Capacitance-voltage profiling and the characterisation of III-V semiconductors using

electrolyte barriers

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

1986 Semicond. Sci. Technol. 1 7

(http://iopscience.iop.org/0268-1242/1/1/002)

Download details:

IP Address: 129.7.158.43

The article was downloaded on 21/08/2010 at 09:22

Please note that terms and conditions apply.

View the table of contents for this issue, or go to the journal homepage for more

Home Search Collections Journals About Contact us My IOPscience

Sernicond. Sci. Technol. 1 (1986) 7-27. Printed in Great Britain

P Blood

Philips Research Laboratories, Redhill, Surrey RH1 5HA, UK

Received 2 1 October 1985

Abstract. This article is a personal review of the principles, capabilities, limitations and potential of the technique of electrochemical capacitance-voltage (C-V) carrier concentration profiling of compound semiconductors and the associated technique of photovoltage absorption spectroscopy. The profiling technique was developed by Ambridge and co-workers to overcome the depth limitation in depletion C-Vprofiling by using an electrolyte barrier to measure the carrier density and to etch the material in a controlled electrolytic process. The electrolyte also provides a transparent barrier which facilitates observation of absorption spectra, hence providing the added capability of band-gap profiling. In this article the basic principles of C-V profiling are summarised, we analyse the balance between measurement accuracy and instrumental depth resolution, and consider the effect of series resistance. In reviewing the principles of electrochemical C-V profiling, we pay particular attention to the electrolyte (Helmholtz) capacitance, the high electrolyte resistance and the definition of contact area. In considering these problems, and those of depth resolution and the influence of deep states, we take account of the use of a fixed low reverse bias in electrochemical C-V profiling compared with an increasing bias in depletion profiling. The interpretation of photovoltage spectra from single layers and heterostructures is described and examples are given of band-gap profiling of laser structures. The article concludes with examples of the characterisation of multiple quantum-well structures including carrier density profiles and photovoltage spectra on structures with periods less than 200 A.

1. Introduction integrating the etch current and applying Faraday’s law. Although this method is destructive, the profile can, in

Analysis of the capacitance-voltage (C-V) behaviour of principle, be measured to unlimited depth. However, the the depletion region of a reverse-biased Schottky barrier requirements for the electrolyte are rather demanding, is a convenient non-destructive method for determining calling for satisfactory barrier and dissolution properties the ‘doping profile’ in a semiconductor. The chief dis- on n- and p-type material, and, while a number of etches advantage of the method is that the maximum depth for profiling 111-V compounds and alloys have been which can be profiled is limited by electrical breakdown at developed, electrochemical profiling of silicon is still in its high reverse bias, and this can be very restrictive in highly infancy. The technique is now widely used for the doped materials where the depletion depths are small. characterisation of 111-V compounds not only because of Originally this was overcome by alternate chemical the enhanced depth capability but also because the etching and profiling with a temporary mercury barrier, electrolyte barrier can be made quickly without any but this process is time consuming and tedious. A better sample processing, thereby avoiding the risk of modifying solution was proposed by Ambridge and co-workers? - an the sample properties. Furthermore, a versatile instrument electrolyte is used to make the barrier and to remove manufactured by Polaron Equipment Ltd, Watford, UK material electrolytically so both processes can be carried (sometimes called the ‘Post Office plotter’ or pop - not out in the same electrochemical cell and controlled because of any sparkling performance in drawing the electronically, using automatic equipment to perform the nationwide distribution of sales outlets of postage stamps repetitive etch/measure cycle and generate a profile plot. but rather in recognition of the affiliation of its originators) The etch depth can be measured continuously by is available commercially.

As well as providing a convenient barrier for C-V i Ambridge and Faktor (1975a, b). measurements, the electrolyte is transparent to radiation

0268-1 242/86/010007 + 2 1 $02.50 0 1986 The Institute of Physics 7

P Blood

at wavelengths shorter than about 1.0 pm, thereby facilitating the observation of a variety of photovoltaic phenomena in GaAs and related alloys. The observation of photovoltage absorption spectra in conjunction with etch profiling is particularly useful for the measurement of band gap and alloy composition in heterostructures for opto-electronic devices. This capability has enhanced the value of the electrolyte- semiconductor contact in the characterisation of 111-V compounds.

The basic principles of electrochemical C-V profiling are documented in a number of original papers by Ambridge and co-workers, but in view of the development of photovoltage spectroscopy and the current widespread use of the instrument for 111-V characterisation it seems worthwhile to review the capabilities, limitations and potential of the electrolyte-semiconductor contact in this area of materials assessment. The review which follows is not a complete survey of published work in this field, but is a personal assessment based primarily, though not exclusively, on the author’s experiences in the characterisation of GaAs/AlGaAs structures.

To provide the necessary fundamental background, and to put electrochemical profiling in context in the field of C-V measurements as a whole, the first sections develop the basic principles of C-V profiling (0 2) with reference to the limitations imposed by the instrumentation and the sample (0 3). Here we extend the analysis of errors in the measurement of carrier density to include considerations of instrumental depth resolution, summarise the influence of deep states and give equations for the effect of series resistance on the measured carrier density. The electrochemical cell has a number of features not encountered in metal-semiconductor contacts such as the Helmholtz-Gouy electrolyte capacitance, the series resistance of the electrolyte and the need to increase the contact area to reduce errors in its definition, all of which have implications for the measurement of C-V characteristics. Furthermore, the electrochemical charac- teristics of the cell determine the etching behaviour which influences the depth resolution, control of the area and overall control of the etch/measure cycle. Published work and some of our own experiences on these topics are brought together in 0 4. In 6 5 we consider the limitations in electrochemical C-V profiling with particular attention to the consequences of the fixed low bias and high electrolyte series resistance encountered in this technique. The principle of photovoltage spectroscopy is outlined in # 6 with examples of applications to heterostructures and composition profiling of laser structures.

Quantum-well structures now represent a significant fraction of the activity on 111-V compounds and in 0 7 we present new results which illustrate the applications of electrochemical C-V profiling to heterostructures with periods of ~ 2 0 0 A, and indicate the importance of photovoltage absorption spectroscopy in measuring the characteristic wavelengths of quantum-well structures and checking reproducibility of the well width. The combination of C-V measurement, photovoltage spec- troscopy and controlled etching is particularly power- ful in the assessment of multiple quantum-well (MQW)

structures for opto-electronic devices such as quantum- well lasers.

In view of their technological importance and the state of the art of their preparation, most of this paper is concerned with layered structures of GaAs/AlGaAs. Quaternary alloys grown on InP are also of importance and are the subject of electrochemical scrutiny in a number of laboratories: most of the principles outlined here are applicable to this material system although, due to absorption in the electrolyte, photovoltage spectra have to be recorded with illumination through the substrate. The limited extent of the author’s experience rather than the need for this modification is responsible for the in- frequent reference to these materials in this review.

The personal conclusion of the author is that, due to the added ability to record photovoltage absorption spectra, the electrolyte-semiconductor contact has assumed a significance in the characterisation of 111-V compounds beyond the enhanced depth profiling capability which was the original motivation for its development. These characterisation techniques are especially appropriate to material for opto-electronic devices and, from recent experience, they will be of considerable value in the characterisation of quantum-well systems.

2. Capacitance-voltage profiling

2.1. Diode capacitance

The upper part of figure 1 is the band diagram of a metal Schottky barrier on an n-type semiconductor containing densities N, and N , of donors and traps, the latter having energy level E , and taken to be donor like, though this is not essential to the argument. A depletion region is established by the combined effect of the built-in voltage V, and applied reverse bias V,, and the electron density distribution n(x) at the edge of the depletion region is as illustrated, producing the charge distribution p(x), made up of positive charge in the semiconductor and an accumulation of electrons in the metal, indicated in the lower part of the figure. The electrostatic potential @ ( x ) at any point in the depletion region is given by Poisson’s equation

d2@/dX2 = - P ( x ) / E E ~ , (1)

that is

which may be integrated by parts to give the total electrostatic potential across the contact:

Since the total net positive semiconductor space charge is of equal magnitude to the total excess electronic charge

8

Electrochemical C-Vprofiling of Ill-V semiconductors

described by a Boltzmann factor it can be shown that

n(x)=Nd eXp[-(xd-X)2/2L~]"2 (6)

with the fall-off of n(x) being characterised by a Debye length

L , = (&&oki"/e2Nd)1/2. (7)

The depletion capacitance is given by C = A dQ/d V where dQ is the charge fluctuation per unit area arising from a modulation dV in the voltage. We will assume that Vb remains constant so that dV, dV. The principal contribution to dQ arises from the fluctu- ation in electronic charge on the shallow donors in the vicinity of the depletion edge causing a fluctuation in the positive space charge e(N,(x)-n(x)). There is another contribution to dQ from the change in occupancy of deep states in the vicinity of x1 Ahere E, crosses E,. States at the interface between the barrier and semiconductor (at x = O ) may also contribute to d e , but this is only significant in the presence of an insulating interfacial layer and for most common materials contacts can be prepared where this layer is very thin (Rhoderick 1978).

If the space-charge profile changes by dp(x) in response to the voltage increment d V then

d Q = I dp(x) d x .m

(8) ' 0

I

Figure 1. Energy band diagram of a Schottky barrier on an n-type semiconductor containing Nd shallow donors and NI donor-like deep states per unit volume at energy level E,. The electron density distribution n ( x ) at the edge of the depletion region, of width xd, is shown, and the plot of p ( x ) indicates the space-charge density distribution for uniform material.

accumulated in the metal we have

1 P ( Y ) dy = 0; .+m

. -m

if we assume that the width of the accumulation region is very small (screening distancezfew angstrom) such that the potential drop in the metal can be neglected, then the electrostatic potential across the barrier is

with p(x)= e(N,(x)- n(x)) and where d@/dx=O for x ~ x , . For uniformly doped material and an abrupt cut- off of n(x) at Xd, p(x)=eN, and the reverse bias band bending, V = - @, is

V= V, + v b = eNdXi/2&&o. (4)

Furthermore, if xd is well defined, integration of the electric field from xd toward the contact gives

I//(x)="eNd(xd-x)2/2&&0 ( 5 )

and since -e@(x) = E,(x) - E,(&) the conduction-band energy increases parabolically with distance into the depletion region. Near xd this analysis neglects the effect of the electrons, but if we take equation ( 5 ) to be a good first approximation to the form of E,(x) then with n(E)

and from equation (3)

1 dV=- 1 x dp(x) d x (9)

&EO ' 0

so that the small signal capacitance is

m O A dp(x) d x Jr x dp(x) d x *

C=

In the absence of deep states it is possible to derive a result for C as a function of V for uniformly doped material with n ( x ) given by equation (6) (see Sze 1981, p 366: neglecting minority carriers gives the result for a Schottky barrier) but for non-uniform distributions of N(x) it is necessary to make three simplifying assumptions, known collectively as the depletion approximation, to obtain an analytic result. It is assumed that the semiconductor can be divided into two distinct regions - (i) a space-charge region immediately below the barrier which is entirely depleted of free carriers and (ii) an interior region which is everywhere neutral - and that (iii) the boundary between these two regions is abrupt. In short, it is assumed that L , g xd so that xd defines precisely the depeletion layer edge; this is equivalent to V $ kT/e. It follows that if we also take the change in deep state occupancy at x, to be abrupt, then equations (8) and (9) become

d Q = u(e,)e&,(x,) dx , + eN,(x,) dxd (1 1)

& E O d V = U(e,)eXINt(X,) dxl f eXdNd(Xd) dXd (12)

where dx, and d x , are the increments in xd and x1 resulting from the voltage increment dV, and u(e,) describes the response of the trap to the voltage increment. The first term in equation (1 1) arises because the deep

9

P Blood

states in the vicinity of x1 emit their trapped electrons to the conduction band at a rate e, where they are removed by the field, and since d V is usually an oscillatory test signal this contribution will only be present when the angular frequency o of the test signal is less than e, so that the traps can respond. Thus we write

u(en) = 1 when o e, u(en) = 0 when o > e,. (13)

I f we first consider the case where the contribution of the deep states is negligible ( N , N , ) then equations ( 1 1) and ( 12) in equation ( I O ) give

c = EEOA/.Yd (14)

so within the depletion approximation C is determined solely by irrespective of the space-charge distribution and the value of N , at .yd. This result is used in C-V profiling instruments to determine the depletion depth.

When deep states are present. we note from equation ( 5 ) that .yd-.yl is given by

for a uniformly doped material, and L is independent of xd. In fact, for small increments 2 will also remain constant in non-uniform material, although 2 will vary as the DC bias is increased. Thus since dx , = dxd equation (10) gives

The effect of deep states is therefore twofold. Firstly. C is frequency dependent through the parameter u(e,) such that at high frequencies, o 9 e, where u(e,) = 0, equation ( 1 6) becomes

c, = &&OA/Xd, ( 1 7 )

identical to equation (14) because the traps cannot respond, and at low frequencies, o ~ e , where u(e,)= l , the capacitance increases by AC to a value C, where

with C,= C, + AC as illustrated in figure 2(a). Unlike c,, c, depends upon both N,/Nd and xl/xd and has a maximum value in a given sample when xl/xd -0, i.e. xd-2, of AC= C,N, /N, . The second feature to note, therefore, is that deep states contribute a depth dependence to C, in addition to the dependence inherent in the depletion capacitance because AC varies with .\'d. When .yd is not much greater than i, c cannot be interpreted in terms of S, using equation (14). In materials of only modest quality the deep state concentration is sufficiently small that these effects are negligible, though this may not be so in implanted or irradiated samples.

I t is usually possible to determine x d from the depletion capacitance using equation (14) but measurement of C is not necessarily straightforward because the test diode may not be an ideal capacitor but

T

I I b

wze," l Frequency,w

\ l b ) I \

I \

Figure 2. Frequency dependence of the measured diode capacitance due to (a ) deep states in the upper half of the band gap with emission rate e, and (b) resistance R, in series with the depletion Capacitance.

may incorporate some series resistance R , and parallel leakage characterised by a conductance RF' . Capacitance is measured in meters and bridges as the out-of-phase com- ponent of the current which flows as a result of an AC

voltage of constant amplitude. In the absence of series resistance this procedure gives C independent of parallel conductance. but when R , is not negligible the measured capacitance is given by the imaginary part of the complex admittance as (Goodman 1963, Bleaney and Bleaney 1976)

C,/C= {[ 1 + (R,/RJ]* + (wIR,C)*I" (19)

\vhere w I is the angular frequency of the test signal. When R , f 0 C, < C due to both series resistance and parallel conductance, and C, becomes frequency dependent such that C, decreases with increasing frequency as shown in figure 2(b). C, is frequency independent when R , is such that

w,R,C 1 + (R,/R,) although C, only takes the true value when additionally R J R , < I . Even when R , is large the parallel conductance is sufficiently small in all useful samples that R,/R, e 1 and equation ( 19) becomes

C,/C=( 1 + W:R;C')-' .

For the decrease in C, to be less than 19'0 R,<R,,= 0. l(27rfiC)-1 and so errors in C are most likely to occur in highly doped material where C is large. The critical value of R,. RSc, is plotted in figure 3 for a total band bending of 1 V in a diode on material with N , = I O l 9 cm-3 as a function of frequency fi for diodes of various diameters. Evaporated metallic contacts are usually 1 mm in

10

Electrochemical C-V profiling of Ill-V semiconductors

Figure 3. Critical values of the series resistance R,, for a 1 % error in C, and N, plotted as a function of frequency for diodes of various areas on material with Nd = 10'' cm-3 and a total reverse band bending of 1 V (C/A = 1 O6 pF cm-').

diameter or less, and the figure shows that a capacitance measurement on a 0.25 mm diameter diode on this material using a meter operating at 1 MHz will not be in serious error if R , < 30 R, which is easily achieved.

2.2. Principle of C-V profiling

I n the depletion approximation x d is well defined and. provided there is no influence of deep states and that the test diode is a good approximation to an ideal capacitor. .\'d can be determined by measuring the diode capacitance (equation (14)). With these assumptions the depletion depth increases by Axd when the bias is increased by A V and from equation (9)

A V = exdN(Xd)AXd/&&O (20)

and the charge increment (equation (8)) is

AQ = eN(Xd)AXd. (2 1) It follows that since

using equations (14) and (20)

AC/A V=-C3/es&,AZN(xd) or

C3 AC -l N(xd)=-- - e&&,A2 ( A V )

so that the measurement of C and AC/A V as functions of V gives N ( q ) as a function of x&

We will not describe here the various methods which have been developed for the measurement of doping profiles based on these equations (see Blood and Orton 1978): the methods commonly employed are similar in that equation (22) is utilised by modulating the voltage at some frequency o2 and measuring the resulting modulation in C. Alternatively C can be measured as a function of V and N(Xd) calculated by numerical differentiation.

All these methods are subject in varying degree to a number of limitations which can be conveniently divided into three classes: (i) fundamental limitations; (ii) limita- tions in the instrument; (iii) limitations due to non-ideal characteristics of the sample.

3. Limitations in depletion profiling

3.1. Fundamental limitations

There are two limitations of a fundamental nature: the maximum depth which can be profiled and the depth resolution.

The maximum depth is limited by the onset of electrical breakdown at high reverse bias in the high-field region of the semiconductor immediately beneath the contact. In GaAs the maximum field is about 4 x lo5 V cm" which corresponds to about 2 x 10l2 charges cm-2 in the depletion region (Sze 1981). In material with N , cm-3 the maximum depth is z 2 O p m whereas for N , z 10l8 cm-3 the range is seriously restricted to ~ 0 . 0 2 pm. Furthermore, since it is not always possible to fabricate ideal diodes with the maximum possible breakdown voltage this limitation can be more restrictive in practice than the theoretical values quoted here.

In the depletion approximation xd is well defined and so the depth resolution should be limited only by the depth increment Ax, in the measurement of AC/AV. In reality the depletion depth deduced from the parallel-plate result is given by a combination of equations (10) and (14),

which represents the mean depth of the differential charge distribution in the measurement of C (Kroemer and Chien 198 1). Since p(x)=e(N,(x)- n(x)), in the limit of d V being very small the extent of dp(x) is determined by the Debye length and equation (6) shows that n(x) falls to 0.05Nd in a distance z 3 L D so the limits of the integral in equation (23) are zxd f 2LD and this represents the fundamental limit to the depth resolution. Further difficulties arise at steps in the impurity profile because the free carriers diffuse down the concentration gradient over a distance of a few L,, establishing a charge dipole within the undepleted material (Kennedy and O'Brien 1969), and as the depletion layer of the surface contact approaches this dipole there is a redistribution of charge both at the

11

P Blood

depletion edge and within the dipole (Johnson and Panousis 197 1).

3.2. Instrumental limitations

The profiling instrument determines the accuracy with which N(xd) and xd are measured and may also determine the depth resolution; ideally, the depth resolution should be limited by the Debye length rather than the instrument. Table 1 gives the contributions of a 30 precision of 1% in the measurement of diameter, capacitance and voltage to the precision in N and x (following Amron 1967).

I E - * I z c_

D

Table 1. Precision in the derived values of N and x,, due to 1% 30 precision in the measured quantities diameter, capacitance and voltage. The fractional capacitance - increment isP=O.l (after Amron 1967).

m IO0 : - - - - -

Contribution to - total precision (%)

Total Diameter C

l I I I V precision (%) 10-2 IO” 100

3a in N 4 13.5 0.02 14 3ainx, 2 0.7 2.1

Although the diode diameter can only be determined to %lo%, in practice this uncertainty affects the absolute accuracy rather than the ‘noise’ in any particular profile plot. The overriding influence on the precision of N is therefore the precision of the measurement of AC, and although there is consequently a temptation to make AC large this introduces errors in the determination of the local value of AC/A V because the C-V curve is not linear and also degrades the depth resolution by increasing the modulation of xd. It is therefore necessary to achieve a balance between these conflicting requirements.

The result of Amron (1967) for the precision in N, denoted 30,, can be simplified when the fractional capacitance step p = AC/C is small to give

30, = @c/p P(0 .1 (24)

where c is the precision in the measurement of C. In figure 4 we have plotted 30, as a function of p for various values of c, together with the error in AC/AV estimated by Amron (1967) for uniformly doped material. This figure shows it is desirable to keep p < 0.1 so that the derivative error is less than the precision due to measurement of C. However, from the result for high-frequency capacitance (equation ( 14))

p = AC/C = -hXd/Xd (25)

and so if p is fixed the depth step Axd will increase in proportion to xd. For example, in a sample with N - 1 0 1 5 c m - 3 d e p l e t e d t o z 1 0 , u m A x d z l , u m f o r ~ = 0 . 1 whereasL.zO.12,um.

In analogue profiling instruments it is common practice to use a modulation voltage of fixed amplitude [AV] rather than the more complex procedure of

tapacltance step, p - A C I C

Figure 4. The 3a precision in N(x) as a function of the fractional capacitance step P=AC/C for various values of the precision in the measurement of C, denoted by c. Also shown is the error in the evaluation of AClAVdue to the non-linearity of the C-V characteristic estimated for uniformly doped material.

controlling AC in some way. The resulting depth modulation is given by equation (20) which, together with equation (25) in equation (24), gives

30,= &ecXjN(xd)/&&o[A V ] . (26)

This shows that the uncertainty in N increases as x; producing noisy plots at large depth as noted by Baxandall et a1 (197 l), and also increases proportional to N itself. From equation (20) the instrumental depth resolution decreases with increasing N but is also inversely proportional to xd and may be poor at shallow depths. It can be shown from equations (7) and (20) that AX, < 3LD when xd exceeds the critical value

X, = f [A V](EEO/N~T)’”. (27)

The performance of this kind of profiler is not optimum because the instrumental resolution at large depths is unnecessarily small, resulting in a poor precision in N.

Profiling with a fixed increment in the electric field A& (Miller 1972) gives a more favourable compromise with a depth modulation proportional to N” and independent of xd:

A X d = &Eo[A&]/eN(Xd) (28)

and a precision in N proportional to N and xd:

30, = \/ZeCXdN(Xd)/&&,[ A& 1. (29)

With complete freedom in spacing the data points it is possible to achieve the optimum depth resolution by

12

Electrochemical C-Vprofiling of Ill-V semiconductors

controlling A x , for each step so that Axd z L D where L D equation (22) we can write is evaluated using the previous value of N . Substituting equation (7) for Axd in equations (24) and ( 2 5 ) gives Nil , , =-- ~ 2 ~ o e [ ~ c m ] - (32)

(30) AVrn 0 2

30, =

and so the penalty for optimum depth resolution throughout the profile is a precision in N which deteriorates as xd and

From this analysis it can be seen that it is difficult to achieve a satisfactory balance between optimum depth resolution and accuracy in the measurement of N in depletion profiling and this arises from the coupling between Ax, , N(xd) and depth according to equation (20).

3.3. Limitations due to the sample

Distortions may be introduced in a C-V profile by deep states in the material and by series resistance and leakage in the test diode.

Even when C is measured at high frequency such that equation (17) applies, the bias may be stepped or modulated at a frequency where the deep states can respond leading to a contribution to the indicated value of N. From an equation of the same form as (12) for the modulation depth A x d in terms of the modulation voltage A V an expression for A V / A C can be determined and it can be shown that the measured density (equation (22)) is (see, e.g., Kimerling 1974)

where umOd(en) is defined as equation (1 3) with w2 as the modulation frequency and N + ( x d ) is the total positive space-charge density at the depletion layer edge: N + ( x d ) = N d ( x d ) when Nt is a deep donor and N + ( x , ) = Nd(Xd)- N t (xd ) when Nt is a deep acceptor. In material where N + is uniform, or when Axd is small, A x l = Axd .

At modulation frequencies where the traps can respond, as xd is increased from xd A. to xd $A. profiling uniform material, the measured density increases by Nt due to thermal emission in the vicinity of x 1 where EF crosses E,. For localised deep donor and acceptor distributions this emission process produces a peak in Nmeas(xd) displaced a distance 1 from the true location of the traps. Additionally the sample with deep acceptors will have a dip in the profile corresponding to the 'compensa- tion' profile N + ( x d ) = Nd(Xd) - Nt(xd) (Kimerling 1974). These features are often apparent on profiles of ion- bombarded material (Schultz 1974).

The contribution of deep states to the profile is determined by the emission rate at the temperature of measurement, the modulation frequency and the relative magnitude of x 1 and xd in equation (31). In the case of sequential point-by-point measurements the profile measured at low temperatures where e,, is small will also depend upon the direction in which the bias is changed (Blood 198 1).

The measured value of N is also modified by series resistance and leakage currents in the test diode. From

where C, is the measured high-frequency capacitance given by equation (19) and V, is the voltage across the complete test diode for a voltage V, across the depletion region; w 2 is the (angular) modulation frequency. It follows from equation (32) that

where the derivative in square brackets is evaluated for changes of V in phase with V,. It can be shown from a consideration of the complex impedance of the circuit that

and since w 2 z ,&,W, the measurement of C imposes the most restrictive conditions on R , so we can assume w2RsC< 1 for values of R , and C such that wlR,C< 10 and consequently

(34)

In effect the capacitive impedance is large at o2 so the fraction of the applied voltage V , appearing across the capacitor itself is determined by the resistive components in the circuit. It then follows from equations (19) and (34) that (33) gives (J P Stagg, private communication)

It follows from our assumption above that N,,,, depends on w 1 but not w2, and following our discussion of the measurement of C if we again assume R,/R I G 1 then

Nrneas/N= [ 1 - ( w I R ~ C ) ~ I - ' (36)

so that N,,,, increases as R , or C increase, and may even change sign. For Nmea, /N< 1.01 it is necessary that w,R ,C < 0.3, and the corresponding critical value R,, = 0.3/2nflC is also plotted in figure 3 as a function of frequency for heavily doped material. Again it is apparent that the measurement of C itself imposes the most stringent condition and diodes for which R , is low enough to measure C correctly will give valid data for N . The error in N will be largest at low bias and in highly doped material where C is large. In fact, with diodes where R , is significant wlR,C will decrease as the bias increases and N,,,, will appear to decrease with increasing xd and may indicate the true value at high bias. The series resistance will also increase the perceived value of xd (equation (1 9)) and as C decreases with bias it is possible that the decrease in w,R,C dominates over the C( V ) dependence and there is a net increase in C with increasing bias so that the profile plot appears to move backwards (Wiley and Miller 1975).

13

P Blood

3.4. Summary

Depletion C-V profiling is convenient, quick and non- destructive. Using evaporated metal contacts the area is well defined even for diameters ~ 0 . 2 5 mm which make C sufficiently small that there are no series resistance effects even in highly doped material. In any case it is often possible to prepare test diodes with series resistance of only a few ohms. The combination of small R , and small area (i.e., small C) permits high measurement frequencies to be used (typically x1 MHz) which reduce the influence of deep states on the measurement. The principal disadvantage of depletion profiling is the limitation to the accessible depth which is set by electrical breakdown at high bias: this is very restrictive in highly doped material. Most profiling instruments are not ideal in achieving a balance between depth resolution and uncertainty in N , and this can lead to considerable scatter at large depletion depths.

4. Electrochemical C-V profiling

The restriction on the maximum accessible depth is the principal limitation of conventional C-V profiling, and to overcome this it was common practice alternately to etch the sample chemically and make profile plots using a temporary mercury Schottky contact (see, e.g., Wood et a1 1979). This was a tedious process and Ambridge and Faktor (1975a, b) developed the use of an electrolyte to make the Schottky barrier and to remove controlled amounts of material by electrochemical etching. Since the sample remains in the same cell for both operations the repetitive process can be controlled automatically and, using Faraday’s law to determine the etch depth from the integrated etch current, a profile can be plotted directly. The principal advantage of the method is that profile depths are not restricted by electrical breakdown and we also show that the method achieves a more satisfactory balance between depletion depth, resolution and accuracy in N . The disadvantages are that the method is destructive, it is difficult to measure and control the area of the electrolyte contact with high precision and reproducibility, and the depth resolution is limited by etching non- uniformity. In Q 6 we review the additional advantages which derive from the capability to make photovoltage measurements through the transparent liquid contact.

Detailed investigations of the dissolution and C-V characteristics of electrolyte-GaAs contacts have been reported by Ambridge et a1 (1973) and Ambridge and Faktor (1974), and an extensive review of this and later related work has been given by Faktor et a1 (1 980).

4.1. Operating principles

The key component is the electrochemical cell, shown diagrammatically in figure 5. The semiconductor slice is held against a sealing ring, which defines the contact area, by means of spring-loaded back contacts. The etching and measuring conditions are controlled by the potential

II l I I*[

Figure 5. Schematic diagram of the electrochemical cell used in the profiler, showing the Pt, saturated calomel (SCE)

and carbon electrodes, and the pump used to agitate the electrolyte and disperse bubbles on the semiconductor surface.

across the cell and this is established by passing a DC current between the semiconductor and the carbon electrode to maintain the required overpotential measured potentiometrically with reference to the saturated calomel electrode (SCE). This procedure ensures that the reference half-cell carries no current and is not polarised. The AC signals are measured with respect to a Pt electrode located near the semiconductor surface to reduce the series resistance due to the electrolyte. A front contact system is available to make the ohmic contact to epitaxial layers on insulating substrates.

It has been common practice to represent the I-V characteristics of the cell either as plots of V as a function of log I or I as a function of the anodic potential, so in figure 6 we have redrawn the characteristics in the more familiar form of a plot of I ( V ) with forward current in the upper RH quadrant for an n-type semiconductor. The voltage is that of the semiconductor back contact with respect to the SCE so a positive anodic potential corresponds to a reverse bias across the depletion region. The voltage for zero current (dark rest potential) is displaced from the origin in this diagram due to the electrochemical potentials associated with the reference electrode and the semiconductor half-cell. A Schottky plot of C-* as a function of V for uniform material is illustrated in the lower part of figure 6: the intercept relative to the rest potential represents the built-in voltage Vb of the electrolyte-semiconductor barrier while the doping level is given by the slope of this curve (an equivalent procedure to equation (22)) at positive going potentials with respect to the rest potential, provided significant reverse current is not drawn.

When the contact is illuminated with photons of energy greater than the band gap of the semiconductor the reverse current is increased as indicated in figure 6 due to a flow of holes or electrons from the semiconductor into the electrolyte in n- or p-type material, respectively. As illustrated, this causes a change in the rest potential which is of opposite sense for n- and p-type material and can therefore be used to indicate the material type.

14

Electrochemical C-V profiling of Ill-V semiconductors

Current

t I I

Voltage

toSCE Dark I

I 1

Jlncreasing i l lumination I v I I

, l 1 * ‘Safe’dissolution l potential

I Rest

Rest (light1 potential (dark1

c-zt ‘ Z e r o b m ’

0 Cathodic

Voltage with respect to S C E

Figure 6. Conventional /-V characteristics of an electrolyte-n-type semiconductor contact, with V measured with respect to the SCE. The rest potentials in the dark and light are indicated, and the region for safe dissolution where I is independent of Vand proportional to the intensity of illumination is shown. The lower part of the figure is a C-’ against Vplot measured for NaOH on IO” GaAs.

Material is dissolved when an anodic current is drawn by a flow of holes from the GaAs, whereas a cathodic current causes deposition of material from the electrolyte onto the semiconductor surface. With p-type material the holes required for the dissolution reaction are obtained from the valence band simply by applying an anodic potential which drives the barrier into forward bias, whereas to etch n-type material the holes are generated by illumination under reverse bias. Smooth removal of n-type material is achieved when the anodic current depends upon the illumination intensity but not upon the potential, as illustrated in figure 6. For a ‘reverse bias’ C ( V ) measurement on p-type material the potential is switched from an anodic (dissolution) to a cathodic value, and to avoid contamination of the sample surface by the cathodic reaction promoted by electrons from the conduction band it is important that the cathodic potential is such that the reverse current during the measurement is very small.

Faraday’s law of electrolysis is used to calculate the depth etched, x,, from the total charge transferred by

integrating the etch current I :

M zFDA .

x, = - I ’ I d t (37)

where M and D are the molecular weight and density of the semiconductor, F is the Faraday constant, A is the dissolution area and z is the charge transferred per molecule dissolved. For GaAs z = 6.

A simplified block diagram of the measurement system is shown in figure 7. The etching and measuring conditions are determined by the cell potential and illumination intensity according to the material type, and the alternating etch-measure sequence is controlled automatically. The etch current is integrated and processed to give the etch depth, which is added to the depletion depth to give the total depth of the depletion edge from the original surface. The depletion depth is obtained from equation (14) by measurement of C at 3 kHz ( ~ 0 . 1 4 V peak-to-peak) and N is derived from equation (22), measuring AC/A V by modulation at 30 Hz ( ~ 0 . 2 8 V peak-to-peak) at a low fixed reverse bias. An example of a profile of n-type GaAs is shown in figure 8: only the first micrometre at most of this sample could be profiled conventionally before breakdown.

voltages C,ACIAV

- L ‘ Sequence

Adder

Cell -tt-

Figure 7 . Block diagram of the electrochemical profiler.

The electrochemical C-V technique has been applied to a wide variety of 111-V compounds and some results have been reported for profiling Si (Sharpe et a1 1979, Sharpe and Lilley 1980). The key to successful

r 7

Large ‘0‘-ring Tiron (MBV 1331

5 10‘6 c

0 1 2 3 Depth l!.tml

Figure 8. Electrochemical C-V profile of a doped GaAs epitaxial layer recorded using the 3 mm sealing ring and Tiron electrolyte.

15

P Blood

electrochemical profiling is the characteristic of the contact itself, and in particular the ability to define the contact area and to control the etching process by bias and illumination with a suitably small dark current under measurement conditions. Given that a suitable electrolyte exists, there are further aspects of the contact, peculiar to the electrolyte-semiconductor system, which must be considered. Firstly the C( V ) characteristics of the system must be dominated by the depletion capacitance of the semiconductor, a requirement which raises fundamental questions about the charge distribution at the contact as well as considerations of the electrolyte resistance, and secondly the contact area must remain constant throughout the etching process without undercutting or significant roughening and without seepage of electrolyte under the sealing ring. We review these equations in the following sections.

4.2. Contact capacitance

As with the metal-n-type semiconductor contact, illustrated in figure 1, there is an accumulation of negative charge in the electrolyte due to ions which is distributed over a distance of several ionic radii (x 10 A) rather than a few angstroms as for electrons in a metal. The existence of this layer of charge was recognised by Helmholtz and the theory was refined by Gouy and Chapman (see Faktor et ai 1980). We cannot necessarily neglect the electrostatic potential in the electrolyte as we did in the derivation of equation (3) for the metal contact, and strictly we should consider the contact as the Helmholtz-Gouy capacitance in series with the depletion capacitance.

Electrochemical C-V profiling is done at fixed low reverse bias, so taking a total band bending of 1 V the largest depletion capacitance encountered will be about 1 pF cm-2 (r?z l O I 9 cm-3). A simple parallel-plate calculation of the Helmholtz capacitance for a spacing of one ionic radius (-6 k) gives 1 0 p F cm-2 (e= 7 at high fields) and more detailed calculations which take account of the decay of the ion concentration with distance from the interface suggest larger values (Faktor er a1 1980). A value of x40pF cm-2 has been measured at 10 kHz by Stagg (1982, unpublished) for 1 M NaOH with a Pt electrode. It would seem that we are justified in neglecting the Helmholtz-Gouy capacitance in all but the most highly doped samples, a practice which is further justified by the observation of linear plots of CP2 as a function of V for this contact system, characteristic of depletion capacitance alone. In fact, a fixed series capacitance will modify xd but not N as derived from AClA V.

The against V plot in figure 6 is for NaOH on GaAs ( 1 7 z lo1’ and indicates a built-in voltage V,>, 1.0 V. This increases with increasing pH of the electrolyte (Redstall et a / 1978), but from our own measurements does not depend strongly on doping level. These barriers are significantly higher than metal barriers on n-GaAs ( V,=0.8 V). We find corresponding low

Table 2. Values of electrolyte resistance measured for 0.1 M Tiron and estimated maximum values of N for an error <20% due to series resistance (J P Stagg 1982, unpublished).

Sealing ring

3 mm 1 mm

RE 650 R 2300 R Nmm 3.5 x IO'^ cm-3 3 X 10’’ cm-3

area. large sealing ring diameters of 1 mm or 3 mm (area 0.07 1 cm2) are used for electrochemical profiling; however the resulting increase in C reduces the critical value for series resistance errors in C, to R,, z0 .2 Q for measurement at 1 MHz on n= 1019 material with the larger ring, as shown in figure 3. This is very restrictive because the electrolyte resistance in the standard cell can be large (we have measured 650 Q for 0.1 M Tiron with 3 mm ring, table 2 ) , so to ease this limitation a lower measuring frequency must be used: 3 kHz is used in the standard instrument which, according to figure 3. means that R , will influence measurements when n > 1019 and R , 2 lo2 Cl.

4.3. Contact area

Ambridge er ai (1980) have identified three components to the contact area, illustrated in figure 9. The central illuminated area A , is the region which is etched in n-type material. while the total wetted area within the sealing ring A , = A c + A , is the area etched and measured in p-type material. The instrument corrects the capacitance measured on n-type material for capacitance of the unetched annular contact of area A , . There is a further outer excess area A , due to seepage of electrolyte under the sealing ring which is particularly troublesome when measuring ‘hi-lo’ profiles, and has been modelled as a frequency-dependent capacitance whose contribution can be reduced by choice of a low-conductivity electrolyte (Ambridge et a/ 1980). The areas A , and A , can be measured and controlled with reasonable accuracy but A , is very variable and depends to some extent on the viscous properties of the electrolyte. Ambridge et a / (1 980) report

Wetted area A q Z A C t A E

V , z 0.4 V in p-type material. and find similar values for Figure Diagrammatic cross Section of the c’, i n both n-type GaAs and Alo,,Ga0,,As. between the sealing ring and the semiconductor sample, To minimise the effect of poor definition of the contact showing the outer excess area due to leakage of electrolyte.

16

Electrochemical C-Vprofiling of Ill-V semiconductors

that Tiron is particularly satisfactory in minimising the effects of the outer area A , , and gives a short-term reproducibility in the area A , of ~ 2 % . Nevertheless, to minimise the fractional uncertainty in the area sealing rings of 1 mm or 3 mm diameter are used -larger than the metallic contacts used in depletion profiling.

These points are apparent in the data of figure 10, which shows measured values of N using Tiron, HCI and NaOH electrolytes with the small sealing ring ( 1 mm) plotted as a function of f i T , the average value measured with Tiron. Tiron and HC1 give similar results, but NaOH gives higher values of N which we attribute to seepage under the ring. The dependence of N / N , upon R, is similar to that predicted by the excess capacitance model of Ambridge et a1 (1980) (see their figure 4), and means that the excess area cannot be compensated simply by using a different value for the area.

*r

0 1015 10’6 1017 10‘8 1019

A, ( c r n - ’ ~

Figure 10. Values of N measured with various electrolytes on different samples of GaAs using the 1 mm diameter sealing ring plotted with respect to the value obtained with Tiron (A,) (J P Stagg 1982, unpublished). 0, 1 M NaOH; x 0.5 M HCI; 0, 0.1 MTiron ( /VT) .

I t is also important that the area remains constant during the etching process so that the profile is not distorted. Principally this means that the crater should remain smooth - this is also an important condition in maintaining good depth resolution. Good uniformity of etching n-type material is achieved using short-wavelength illumination (-550 nm) which is strongly absorbed at the surface producing a photocurrent which is largely indepen- dent of the depletion width and diffusion length, both of which could vary across the crater. Dissolution by draw- ing a dark current in reverse bias must also be avoided because this leads to severe pitting and an increase in the contact area (Ambridge and Faktor 1974). A ‘Talysurf’ trace of the etched crater gives a useful indication of gross roughness and provides a measurement of crater depth which can be compared with the indicated depth, making due allowance for the depletion depth.

4.4. Comments on electrolytes

Initial C-V experiments by Ambridge and Faktor (1974, 1975a, b) used KOH electrolyte but, to reduce the effect of the outer excess area, Tiron (Faktor and Stephenson 1978) with a higher resistance was later adopted as the

preferred electrolyte for GaAs (Ambridge et ai 19801, although the higher electrolyte resistance imposes a lower limit on the maximum value of C which can be measured without R , errors, and hence limits the maximum value of ,V which can be accurately profiled. Ammonium tartrate solution has been suggested for profiling GaAs, AIGaAs, GaP and GaAsP, although the area definition is poor: we have etched some n-type samples of GaInP with this solution but there were serious non-uniformities on p-type material. We have also used NaOH for profiling AIGaAs, although again there can be problems defining the area accurately. HCI is recommended for InP-based materials and we have used it occasionally on GaAs.

5. Limitations of electrochemical C-W profiling

5.1. Depth resolution and accuracy

Electrochemical profiling overcomes the fundamental depth limitation in depletion profiling and in principle offers the capability to measure to any depth. The fundamental Debye length limit to the depth resolution remains because the smearing of the edge of the space- charge distribution is determined by the doping level in the vicinity of .yd.

The influence of instrumental limitations on the profile is rather different for electrochemical profiling compared with depletion methods. Since the etch step Ax, can be made very small, the limiting depth resolution is due to the roughness of the etched crater dx, and the depletion depth modulation Ax,:

(A-Y,,t)2 = (&Ye)* + (AX,)2 . (38)

The measurement is made at a small fixed applied bias with constant modulation amplitude [ A V ] , and if we assume the doping density is approximately uniform over the depletion region, then equations (4) and (20) give

and combining this with equation (7) for L, gives

At room temperature, and with V, + Vb z 1.0 V, modulation of 0.28 V peak-to-peak gives Ax,, z 1.2LD5 so since A s , is less than a few Debye lengths and independent of N the depth resolution for AC/AV is always determined by the Debye length rather than the modulation. The overall instrumental depth resolution is therefore controlled primarily by the influence of the etching process on the flatness of the crater. Our observations suggest that the amplitudes of depth undulations in the crater are proportional to the mean etch depth and amount to ~5-10% of the depth etched.

The precision of the differential capacitance measurement of N can be estimated (assuming N to be uniform over S,) by substituting equation (4) into equation

17

P Blood

(26) to eliminate ,V:

The uncertainty in N due to imprecise measurement of C is independent of N and the depletion depth. However, in the case of electrochemical profiling there is the possibility of further uncertainty in the value of N within a given profile due to crater roughness, contributions from the sides of the crater and gradual seepage of electrolyte under the sealing ring, although these are difficult to quantify.

5.2. Influence of deep states

The sensitivity to deep states differs from that of depletion profiling because the measurement frequencies are lower and because the depletion depth remains small, and constant in uniform material, so that the term XI/&, = 1 - @.yd can be much less than unity (equation (3 l)). In fact, these two effects are linked through the energy level of the trap which determines both e, and A. Considering first the influence of /I, when u(e,)= 1 equation (18) gives the capacitance as

where C, is independent of N, (equation (17)). and equation (3 I ) gives

(43)

where we have taken the simple example of a donor-like trap. For this example we assume the material is uniform, so that equations (4) and (15) give

(44)

and we assume E , is sufficiently close to the conduction band that it is reasonable to make the approximation E , - E , 2 E, - E,. Figure I 1 shows xl/.Yd. co/c, and Nmeas/Nd as functions of E , - E, calculated from equations (44), (42) and (43) for V = V, + V, = 1 V and 10 V and with the specific value of N , = 0.1 Nd. Since the perturbations of the measured quantities scale approximately as N,/Nd these plots indicate the relative magnitudes of the effects in a given sample. We have calculated the emission rate of the trap at 300 K for the specific example of a capture cross section of IO-I5 cm2 using the detailed balance equation (Blood and Harris 1984; equation (6)) and this is given in the upper part of figure 1 I .

With the small fixed bias used in the profiler x1/Xd

becomes small as E , - E , increases, causing an increase in C, away from its true value and a decrease in N,,,, towards the true value. The capacitance is measured at f, = 3 kHz so that only traps with E,-E, < 0 . 3 5 eV will respond and the maximum error in C, (and XY) will be z 6% for N,/Nd = 0.1. N,,,, is obtained by modulation at f2 = 30 Hz and will therefore deviate from Nd by at least 3% up to the maximum possible error of 10% (= N,/N,),

\1 f.30 H Z

l . 0 L . .

l . l r

””- 1 v

1.0

Figure 11. Calculations of the influence of deep states on the measurement of C and N as a function of trap energy level E, - ,Et . In these examples we have taken NI =0.1 Nd and have assumed that E, - E F is negligibly small. The upper plot indicates the relation between e, and E, -E, for an electron capture cross section of I 0-15 cm’.

due to traps shallower than ~ 0 . 4 8 eV. Since V, remains fixed and .ul/.ud is independent of Nd these perturbations will remain constant throughout an etch profile for a given trap energy level and concentration.

The lines calculated for V= 10 V indicate the changes which occur in .Yl/.Yd and the measured quantities as the bias is increased for a depletion profile. The energy level positions for traps influencing a measurement of C at 1 MHz and N with modulation at 3 kHz are marked on the figure. I n accordance with equations (16) and (3 1) the perturbations in C, and N,,,, decrease and increase, respectively, as V, increases.

Taking account of both the different measuring frequencies and the effect of the DC bias, we conlcude from figure 1 1 that in the presence of deep states depletion profiling will give a more reliable value of x,, because the bias is greater and the capacitance is measured at a higher frequency than in electrochemical profiling, restricting the effect to only shallow traps. Electrochemical profiling

18

Electrochemical C-Vprofiling of Ill-V semiconductors

gives a more accurate value of Nd throughout the profile because V remains small, and although this method is sensitive to deeper traps because of the lower modulation frequency these have a smaller effect on N,,,, because of their larger l. values.

5.3. Series resistance

Because of the large series resistance of the electrolyte (table 2) and the large capacitance due to the contact area. series resistance errors are of greater concern in electrochemical C-V profiling than in depletion profiling. Although the measuring frequencies are relatively low to reduce these errors, large values of C will be encountered because the profiler can be used on highly doped materials where depletion profiling is of little value due to electrical breakdown. The dependence of N on the fourth power of R , (equation (36)) has been verified experimentally (Stagg 1982. unpublished results) by inserting carbon resistors in series with the cell. Figure 12 shows that as predicted [ 1 - (.Vmea,/,V)~ varies linearly with R , with a slope consistent with C calculated for the doping level and an intercept which gives R , = 2.75 k n due to contact and electrolyte. in agreement with the value in table 2 . In table 2 we give the maximum values of N which can be measured with a series resistance error less than 20% for the values of R , measured for 0.1 M Tiron. These limits can be increased by using a more conductive electrolyte, but contact area errors may then be introduced.

Figure 12. Plot of [ l as a function of the resistance RI added in series with the electrochemical cell. The linearity of the plot confirms equation (36) for the effect of series resistance, and the intercept gives R,, the resistance of electrolyte and back contact (J P Stagg, unpublished).

Series resistance will distort the profile in a different way to depletion profiling. For example, with a uniformly doped layer on a conducting substrate R, is due to the electrolyte and contact and remains constant through the profile: likewise, since the measurement is done at fixed reverse bias. C also remains constant. The errors in both N

and C therefore remain fixed. resulting in values of N and .yd which are larger than their true values but the indicated profile remains flat as illustrated in figure 13. This contrasts with depletion profiling where C decreases and so the errors decrease through the plot (Wiley and Miller 1975). The error in the electrochemical plot is more difficult to detect, so it is useful to check that the indicated depletion depth and doping level are consistent (equation (4)). When profiling layers on semi-insulating substrates R , increases as the depletion edge approaches the substrate, which leads to an apparent increase in N . although this is often preceeded by a decrease due to part of the etch area penetrating through to the substrate as a result of non-uniform etching.

c x

m c 0

. _

I Depletion I I p r o f l l e I l \ \ \

J"" t;"" \ \

Electrochemical p r o f i l e

I m p u r i t y p r o f l l e

Figure 13. Distortion of a uniform profile by a large series resistance for depletion and electrochemical C- V profiling.

Errors will also be introduced by a high parallel conductance (G=R;') - which, if acting alone, serves to decrease N,,,, (equation (35)). Furthermore, in highly doped samples there is only a small voltage range over which G is acceptably small and this may be less than the voltage swing applied to measure C and AC/A V. While this source of error is not in principle unique to the electrolyte barrier, it is rarely encountered in depletion profiling because this technique is not usually applied to highly doped samples.

5.4. Summary

I n summary, the electrochemical profiler is not limited by diode breakdown and as a consequence of operation at fixed bias the accuracy in N is independent of N and depth and the depth resolution of the differential capacitance measurement is always limited by the Debye length rather than the instrument. Etching uniformity is the principal instrumental limit to the depth resolution, and area definition limits the absolute accuracy. Helmholtz capacitance and electrolyte resistance may limit operation of the instrument on highly doped material where C is large. and the choice of low operating frequencies to minimise R , effects results in increased sensitivity to deep

19

P Blood

states in the measurement of C and x d , although the low applied bias means that N is not seriously affected.

6. Photovoltage spectroscopy

An advantage of an electrolyte contact is that it is transparent to radiation at wavelengths below z 1.2 p m where there is negligible absorption by water. With the addition of a variable monochromatic light source the electrochemical cell becomes a powerful tool for the study of the photovoltaic behaviour of materials with E , 2 1 eV.

6.1. Basic principles

The band diagram of a transparent contact on n-type material under illumination with light with hv > E, is shown in figure 14. Photogenerated electrons and holes are separated by the electric field such that for n- and p- type material holes and electrons, respectively, are swept to the front contact. The sign of the photocurrent is therefore indicative of the semiconductor type in the vicinity of the contact, and this is manifest in the change in the rest potential which is observed with the broad band source used for etching (see figure 6).

electrode Transparenl

_Nv,

Figure 14. Band diagram of a transparent contact on an n-type semiconductor indicating the drift and diffusion components to the photocurrent.

For an incident photon flux F at wavelength A, the photocurrent density JP, produced in a semiconductor with diffusion length L , absorption coefficient a(A) and contact depletion width xd is made up of a drift component due to electron-hole pairs separated in the region 0 < S <.vd and a component due to the diffusion of minority carriers beyond s d to the depletion edge where they are then swept out by the field (see figure 14). These contributions combine to give (Stagg 1982)

for a ( i ) s d < 1 and with the thickness of undepleted material >4L; T is the transmission factor of the contact. The absorption coefficient a z lo4 cm" at photon energies above the absorption edge, and since x d z 1 p m t h e condition a(l).yd < 1 is satisfied for the initial part of the absorption edge at lower photon energies. Furthermore, since L z 1 pm then at the onset of absorption a ( i ) L < I and equation (45) can be written

Jph(2) = eFT(L f Xd)a(A) (46)

so JP&) is proportional to a(A) and the spectral response of the photocurrent defines the absorption edge, and hence the band gap, of the near-surface material.

It is often desirable to measure an open-circuit photovoltage rather than a current to avoid electrochemical etching or deposition at the interface with the sample. In this case the photogenerated carriers separated by the field build up charge on each side of the depletion region causing a reduction in the band bending which in turn causes a forward current to flow through the contact. In the steady state an open circuit voltage V,, is established which sets up a forward current which is equal and opposite to the photocurrent. For a barrier with ideality factor n, a series resistance R , and leakage R , the net current is (following Rhoderick 1978)

xexp -(V--ItOtRs) (47) e ( nkT

so that when I,,, = AJ,,, = 0

and if the photovoltage is small such that V, < kT/e then

which, with equation (46), shows that under small signal conditions and a L , a x d < 1, the photovoltage is proportional to both a and the photon flux F :

The open-circuit photovoltage is independent of R , but its magnitude is influenced by the leakage current of the diode as well as the barrier height (through lo), the diffusion length and depletion depth.

6.2. Applications of photovoltage spectroscopy

We have built a system for measuring photovoltage spectra in GaAs and AlGaAs in conjunction with electrochemical profiling using a light pipe and remote- controlled prism to introduce chopped monochromatic radiation through the window of the cell without removing it from the instrument. The photovoltage signal is detected between the back contacts and the Pt electrode using a

20

Electrochemical C-Vprofiling of Ill-V semiconductors

lock-in amplifier with an input impedance of 100 MR. The cell receptacle is screened to reduce pick-up and when very high sensitivity is required the electrodes are connected directly to a battery-powered high-impedance pre-amplifier within the screen.

The photovoltage spectra in figure 15, recorded for samples of GaAs and A10,,,Gao,8,As, show the shift of absorption edge with alloy composition due to difference in band gap. In direct gap materials a(hv) is proportional to ( ~ v - E , ) ” ~ (Pankove 1971) and in principle an - extrapolation of a2(hv) should locate E,. In practice these g plots are not usually linear, probably because of the effect 6 of electric field on the band gap (the Franz-Keldysh $ effect) and impurity tails in highly doped material. Klug g and Neuman (1976) have used a linear extrapolation and we have found that the wavelength of the half-height of the edge gives quite good agreement with luminescence data for AlGaAs doped at =lo’’ cm-3. Despite these reservations, these measurements provide a quick self- consistent method for checking alloy composition.

Wavelength lnm)

Figure 15. Surface photovoltage spectra from n-GaAs and n-AI,Ga, -,As. Three common methods of identifying the band edge are indicated: the ’break point’ gives x z 14.8%, a linear extrapolation gives x % 14.2% and the half-height position gives x z 15.5%.

This technique has been applied to the characterisation of GaAslAlGaAs heterostructures by Wakefield et a1 (1 979): by periodically interrupting the electrochemical profiling process, it is possible to record photovoltage spectra at various etch depths through the structure and hence obtain the local band gap and composition.

Figure 16 shows a selection of photovoltage spectra recorded at different depths while performing an etching profile of an AlGaAs/GaAs double heterostructure laser. The initial spectrum (1) indicates a p-type GaAs contact layer and subsequent etching reveals in sequence (2) the p- type AlGaAs cladding layer, (3) the n-type GaAs active region, (4) the active region and the lower-n-type AlGaAs cladding layer (the contact depletion region includes both

4 4 4 4 4

Figure 16. Photovoltage spectra recorded a t the locations indicated by interrupting an etch profile through a GaAs/AIGaAs DH laser structure. A positive signal corresponds to an n-type surface photovoltage.

the GaAs and AIGaAs) and finally (5) the n-type AlGaAs layer alone.

Stagg et a1 (1982) have used this procedure to construct composition profiles in conjunction with doping profiles for DH laser structures grown by molecular beam epitaxy. Figure 17(a) shows data for a structure where, due to surface accumulation of the Sn n-type dopant during growth, the p-n junction is displaced from the metallurgical junction which delineates the upper interface of the GaAs active region. Notice also the increase in the n-type doping level at the lower active region interface caused by the reduction in the growth rate when the A1 flux is turned off (the growth rate is proportional to the total flux of group- I11 elements). Similar experiments have shown that the junction is correctly located when the p-doping and n- doping levels are similar (figure 17(b)) or when Si is used to dope the n-type layers. The interpretation of these measurements is unambiguous because the determination of composition, type and doping level are made together on the same structure with a common depth scale.

The depth resolution in the vicinity of the active region is often degraded by crater roughness obscuring useful information. In our experience a slow chemical etch (e.g., 5H2S0, : H 2 0 : H 2 0 2 ) leaves a relatively smooth surface so we use this to remove most of the upper cladding layer then profile electrochemically across the active region with an expanded depth scale and reduced crater roughness.

Although we have concentrated attention on the photovoltage generated at the electrolyte-semiconductor contact - the surface photovoltage - photovoltages may also be set up within the sample wherever electron-hole pairs are generated and separated by band-bending

21

P Blood

Carrier concentrati k m - 7

AI content ( X )

01

1 0 ' ~ ~ P i n la1

r

Depth (pm1

Figure 17. Doping profiles and composition profiles for two DH laser structures ( a ) with and (b) without a displaced junction and active region (Stagg et a/ 1982).

regions. Figure 18 shows the band diagram and photovoltage spectrum of a single heterostructure of p- type GaAs and AlGaAs grown on an n+ GaAs substrate. The dominant feature of the spectrum is an edge at s 5 9 0 nm produced at the surface contact with the AlGaAs ( 2 5 2 % ) but there is also a signal of opposite sign which persists at longer wavelength and cuts off at 880 nm. This is generated at the buried GaAs p-n junction by photons of energy less than the band gap of the AlGaAs which are not absorbed in the upper layer of the structure. Since the measurement is made under open- circuit conditions it is only necessary for charge to be redistributed across each band-bending region. unlike a photocurrent experiment where current must flow through the sample and the external circuit. The observed photovoltage is simply the algebraic sum of the voltages generated throughout the sample at a given wavelength. It is possible that a photovoltage signal is also generated at i < 600 nm by the band bending at the heterobarrier and this will oppose the surface photovoltage signal, but since the light is attenuated in the material at these wavelengths the surface signal will always be dominant. We do not anticipate a strong photovoltage signal from the GaAs at this interface because the sense of the band bending is such that the minority carriers generated in the GaAs are

KLB 2 4 6

t

not swept across the barrier region, although there may be a small effect due to accumulation of holes at the valence- band spike which is of the same sign as the p-n junction signal. I t can be seen that there will be a negligibly small signal from narrow gap material in a double heterostructure even though attenuation of the excitation through the upper cladding layer is small. Spectrum ( 2 ) in figure 16, recorded in the upper cladding layer of the DH

laser. gives no indication of the GaAs active region in the structure. even though this material is photoexcited. Notice also that though the GaAs signal (1 E 880 nm) in figure 18 is of opposite sense to the surface signal from the p-AIGaAs. it cannot be interpreted simply as an 'n-GaAs' signal as if it were at the surface. The sign of the voltage indicates the sense of the band bending and the positive- going voltage is due to photogenerated carriers from both n and p sides of the junction.

The techniques described are applicable to materials with E , 3 1.2 eV, but in narrower gap materials, such as the quaternary alloys used in long-wavelength lasers, there is strong absorption in the aqueous electrolyte in the vicinity of the band edge. In this case photovoltage spectra can be obtained by illumination through the substrate, provided it is transparent (as it is for GaInAsP on InP), to generate a signal at the electrolyte contact.

0 I - I I 1

700 800 900

aJ m

f > +

a .c J Wavelength lnml

hc lh " "- - ""

P - 1 P- I "- E lec t ro l y te l AlGaAs , GaAs , GaAs

Figure 18. Photovoltage spectrum from a p-type AIGaAs/GaAs single heterostructure on an n-type GaAs substrate showing the signal from the buried GaAs p-n junction.

22

Electrochemical C-V profiling of Ill-V semiconductors

7. Thin multilayer structures t In this section we describe some applications of the electrochemical profiler to the assessment of multiple quantum-well (MQW) structures, with examples taken from recent work in our laboratory using samples grown by molecular beam epitaxy.

7.1. C-V profiling

Figure 19 is an electrochemical C-V profile through a single n-type AIGaAs-GaAs heterobarrier showing depletion of carriers in the AlGaAs and accumulation in the GaAs due to the form of the conduction-band profile

l D 94

1017 I I I 1 0 0 1 0.2 0.3

Depth (pm1

Figure 19. Electrochemical C-Vprofile through an n-type AIGaAs-GaAs heterobarrier.

across the interface illustrated in figure 20. Due to the averaging effect of the Debye tail the measured C-V profile ;(.v) does not correspond to the true free-carrier profile /?(S), and n(x) does not correspond to the impurity profile because of carrier diffusion in the region where the bands are bent. Since the band bending at the contact in an electrochemical profile is much greater than kT/e, this measurement should give the same results for i ( x ) as a depletion profile and this is confirmed in the simulations of Whiteaway (1983). A detailed analysis of a profile such as figure 19 requires solution of Poisson’s equation for the assumed doping profile in each layer and the assumed discontinuity AEc (e.g., Whiteaway 1983, Missous and Rhoderick 1985). However, Kroemer and Chien (198 1) have shown that the Debye averaging process conserves both the charge increment and its total moment throughout the profile so the electrostatic potential t,b across the barrier can be calculated using equation (3) with /?(.v) replaced by i ( x ) and the origin transferred to the interface so that equation (2) is satisfied. With @ thus

w l

Narrow gap V W Ide gap

Figure 20. Conduction-band (E,) diagram and plots of the actual, n ( x ) , and perceived, ? ( x ) , free-carrier profiles for GaAs ( a ) and a AlGaAs (b) heterobarrier. Vda and V,, are the diffusion potentials on each side of the barrier (after Whiteaway 1983).

determined, the discontinuity may be calculated by noting from figure 20 that

e$ = AEc + (Eca - EF) - (Ecb - EF).

Experiments to measure AEc by this method have used data for r i (x) obtained by depletion C-V profiling (e.g., Kroemer et a1 1980), and while in principle these data could also be taken from an electrochemical C-V profile provided the etch step ( A x , ) and the roughening (dx,) are sufficiently small, the method is very sensitive to the diode area. Unlike a depletion profile where h(x) and x are both obtained from a capacitance measurement and t,b is independent of the measurement of area, in an electrochemical profile where the depth scale is obtained predominantly from the dissolution current the integral in equation (3) depends upon i ( x ) obtained from equation ( 2 2 ) and s d . u z [ x l 2 obtained from equation (37), which combine to give I C / K A - ~ . Even if A can be determined to sufficient accuracy, we emphasise that the substitution of ;(.v) for /?(.v) is valid only for averaging by the Debye tail and will not be valid if the profile is smeared out by etch roughening, so although the discontinuity is evident in a profile such as figure 19 this is probably not the preferred source of data for i ( x ) to determine AEc,

Figure 21 shows a profile recorded using a 1 mm sealing ring on an MQW structure with 60 GaAs wells separated by A10,,,Gao,,3As barriers and doped p-type throughout with Be: the profile shows 60 spikes spaced 184 8, apart, which we associate with carrier accumulation in the wells, as in figure 19. The striking feature is that the wells are clearly resolved even at a depth of 1.2 pm where our usual roughness criterion suggests A Y , z 1000 A and it seems that the multilayer structure

23

P Blood

L

u 0 t - 6 0 - p e r ~ o d m KLB 266 - A X e ’ 3 5 R 10 ‘6 0 1 I I l l l

0 4 0.8 1.2

Depth (pm1

Figure 21. Electrochemical C-V profile through a 60-period GaAs/AIGaAs MOW structure doped with a constant Be flux. The etch step between data points was Ax, = 3 5 A.

itself is smoothing out the etch. It is also noteworthy that the peak spacing averaged over the first 10 and last 10 wells is 182 A and 186 A, respectively, indicating that the depth scale is accurately maintained throughout the profile (assuming reproducibility in the period of the structure). Figure 22 is part of a profile recorded on a similar sample at higher depth resolution. The profiles for a set of structures all with 60 GaAs wells and with the same period but doped throughout with different concentrations of Be are shown in figure 23 . The two samples with the lowest doping (< 10’’ cm-3) have flat profiles whereas the other samples show a damped fluctuating signal, due to the wells, but not clearly resolved because of the large etch depth increment during profiling.

To interpret the profiles in figure 23 we must consider the valence-band diagram of a multilayer GaAs/AlGaAs structure. shown in figure 24. When the layers are thick (say z 1 pm) there is accumulation and depletion of mobile holes in the GaAs and AIGaAs, respectively, on each side of the valence-band discontinuity AE,. Taking A E , z 0 . 2 5 A E g (Dawson et a/ 1985), we estimate A E , s O . 1 1 eV for our samples so the thinnest depletion region ( d ) is x 150 A wide in the most highly doped sample ( s 3 x 10’’ cm-3 in AIGaAs). (We have assumed the band bending in the barriers is zOSAE,.) In a multiple quantum-well structure with barriers only 175 8, wide the barriers are therefore depleted and all the mobile charge

resides in the wells as depicted in the lower part of the figure. In less highly doped samples d will be even greater and the band bending over h & , will be less. Moreover, since L , 5 5 5 A, the accumulation regions associated with each interface merge to give an approximately uniform accumulation of holes in the well. When the structure is depleted by an external contact the space-charge density is approximately uniform, being determined by the impurity distribution. For N , = 2 x IO” we can estimate from equation (4) that for V, + V,, ~ 0 . 4 V, as used for the profile, xd x 500 ii and the contact depletion extends over several wells.

We have shown in 9 5 that in principle the depth resolution of the C-V measurement is limited by the Debye length. but since the carriers are confined over a distance L , which in these structures is less than L D (> 80 A ) the resolution will be controlled by the relative magnitudes of the etch step Ax, and depletion modulation A.yd compared with L , and Lb.

From equation (20) we have estimated Axd for I/, + Vb = O S V and AV=O.28 V peak-to-peak as used in the instrument for the average doping levels indicated by each of the plots in figure 23. The values given on the figure show that only in the more highly doped samples is A.yd sufficiently small to resolve each period (Z200 A) of the structure, but since A x , E 100 A the carrier accumu- lation is not well resolved into continuous peaks. In figures

Depth Ipml

Figure 22. Part of an electrochemical C-Vprofile through a 60-period MOW structure similar to that in figure 2 1 recorded with a small etch step Axe z 10 A.

24

Electrochemical C-Vprofiling of Ill-V semiconductors

I I I

1 o'* E

Axd=1688(

Axd=306J(

10l6

Depth Ipml

Figure 23. Electrochemical C-Vprofiles of a set of similar st structures doped throughout at various concentrations with Be. The etch step was x, z 83 A and the depletion step, estimated from the averaged measured doping level, is shown on each plot.

i A lGaAs 1 GaAs A lGaAs

l !

is conserved in the Debye averaging of the profile at each interface (Kroemer and Chien 1981), the integrated charge under each peak in figure 22 should be equal to the dopant concentration per unit area per period. With a small correction for overlapping peaks the charge per peak is about 5.7 x 10" cm-*, and the charge per period, calculated from the observed AlGaAs doping level and period. and with allowance for the higher doping level in the GaAs due to the lower growth rate, is estimated to be 5.5 x I O " cm-2. These are in reasonable agreement: the true doping level in the GaAs may be even higher if there is some preferential incorporation of compensating centres in the AIGaAs. The depletion step could be reduced by reducing A V : for example, if A V=O.l V peak-to-peak then Axd z 50 A for the most highly doped sample in figure 23.

Although we have made a number of simplifying assumptions, the arguments presented here account for the general features of our profiles. Charge accumulation in quantum wells can be observed when the doping density is sufficiently high that Axd is less than the well spacing for the voltage step used in the measurement, and when the etch step Ax, is less than the well width. Our observations imply that the roughness of the etch crater dx, is much smaller in these multilayer structures than in homogeneous samples and we interpret the damping of the oscillations in the profile to be caused by an increase in dx, with increasing etch depth (e.g., in figure 23).

7.2. Photovoltage spectroscopy

Another aspect of the characterisation of MQW structures using the electrochemical cell is the observation of the absorption spectrum of the MQW using photovoltage (PV) spectroscopy. The spectrum in figure 25 for the least doped sample of figure 23 has two groups of two peaks corresponding to the excitonic transitions between electrons and light and heavy holes for the n = 1 and n = 2 confined particle states (Dingle 1975). With correction for the binding energy of the 2D exciton (x9 meV) and the

Figure 24. Valence-band diagram of an AIGaAsIGaAs multilayer structure where the layer thicknesses, L, and Lb in wells and barriers, respectively, are greater than and less than the depletion and accumulation distances d. ( a ) Thick layers: (b ) quantum well.

21 and 22 Ax, has been reduced to 35 A and 10 A, respect- ively, and the peaks then emerge as well defined features. Since the contact depletion depth is greater than the period of the structure and since the charge increment

Wavelength (nml

n = l

t

Figure 25. Surface photovoltage spectrum of a p-type MOW structure with 55 A wide GaAs wells (same as the low doped sample of figure 23).

25

P Blood

AlGaAs composition obtained from a surface PV spectrum. i t is possible to use these data to derive a value for the well width assuming independent wells: for this sample we obtain L , = 55 & 1.5 8, (using the same analysis as Dawson er a1 ( I 985)). We have assumed that there is no significant shift of the absorption peaks due to the electric field in the depletion region.

An important application of this technique is the characterisation of MQW laser structures. Adopting the same principle as 'band-gap profiling', it is possible to determine the composition of cladding and waveguide regions, and the wavelengths of the absorption peaks of the MQW active region as illustrated in figure 26 (Blood er a1 1985a). It is then possible to make direct comparison with the observed emission energies of the same structures processed into lasers (Woodbridge et a1 1984), without recourse to estimated well widths and theoretical calculations of the associated transition energies.

A B C

550 600 650 700 7 5 0 800

Wavelength (nm)

Figure 26. Photovoltage spectra recorded at various stages during electrochemical profiling of a MQW separate confinement heterostructure laser (Blood et a/ 1985a).

It is interesting to speculate on the origin of the photovoltage in these structures. If the photoexcited e-h pairs remain confined in their original wells then the redistribution of charge by the field can only occur within each well so the observed photovoltage is due to dipoles set up across individual wells. However, the electric field may enhance the emission rate of carriers from the well, probably by tunnelling, so that the dipole is set up across the complete depletion region. Because the substrate is not perfectly aligned the wells are not laterally continuous, and the etch itself is not smooth within a barrier width so it is also possible for charge to be extracted along the wells where they are penetrated by the electrolyte.

It is not possible to deduce an absolute value for the absorption coefficient from these experiments because, as equation (50) shows, the photovoltage depends upon wavelength-independent factors such as the depletion depth, barrier height (determines J,,) and the mechanism of carrier transport as discussed above. However, it is

possible to use the signal from a buried p-n junction, as shown in figure 18, to monitor the light transmitted through an MQW using the structure indicated in figure 27.

GoAs

Figure 27. Schematic diagram of a structure with a GaAs p-n junction behind a Maw sample where it acts as a detector for transmitted light. The associated band diagram is shown in the lower part of the diagram.

Following the derivation of equation (50), the photovoltage from the junction is (Blood 1985)

where TMQw(A), R(A) and F(A) are the transmission through the MQW, the junction spectral response and incident flux. respectively. The signal from this structure (figure 28) shows a doublet feature near A = 845 nm due to absorption in the MQW reducing the light intensity incident on the junction, and since F(A) and R(A) are slowly varying functions of A the spectrum below 850 nm follows qualitatively the transmission spectrum TMQw(A). A structure without the MQW gives a similar signal to that

Sample 157 100-perlod naw structure

. Structure 4 without Mak

- 0 v/---- I

P I $ 0

1 - I I

0 800 900

OI

- 0 0 r: a c wavelength lnm)

I / Gmplete structure

Figure 28. Photovoltage spectrum from the structure in figure 27. The surface photovoltage signal at 680 n m is due to the electrolyte barrier with the upper GaAlAs layer and the signal from the buried GaAs p-n junction is modulated by the transmission spectrum of the Maw. The spectrum of the same sample with the Maw structure, layers ( a ) t o ( b ) in figure 27, removed is also shown (see figure 18).

26

Electrochemical C-V profiling of Ill-V semiconductors

shown in figure 18, and this can be used as a reference giving the spectral form of F(A)R(A) so that if the junction response is linear with intensity the absolute transmitted fraction can be obtained from a pair of normalised plots as the ratio T(A)= Vl(A)/V2(A) as illustrated in figure 28. It has been shown that the spectra of TMq,(A) obtained in this way are in good agreement with the results of conventional transmission spectra from thinned samples (Blood 1985). This technique has been used to characterise MQW structures for studies of non-linear and bistable optical behaviour (Blood et a1 1985b, Miller et a1 1986).

7.3. Summary

The experiments described in this section show that the electrochemical profiler is a valuable tool in the characterisation of thin layer structures. When the etch and depletion steps are sufficiently small it is possible to resolve quantum-well features on a scale of Q 100 A and it does seem that crater roughening is significantly reduced when etching these samples permitting resolved profiles to be recorded over many periods of the structure. The capability of recording photovoltage spectra using the standard cell is especially significant for the characterisation of MQW structures because it is a rapid method of comparing well widths, and at the same time giving data on AlGaAs composition. The method permits the absorption edge in MQW lasers to be located directly and it can be extended to obtain the absorption coefficient using suitable structures.

Acknowledgments

The work on multiple quantum-well structures described in this paper was done in collaboration with a number of colleagues, particularly K Woodbridge and J T Bellchambers who, respectively, grew the samples and gave practical assistance with the measurements. The author also acknowledges useful discussions with P Dawson and G Duggan on optical absorption and confined particle transitions. As indicated in the text, some of the work on the performance of the profiler was done by J P Stagg while at Philips Research Laboratories and his contribution to this field is gratefully acknowledged. Thanks are also due to T Ambridge (BTRL) for helpful conversations, correspondence and communications concerning this article.

References

Ambridge T. Elliott C R and Faktor M M 1973 J . Appl.

Ambridge T and Faktor M M 1974 J. Appl. Electrochem. 4

- 1975a J. Appl. Electrochem. 5 319-28 - 1975b Gallium Arsenide and Related Compounds 1974

ed. J Bok (Inst. Phvs. ConJ Ser. 24) pp 320-30 Ambridge T. Stevenson J L and Redstall R M 1980

J. Electrochem. Soc. 127 222-8

Electrochem. 3 1 - 15

135-42

Amron I 1967 Electrochem. Technol. 5 94-8 Baxandall P J. Colliver D J and Fray A F 1971 J . Phys. E: Sci.

Bleaney B I and Bleaney B 1976 Electricity and Magnetism

Blood P 198 1 Gallium Arsenide and Related Compounds 1980

Instrum. 4 2 13-2 1

(Oxford: University Press) 3rd edn

ed. H W Thim (Inst. Phys. Conf: Ser. 56) pp 25 1-8 - 1985 J . Appl. PhJ’S. 58 2288-95 Blood P, Fletcher E D, Woodbridge K. Dawson P and Hulyer

P J 1985a Gallium Arsenide and Related Compounds 1984 ed. B de Cremoux (Inst. Phys. Conf: Ser. 74) pp 427-32

Blood P and Harris J J 1984J. Appl. Phw. 56 993-1007 Blood P, Miller A and Woodbridge K 1985b Toward

Semiconductor Integrated Optoelectronics (London: IEE) Technical Digest 1985129

Blood P and Orton J W 1978 Rep. Prog. Phys. 41 157-257 Dawson P. Duggan G. Ralph H I. Woodbridge K and ’t Hooft

G W 1985 Superlattices and Microstructures l 23 1-5 Dingle R 1975 Festkorperprobleme (Adcances in Solid State

Physics) vol. 15 ed. H J Queisser (Braunschweig: Pergamon-Vieweg) pp 2 1-48

Current Topics in Materials Science ed. E Kaldis (Amsterdam: North-Holland) vol. 6 pp 1-107

Faktor M M, Ambridge T, Elliott C R and Regnault J C 1980

Faktor M M and Stevenson J L 1978 J . Electrochem. Soc. 125

Goodman A M 1963 J . Appl. Phys. 34 329-38 Johnson W C and Panousis P T 197 1 I E E E Trans. Electron

Kennedy D P and O’Brien R R 1969 IBM J . Res. Dev. 13

Kimerling L C 1974 J . Appl. Phys. 45 1839-45 Klug H P and Neumann H 1976 Exp. Tech. Phys. 23 605-10 Kroemer H and Chien W Y 198 l Solid State Electron. 24

Kroemer H. Chien W Y, Harris J S and Edwall D P 1980 Appl.

Miller A, Steward G, Blood P and Woodbridge K 1986 Opt.

Miller G L 1972 IEEE Trans. Electron Devices ED-l9 1103-8 Missous M and Rhoderick E H 1985 Solid State Electron. 28

Pankove J I 197 1 Optical Processes in Semiconductors (New

Redstall R M, Regnault J C and Stephenson J L 1978

62 1-9

Devices ED-l8 965-73

212-4

655-60

Phys. Lett. 36 295-7

Acta 36 to be published

233-7

York: Dover)

Electrochem. Soc. Con$ Proc. 78-3 293 (see also Faktor et al 1980; figure 49)

Rhoderick E H 1978 Metal-Semiconductor Contacts (Oxford: University Press)

Schultz M 1974 Appl. Phj’s. 4 225-36 Sharpe C D and Lilley P 1980 J . Electrochem. Soc. 127

Sharpe C D, Lilley P, Elliott C R and Ambridge T 1979

Stagg J P 1982 J . Appl. Phys. 53 3680-5 (his analysis follows

1918-22

Electron. Lett. 15 622-4

from Hovel H J in Semiconductors and Semimetals ed. R K Willardson and A C Beer (New York: Academic) (1975) vol. 1 1 p 114)

J. Physique 43 suppl. 12 C5 377-82

Wiley) 2nd edn

1979 Appl. Ph.vs. Lett. 35 347-9

Stagg J P, Huyler P J, Foxon C T and Ashenford D 1982

Sze S M 198 1 Physics of Semiconductor Devices (New York:

Wakefield B, Stevenson J L, Redstall R M and Ambridge T

Whiteaway J E A 1983 I E E Proc. I30 pt I 165-70 Wiley J D and Miller G L 1975 IEEE Trans. Electron Devices

Wood C E C, Woodcock J and Harris J J 1979 Gallium ED-22 265-72

Arsenide and Related Compounds 1978 ed. C M Wolfe (Inst. Phq’s. ConJ Ser. 45) pp 28-37

Woodbridge K, Blood P, Fletcher E D and Hulyer P J 1984 Appl. Ph.w Lett. 45 16-8

27