1030 Applied Surface Science 33/34 (1988) 1030-1036 North-Holland. Amsterdam

C H A R G E - D I S C H A R G E D Y N A M I C S OF D I S O R D E R I N D U C E D GAP S T A T E C O N T I N U U M AT C O M P O U N D S E M I C O N D U C T O R - I N S U L A T O R I N T E R F A C E S

Li HE, Hideki H A S E G A W A , Ji-kui LUO and Hideo O H N O

Department of Electrical Engineering, Facul(v of Engineering, Hokkaido Universi(v, Sapporo 060, Japan

Received 23 August 1987; accepted for publication 13 October 1987

Based on the recently proposed disorder-induced gap state (DIGS) model for interface states. the charge-discharge dynamics of interface state continuum at insulator-semiconductor (I S) interfaces are theoretically analyzed and compared with the experiments on InP and lnGaAs MIS structures. The concept of occupation boundary used in the analysis clarifies the physics involved and simplifies the simulation of complex processes. By assuming a particular type of DIGS distribution in energy and in space, the observed complex hysteresis behavior and frequency dispersion of MIS capacitance in MIS C-V curves as well as the currenl drift behavior of MISFET's are completely reproduced on computer, offering a unified understanding of a wide variety of phenomena associated with I S interfaces.

1. Introduction

The insulator semiconductor ( I -S ) interface is a basic cons t i tuent s t ructure of any integrated device for surface passivat ion as well as for gate technology in InP and I n G a A s MIS ( m e t a l - i n s u l a t o r - s e m i c o n d u c t o r ) FET's . As the technology goes further down to atomic scale sizes in the future, the control of the I - S interface properties becomes more and more crucial due to increased device surface to volume ratio.

In view of such increasing impor tance of I - S interface control, the present paper analyzes the charge-discharge dynamics of interface state c o n t i n u u m at

InP and I n G a A s I - S interfaces both theoretically and experimental ly. The recently proposed disorder- induced gap state (DIGS) model [1,2] is used as the basic model, and the occupat ion bounda ry is calculated on computer .

The observed complex hysteresis behavior and frequency dispersion of capacitance in MIS C - V curves as well as the drain current drift behavior of M I S F E T ' s are completely reproduced for the first t ime on compute r by assuming a part icular type of D I G S dis t r ibut ion in energy and in space. The present work offers a unified under s t and ing and descr ipt ion of a wide variety of phenomena associated with I S interface used for surface passivat ion and MIS gate structures.

0169-4332/88 /$03 .50 © Elsevier Science Publishers B.V. (Nor th -Hol land Physics Publishing Division)

Li He et aL / Charge- discharge dynamics of DIGS continuum at I - S interfaces 1031

2. Theory of charge-discharge dynamics of DIGS continuum

Fig. l a illustrates the basic concept of the DIGS model used for the theoretical analysis. In short, processing-induced distortion of length and angle of the local bonds in the interface region results in incomplete separation of bonding and anti-bonding states, and forms donor-like bonding states and acceptor-like anti-bonding states in the energy gap that are distributed both in energy and in space, forming a DIGS continuum. The energy boundary, Eiao, where charge neutrality is achieved, is given by the hydrid orbital energy of the sp 3 bond [1]. Evidence for microstructural disorder has been presented elsewhere [2].

The charge-discharge dynamics of the DIGS continuum can be analyzed by the Shockley-Read-Hal l (SRH) statistics. States in the insulator com- municate with the carriers in the semiconductor bands via tunneling-assisted capture and emission processes. For tunneling decay of wavefunctions into an insulator, the effective cross-section of the states located at a distance x from the interface is reduced as o0 exp( -X/Xo) where o 0 is the cross-section of the states at the interface and x 0 is the tunneling decay length [3]. On the other hand, since the spatial extension of the states in a semiconductor region is much smaller than the de Broglie wavelength of the carriers, being one to several monolayers as determined by our cross-sectional TEM study [2], charge-discharge transients of states in this region can be regarded to take place at the interface.

i / i / i / i / / / / /

* / H-~C • o , i

i{:.'a Ev L ass,,me EFCt) q

. ..;.~ii a ~ " v Foccupa t ,o n~bo u n da ry~ (a)

E I interface charge j

E ~ w,I

A D'D r x< F ......... Ev [ C-V curves ] Nss distribution

o (b) (c)

I Imodified EF(t) 1

Fig. 1. (a) DIGS model, (b) occupation boundary and (c) procedure for simulation of MIS C- / / c u r v e s .

1032 Li He et al. / Charge - discharge dynamics of DIGS continuum at I - S interfaces

The analysis focuses attention on the occupation boundary separating occupied and unoccupied states on the E-x planes as schematically shown in fig. lb for an n-type semiconductor. When the bias moves the interface Fermi level, Ev(t), upwards (capture direction of bias sweep), the occupation boundary moves as shown by CD and C ' D ' in fig. lb, as more electrons are captured. The vertical portion of the boundary reflects the energy-independent nature of the capture process. On the other hand, when Ev(t ) is moved downward (emission direction), the occupation boundary moves as shown by C ' E ' and CE in fig. lb. The energy-dependent slanted portion of the boundary reflects the energy-dependent nature of the emission process modified by tunneling.

It can be shown from the rate equation based on SRH statistics, that the occupation boundaries for capture and emission of majority carriers are given approximately by the following equations:

=

x=x~(E, t)=Xo~ ln{%.VthnN~exp[-(E~-E)/kT](t-to) ), (2) where t o is the time when the state at E initiates capture or emission.

The mechanism for the C - V hysteresis can be explained as follows. In the same energy interval between Evl and EF2 in fig. lb, the states in the area C D D ' C ' capture electrons in the capture direction, whereas the states in the area C E E ' C ' emit electrons in the emission direction. Then the charge in the black region remains unemitted and shifts the C - V curve.

Actual calculation of MIS C V curves requires a computer simulation, since the variation of the boundary with time should be determined so as to become consistent with the given bias voltage waveform. Additional complica- tions come from minority carrier processes and from the presence of an electric field in the insulator. The procedure for simulation is shown in fig. lc.

Once the occupation boundary is calculated, the small signal admittance Y(j~0) of the DIGS continuum can be calculated through

+ o o + ~

=J'°q2f fo {[N,(E, x)/(1 x))] dr(e, x)/dEv) dx dE. (3)

The drain current drift behavior can be described by the capture process of the channel electrons under the condition of a fixed gate bias.

3. Comparison between theory and experiment

Charge-discharge dynamics of interface states were experimentally ob- served on C V curves of MIS capacitors as well as on the current drift

Li He et a L / Charge- discharge dynamics of DIGS continuum at I - S interfaces 1033

behavior of MISFET's. MIS capacitors and MISFET's were fabricated on (100) oriented InP and InGaAs, using an A1203/anodic native oxide double- layer insulator. The anodization process has already been described elsewhere [4]. The thickness of A1203 was typically 1500 ]k and that of the native oxide layer was 100 .~.

Using the procedure in fig. lc, MIS C - V curves were calculated for various possible energy and spatial distributions of the DIGS continuum and for various possible values of their dynamic parameters. The simulated C - V curves were sensitive to the shape of energy and spatial distributions of the state continuum, so that only a particular functional form of distribution could be selected. After many trials, it was found that the experimentally observed C - V curves with their voltage swing speed and magnitude depen- dences and their hysteresis can be reproduced by the following energy and spatial distribution:

Nb( E, x) = N O exp[( [ E - E H O [ / E 0 b ) nb ] e x p ( - x / x b ), (4a)

N ~ ( E , x ) = U o exp[( I E - E , o I/E0a)""] e x p ( - x / x ~ ) , (4b)

where N b is the density of donor-like bonding states and Nl" is that of the acceptor-like anti-bonding states. EHO is the charge neutrality boundary of these states. The distribution is U-shaped in energy, becoming minimum at

%(lnGaAs) (V) 8 6 4 2 0 2

' ~ ~ ' C n / '

t - - InP experirnenta[ 1.0 . . . . lnGaAs experimental

• lnP colculated 0.9 o [nGa~ calculated

72rnV/sec ~

I i I I I I I

-3 -2 -1 0

Vc,(lnP) (V)

4 6 8 i i i

0.5

-0.4

I I I I I

1 2 3

Fig. 2. M e a s u r e d a n d s imu la t ed C - V curves for I n P a n d I n G a A s u n d e r va r i ous sweep speeds . A

s ingle set of p a r a m e t e r s were used for s imu la t ion . InP: Xon = 3.40 .~, Xop = 0.176Xon, Oo. = aOp = 5.0 X 1 0 - 1 4 c m 2 , E H O = Ec _ 0 .364 eV, Eob = 0 .210 eV, Eoa = 0 .180 eV, n b = n a = 1.60, x b = X

= 20.0X0n , N o = 9.6 × 1 0 ] 7 c m - 3 eV -1 . I n G a A s : E H o = E c - 0 . 2 0 eV.

] 034 Li He et al. / Charge- discharge dynamics of DIGS continuum at 1 S interfaces

1 0 l ~ - - , ~ r - - - t rue Nss \ / - tn f~ -~ -exper ,menta [ , , /' - L • calculated \ ~

p - - t r ue Nss \,~ g,/ -InGaAs .~--experimenta[\~ ~.~ .,,

1013 - L, o calculated ~ f l f

2 Z - % _ , , 8omv,s E

2 1 o _ . , , ,,

0.72 mWsec ~

72 mV/sec

l d 1 I I I I J i I I I

-1.0 - 0 8 -0.6 -0.4 -0.2 0 E- Ec(eV )

Fig. 3. Measured and simulated apparent N, s distributions versus true N~ distributions for lnP and InGaAs I S interfaces.

EHO , and exponentially decaying in space. The parameters N 0, Eno , E0b, E0,, n b, n~, x b and x~ characterize the distribution.

The experimental and simulated C V curves and the corresponding N,~ distributions derived by Terman's method are compared in figs. 2 and 3,

1.0

0.8

0.6

O.4

0.2

l n G a A s - MISFET .... simu~ted z~.no experimental

-.~.~ ...... ~_ (300t 4hrs)

"~3. ~ Lr" --[3 [3._ £3CL q343~ ~[3 _

" ~ ( as-grown ) --o.o.

,anodic double layer

. - M ~ layer Vd = 2 V . . . . . . . . . . . . Vg 3V F----~. ~

: [ : .SHn P " i . i . . 0

0 i I I I I i I i I I

10 -° 10 -4 10- 2 100 102 104

Time (sec)

Fig. 4. Measured and simulated drain current drift behavior for an lnGaAs MISFET having the device structure in the inset.

Li He et al. / Charge- discharge dynamics of DIGS continuum at 1 - S interfaces 1035

respectively, for InP and InGaAs MIS capacitors with different bias sweep conditions. It should be noted that a single set of parameters characterizing the distribution and the dynamic behavior were used to produce all the simulated C - V curves. Agreement between theory and experiment is thus impressive. It is also clear that apparent state distributions are very much distorted from the " t rue" distributions calculated from eqs. (4a) and (4b), indicating problems with Terman's method.

The measured and simulated values of interface state admittance also agreed very well as discussed previously [5,6]. Fig, 4 shows the measured and simulated characteristics of the drain current drift behavior for an InGaAs MISFET whose structure is shown in the inset. Again excellent agreement is seen between experiment and theory.

4. Discussion and conclusions

The mechanism of C - V hysteresis has previously been attributed to "s low" traps in the insulator [3] that are different from "fas t" interface states that cause frequency dispersion of small signal admittance [7]. The current drift of MISFET's has been attributed previously to special insulator traps situated above E c [8], to the special band structure of the native oxide [9], or to Van Vechten's hopping mechanism in the semiconductor [10]. The present result provides, for the first time, a unified quantitative basis that attributes all these phenomena to the same DIGS continuum, covering an extremely wide range of time constants and showing wide varieties of behavior depending on the measurement conditions. The experimental results on C - V curves with hyster- esis, frequency dispersion of small signal admittance and drain current drift of MISFET's can only be fitted consistently with the distribution of DIGS, as shown in eq. (4).

Acknowledgments

The present work is financially supported by a Scientific Research Grand- in-Aid for Specially Promoted Research on "The Properties of Compound Semiconductor-Insulator Interface and Its Applications" and by a Grand-in- Aid for Special Project Research on "Alloy Semiconductor Physics and Electronics" from the Ministry of Education, Science and Culture.

References

[1] H. Hasegawa and H. Ohno, J. Vacuum Sci. Technol. B 4 (1986) 1130. [2] H. Hasegawa, L. He, H. Ohno, T. Sawada, T. Haga, Y. Abe and H. Takahashi, J. Vacuum

Sci. Technol. B 5 (1987) 1097.

1036 Li H e et al. / Charge - discharge dynamics o f D I G S continuum at 1 - S interfaces

[3] F.P. Heiman and G. Warfield, IEEE Trans. Electron Devices ED-12 (1965) 167. [4] T. Sawada, S. Itagaki, H. Hasegawa and H. Ohno, IEEE Trans. Electron Devices ED-31

(1984) 1038. [5] T. Sawada and H. Hasegawa, Phys. Status Solidi (a) 54 (1979) 698. [6] H. Hasegawa and T. Sawada, IEEE Trans. Electron Devices ED-27 (1980) 1055. [7] E.H. Nicollian and Goetzberger, Bell Systems Tech. J. 46 (1967) 1055. [8] M. Okamura and T. Kobayasi, Japan. J. Appl. Phys. 19 (1980) 2143. [9] S.M. Goodnick, T. Hwang and C.W. Wilmsen, Appl. Phys. Letters 44 (1984) 453.

[10] J.A. van Vechten and J.F. Wager, J. Appl. Phys. 57 (1985) 1965.