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Materials Science in Semiconductor Processing 8 (2005) 261–266

Simultaneous optical measurement of Ge content and Borondoping in strained epitaxial films using a novel

data-analysis technique

Stephen Morrisa,�, Paul Fougeresb, Stephanie Bozzo-Escoubasc, Sylvie Bodnard,Stephane Gaillardd

aTherma-Wave Inc., 1250 Reliance Way, Fremont, CA 94539, USAbTherma-Wave Inc., Hameau du Parc Bat D16, Chem. Departmental 56C, F-13790 Rousset, France

cLaboratoire TECSEN, FST de St Jerome, F-13397 Marseille, FrancedAtmel Fab 7, Z.I. de Rousset, F-13106 Rousset, France

Available online 18 October 2004

Abstract

We present a novel technique, based on a proprietary approach to analyzing the raw optical data, which is able to

decouple the effects of Ge and B on the optical properties of a B-doped SiGe film. An example is given of the

application of this technique to measure the two material fractions, plus the thickness, simultaneously and

independently on a standard Opti-Probes film-thickness tool.

Three sets of doped epitaxial SiGe layers were grown, each with a nominally fixed Ge-content but with the Boron

levels varying from zero to �1� 1020 cm�3. Two sets consisted of single-layer films on c-Si substrates, the other

consisted of similar films capped with undoped epi-Si layers.

The Ge-fractions found were in good agreement with XRD and SIMS whilst the calculated ‘‘doping parameter’’ was

found to follow a monotonic relationship with changes in Boron concentration in each case.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Epitaxy; Composition; Doping; Measurement

1. Introduction

When growing epitaxial SiGe films it is helpful to have

a method for measuring the thickness and Germanium

fraction to facilitate process control. This can be done

optically, using a method such as spectrophotometry or

spectroscopic ellipsometry, and is a routine application

[1] where the films are either undoped or have a known

level of Boron doping. However, where the doping level

e front matter r 2004 Elsevier Ltd. All rights reserve

ssp.2004.09.040

ing author. Tel.: +44 1743 365 445; fax:

7

ess: smorris@thermawave.com (S. Morris).

may be subject to change independently from the

Germanium fraction, the measurement becomes more

complex because of the effect that the Boron has on the

optical properties of the material. Changes in Boron

level, if unaccounted for, can introduce significant errors

in the measurement of Germanium fraction, or thick-

ness, or both.

Hitherto there has not been an accepted optical

method for characterizing both Germanium fraction

and Boron level simultaneously, and measurements have

of necessity been made with the assumption that one of

these is fixed and only the other must be determined. We

present here a novel technique, based on a proprietary

d.

ARTICLE IN PRESSS. Morris et al. / Materials Science in Semiconductor Processing 8 (2005) 261–266262

approach to analyzing the raw optical data, which is

able to decouple the effects of each element on the film’s

optical properties and so measure the two fractions, plus

the thickness, simultaneously and independently on a

standard Opti-Probes film-thickness tool.

Fig. 1. Plots of the �2ðEÞ curves for a set of undoped SiGe films

with varying Ge-fraction.

2. Effects of doping upon optical properties of Si and

SiGe

In order to understand how the presence of doping

affects the optical measurement of epitaxial SiGe (or

indeed Si) films, it is helpful to examine the complex

dielectric function, �ðEÞ, and in particular its imaginary

part �2ðEÞ: Together with the real part �1ðEÞ; this is

related to the more familiar nðlÞ and kðlÞ curves throughthe relations

�1 þ i�2 ¼ ðn þ ikÞ2 (1)

and

E ¼ hc=l: (2)

Fig. 1 shows a set of �2ðEÞ dielectric functions for

undoped SiGe alloys with the Germanium fraction

varying from 0% to 25%. It can be seen that the two

strong features in the visible photon range, E1 and E2,

change in height and energy as the Germanium fraction

changes. Hence, if an optical method can determine the

�2ðEÞ curve of such a material, in the absence of doping

the Germanium fraction can be deduced simply by

correlating the peak heights and positions, or else by

interpolating the curve between those obtained from

reference films with known Germanium fraction.

However, if the materials are doped (either p-type or

n-type), this also has an effect on the shape of the �2ðEÞ

curve, which consists mainly of suppressing the E1 and

E2 features [2,3]. Fig. 2 illustrates this in the case of a

Silicon sample, and Fig. 3 shows the �2ðEÞ curves for a

set of doped SiGe films with nominally the same Ge-

fraction. The modifications to the �2ðEÞ curve caused by

doping lead to errors in the calculated Ge-fraction if the

doping is not explicitly accounted for. Even so, the fact

that the effect of doping is much more localized in the

vicinity of the peaks than the effect of changes in Ge-

fraction means that the effect of doping upon the curve

is qualitatively different from the effect of changes in

Ge-fraction. This leads directly to the supposition that

the measurement of the two parameters can be

decoupled by use of an appropriate method.

Fig. 2. Measured e2 curves for a nominally undoped Silicon

substrate and an epitaxially-grown Si film doped with Boron to

�2.5� 1019 cm�3, respectively.

3. Principle of method

We have successfully decoupled the effect of doping

upon the �2ðEÞ optical properties from the effect of

changing Germanium content by introducing a ‘‘pertur-

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Fig. 3. Plots of the �2ðEÞ curves for a set of SiGe films where the

Ge-fraction is nominally the same (21%), but Boron levels vary

from zero to �1� 1020 cm�3. In practice there is also some

variation in Ge-fraction from sample to sample, which accounts

for the fact that the curves do not all appear in strict sequence.

S. Morris et al. / Materials Science in Semiconductor Processing 8 (2005) 261–266 263

bation function’’, D�2ðEÞ; to represent the effect of the

doping. This recognizes the separable form of the

Kramers–Kronig transform used to obtain �1ðEÞ from

�2ðEÞ; viz.

�1ðE0Þ ¼ 1þ

Z 1

0

E�2ðEÞ

E2 � E20

dE (3)

and hence

�1ðE0Þ þ D�1ðE0Þ ¼ 1þ

Z 1

0

Eð�2ðEÞ þ D�2ðEÞÞ

E2 � E20

dE

) D�1ðE0Þ ¼

Z 1

0

ED�2ðEÞ

E2 � E20

dE: ð4Þ

Unlike �2ðEÞ itself, which is only known within the range

of photon energies for which optical data is available,

D�2ðEÞ may be defined in such a way that it is known at

all values of E from 0 to N and can therefore be

transformed precisely. We parameterize D�2ðEÞ in such a

way that the parameters can be regressed upon and

correlated with the doping level of the material. After

transforming it, we combine the function D�1ðEÞ so

calculated with the �1ðEÞ function for the undoped

material, and so obtain the full dielectric function and

hence n and k for the doped material. Note that this

approach is proprietary and a patent application has

been filed.

A simple example of the application of this technique

to a doped Silicon film is given in Fig. 4. Here, we simply

show the measured reflectivity (at near-normal inci-

dence) of the film, normalized to that of an undoped

reference having a thin native Oxide layer. In Fig. 4(a)

the raw data is compared to the calculated reflectivity of

an undoped sample, and it can be seen that the

agreement is very poor. The strongest discrepancies are

the sharp feature at �365 nm, which corresponds to the

energy (�3.4 eV) of the E1 peak in the �2ðEÞ curve, and

the general shift in the overall reflectance level which is

positive below this wavelength and negative above it. In

Fig. 4(b) we show the calculated reflectivity obtained

when a simple D�2ðEÞ function (using two floating

parameters) is employed to suppress the E1 peak,

making no other changes. It can be seen that not only

is the strong feature at �365 nm now fitted very well, but

also the shift in reflectance in the visible part of the

spectrum is accounted for. This is because even though

the effect of doping upon �2ðEÞ is local in energy, the

Kramers–Kronig transform propagates the effect to all

energies and hence all wavelengths. Finally, we show in

Fig. 4(c) the effect of a more general D�2ðEÞ function

using eight floating parameters and affecting the vicinity

of the E2 peak as well as just E1. It can be seen that only

marginal further improvement is obtained. This is

thought to be for two reasons. Firstly, the changes in

the height of the E2 peak, though similar in magnitude

to the E1 peak, are smaller as a percentage of the peak

height because the peak itself is bigger. Secondly, as the

effect of the local peak structure upon the rest of the

curve scales as ðE2 � E20Þ

�1 (from Eq. (3)), the E2 peak

clearly has less of an effect than E1 at lower photon

energies in the visible part of the spectrum.

4. Experimental details

4.1. Analysis of samples

In the present work, three sets of doped epitaxial SiGe

layers were grown, each with a nominally fixed Ge-

content but with the Boron levels varying from zero to

�1� 1020 cm�3. Two sets consisted of single-layer

films (�300 A thick) on c-Si substrates, the other

consisted of similar films capped with undoped �600 A

epi-Si layers.

The layers were deposited in an Applied Materials Epi

Centuras 200mm RTP chamber, using SiH4 and GeH4

as gas precursors and B2H6 for doping. Thicknesses were

measured by a conventional Philips DCD Pros XRD

tool, using Vegard’s law for calculating Ge content. This

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0.98

0.99

1.00

1.01

1.02

1.03

1.04

200 400 600 800

Wavelength (nm)

No

rmal

ized

ref

lect

ance

0.98

0.99

1.00

1.01

1.02

1.03

1.04

200 400 600 800

Wavelength (nm)

No

rmal

ized

ref

lect

ance

(a) (b)

0.98

0.99

1.00

1.01

1.02

1.03

1.04

200 400 600 800

Wavelength (nm)

No

rmal

ized

ref

lect

ance

(c)

Fig. 4. (a) Raw data (represented by individual points) for the reflectance of a doped Si film, with the calculated reflectance of an

undoped film superimposed (continuous line). The reflectance is normalized to that of an undoped Si reference sample, so that a

normalized reflectance of 1.0 corresponds to the reference film reflectance. Note the prominent feature at �365 nm corresponding to

the E1 peak energy of �3.4 eV. (b) The same raw data, with a calculated curve that incorporates a first-order modification to the �2ðEÞ

curve consisting of a simple suppression of the E1 peak. (c) The same raw data, with a calculated curve that incorporates higher-order

modifications to the �2ðEÞ curve affecting both the E1 and E2 peaks.

S. Morris et al. / Materials Science in Semiconductor Processing 8 (2005) 261–266264

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15

20

25

0.00 0.80 1.00 1.50 2.00

Doping level (from SIMS) X 1E20cm-3

% G

e

Do

pin

g p

aram

eter

(ar

b. u

nit

s)

%Ge (OP) %Ge (SIMS) Doping parameter

Fig. 5. Results for Germanium fraction and ‘‘doping parameter’’ for a set of single-layer SiGe films with varying doping levels (as

separately measured using SIMS). The SIMS results for Germanium fraction are also shown for comparison.

0

5

10

15

20

25

0 50% 75% 80% 100%

Doping level (% of Max)

% G

e

Do

pin

g p

aram

eter

(ar

b. u

nit

s)

%Ge Doping parameter

Fig. 6. Results for Germanium fraction and ‘‘doping parameter’’ for a set of SiGe films with varying doping levels buried under

�600 A Si caps. As no SIMS data was taken for these samples, the x-axis shows just the expected doping levels, where the maximum

doping level is �1� 1020 cm�3.

S. Morris et al. / Materials Science in Semiconductor Processing 8 (2005) 261–266 265

technique is, however, known not to be reliable for

measuring Germanium fractions of doped films [4].

Optical data from two of the sample sets (the capped

set and one of the uncapped sets) was collected on a

standard Therma-Wave Opti-Probes 5240 production

metrology tool in Atmel Fab 7, using the tool’s beam-

profile reflectometry (BPRs), broad-band spectropho-

tometry (BB) and spectroscopic ellipsometry (SE)

technologies. The third set was measured on an Opti-

Probe 7341 tool at Therma-Wave. In each case, only the

Broad-Band data was used for the modelling, for the

reasons cited in Ref. [1]. After the results had been

obtained, the set of uncapped samples measured at

Therma-Wave was sent to an independent laboratory

for SIMS analysis.

4.2. Modelling of results

The optical data from the samples was analyzed by

combining an alloy model for the undoped SiGe

material with a parameterized representation of the

D�2ðEÞ function. The best-fit solution was found by

simultaneously optimizing the Germanium alloy frac-

tion and the parameters representing D�2ðEÞ: Followingthe principle illustrated in Fig. 4, only the suppression of

the E1 peak was modelled.

4.3. Comparison with other techniques

Figs. 5 and 6 show the results for Germanium fraction

and doping parameter for each sample set. Fig. 5

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Table 1

Comparison between XRD and Opti-Probe measurements of

thickness for the single-layer SiGe films measured at Atmel

XRD (A) Opti-Probe,

no account

of doping

(A)

Opti-Probe,

with

doping

model (A)

Undoped 310 308 308

25% max 318 305 308

50% max 325 305 307

75% max 325 301 318

Max dopinga 332 300 329

aMax doping is �1� 1020 cm�3.

S. Morris et al. / Materials Science in Semiconductor Processing 8 (2005) 261–266266

incorporates the SIMS data for comparison. In each

case the Germanium fraction found by the Opti-Probe

was in good agreement with expectation, and the E1

peak suppression was found to follow a monotonic

relationship with changes in Boron concentration. In

Fig. 5 the agreement between the Opti-Probe and SIMS

is excellent for the doped samples, but there is a puzzling

discrepancy for the undoped sample where the Opti-

Probe measurement had been calibrated to match with

XRD. Although the latter technique is not considered

reliable for %Ge of doped films, a comparison was

made between the layer thickness measurements on the

Opti-Probe and by XRD for the single-layer films

measured at Atmel, and the new model was found

greatly to improve the matching as shown in Table 1.

5. Conclusions

It has been shown that, by the application of a novel

data analysis technique which exploits a fundamental

principle of optical physics, we can decouple the effects

on the optical properties on SiGe of varying Ge-content

and B-doping level and hence determine both quantities,

together with the film thickness, simultaneously. The

method has been demonstrated both for single-layer

films and for more typical structures incorporating an

epitaxial Si cap.

Acknowledgements

We would like to express particular thanks to Heath

Pois and Jon Opsal of Therma-Wave Inc. for many

stimulating discussions, and to Laurent D’Emmanuele

of Atmel for assistance in characterizing the samples

used in this work.

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