Surface photovoltage and internal photoemission at the anodized InSb surface

SURFACE

SCIENCE 34 (1973) 337-367 8 North-Holland

SURFACE

PHOTOVOLTAGE

PHOTOEMISSION

Publishing Co.

AND INTERNAL

AT THE ANODIZED

InSb SURFACE

D. L. LILE Naval Electronics

Laboratory

Center, San Diego, California 9215.2, U.S.A.

Received 10 April 1972; revised manuscript

received 26 July 1972

Surface photovoltage measurements have been made as a function of wavelength and temperature on a number of variously doped samples of n- and p-type InSb in the carrier concentration range of 8.9 x 1013 to 1.O x 101a cm-a. The measurements were made using an MIS sandwich employing for the dielectric an anodically formed layer of Inz 03. Differential capacitance measurements have shown that, when cooled in the dark, the surface of the n-type material is near flat band whereas that of the p-type is depleted. Illumination with photons of energy in excess of N 1.5 eV leads to a shift of the surface potential to larger negative values presumably as a result of optical activation of electrons from fast interfacial surface states to slow states near the InSb surface. Internal photoemission measurements lend support to this model and suggest that, in the absence of any applied bias an internal field within the oxide causes the electrons excited from the semiconductor to move towards the metal. A theory for the surface photovoltage in the presence of a continuum of surface states is developed. It is concluded from theory, and supported by experiment, that surface trapping as well as recombination can exert a considerable influence on the photovohaic response.

1. Introduction The surface photovoltage, the change in surface potential accompanying the redistribution of optically excited electron hole pairs in the surface field of a semiconductor, was first treated theoretically by Brattain and Bardeenr). Although good agreement was obtained with measurements made on single crystal specimens of Ge their theoretical model was rather idealized in that it employed a highly specific discrete surface state distribution as well as a net trapped surface charge density which was invariant with illumination, These restrictions were subsequently relaxed by Garrett and Brattain2-Q) who extended the theory to include both the contribution of the space-charge region to the redistribution of the injected carriers as well as a continuous rather than discrete distribution of surface states. More recently an attempt has been made to extend the theory to the case of high injection levels59 6, and to more precisely define the trapping and recombination processes at the semiconductor surface’). Despite these theoretical refinements quantitative assessments of the contribution of surface states to the photovoltage are lacking. The reason for this is mainly 337

338

D.L.

due to the fact that the more rigorous

LILE

theoretical

treatments

result in com-

plicated expressions for the photovoltage which are difficult to compare with experiment and which involve many parameters the values of which are rarely known precisely. In particular, the parameters of surface states and hence their contribution to the measured photovoltage is often unknown. Despite this the surface photovoltage has been used successfully for the determination of recombination ratessjg) and also has found acceptance as a practical mechanism for the detection of infrared radiation; highly sensitive surface photovoltaic detectors having been fabricated from both Schottky barrierslo) and MIS 11) (metal-insulator-semiconductor) structures on a variety of semiconductors. This paper reports the results of spectral measurements of surface photovoltage made on InSb MIS diodes both as a function of carrier concentration and of temperature. Asymptotic approximations to a rigorous theoretical treatment are presented with particular emphasis being placed on the role played by surface states in the photovoltaic generation process. Explicit relationships are developed which allow the significance of surface states to be assessed in any particular instance. It is concluded that only in special cases will it be valid to neglect the effects of surface states in interpreting surface photovoltage measurements; in the present case they appear to dominate the response. Internal photoemission spectra for the anodic In,O,-InSb interface are presented which correlate with previously reported drift phenomena observed in the photovoltaic response of this system at photon energies in excess of - 1.5 eV. 2. Theory of the surface photovoltage The theory of the surface photovoltage has been treated to various levels of sophistication by a number of authors L 4-7p12$ls). The present treatment, which draws heavily on this previous work (particularly on ref. 4) is an attempt to simplify the final expressions to the point where meaningful comparisons with experiment can more readily be made. It is shown in the appendix that the surface photovoltage generated in the surface field of a semiconductor may be written, for the small signal case, in the form + 2 [,X,/CT (q, + pJ]+ sinh’ +v, - cub cash q,

A$,=-

x F(vs,ut,)A, x

aQ,s f C%kT (4 + Pb>li av s

s1

[sinh (vs + u,,) - sinh ub] + cash ub F (vs, ub) ‘+v2

-1

,

(1)

SURFACEPHOTOVOLTAGEAT

339

InSb SURFACES

where v, is the semiconductor surface potential in dimensionless units of kT/q, the positive signs applying for v, < 0. An * is the excess carrier density at the edge of the space charge region, n,, and pb are the electron and hole densities respectively beyond the space-charge region, ni is the intrinsic carrier density, z+, is the reduced bulk potential, Q,, is the trapped surface charge, F(v,, ub) is a function defined in the appendix and A, is a dimensionless parameter describing the statistics of charge rearrangement between the surface states during illumination. All parameters used in this treatment are listed and discussed more fully in the appendix. Garrett and Brattain4) have shown that for a continuous distribution of surface states N,,(E), where the energy E in units of kT is measured positive downwards on a conventional band diagram from a value at the surface coincident with the intrinsic Fermi level:

8QSS

q=-

s

qN,s(~1ds

(2)

4 cash’ [+ (E + us)] ’

and

c@,,(E) n d& dQ,s -ub ayp=e s 4 cosh2 [+ (E + us)] ’ where

(3)

+

sinhu,.

n = cash u,, tanh

(yP- 1) is the injected hole excess normalized to the bulk hole density and the integral is taken over all states lying between the conduction and valence bands edges. rVand rc (which in general will be functions of E) are parameters analogous to those introduced by Shockley and Readi4) to describe the bulk recombination process. They describe, respectively, the probability that an electron will be emitted by a trap into the valence band or captured by a trap from the conduction band. One would expect rv
(sr),

(4)

(sr) A,,

(5)

aQ,,/av,, --f - 4N,, and aQss/aYP+ 0,, where (l,,=eeubn

with

&=-us,

340

D. L. LILE

i.e., A,, = eeub cash ut, {tanh [ - U, + In (rJr,)*] z-e

+ tanh ui,}

(6a)

-“~ sinh [v, - In (rV/rJi] cash [us - In (ry/rC)*] ’

The value of rv/rc appearing in eq. (6) is appropriate to the trapping centers at the Fermi level. It can be seen from eqs. (4) and (5) that ,4,, as defined by eq. (27) in the appendix, is identical with that defined by eq. (6) above. The parameter A,, of eq. (1) determines, in part, the contribution of surface states to the photovoltage. Inspection of eq. (6) shows that for values of v, appropriate to strong accumulation the function eub& approaches asymptotically a value T e-lUbl, whereas in inversion it has a value _telubl, the upper sign referring to n-type material, the lower to p-type. For large positive values of surface potential the quasi Fermi level for electrons thus determines the trap occupancy and Q,, becomes more negative on illumination. At large negative surface potentials the hole Fermi level controls the surface state occupancy and @,,/13y, is positive. Going from accumulation to inversion the term eUb,10 changes sign at a value of v,=ln(r,/r,)9 and increases in magnitude by a factor of 2 sinhlu,l. For all values of surface potential outside the range 0< 1v,J< Iln(ry/r,)tl both terms in the numerator of eq. (1) will have the same sign and the surface state term will enhance the photovoltaic response. The transition between the two limiting values of eub,4,,, for large Iv,l, occurs exponentially in 12v,( in the depletion region over a range of surface potential centered on [ -z~,+ln(r,/~~)~]. Fig. 1

exp

(u,) 10

cash u,,

--0.5 I -14.0

-10.0

-6.0 REDUCED

-2.0 SURFACE

0

2.0

I

I 6.0

POTENTIAL

Fig. 1. Dependence of the surface state parameter Ao on the reduced surface potential vS for various values of the trapping parameter ratio rv/rc.The curves were calculated for a reduced bulk potential ub = 5.0.

SURFACEPHOTOVOLTAGEAT

341

InSb SURFACES

for three values of the ratio r,/r,. The parameter

shows this behavior

A,, and

hence the contribution of the surface state term in the numerator of eq. (1) clearly increases with increasing depletion. From eq. (6) it can be seen that only if r,,= r, is this contribution to the photovoltage zero at v,=O; in all other cases the traps become the dominant source of the photovoltage. From eq. (I), at flat band, the space-charge contribution goes to zero and from eqs. (1) and (6) for v,=O

A$, =

kT An” __ ni

4

rV - r, rc cub + rv eTub> .

(7)

Although Buimistrov et alis) have treated the surface state contribution to the photovoltage at flat band, it is worth emphasizing that the flat band signal can be either positive or negative, depending on the ratio rv/rc in eq. (7). This means that trapping away from flat band can either enhance or degrade the space-charge response with the result that displacement of the zero photovoltage point can be towards depletion rather than always toward accumulation as has been often implied by previous treatments. The direction of the shift depends simply on whether holes or electrons are more readily trapped by the surface states. Consider now the expression for the photovoltage given by eq. (1). For large values of surface potential 1~~1,the first terms in both the numerator and denominator of eq. (1) are dominant no matter how large is aQss/dvs. This can be understood from inspection of eqs. (25) and (26) in the appendix; both space-charge terms in eq. (1) increase rapidly with increasing magnitude of surface potential whereas from fig. 1 the surface state contribution in the Also the numerator rapidly saturates in accumulation and inversion. Fermi level at the surface passes outside the forbidden bandgap and thus by definition it is to be expected that aQ,,/av, is zero. In these regions eq. (1) takes the form 2 sinh’ zsiv

,+_!?A? 4

ni

smh (vS + ui,) - sinhu,

.

In accumulation layers i.e., where ub and vS have the same sign, an expansion of the hyperbolic functions reduces eq. (8) to

A$,

=

+

kT!!!?e-l”bl 4

=-

4

kT An*

~~.- ~ 4 nb

(9) for an n-type semiconductor.

342

Similarly

D. L. LILE

in the inversion A,),

=

-j-

regime

“,’ “*

ebbi

ni

kT An* ___ 4 Pb

(10) for n-type material.

The photovoltage generated in an extrinsic semiconductor in inversion is thus much larger than that generated in an accumulation layer. In the intermediate range of depletion the asymptotes of eq. (8) are not reached; furthermore, the surface state terms in eq. (1) are not generally negligible. Eq. (1) may be reduced however by a first order expansion of the hyperbolic functions to give in the depletion regime kTAn” A$, = ___

f K elYS1- cub &

aQssjaV, ’

K eiub’ - 8Qss/dv,

qni

(11)

where K = [cc,,kT (nb + pb)]* (,,h

eiUb’ Iv,lf)-l

,

and the positive sign, unless otherwise noted, refers throughout this treatment to n-type material. From eq. (6) and fig. 1 it can be seen that eUb& increases with increasing surface potential into depletion. Specifically, if in depletion

(12a) for

v,
0

3 for n-type

and

v, > In

3rc

EcokT

0

3

5 rc

for p-type,

+

(nb+ PI,) 2 IVSI

Wb)

explvsl

elsewhere, then the surface state term in the numerator neglected and kTAn* + K exp Iv,1 A$,~ K exphl - aQss/avs 4%

of eq. (11) may be

’

(13)

i.e., the photovoltage varies exponentially with surface potential. This equation will apply for all Iv,1 in depletion less than that at which

SURFACEPHOTOVOLTAGEAT

InSb

SURFACES

343

inequality (12a) holds. If (12a) is satisfied at vsw - ~~+ln(~“~~~~~ then, because A, is essentially constant beyond this point, eq. (13) will apply at all v,. By numerical substitution in eqs. (12a) and (12b) however, it is readily apparent that for other than extremely small surface trapping the surface state term in the numerator of eq. (11) can only be neglected if r, $rV on n-type material or r,
where ( V,l is the magnitude of the surface potential in volts. However, the inequality in eq. (14), (which requires the differential space-charge capacitance to be much greater than the capacitance associated with surface states) is unaffected by the rV/rCratio. For typical values of surface state densities the neglect of the surface state term in the denominator of eq. (13) would not seem warranted except for relatively impure samples at or above room temperature. The surface state term will usually dominate, in which case

If, in addition, the surface state term in the numerator is also dominant, then eq. (1) takes the form (17) and the photovoltage becomes independent of trap density with a dependence on surface potential governed by .4, i.e., the photovoltage increases exponentially in 12v,l to a value

The above developed arguments suggest that the rather complicated photovoltage expression of eq. (1) can be simplified to provide experimentally

344

D. L. LILE

verifiable relationships. In any particular case consideration of the inequalities (12) and (14) should suffice to show which terms, if any, in eq. (1) may be neglected. As an illustration of the above treatment fig. 2 shows a plot of photovoltage versus surface potential for material parameters appropriate to InSb with 2 x 1016 donor impurities/cm3 at 77°K. Surface state densities and trapping probability coefficients for these curves were intentionally chosen so as to illustrate the limiting forms of eq. (1). Curve (a) is for zero surface trapping where the first terms in both the numerator and denominator dominate eq. (1) and the depletion approximation of eq. (15) is applicable. Curve (b) is for the case of an infinite surface state density where the second terms of both numerator and denominator of eq. (1) dominate and eq. (17) applies. Curves (c) and (d) represent intermediate surface state densities. To calculate curve (c): aQ,,/av, was chosen sufficiently small that the space charge term dominates the denominator of eq. (1) i.e., that inequality (14) applies and r, was set equal to rc so that inequality (12a) does not hold. In curve (d) @,,/a~, was chosen sufficiently large so that the surface state term dominates the denominator of eq. (11) whereas rc was chosen much smaller than r, so that inequality (12) applies. From the curves in fig. 2 it can be seen that except for unrealistically small values of surface state density the contribution of surface states to the photovoltage cannot be ne-

I

I

I

I

I -40.0

I

-20.0

-30.0 REDUCED

SURFACE

-10.0 POTENTIAL

0.0

10.0

(I’,)

Fig. 2. Variation of the surface photovoltage with reduced surface potential for various values of surface state density on n-type InSb of carrier concentration 2 x lOI cm-s at 77 “K. Values of aQ,,/qh: (a) Zero, (b) -+ co, (c) 108 cm-2 and rv = rC, (d) 1012cm-2 and and rv % rc. Negative photovoltages are shown dotted.

SURFACEPHOTOVOLTAGEAT

glected.

Furthermore

345

InSb SURFACES

it can be seen that the effect of surface states can be

to either enhance or degrade the magnitude of the photovoltage. This is in agreement with the conclusions of Frank1 and Ulmer’) but in marked contradiction with those of a number of previous authors. The above treatment given in terms of a continuum of surface states is to be compared with the case of a discrete trap distribution as treated by Frank1 and Ulmer r). If iV,, (E), is not varying slowly, as assumed here, then the integrands in eqs. (2) and (3) will be dominated by their numerators rather than the denominators. In terms of the parameters employed by Frank1 and Ulmer and for a delta function distribution of N, states at an energy E= - w:,eqs. (2) and (3) become

dQ,S

ay,=-epub cash

c:)t]

ur,

+ tanh ubr$y

(18) and

dQ,s

- qN,

av,

4 cosh2 4 (us - w;) ’

(19)

From these equations (as well as the plotted curves in fig. 2 of ref. 7) it can be seen that ~Q,,/~v, will exhibit a relatively sharp peak as the Fermi level sweeps through the traps at u,= wi resulting in a corresponding maximum in ~Q,,/+J,. The contribution of the surface states to the photovoltage is therefore a maximum for u, = w: and is again determined by the inequalities (12) and (14) with v, set equal to (w; -ub). From eq. (18) it is apparent that 8QSS/8yP goes to zero at vS=u,,- w; + +ln(rJr,) rather than at v,= ln(r,/r,)* as for a continuous distribution. The consequence pointed out by Frank1 and UlmerT), is that only for w: -ln(r,/r,)-u, will the discrete state model allow a shift of the zero photovoltage point into depletion whereas, as can be seen from eq. (7) and fig. 2, with a continuum of donor states on n-type material or acceptors on p-type this is a likely occurrence. In addition for rv=r, the continuum model allows no shift of the zero photovoltage point whereas appreciable shifts occur in the discrete state model. In addition to their role as trapping centers, the surface states also control the rate of carrier recombination at the surface and hence determine An* through eq. (32) in the appendix. Frank1 and Ulmer7) have included this implicitly in their treatment for a discrete surface state distribution and Garrett and Brattain*) analysed the problem for a continuum of surface

346

D.L.LILE

states. The latter authors velocity is given by S* = cash ub

showed that in general

N,, (e) (ryrJ3 s cash [E + In (r,/r,)*]

the surface recombination

ds

+ cash [a, - In (rJr,)*]

’

(20)

which reduces to the expression given in eq. (16) of ref. 7 for a discrete level at E= -WI. If N,, is continuous rather than discrete eq. (20) has no simple solution and, lacking information on N,,(r,r,)*, cannot be evaluated. Qualitatively, however, S* will increase exponentially in v, to a peak value at v, N In (r”/r,)* - ub beyond which it falls again. The recombination velocity given above is an effective value defined by U/An* where CTis the per unit area rate of carrier transport into the spacecharge layer. For small values of surface recombination the effective rate of surface recombination given by S* equals the actual recombination rate at the surface proper. However, at large rates of recombination the transport of carriers through the surface space-charge layer may become the limiting mechanism. Garrett and Brattain4) have shown that for a depleted surface on n-type material equality of the effective and actual recombination velocities requires exp (h

- t-M)

3

which for bulk InSb at 77°K with nt, =2 x 1016 and 1v,I =2u, requires that S* be less than N 3.0 x lo9 cm/set. As will be seen later, this condition is apparently satisfied in the present case.

3. Device preparation and experimental procedure MIS devices were prepared from both single crystal bulk and polycrystalline thin film samples of InSb with net donor concentrations in the range 8.9 x 1013 to 1.0 x 10” cm- 3. A small number of p-type films intentionally doped with Cu were also studied. Film samples, 1.0 to 8 urn thick, deposited on glass substrates, were prepared by microzone crystallization of thermally evaporated In and Sbm). InSb layers prepared in this way are polycrystalline as a result of multiple twinning which occurs during the growth process. Net donor densities 225 x 1015 cme3 and electron Hall mobilities 5 1 x lo5 cm’/V-set are observed typically in these layers at 77°K. MIS diodes were fabricated by first overcoating the InSb with an insulating layer approximately 600 A in thickness formed by the anodic oxidation of the semiconductor in a 0.1 N aqueous solution of KOHi7). This process is believed to lead to the formation of an insulating layer of In,O, as a result

SURFACEPHOTOVOLTAGEAT

InSb

SURFACES

341

of the solubility of the oxides of Sb in the KOH electrolyte. The anodization was followed by the evaporation onto the oxide of a semitransparent layer of some suitable conductor such as Ni or Al. The devices were completed by making ohmic contact to both the semitransparent counter-electrode and the InSb with In solder. Photovoltages generated between the surface and bulk of the InSb are capacitively coupled to the metal electrode and appear as a change in potential between the metal and semiconductor contacts. An array of eight l-mm diameter thin film devices prepared in this way is shown in fig. 3. The Al contact land shown was necessary to ALUMINUM LAND ANOOIC

(OVER

CONTACT NICKEL)

OXIDE

SE~ITRANSP~RENT

NICKEL (a)

ACTIVE

ALUMINUM

DEVICE

SEMICONDUCTOR

(b,’ Fig. 3.

(a) Eight-element

thin film MIS diode array; (b) cross section of single device on XX’.

bridge the step which occurs at the edge of the semiconductor film. Measurements were made on the devices in an evacuated optical dewar, the diodes being mounted behind a NaCl window on a shielded Cu cold finger which could be temperature controlled from * 20 “K to above 300 “K. At all temperratures the devices were exposed to a 180” background at N 80 “K save for an approximately 30” FOV to the ambient. A Nernst glower, 525 Hz mechanical chopper and prism monochromator were used to supply amplitude modulated monochromatic radiation of wavelength from 1 to 10 pm at an intensity 5 100 l.tW/cm’ at the sample

348

D. L. LILE

surface. A calibrated thermocouple served as a reference and a phase locked amplifier with an input impedance of 10 MR was used to measure the photovoltages generated between the semiconductor and metal contacts of the MIS devices. At the 525 Hz frequency of measurement used in the present study this impedance was sufficiently large compared with that of the MIS diodes that essentially all the surface photovoltage generated in the InSb appeared between the metal and semiconductor contacts. DC photoemission currents through the insulator were measured using a Keithley electrometer. Illumination for the measurements was obtained from a mercury arc lamp. High frequency (1 MHz) differential capacitance versus bias (typically 40-80 Hz) measurements were made on the diodes using a Boonton C/Y meter driving a Tektronix 7704 oscilloscope. Hall measurements, using standard dc techniques, were used to determine carrier concentrations and mobilities in the semiconductor samples. 4. Experimental results and discussion In agreement with the results of Phelan and Dimmockrs) on similarly anodized n-type InSb photodiodes, we have observed that when initially cooled to -80°K in the dark the photoresponse of these devices is quite small. If the cooled devices are expased to radiation of energy 2 1.5 eV however the response to radiation of all wavelength (of energy greater than the fundamental gap) can be made to increase to a peak. Further short wavelength irradiation (hvk 1.5 eV) then leads to a slight decay. This behavior, which has been reported previouslyl*-20) is shown in fig. 4 for a typical n-type device at - 80°K. Differential capacitance-bias measurements on these devices at 1 MHz have given results also in agreement with previous observations 2oT21). These measurements indicate that, when cooled to -80°K in the dark the surface of the n-type InSb is near flat band with a surface potential of less than a few kT/q. Subsequent exposure to photons of energy 2 1.5 eV causes the surface potential to increase to a value of - -20 kT/q at the peak in photosensitivity shown in fig. 4. This suggests that, aside from any compensation that may exist, the surface states at the InSb-In,O, interface are possibly donor-like. Apart from the purest bulk sample, the n-type InSb used in these experiments is degenerate at 77°K with the Fermi level within the conduction band. Any acceptor states located between the conduction and valence band edges at the surface would thus be below the Fermi level and hence would be expected to be full and lead, in the absence of any initial charge exchange with the oxide, to depletion of the InSb surface. That this is not observed is taken to indicate the net donor nature of the traps. A possible consequence of this would be

SURFACE

PHOTOVOLTAGE

AT

InSb

349

SURFACES

that, on more pure n-type material or at higher temperatures where the Fermi level in the bulk lies well outside the conduction band, the surface states would acquire a positive charge with a consequent accumulation of the InSb surface. Such an accumulation layer on pure n-type material has, in fact, been reported by Axt and RogerszO). Fig. 5 shows the total electronic charge trapped in surface states (indeterminate to the extent of an additive constant) together with the effective 4.0

I

I

1

I

I

I

I

0

20

40

60

I

I

I

1

I

I

I 100

I 120

I 140

160

80 TIME

I -4

IIIIIIIII -8

-12

-16

I 180

IMIN) -20

I -24

I -26

vs (DIMENSIONLESS)

Fig. 4. Variation of surface photovoltage with time for a typical sample of InSb at 80°K. The photovoltage was measured at 1.65 Mm while the device was subjected to a background radiation of energy 2 1.5 eV. Time is measured from the instant at which the higher energy radiation is applied and the vs scale shows the corresponding increase of surface potential with time derived as described in the main text.

surface state distribution given by the derivative of Q,, with respect to v, as determined from the C/V measurements for a typical n-type InSb-In,O, interface following drifting to its photosensitivity peak at N 80 “K. Both the shape of this distribution and the quiescent (zero bias) surface potential are in good agreement with the results reported by Lile and Andersonas) on the polycrystalline InSb-Al,O, interface and are within a factor of two of the --results of Davis2s) on the (111) surface of single crystal InSb. Prior to exposure to short wavelength radiation after cooling, the dif-

350

D. L. LILE

ferential capacitance minimum could not be reached and thus the state distribution could not be determined. The general shape of the C/V curve, however, was similar to that observed following drifting which suggests that only the surface potential and not the fast state distribution is changed

lo-: J

VALENCE BAND

10’0

1

I -28.0 REDUCED

I

I -20.0 SURFACE

I

I

I

-12.0 POTENTIAL

I -4.0 b,)

Fig. 5. Dependence on surface potential of charge trapped in surface states (shown dashed) and its derivative lQss/qhe for InSb following drifting to its peak photo-voltaic response at - 80°K.

by illumination. A conclusion similar to this was also reached by Pagniaa4) from the observed drift of the field effect conductance of InSb with illumination. Attempts to vary the surface parameters by etching and mechanical polishing of the InSb films prior to device preparation were unsuccessful. This suggests that the surface characteristics of the films, in the present

InSb

SURFACEPHOTOVOLTAGEAT

351

SURFACES

case, are primarily determined by the electrochemical process of anodization. The drift of the surface of InSb on exposure to high energy radiation has been observed previously by a number of authors using a variety of experimental techniquesis-21*24-ss) and h as, in general, been interpreted in terms of light activated trapping of electrons in an oxide layer near the semiconductor surface, the source of the electrons being states located within

K

0

1.0 PHOTON

Fig. 6.

Internal

2.0 ENERGY

3.0 Wl

photoemissive yield versus photon energy for an anodized diode in the absence of applied bias.

InSb MIS

a mean free path of the surface. However with the surface state densities shown in fig. 5 the majority of these electrons would seem to originate from interfacial surface states. Fig. 5 shows that a change from flat band to a surface potential of - 20.0 kT/q requires in the present case the removal of at least 2 x 10” electrons/cm’ from fast states and of only 1.3 x 1O’l electrons/cm’ from the space charge region. This also implies an oxide trap density of at least 2 x 101’ cmm2 3 in close agreement with N IO” oxide trap/cm’ deduced

352

D. L. LILE

by Hung and Yonzl) on similarly anodized InSb. Although in the present case the oxide was intentionally formed by anodization, evidence existsa4) to suggest that a similar effect occurs on the “free” surface of InSb as a result of charge transfer into states in the thermal oxide which exists in general on the surface of this material. Fig. 6 shows dc photocurrent measurements made on MIS diodes at 300°K and 80°K. The photoemissive yield curves (which include no correction for optical attenuation in the metal and oxide) were measured without an applied bias and correspond to electron flow from the semiconductor, through the In,O, into the metal. These spectra were stable at 300°K; at 80 “K they showed a slight increase with time for energies in excess of approximately 2.5 eV. This effect may account for part of the superlinearity of Y shown in fig. 6. Fig. 6 shows that the yield is large and that it has a cubic energy dependence over most of the measured range. Theories of photoelectric emission from semiconductors into vacuum27) predict, near threshold, a power law dependence for the yield of the form Y = C,(hv

- E,)“,

(21)

where the exponent n and the threshold E,, depend on the excitation and escape mechanism involved. Experimental vacuum yield spectra in general obey eq. (21) with typical values of n- 3.0. Fischer2*) has shown that no unambiguous choice can be made between the various possible carrier generation mechanisms in the semiconductor based only on the shape of the spectral yield curve. It seems probable that the cubic part of a yield spectrum results from direct transitions into vacuum of electrons excited from the top of the semiconductor valence band. Internal photoemission measurements involving electron excitation into a solid have been reported for the thermal SiOZ-Si systemag,sO). In analogy with photoemission into vacuum, the yield has a power law dependence on photon energy with it typically in the range of 2.0 to 3.0. In the absence of a detailed knowledge of the density of states function for the conduction band of the insulator, the interpretation of such data is difficult. In practice the usual procedure is to fit the experimental yield to a power law which is then extrapolated to give a value for the threshold energy E,,. Fig. 6 shows that in the present case, at 300”K, the photo-emissive yield has a cubic dependence on photon energy with E, - 1.3 eV. Following previously reported studies of the Si-SiO, system31), this threshold can be related to the energy separation between the top of the valence band in InSb and the bottom of the conduction band in the In,O,. Interpretation of the data obtained at 80°K is, however, more difficult. At low yields the

SURFACEPHOTOVOLTAGEAT

exponent

is cubic and the threshold

InSb

SURFACES

353

energy is N 1.63 eV; at higher yields the

cubic dependence has a larger slope (close to that at 300 OK) with a threshold of -2.45 eV. It is clear that at 80°K the absolute threshold for injection32) into the In,O, occurs at N 1.6 eV. This value is very close to the 1.5 eV threshold observed for the onset of light-induced drifting of the semiconductor surface potential. It supports the contention that the conversion of the InSb surface towards p-type with illumination is associated with light activated injection of electrons into the conduction band of the oxide. The finite current flow through the oxide at zero bias shown in fig. 6 also indicates that either the mean free path of electrons in the In,O, is greater than the oxide thickness (i.e., 2 600 8) or that at zero applied bias there exists within the oxide a built-in field directed such that electrons excited into the oxide drift towards the metal electrode. Similar measurements made on p-type samples show that, in agreement with previous observations 1*~25,33), the cooled p-type material is depleted and exhibits a large photoresponse. Depletion of the surface of the p-type material prior to illumination is, of course, further evidence for the donorlike nature of the surface traps which in this case would all be above the Fermi level at flat band. Short wavelength irradiation (hvz 1.5 eV) leads in this case, to a flattening of the bands with a corresponding reduction in the magnitude of the photovoltage, the probable result of electron injection from the interfacial surface states into the oxide. Disagreement still exists in the literature over the quiescent condition of the InSb surface. (For a discussion of this see, for example, refs. 20 and 21.) From the above it would seem that an important parameter that is often omitted is the previous illumination history for the surface under study. It has been reported that the effect of illumination, on both p- and n-type material is to drive the surface more p-type l8 -21’ 21-26). The above described model involving optically activated electron transfer from fast interfacial donor surface states, via the conduction band of the oxide into electron traps in the oxide appears to explain this effect as well as that of occasionally reported accumulation layers on relatively pure n-type material201 33) and depletion or inversion layers observed on p-type samples prior to illumination rs,25,33 )* Fig. 7 shows the photovoltaic spectral response of a typical InSb MIS diode following illumination-induced drifting to its peak response at 80 “K. The approximately linear increase of detectivity with increasing wavelength shown in fig. 7 for 254.0 urn is a characteristic of an ideal quantum detector whose output is proportional to the rate of arrival of incident photons. The rapid fall in photovoltage at the fundamental edge at -5.5um is consistent with the generally accepted value for the fundamental bandgap of

354

D.

L.LILE

InSb at -77°K. Peak responsivities in excess of 4 x 103 V/W have been observed in these devices of IOF2 cm2 area. When sufficiently large to be measured the noise of these diodes was found to vary inversely with frequency. In general, however, the noise signal was below the limit of sensitivity of the equipment (N 20 nV) and thus detectivity values shown in fig. 7 are based on system limited noise. Early in this section it was reasoned that the states at the InSb surface appear to be donor-like so that r,>> r,. This suggests that the surface state PHOTON

1.0

0.8

0.6

ENERGY

0.4

kV) 0.3

a

WAVELENGTH,

Fig. 7.

Spectral

detectivity

P

of high purity [Nd(net) = 8.9 InSb MIS diode at N 80’K.

X

1013cm-3l

single Ct’YStal

term in the numerator of eq. fll) may be neglected for all but very large negative values of v,. Moreover, with the measured values of surface state densities shown in fig. 5 the inequality in eq. (14) will only be satisfied for very large values of ptb.Specifically, at 80°K the surface state term dominates the denominator of eq. (13) for all carrier concentrations n,s lo’* cme3. This implies the assumption that the surface states measured by the C/Y technique are the same as those which contribute to the photoeffect. Since the capacitance and photovoltage were measured at similar frequencies this would not seem to be too unrealistic an assumption. Aside from determining the

SJRFACEPHOTOVOLTAGEAT

quiescent

surface

potential

InSb SURFACES

the slow oxide traps are probably

355

not involved

in these measurements. With these constraints eq. (1) reduces to eq. (16) for surface potential values appropriate to depletion. If the not unreasonable assumption is made that the optically-activated transfer of electrons between the fast surface states and the slow oxide traps occurs at a constant rate (i.e., aQ_/at a constant) then the time scale in fig. 4 may be replotted as surface potential using the experimentally determined dependence of trapped surface charge on surface potential shown in fig. 5. For this we take the peak response to occur at v, = - 20.0 as measured and arbitrarily assume that at t =O, v, -2.0. This scale change is shown in fig. 4. Consequently it is possible to calculate the relative dependence of A$, on surface potential from fig. 4 and to calculate the variation of the surface excess of injected carriers An * with v, through eq. (16) and the surface state results shown in fig. 5. The dependence of S* on v, can be calculated by the use of eq. (34) in the appendix and with the additional assumption that S* 9 l,/z,. For realistic estimates of the specimens measured at 80°K a peak photovoltage of 10 V at v, = -20.0 for an illumination intensity of 1 W cmm2 at 1.65 urn is considered as typical. Moreover, the overall quantum efficiency of the diodes 6 is assumed to be 25x11). Fig. 8 shows the behavior of S* determined by means of the above described procedure, assumptions and eq. (16). In order to fit the observed photovoltage data with the theory presented here requires a surface recombination velocity which increases nearly exponentially with increasing surface potential into depletion. No definitive experimental data exists as yet, to this author’s knowledge, on the surface recombination rate on InSb. Hilsum et al.34) arrived at a value of IO6 cm/set from photoelectromagnetic and photoconductive measurements made on bulk material at room temperature and Davis 23) has tentatively proposed a value of 6 x lo4 cm/set deduced from a spectral photoconductivity measurement on the (iii) surface of this material at 79°K. These results, as well as qualitative arguments that have been made concerning plasma generation in thin films of InSb35) suggest that the surface recombination velocity is large. Its absolute magnitude however, even allowing for preparative variables, is unknown, and so is its dependence on surface potential. Although experimental evidence is lacking, theory does lend some support to the results shown in fig. 8. If we assume N,, to be a constant independent of a, eq. (20) may be evaluated using the integral relationship developed by Garrett and Brattaind) to give

(22)

356

D. L. LILE

where the assumption has been made that (TJ,) is also independent of E and that [us-In(r,/r,) *] -2 > as before. Although eq. (22) is based on a uniform distribution of surface states it is of interest that, in general, a first order solution of eq. (20) results in an exponential dependence of S* on v, for values of [us-- ln(r,/r,)*] not close to zerols). Thus the ShockleyRead recombination model14) does lend some credence to the exponential dependence of S* on v, shown in fig. 8. Fig. 9 shows how the peak drifted photovoltaic response well away from the fundamental edge varies with net donor density for a number of bulk

103

I

-10.0

I

I -14.0

I

I REDUCED

Fig. 8.

I

I

I

-22.0

-18.0 SURFACE

I -26.0

I

I -30.0

POTENTIAL

Surface potential dependence of the effective surface recombination velocity on InSb required for a theoretical fit of the experimentally measured surface photovoltage at - 80°K.

SURFACE

PHOTOVOLTAGE

AT

InSb

357

SURFACES

and thin film samples at - 80°K. It can be seen that below a value of q, - 1 x 1Ol6 cmB3 there is very little dependence of A+, on doping level whereas above this density the response varies approximately inversely with nb. This can be seen to be in poor agreement with the expected l/J&, behavior predicted by eq. (16). The data shown in fig. 9 however, are conconsidered to be inconclusive. All the samples were measured at the same illumination intensity which, providing the surface recombination velocity is

0 0

0

l

00

l

10-l1 10'3

0

FILM

l

BULK

I

10'4

DEVICES DEVICES

I

I

10'5

10'6

ELECTRON

I

I

10'7 DENSITY

1018

I

I

10'9

(cm -3

Fig. 9. R~ponsivity at 1.65 pm versus net donor density for a number of thin film and bulk MIS diodes at * 80°K. Device area is approximately 0.01 cm2 and all samples were measured at approximately the same illumination intensity.

358

D. L. LILE

large so that eq. (34) applies, suggests a similarly constant carrier injection level independent of the widely varying mobilities and probable bulk lifetimes of these samples. Similarly, variations in absorption coefficient in the high surface recombination regime should be relatively unimportant. However, variations between samples in such parameters as 6, S* and aQ,,/aV, could be significant, Moreover, any inadequacy of the theory in not accounting for carrier degeneracy will increase with increasing carrier density. Further difficulties are attendant on the temperature dependence of the

-

lo-3

HEATED

I 140

I

II 120

I 100

II

11 80

1 60

11 40

20

TEMPERATURE(K)

Fig. 10. Temperature dependence of surface photovoltage on a high purity single crystal sample of InSb prior (AB) and following (DE) exposure to high energy (2 1.5 eV) radiation. Measurement was made at a wavelength of 1.65 pm.

SURFACE

PHOTOVOLTAGE

AT

InSb

SURFACES

359

photovoltage. Fig. 10 shows this for the purest bulk sample studied. On initially cooling, the photovoltage rises rapidly with decreasing temperature as shown by curve AB. Exposure to short wavelength radiation at 80°K leads to the increase in response discussed previously. After this radiation is removed the temperature dependence follows curve DE. The variation with temperature shown in fig. 10 is quite reproducible in that the photovoltage can be cycled continuously back and forth along the line DE by cycling the temperature. Furthermore the photovoltage could be returned to its original value (curve AB) by warming the diode to room temperature and then retooling. Apart from the magnitude of the signal, behavior essentially identical to this was observed on all the samples studied, both bulk and thin film. Inspection of eqs. (16) and (22) indicates that unless @,,/8V, or S*e’” varies markedly with temperature the photovoltage should be relatively insensitive to changes in T. The similar slopes of the curves in fig. 10 before and after drifting also suggests that whatever determines the decrease in photovoltage with increasing temperature is relatively independent of quiescent surface potential. It is of interest that similar behavior to that shown in fig. 10 was also observed by Buimistrov et a1.12) on high purity samples of p-type silicon. In that case, however, the photovoltage was supposedly observed at flat band so that preferential surface trapping was the only source of the measured signal. As in the present treatment, the theoretical expression for the photovoltage contained explicitly only weak temperature dependence. To explain the observed large photovoltage changes it was necessary to consider a multilevel distribution of discrete trapping levels whose net effective trapping cross-section decreases with decreasing temperature. It is felt that in the present case so little is known about the trapping parameters r, and rc, other than their probable proportionality to Tt 2,14336) that attempts to fit the data by a judicious choice of surface parameters would be unrealistic. However, two salient features of the results seem worthy of comment. It can be seen from fig. 5 that the surface state density increases for both larger and smaller values of surface potential around the drifted quiescent value of - - 20.0 kT/q. Thus any change in surface potential with temperature would lead to an increase in 8Qss/~vs and thus a reduction in photovoltage through its inverse dependence on 8Q,,/aV, in eq. (16). Moreover, any change in aQ,,/aV, (which up to this point has been tacitly assumed temperature independent) with temperature will lead to a rapid change in photovoltage through both its contribution to surface recombination [eq. (22)] and its explicit presence in eq. (16). It is of interest that Yamagishi3’) has indeed observed a pronounced flattening of the bands with increasing temperature at the (111) Si surface and Luby et al.ss) and Schwartz et a1.3g) using MOS techniques have measured pronounced

360

D. L. LILE

increases in surface state density on going from N 77°K to room temperature for both the SiO,-Si and SiO,-InAs interfaces. Appendix SYMBOLS 6 60 k T R Izb,

Pb

Pn9

Pup

An,

AP

An* Y”, Yp

N,,(E) (= a&/q&,) K

s* I;“* 20

1 1,2 LD

X

d

All/s ‘4, no *,, rv V

-

Relative, absolute dielectric constant (F/cm) Boltzmann’s constant (J/OK) Absolute temperature (OK) Magnitude of the electronic charge (C) Planck’s constant (J-set) Electron, hoIe bulk densities (cme3) Electron, hole mobilities (cm’/V-set) Excess carrier densities (cmm3) Excess electron (and hole) concentration at edge of space-charge region (cmv3) - Ratio of electron, hole densities to the thermal equilibrium values - Fermi level at thermal equilibrium - Electron, hole quasi-Fermi levels - Surface, bulk potentials (see fig. 11) - Surface potential -Per unit area electronic charge in surface states, space charge (C/cm2) - Energy in dimensionless units of kT measured from intrinsic Fermi level at surface - Surface

density at E (cmT2) parameter (C/cm2) - Effective surface recombination velocity (cm/set) - Bulk carrier lifetime (set) - Ambipolar diffusion coefficient (cm2/sec) - Ambipolar diffusion length (cm) State

- Space-charge

- Surface diffusion lengths (cm) Debye length (cm) - Distance from surface into semiconductor (cm) - Semiconductor thickness (cm) - Surface photovoltage (V), i.e., change in surface potential with illumination - Surface state parameters [see eqs. (3), (5) and (6)] - Trapping probability coefficients (cm3/sec) - Optical frequency of radiation (set-‘) -

SURFACEPHOTOVOLTAGEAT

- Actual, - Overall

4 43 4 &J

THEBASIC PHOTOVOLTAGE

InSb

361

SURFACES

effective illumination diode, semiconductor

intensities quantum

(W/cm’) efficiencies

EQUATION

Fig. 11 shows the conventional band diagram appropriate to the surface region of a semiconductor in the presence of injected carrier excesses An(x) and Ap(x). This figure has been drawn on the assumption that the semiconductor is n-type and the surface is depleted. The expressions to be developed here however, are quite general and applicable to both p- and n-type material for positive and negative values of surface potential. To simplify the analysis the usual assumptions are made of complete impurity ionization and non-degeneracy of the carrier species. Although the latter is not valid for InSb at electron densities in excess of approximately 5 x 101’ cme3 at 80°K the resulting error should not be large for values of surface potential appropriate to surface depletion. This, however, may not be the case if an attempt is made to apply this theory to very narrow gap materials or to those which contain a very high concentration of electrically active impurities. In drawing the band diagram of fig. 11, it has been implicitly assumed that the quasi equilibrium approximation introduced by Garrett and Brattains) is valid. This assumption, which results in an appreciable simplification of the mathematics, states that, in the presence of carrierinjection the electrons and holes remain in thermal equilibrium with their

CONDUCTION

VALENCE

BAND

BAND

t--i+ Fig. 11. Energy level diagram appropriate to the surface region of a semiconductor in the presence of an equilibrium excess of injected electron hole pairs.

362

D.L.

LILE

respective bands and thus that 4, and 4, may be considered as constant throughout the space charge region. With this assumption the normalized carrier excesses n(x)

+ An (x)

Yn (x) =

=exp&(A-db), n (4

and yp (x) = P(X) + AP (x) P (x)

= exp $

(40 - 4,))

are independent of position within the space charge region. Combined the fact that electrical neutrality requires An = Ap in the bulk, gives

with

Yp - 1 ___ = exp (2~~). Y” - 1 Using this relationship it is readily showns) equation that the space charge per unit area

Q,,= _+[w&- (nts + PJ’

from a solution

F2 (vs, ut,) + 4 (Y, - I)

of Poisson’s

eeub sinh’ +v, cash 1.4~

t 1 ’

(234

where the F function

~

F(vs,ub)= ,/2 and the positive

cash (v, + I+,) cash ub

1, C=b) 3

- v, tanh ur, - 1

sign applies for v, < 0, i.e.

Q,,= k [%kTh

+ Pd+F(%

ub,

I’,>,

(23~)

where F(v,, ub, y,,) equals the terms within the square brackets in eq. (23a). Because illumination creates electrons and holes in equal numbers the total charge per unit area in the semiconductor surface, QT (= Q,, + Q,,), can be assumed invariant with illumination; i.e. dQ,=$dy,+gdv,=O. P

s

At low levels of carrier injection dy, -+ Ap (x)/p (x) and the small signal photovoltage, with the formalism introduced by Frank1 and Ulmer’), is given by A$, = kT Av 4

SURFACE

PHOTOVOLTAG~

AT

I&b

363

SURFACES

Now &T= (Q,, f Q,,) where Q,, is the per unit area net charge in surface traps. kT aQ,,iay, + a&,,iay, (24) :, A& = - --; (yP - 1) d&s,/% + ~Qsslavs yp+l ’

1

and

+ ~kc&T cnb + Pb)]’ sinhb’s+ ub) _ aQ,o --= cash tit, atf, F (% ub, YP)

u

tanh

b

~, 1

+ 2&Y - 1) emubsinh $v, cash +Y, cash at,

Gw

where the positive signs again appIy for negative v,. If, in addition, the dimensionless parameter A, defined by

is introduced into eq. (24), then kT A& Ipp-)z= - -4 (Yp - 1) x

2 [q,kT(n, ' [.x&T

+ p,)]’

e-*b sink’ j+, -

cOSh

i&

(nb + J$)]+ [sinh (Vs+ ti,,) - sinh u,,] +

1 cw

F (V,, ub) ii0&&,jaV, Cdl

Ub

F

(I’,,

u,)&#,,~Vs

.

&, defined by eq. (27), is considered further in eq. (4) through eq. f6) in the main text. THE EXCESSCARRIER DENSITY yp,the normalized carrier excess, is determined in the static case by a solution of the time independent diffusion equation, i.e., (in one dimension} d2An

D* Gfp*Ean=---

aAn

An 5b

&,aZ, hv

exp (-

Rx),

(29)

where I)* and I”* are the ambipolar diffusivity and mobility respectively. In writing eq. (29) the implicit assumptions have been made that AB and Ap are equal, i.e., that quasi neutrality exists throughout the region of interest, that bulk recombination is linear in An and that absorption proceeds exponentially into the sample, i.e., primarily that internal reflections are absent within the material. If we neglect the influence of the surface fieId on the optical absorption coefhcient and assume a homogeneous sampfe, this requires that a& I where d is the thickness of the sample in the x direction.

364

D. L. LILE

TO avoid the difficult problem of solving eq. (29) in the high field region near the surface the usual assumption is made that the extent of the space charge region, characterized by the Debye length L,, is small compared with both the absorption length for light and the ambipolar diffusion length I, for excess carriers, i.e., L, 4 ct- ’

and

A,, .

(30)

This assumption, which amounts to neglecting generation and bulk recombination within the space charge region, together with the condition that the rate of surface recombination and the electric field in the surface region are not too large, is sufficient to validate the quasi-equilibrium approximation made earlier, namely, that carrier flow normal to the surface within the space charge layer is negligible. As has been discussed by Frankl40) the above assumption may be quite restrictive except at very low levels of carrier injection. Nevertheless Johnsons) and others41) have had acceptable success in fitting the quasi equilibrium theory to experimental data at very large levels of carrier injection. Furthermore it is unlikely that inequality (30) will be satisfied by many large gap semiconductors. These materials often have small values of carrier mobility and low carrier concentrations which both act to invalidate the above inequality. Subject to the inequality in (30), eq. (29) can be solved for the quasi field free region of the semiconductor, L,
An 4

and X=LD

An - ~ A, X=(d-LD) ’

where I,, 2 are the surface diffusion lengths D*/ST and D *IS; respectively at the surfaces x = 0 and x = d. ST and S: are the associated effective recombination velocities. The solution for the carrier excess at the edge of the space charge region is then An* = where A* = 2~ and

A* -

~,a~,% hv(c&; - 1) ’

(31)

InSb SURFACES

SURFACEPHOTOVOLTAGEAT

It can be seen from eq. (3 1) that An * is a non-trivial

function

365

of the material

parameters. Considerable simplification is possible if the sample is sufficiently thick in the x direction (i.e., d%&) so that recombination at the unilluminated surface can be neglected. Although this is most certainly true for typical bulk sample geometries its validity for thin films is questionable. Using the measured value of 2.0 urn for & in the present InSb filmsas), An * was evaluated using eq. (31). With representative values for the remaining parameters it was found that An * changed by less than 20% for values of d going from i, to infinity. For this reason the simplifying assumption is made that d$>,, in which case eq. (31) reduces to GcdA,z,

An* =

ST

hv (a& + 1) (A, + STZJ ’

(32)

where 6 is the overall quantum efficiency and I is the illumination intensity incident on the MIS diode. These parameters are related to 6, and I, by 61=&Z, and serve the purpose of relating An * to the experimentally measurable incident radiation. 6 includes implicitly 6, as well as any additional energy loss mechanisms such as result from reflection and absorption of the incident radiation in the metal and dielectric layersas). From eq. (32) for ~2, $1 and cc, $ pP

An* N

6z

and An* N-

1 +

qzb

~ hi 1IkT,up 61 hvS*

for

for

S*+O

(33)

S*+co.

Thus for large rates of surface recombination the carrier excess and hence the surface photovoltage becomes independent of carrier mobility and bulk lifetime. At lower values of S* an increasing mobility would be expected to result in a decreasing photovoltage through an increased loss of carriers from the surface by diffusion into the bulk. Acknowledgements It is a pleasure to acknowledge the continuing interest and assistance of my colleague H. H. Wieder during the course of this investigation; in addition thanks are due A. R. Clawson and D. A. Collins for supplying the InSb films used in the work.

366

1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

D. L. LILE

W. H. Brattain and J. Bardeen, Bell System Tech. J. 32 (1953) 1. C. G. B. Garrett and W. H. Brattain, Phys. Rev. 99 (1955) 376. W. H. Brattain and C. G. B. Garrett, Bell System Tech. J. 35 (1956) 1019. C. G. B. Garrett and W. H. Brattain, Bell System Tech. J. 35 (1956) 1041. E. 0. Johnson, Phys. Rev. 111 (1958) 153. M. Bujatti, Proc. IEEE 53 (1965) 395. D. R. Frank1 and E. A. Ulmer, Surface Sci. 6 (1966) 115. A. Quilliet and P. Gosar, J. Phys. Radium 21 (1960) 575. A. M. Goodman, J. Appl. Phys. 32 (1961) 2550. E. M. Logothetis, H. Holloway, A. J. Varga and E. Wilkes, Appl. Phys. Letters 19 (1971) 318. 11) R. J. Phelan Jr. and J. 0. Dimmock, Appl. Phys. Letters 10 (1967) 55. 12) V. M. Buimistrov, A. P. Garbon and V. G. Litovchenko, Surface Sci. 3 (1965) 445. 13) A. Many, Y. Goldstein and N. B. Grover, Semiconductor Surfaces (North-Holland, Amsterdam, 1965). 14) W. Shockley and W. T. Read, Jr., Phys. Rev. 87 (1952) 835. 15) J. Shappir and A. Many, Surface Sci. 14 (1969) 169. 16) For a review of this method of film preparation see: A. R. Billings, J. Vacuum Sci. Technol. 6 (1969) 757. 17) This process, which has been reported by a number of authors [see for example, T. Sakurai, T. Suzuki and Y. Noguchi, Japan. J. Appl. Phys. 7 (1968) 14911 was found (R. F. Potter, private communication) to result in the growth of approximately 30 A of oxideforeachvolt of biasappliedduringanodizationinambientfluorescentillumination. 18) R. J. Phelan, Jr. and J. 0. Dimmock, Appl. Phys. Letters 11 (1967) 359. 19) W. E. Krag, R. J. Phelan, Jr. and J. 0. Dimmock, J. Appl. Phys. 40 (1969) 3661. 20) C. J. Axt and C. G. Rogers, J. Appl. Phys. 41 (1970) 3423. 21) R. Y. Hung and E. T. Yon, J. Appl. Phys. 41 (1970) 2185. 22) D. L. Lile and J. C. Anderson, Brit. J. Appl. Phys. 2 (1969) 839. 23) J. L. Davis, Surface Sci. 2 (1964) 33. 24) H. Pagnia, Surface Sci. 10 (1968) 239. 25) R. K. Mueller and R. L. Jacobson, J. Appl. Phys. 35 (1964) 1524. 26) R. Glosser and B. 0. Seraphin, Z. Naturforsch. 24 (1969) 1320. 27) E. 0. Kane, Phys. Rev. 127 (1962) 131. 28) T. E. Fischer, Surface Sci. 13 (1969) 30. 29) R. Williams, Phys. Rev. A 140 (1965) 569. 30) R. J. Powell, J. Appl. Phys. 40 (1969) 5093. 31) B. E. Deal, E. H. Snow and C. A. Mead, J. Phys. Chem. Solids 27 (1966) 1873. 32) The optical bandgap of indium oxide has been reported as 3.75 eV [R. L. Weiher and R. P. Ley, J. Appl. Phys. 37 (1966) 2991, hence for energies in excess of this, photoconduction in the oxide may be significant. In addition, optical activation of electrons from surface states could extend the photoemissive threshold to lower energies than would be necessary for direct transitions from the valence band. This could account for the photoemissive “tail” evident in fig. 6 at 80°K. 33) L. L. Chang and W. E. Howard, Appl. Phys. Letters 7 (1965) 210. 34) C. Hilsum, D. J. Oliver and G. Rickayzen, J. Electron. 1 (1955) 134. 35) D. L. Lile, Solid State Electron. 14 (1971) 855. 36) D. T. Stevenson and R. J. Keyes, Physica 20 (1954) 1041. 37) H. Yamagishi, J. Phys. Sot. Japan 25 (1968) 766. 38) S. Luby, R. N. Lovjagin, N. Doshdikova, L. N. Alexandrov and J. Cervenak, Solid State Electron. 13 (1970) 1097. 39) R. J. Schwartz, R. C. Dockerty and H. W. Thompson, Jr., Solid State Electron. 14 (1971) 115.

SURFACEPHOTOVOLTAGEAT

InSb

SURFACES

361

40) D. R. Frankl, Surface Sci. 3 (1965) 101. 41) A. Waxman, Solid State Electron. 9 (1966) 303. 42) D. L. Lile and H. H. Wieder, Proc. Intern. Conf. on Thin Films, held in Venice in May 1972 and to be published in Thin Solid Films.