( 1 ) bandgap 2 .48529751 13 .29937564 3 .64683090 x ( 2 ) l i n e w i d t h A 2 .27551271 1 . 6 2 2 2 6 8 9 4 1 . 2 7 3 6 8 3 2 2 x ( 3 ) ~ 2 1 ~ 2 -27710568 - 0 5 9 5 1 4 1 2 .09017290 -24395515 -30028804 x(4) ~ 3 1 ~ 2 -07497750 -0214743 6 .08259370 -14654133 -28739120 v a 1 2 -. 26467852 v a 1 3 -87925691 v a 1 4 ************ v a 2 3 235.61839778 v a 2 4 - .01315118 va34 -03526802 vext -04136887

INITIAL CO -ORDINATES 1 . 4 0 0 0 2 - 5 0 0 0 3 - 6 0 0 0 4 . 6 0 0 0

OSUM O F SQUARES = 9.44207804D+00 I*** MAXIMUM NUMBER OF ITERATIONS EXCEEDED ORESULTS AT ITERATION 5 0 0 , 505 FUNCTION EVALUATIONS OSUM OF SQUARES = 7.31886878D-01 -

fit data y d i f f .66320 - 7 7 3 7 2 - -11053 - 2 9 1 7 1 .28372 .00800

-40275 -48367 -. 08092 .OOOOO .OOOOO a 00000 -40300 - 51248 -. 10948 .OOOOO .OOOOO -00000 -40292 -51366 -. 11074 - 00000 -00000 - 00000 -40284 -46474 - -06190 .OOOOO .OOOOO -00000 -40296 -52957 -. 12661 .OOOOO .OOOOO .OOOOO -40466 - 56137 - ,15670 .OOOOO . 00000 -00000 .40463 - 52059 -. 11596 -10163 -20623 - -10460 .38320 -39790 -.01470 .OOOOO .OOOOO .OOOOO .38308 -44122 -. 05814 .OOOOO .OOOOO .OOOOO .38341 -29655 .08687 .OOOOO .OOOOO .OOOOO -38297 -35568 .02728 .OOOOO .OOOOO -00000 ,38335 - 38753 - ,00419 .OOOOO .OOOOO .OOOOO -38348 -36115 -02233 .OOOOO .OOOOO .OOOOO .38320 - 3 9518 - .01198 .OOOOO -00000 -00000 .41919 -32316 .09603 . 00000 .OOOOO -00000 -41972 -18700 -23271 -00000 .OOOOO -00000 -42018 -22184 -19034 .OOOOO .OOOOO .OOOOO -41944 - 18555 -23390 .OOOOO .OOOOO -00000 -41925 -11381 -30545 .OOOOO ,00000 .OOOOO -41993 ,27470 -14523 .OOOOO .OOOOO .OOOOO ,41803 -20442 .21361 .OOOOO .OOOOO .OOOOO

total spec .731887D+00 5 -42132 -7318860775264589 variance, sd of parameters x ( 1 ) bandgap 2-47120072 .00002746 -00524050 x (2) linewidthA2 -00265988 .00000042 .00064990 x ( 3 ) ~ 2 1 ~ 2 -29909894 .00034818 -00052755 -01865958 -02296835 x(4) ~ 3 1 ~ 2 -03678971 .00004898 .00018837 -00699832 -01372484 va12 - .00000013 va13 -00002050 va14 -.00000004 va2 3 - 00000101 va24 -00000131 va3 4 -00001586 vext -01463374 INITIAL CO-ORDINATES

1 -5000 2 .2000 3 1.0000 4 3 .oooo

OSUM OF SQUARES = 5.05167860D+01 I*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY OFSS'ZTLTS AT ITERATION 222, 227 FUNCTION EVALUATIONS OSUM OF SQUARES = 2.03521411Di-00

fit data ydif f -54382 -77372 - -22990 -28175 .28372 -. 00197 -54378 .53103 -01275 ,28178 .I9666 ,08512 .54377 .61569 - .07192 .28182 -33470 -. 05288 .53559 - 89714 - .36155 .27284 -39540 -. 12256 .53558 -71246 -. 17688 -27283 -35204 -. 07920 -53558 -89729 - -36171 -27283 -34170 -. 06887 -53558 -86958 - -33400 -27283 .30960 -. 03677 -53559 -96426 - -42867 -27283 ,36293 -. 09009 -53553 .85439 -.31886 .27279 .44156 -. 16876 -53553 -90065 -.36512 .27279 .49877 -. 22599 -52953 -64636 -. 11683 .26658 .07082 -19576 -52954 .54274 -. 01320 .26663 -19994 -06669 -52954 .GO884 -. 07930 .26657 -39026 - -12369 .52953 ,46515 .06438 ,26658 -03778 -22880 .52948 -65500 -. 12552 -26654 -13789 -12865 .52949 -62577 - -09628 -26654 .I2434 .I4221 .52491 -48367 -04124 .OOOOO .OOOOO .OOOOO -52491 -51248 .01243 .OOOOO .OOOOO .OOOOO

-52491 .51366 -01125 .OOOOO .OOOOO .OOOOO -52491 .46474 -06016 .OOOOO .OOOOO .OOOOO .52492 .52957 -. 00466 -00000 .OOOOO .OOOOO .52499 .56137 -.03638 .OOOOO .OOOOO .OOOOO -52498 .52059 .00439 .26222 -20623 -05600 .52229 -39790 .I243 9 -00000 .OOOOO .OOOOO -52228 ,44122 -08106 .OOOOO .OOOOO .OOOOO -52228 -29655 -22574 .OOOOO .OOOOO -00000 -52227 -35568 .I6658 .OOOOO -00000 .OOOOO -52228 .38753 -13475 .OOOOO .OOOOO .OOOOO -52243 -36115 -16128 -00000 .OOOOO .OOOOO -52242 .3 9518 ,12723 .OOOOO .OOOOO .OOOOO -51661 .32316 -19346 .OOOOO .OOOOO .OOOOO -51668 .I8700 -32967 -00000 ,00000 .OOOOO .51673 -22184 ,29488 .OOOOO .OOOOO .OOOOO -51665 -18555 -33110 .OOOOO .OOOOO .OOOOO -51662 -11381 -40281 .OOOOO .OOOOO .OOOOO -51688 .27470 -24218 .OOOOO .OOOOO .OOOOO .51667 -20442 -31224 -00000 -00000 ,00000

total spec .203521D+01 15.07547 2 -0352l410553703 variance, sd of parameters

x ( 1) bandgap 2 -45991738 3 -48006736 1.86549387 x (2) linewidthA2 .I9152620 -44035411 .66359182 x(3) 321A2 -27773135 .03056397 .04630904 -17482553 -21519536 x(4) ~ 3 1 ~ 2 .07074862 -01034328 .03978183 -10170190 -19945384 va12 -28886095 va13 -32058751 va14 -31.10190759 va2 3 29.55305041 va24 -01727507 va34 -01730064 vext -04070428 INITIAL CO -ORDINATES

1 1.0400 2 -0040 3 -3000 4 -4000

OSUM OF SQUARES = 4.80868635D+00 l*** SUM OF SQUARES CONVERGED TO DESIRED ACCURACY ORESULTS AT ITERATION 71, 76 FUNCTION EVALUATIONS OSUM OF SQUARES = 1.93901826D+OO

fit data ydiff -54362 .77372 -. 23010 .28905 .28372 -00534 -54358 -53103 -01255 -28915 -19666 -09249 -54356 -61569 -. 07213 -28922 -33470 -. 04549 -53115 .a9714 -. 36599 .27435 .39540 -.I2105 .53 114 -71246 - -18132 -27434 -35204 - -07769 .53113 .a9729 - .36615 -27434 -34170 -. 06736 -53 114 -86958 -. 33844 -27433 -30960 -. 03527 .53115 .96426 -. 43311 .27434 -36293 -. 08858 ,53105 ,85439 - -32334 ,27427 .44156 - -16729 -53105 -90065 - -36960 -27425 -49877 - .22452 .51975 .6463 6 - .I2661 -26225 -07082 -19143 .51976 .54274 - -02297 -26234 -19994 -06240 .51976 -60884 -. 08909 -26221 -39026 -. 12805 .51975 .46515 .05460 -26225 -03778 -22446 .51964 .65500 -. 13536 .26216 .I3789 -12427 ,51966 -62577 -. 10611 -26217 .I2434 ,13783 .51074 -48367 .02708 .OOOOO .OOOOO .OOOOO .5107S .51248 -. 00173 .OOOOO -00000 .OOOOO .S1075 -51366 -. 00291 .OOOOO .OOOOO .OOOOO .51074 -46474 .04600 .OOOOO .OOOOO .OOOOO

,51076 -52957 - - 01881 . O O O O O . O O O O O . O O O O O -51089 -56137 - , 05047 . 00000 . O O O O O . O O O O O .51089 -52059 -. 00970 -25386 -20623 -04763 . S O 5 7 7 - 3 9790 ,10786 . O O O O O ,00000 . O O O O O ,50575 .44122 ,06453 . O O O O O -00000 . O O O O O -50576 -29655 , 2 0 9 2 1 . O O O O O . O O O O O , 00000 -50573 , 35568 ,15004 . O O O O O . O O O O O . O O O O O ,50576 -38753 ,11822 . O O O O O . O O O O O . O O O O O . S O 6 0 3 -36115 ,14488 . O O O O O . O O O O O . O O O O O - 50601 -39518 ,11083 . O O O O O . O O O O O . O O O O O -49586 -32316 , 17271 . O O O O O . O O O O O . O O O O O .49598 - 1 8 7 0 0 -30897 - 0 0 0 0 0 . O O O O O . O O O O O .49607 ,22184 ,27422 . O O O O O . O O O O O . O O O O O -49592 -18555 - 3 1 0 3 8 - 0 0 0 0 0 . O O O O O . O O O O O -49587 .I1381 -38207 . O O O O O . O O O O O . O O O O O -49632 -27470 -22162 . O O O O O . O O O O O - 0 0 0 0 0 ,49594 -20442 -29151 . O O O O O . O O O O O . O O O O O

t o t a l spec -193 9 0 2 D + O l 14.36292 1 . 9 3 9 O l 8 2 6 2 6 2 1 0 4 variance, sd of parameters x ( 1 ) bandgap 2.46113358 -30432989 -55166103 x ( 2 ) l i n e w i d t h A 2 .09568704 -03696625 . I9226608 x(3) B 2 1 A 2 -26528082 .00806810 -01222439 -06982258 -11056396 x(4) ~ 3 1 ~ 2 -06829083 .00330399 . O x 2 7 0 7 6 4 -05748031 -11272816 va12 .02025018 va13 -04629437 va14 - -89201272 va23 -74919375 va24 . 0 0 2 5 4 0 0 9 va34 .00466973 vext -03878037

*** NOFWAL TERMINATION

6

Appendix 11

L02/L01

+ Fitl (xi)

A L03lL01

Fit2

P o l y . (L02n01) - - Poly. (Fit1 (xi))

P o l y . (L03kOl) - - Poly. (Fit2)

Figu= 17. Band Area Ratio vs Wave!ength: Wire dp=8 nm, ss-polarization

Figure 13. Band Area Ratio vs Wavelength: Wire dp =S.Snm, ss-polarization

Figure 19. Band Area Ratio vs. Wavelength: Wire dp = 10 nm, pp-polarization

LO2JLO1 I i Fit1 (xi)

I A L03L01 A Fit2 - Poty. (L02lL01) - - Poty. (Fit1 (xi))

i - Poly. (L03L01)

!- - Poly. (Fit2)

480 490 500

Wavelength (nm)

Figure 24 Band Area Ratio vs. Wavelength: Wire dp=8 nm, pp-polarization

L02lL01

: Fitl (xi)

I A L03lL01

Fit2 I - Poly. (LOULO 1 ) ! - - Poly. (Fitl (xi)) t

I P o l y . (LOWLO1 ) ' I - -- Poly- (Fit2)

480 490 Wavelength (nm)