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Electronic properties of clean cleaved {110} GaAs surfaces
SURFACE
SCIENCE 26 (1971) 587-604 8 North-Holland
ELECTRONIC
P~OPERT~S
Publishing Co.
OF CLEAN
CLEAVED
(11Oj GaAs SURFACES *
J. H. DINAN**,
L. K. GALBRAITH
and T. E. FISCHER
Beeton Center, Yale University, New Haven, Connecticut 06520, U.S.A
Received 8 December
1970; revised manuscript
received 17 February 1971
Photoelectric emission, contact potentials and surface photovoltages have been measured on clean, cleaved {llO) surfaces of n-and p-type GaAs between 77°K and 350°K. Roomtemperature work-function values depend on bulk doping and range from 4.70eY to 5.53 eV. Ionization energy is in agreement with values reported by Gobeli and Allen. P-type samples show no band bending, no surface photovoltage and small temperaturedependence of the work function. N-type samples show large band bending (0.8 eV at room temperature in the dark) that depends strongly on illumination and temperature. Surface photovoltage is due to interband transitions in the bulk. Results are interpreted in terms of a band of surface acceptors with a density of at least 2 x 1013cm-2 eV-1 at a lower band-edge which lies 0.85 eV below the conduction band edge.
1. Introduction This paper presents results of an investigation of electronic properties of clean cleaved { 1101 surfaces of GaAs. Measurements performed include photoelectric emission, contact potentials by the Kelvin method, and their variation with temperature between 370°K and 77°K as well as with illumination (surface photovoItage). Crystals with bulk doping levels ranging from 3.6 x 10” cmW3 p-type to 2.7 x lOI7 cmT3 n-type were used. The aim of the investigation was an experimental determination of those quantities needed to completely specify an energy-level diagram for the region near the surface (fig. 1). The approach was similar to that used for siliconl) by Allen and Gobeli who measured work functions 4 and photoelectric yield spectra for crystals with a wide range of bulk dopings. They equated ionization energy { with measured photoelectric threshold energy and calculated surface potential from (I&-E,), = 5 - 4. Band bending Vis given by (EF - _E,), - (_!&-I?& where bulk potential is calculated from bulk doping. From these, the charge density in surface states and, finally, information on the spectrum of surface * Supported by Night Vision Laboratory, Fort Belvoir, Va., under Contract No. DAAK 02-68-C-0232 and National Science Foundation Institutional Grant No. Gu-1658. ** Present address: Night Vision Laboratory, Fort Belvoir, Virginia 22060, U.S.A. 587
588
J. H. DINAN,
L. K. GALBRAITH
AND
T. E. FISCHER
states are obtained. Our method of determining (_!$ - I&), and t differs from that of Allen and Gobeli. Energy distributions are used in preference to yield spectra2). This method has the advantage of being free from assumptions about the optical excitation process and the significance of the threshold. Electronic properties of GaAs surfaces have been studied before. From photoelectric energy-distribution measurements on broken surfaces on n-type material, Hanemans) deduced a value of (E,-E,),=0.3 eV, which implied a band bending of about 1 eV. Gobeli and Allen4) measured contact-potentials and photoelectric yields for cleaved surfaces of two n-type crystals of nearly identical doping. They found a band bending of 0.6 eV and predicted Fermi-level clamping by a surface-state density of at least 10” cm-‘. Van
Ga As
Vacuum
Fig. 1. Energy-level diagram for the region near the (1 lo} surface on n-type GaAs. EF is the Fermi level, E, the conduction band edge, Es the lower edge of the band of surface acceptors, U,,, the asymptotic potential energy of electrons in vacuum, V the amount of band bending, D the depth of the space-charge layer, x the electron affinity, 4 the work function and r the ionization energy.
Laar and Scheer5) extended these measurements to a wider range of dopings. They observed no significant variation in spectral character or threshold and found that for non-degenerate samples A4 =A (J&&. These results are inconsistent with clamping and they estimate a surface-state density of 5 2 x x 1O’l cme2. Field-electron emission measurements by Hughes and Whites) on n-type material indicate band bending of 0.6 eV and a density of at least 2.8 x 1013 acceptors/cm2 on the { 11 l} surface. Arsen’eva-Geil, Wang and KaskT>s) and, more recently, Wojasg) have observed changes in photoelectric yield and shifts of I-V characteristics caused by additional longer-wavelength illumination that could not by itself cause photoemission. These measurements were interpreted as evidence for downward band bending on p-type material and upward band bending on n-type material.
ELECTRONIC
PROPERTIES
2. Experimental
OF (1 io}
GaAs
SURFACES
589
apparatus and procedure
All photoemission measurements and absolute work function measurements were performed in an ion-pumped stainless-steel chamber containing a photoemission retarding-potential analyzer, a cleaver and anvil, a Kelvin probe for contact-potential measurements, a cesium-ion gunlo), and a sample holder that could be rotated to face any of these elements. The CaAs samples were cut from slices obtained from the Monsanto Company. Each sample was a bar with cross section 3 mm x 8 mm and length 25 mm with a (110) direction along the length of the bar. Samples were chemically etched and mounted between sapphire slabs which provided electrical but not thermal isolation from a copper clamp. In some instances ohmic contacts were made by diffusion of indium. The copper clamp insured adequate heat transfer between sample and stainless-steel tubes through which liquid nitrogen was circulated for low-temperature measurements, A thermocouple attached to the clamp near the sample indicated a base temperature of 11Ort 10°K about 40 min after circulation had begun. A tungsten single-crystal ribbon was mounted on the rotatable holder and used to calibrate the energy analyzer and Kelvin probe.
Fig. 2.
Energy analyzer for photoemission
measurements.
Work functions were measured by vibrating a 1 mm diameter molybdenum rod first in front of the cleaved surface and then in front of the tungsten ribbon whose work function could be established to within &0.03 eV by photoelectric yield measurements. Contact potentials could be measured with an accuracy of 0.005 V. The energy analyzer (fig. 2) consists of three independent electrodes: a Co-Netic cylinder, a hemispherical collector, and a cage formed by a CoNetic back plate and a hemispherical grid. Energy sorting is done in the region between grid and collector by applying a ramp voltage to the sample and cage. This closely approximates the ideal spherical-capacitor retardingfield configuration. It was originally intended to bias the cage until the cavity defined by it and the sample was field free. However, stray light reaching the
590
J. H.DINAN,
L. K.GALBRAITH
AND T.E.
FISCHER
cage caused spurious current to the collector and necessitated an alternate mode of operation. Maintaining the cage at a constant positive potential of about three volts with respect to the sample isolated electrons emitted by the cage from those emitted by the sample. Negligible degradation of resolution occurred as a result of this modification. Magnetic fields in the analyzer were reduced to below 10 mG by enclosing the elements in the Co-Netic cylinder. All electrodes were electroplated with gold to reduce contact-potential differences. Energy distributions obtained by ac and dc electronic differentiating techniques were found to be identical; the dc technique was used for all measurements reported here. Energy resolution is limited mainly by inhomogeneity of the work function of the collector and by the bandwidth of the light and was determined from the energy distributions of the tungsten ribbon. Pressure in the vacuum chamber during cleavage and measurement was less than 5 x lo-” torr. A detailed investigation of changes in contact potential caused by illumination or by cooling was performed in a separate apparatus. The ion-pumped stainless-steel system had a base pressure of lo-” torr. A vibrating probe consisting of a 2 mm diameter quartz rod with a semi-transparent gold electrode evaporated onto one end could detect 0.2 mV changes in contact potential. Sample temperature could be measured with an accuracy of + 2 “K. No provision for absolute calibration of work functions was available in this system. 3. Experimental
results
In this section, results are presented of measurements taken on the four GaAs single crystals whose bulk doping levels are listed in table 1. The ex.perimental procedure followed for each crystal was to expose a fresh surface by cleaving, to record yield and energy-distribution curves for the sample and for the tungsten ribbon, and finally to measure contact potentials between sample and ribbon with the Kelvin probe. 3.1. PHOTOELECTRIC EMISSION Photoelectric yield spectra were similar to those reported by Gobeli and Allend). A set of energy-distribution curves all taken at room temperature at hv = 6.20 eV is shown in fig. 3. The high-energy edge of a distribution from the tungsten ribbon at the same photon energy is also shown. The latter is a resolution-broadened replica of the Fermi-Dirac distribution. The retarding voltage at which this curve is at half-maximum represents the energy E=E,+hv.
(1)
5.37 & 0.05 5.53 f 0.02
4.70 f 0.1 4.78 ItO. 0.11 -0.06
I .41 1.33
(eV)
(EF-&)b
Bulk potential
4
0.08 rtr 0.03 -0.08 rt 0.03
0.61 Ifi 0.07 0.55 j, 0.10
(eV)
(EF-&IS
Surface potential
5
0 0
0.80 i 0.07 0.78 It 0.08
Band bending
6
5.45 rt 0.07 5.45 zt 0.07
5.38 i 0.10 5.38 + 0.10
.-
Ionization energy
7
without illumination
4.03 & 0.07 4.03 & 0.07
3.95 fO.10 3.95 hO.10
_____
Electron aflinity
a
Values for carrier concentration are those supplied by Monsanto and were not remeasured. The large uncertainties given for n-type crystals represent real variations of the quantities across a surface of the sample. Band binding V and electron affinity x are calculated using the value of 1.43 eV for the band gap given in ref. 12.
C A
2.7 x 1017n 1.7 x lOian 1.0 x 1017p 3.6 x 10lg p
Work function
Carrier concentration and type (cm-s)
Sample
_-.
3
2
E B
TABLE 1
of cleaved {110) surfaces of GaAs at room temperature
1
Electronic properties
ti 8
F z
;
c 6
8
8
% 6 3 d z
Fr!
J. H.DINAN,
592
L. K.GALBRAITH
AND T. E. FISCHER
Even if the work function of the collector changes because of changing vacuum conditions, valid comparison of semiconductor energy-distribution curves is possible if the retarding-voltage scale is calibrated each time by registering
the position
of the Fermi level in accordance
with eq. (1).
The energy-distributions from the metal can also be used to estimate the energy resolution AE,,, of the apparatus. In principle, the high-energy edge of such a distribution rises from 10% to 90% of maximum within about 4kT(lOO meV at room temperature). In reality, this width is 4kT+ AE,,,. For our apparatus, the resolution was determined to be 0.1 eV while measurements were being made on samples B and E, 0.15 eV for sample A, and 0.25 eV for sample
C.
E-E,-
hv
Fig. 3. Energy distribution curves from the (110) surface of GaAs and from tungsten (only the high-energy edge is shown for W). Samples A, B, C and E are identified in table 1. Photon energy was 6.20 eV. The marks below the base line indicate the location of E, for each sample as determined from fig. 7. The limits of the variation of E, over the surface of B and E are shown. L is the low-energy edge of each curve.
Notice that the shape and the width of the energy distributions vary from one sample to the other. The distributions for samples A and C have a relatively well-defined high-energy end. Distribution C is wider than distribution A by the difference in experimental energy resolution. Despite the better experimental resolution, the distributions for the two n-type samples (B and E) are wider than distribution A and have extended high-energy tails. Notice also that the curves are displaced with respect to each other and with respect to the metal curve, and that the displacement from the metal curve is least for the degenerate p-type. An immediate conclusion is that the position of the bands at the surface depends upon bulk doping and therefore that complete clamping of the Fermi level does not occur.
ELECTRONICPROPERTIESOF
593
{110)GaAs SURFACES
3.2. EFFECTS OF ADDITIONAL ILLUMINATION ON PHOTOEMISSION Additional longer-wavelength illumination provided by either a tungstenfilament lamp or by a He-Ne laser (1 mW) had no effect on photoemission from p-type samples. For n-type samples, we observed: (1) an increase in emitted current by as much as 20x, (2) a shift of the energy-distribution curves toward lower energies, and (3) a narrowing of the distributions. Wojasg) has observed (1) and (2) and has interpreted (2) as a reduction in band bending. The lower barrier for escape of photoelectrons gives rise to (1). If the samples were not homogeneously doped, one could expect variations in band bending parallel to the surface. Such a variation would result in the unusually broad distributions mentioned in 3.1. Reduction of this component of band bending by additional illumination would give rise to (3). Variation of band bending parallel to the surface would cause similar variations in the work function, provided that the electron affinity is a well-defined material constant. 3.3. WORK FUNCTION MEASUREMENTS Values for the work function of the four samples measured at room temperature in the dark are listed in table 1. The work function of sample A was found to vary by only 0.005 eV across its surface. The uncertainty of 0.02 eV given in table 1 is the limit of accuracy as discussed in section 2. Uncertainties given for the other samples represent real variations across the surfaces and are attributed
to inhomogeneities
in doping.
3.4. EFFECTS OF ILLUMINATIONON WORK FUNCTION Illumination
had no effect on the work functions
of p-type
crystals
but
caused a decrease in the average work function as well as in the variation over the surfaces of n-type crystals. Typical changes in work function at room temperature and at 77°K are shown in fig. 4 for sample B as a function of intensity of illumination from a He-Ne laser. If x and 5 are not affected by illumination, then changes in 4 are due to changes in band bending and this effect is known as the surface photovoltage effect. The data in fig. 4 can be described by an equation of the form
Ag$=AJI=-.
Z is the light intensity,
“~71n(~)~
C(n), I0 and 12are empirical
+ 1).
parameters
giving best fit
594 to
J.H.DINAN,
L.K.GALBRAITH
AND
T.E.FISCHER
the curves. For the curves in fig. 4, values are n = 0.83 at room temperature,
&/C(A) = 1 x 1o-4 I,,, I&(A)
= 3.55 x lo-’
I,,,
IZ= 1.4at 77°K.
Imaxis the maximum available light intensity, of the order of 10” photons persecond.
0.1 I-
i
I
-6
I
-7 log,,,
I
-6
-5
,
-4
i
-3
,
-2
,
,
-1
0
Light intensity ~arbitrary)
Eig. 4. Surface photovoltage
of the (110) surface of n-type GaAs, ND-NA = 1.7 x lOle cm-a, at 77°K (curve 1) and at 294°K (curve 2). Source of illumination was a 1 mW He-Ne laser (hv = 1.96 eV). Curves are calculated from A# = V* In(CZ/Zo + 1)with parameters V* = 0.00965 eV and lo/C = 3.55 x IO-7 for T= 77”K, and V* = 0.021 eV and Jo/C = lo-* for T= 294’K.
Surface photovoltage could be due to light absorption in the bulk within a diffusion length of the space-charge layer or to absorption by carriers in surface statesll). The latter phenomenon can occur at hv < EG. Measurements have been made of surface photovoltage on sample B caused by illumination 5
5
C(~)/l,(78’10 T-----
4ci
-3-
E?
-2
1.40
I 1.42
I 1.44
I 1.46
I 1.46
I 1.50
I 1.52
I 1.54
I 1.56
hu (eV) Fig. 5.
Spectral dependence of surface photovoltage of the {I 10) surface of n-type GaAs; = 1.7 x 10x6cm-3 at 77°K and at 294°K. Values for C/IO are determined as in section 3.4. Also shown are values of the optical absorption coefficient a after Sturgelaf. ND-NA
ELECTRONICPROPERTIESOF
of various
photon
energies.
{llO} GaAs SURFACES
It was found that eq. (2) correctly
595
describes
the
results for all hv > E,. In fig. 5, surface photovoltages at photon energies near EG are shown for sample B at two temperatures. Also shown are absorption coefficients for GaAs taken from Sturge12). For hv
A (3.6xlO"pj
50
100 150 200 250 300 350 400
T (“K) Fig. 6. Temperature dependence of the work function of {110) surfaces of GaAs crystals whose bulk doping-levels are given. For sample E, $ incresaes to $1 when the sample is cooled rapidly in the dark. If the sample is illuminated while cold, 4 decreases to $2 in < 0.2 set, then decreases to &u after an additional 20 sec. Arrows show the direction of the only changes observed.
Relative temperature-dependence was measured in the more sensitive apparatus used to measure illumination-dependence. For p-type crystals, the measured temperature-dependence of C#Jcan be accounted for by the temperature-dependence of the value of < and of the location of EF in the gap in the bulk. For n-type crystals, the behavior was considerably more complicated as illustrated for sample E in fig. 6. Rapid
596
J. H.DINAN,
L. K.GALBRAJTH
AND T.E.
FISCHER
cooling (in 2 min) resulted in an increase in 4 by about 30 meV, as shown by the dashed line. When the sample was kept at low temperature, 4 drifted very slowly (50 meV/hr) toward lower values. Illumination of the sample surface with the He-Ne laser then caused 4 to drop rapidly (r-O.2 set) to the value 42 and then more slowly (r-20 set) to a value &, which was 0.15 eV below +2. Switching off the light caused the work function to return to 4Z in about 10 min, from where it drifted to higher values at less than 50 meV/hr. Such drifts may have been caused by contamination. The transition between 42 and dill was repeatable. No transition from $Z to 4i was observed. This phenomenon is very similar to that reported by Klein13) for heavily doped p-type GaAs covered with Cs-0 layers and also to that reported for cesiated annealed surfaces14) of n-type GaAs.
4. interpretation
of results
In this section, values for the quantities which characterize level diagram of fig. 1 are obtained according to the method ref. 2 with certain improvements described below. 4.1. SURFACEPOTENTIALANDBAND
the energypresented in
BENDING
If band bending occurs at a surface, care must be taken in determining surface potentials from energy distribution curves. Unequivocal interpretation of curves for n-type crystals is possible because electrons photo-excited at the surface lie higher in energy than those excited deeper in the bulk. In order to determine the surface potential from the curves shown in fig. 3, it is necessary to locate the position of the valence band edge E,, with respect to each of the distributions. It is not known a priori whether the high-energy edges of these curves are the result of interband transitions which may be direct or indirect or of transitions out of surface states. According to available band structure information, direct interband transitions from E, in GaAs occur for photon energies near 4.4 eV, which is below threshold for clean surfaces. However, energy distributions at this photon energy can be recorded if fractional monolayers of cesium are deposited onto the surface. Highenergy edges of curves taken from sample C at hv=4.43 eV and at 6.20 eV are shown in fig. 7 on a scale which would superimpose identical initial states. The use of curves taken from sample C guarantees that deformation due to band bending either normal to or parallel to the surface will be minimal. The fact that the edge of the 4.43 eV curve is abrupt and well defined and lies higher in energy than the edge of the 6.20 eV curve implies that direct interband transitions predominate in GaAs. The exact location of E, on the abscissa of fig. 7 is determined by taking into account the energy resolution
ELECTRONICPROPERTIESOF
obtained
previously.
{llO}
GaAs
597
SURFACES
at + AE,,, below the high-energy
It is located
cutoff of
the 4.43 eV curve. It is reasonable to assume that the energy separation between E, and the initial state for transitions at 6.20 eV is not distorted by the application of cesium to the crystal surface. Then, if the 6.20 eV curves for clean and cesiated surfaces are normalized to the respective yields and superimposed in such a way that the high-energy edges coincide, the location of E, with respect to the energy distribution for the clean surface has been determined. This procedure was followed for each curve in fig. 3.
-cesioted . ..clean
-1.5
-I
E-E,
-0.5
0
- hu
Fig. 7. Energy-distribution curves at hv = 4.43 eV and at 6.20 eV for clean and cesiated (110) surfaces of GaAs doped with NA = 1.7 x 1017 cm-3 (sample C). Dotted line is the distribution from the clean surface. Solid lines are high-energy portions of distributions from a cesiated surface. The high-energy edge of the distribution at hv = 4.43 eV represents direct transitions from the valence band edge and determines the origin of the abscissa. The x 10 curve for the cesiated surface and the curve for the clean surface are normalized to their respective yields.
Values for (Er-E,), determined from fig. 3 must be corrected by an amount equal to the surface photovoltage due to the light used for photoemission. At hv=6.20 eV, approximately 10” photons cm-’ set-’ were absorbed by the crystals. This is about lo4 times smaller than I,,,,, in fig. 4. Since surface photovoltage is independent of hv for hv > E, the value of A V at 10m4 in fig. 4 (0.02 eV at room temperature) is a good measure of the correction for sample B. Extrapolation of data obtained at hv= 1.96 eV to hv=6.20 eV is reasonable because surface photovoltage is due to interband transitions and the penetration depth of the light for both photon energies is less than the depth of the space-charge layer. Corrected values for surface potential are given for samples B and E in table 1. Also listed are values for the band bending V given by the difference between surface and bulk potentials. For p-type
crystals,
the bands
may bend
downward
at the surface,
in
598
J. H. DINAN.
which case electrons bulk rather
L. K. GALBRAITH
responsible
AND T. E. FISCHER
for the curves in fig. 3 might originate
than at the surface and the quantity
(EF-_!$)
determined
in the from
fig. 3 would not correspond to (E, - E,),. For sample C, however, the depth of the space-charge layer is calculated to be 1100 8, and 370 w for band bendings of 1 eV and 0.1 eV respectively. In either case the space-charge layer is deeper than the penetration depth of 6.2 eV radiation (x 100 A) and energy distribution curves can be expected to be characteristic of the surface. For sample C, (Er-E,), determined from fig. 3 is equat to (Er -Ev),, and the bands are therefore flat up to the surface. According to fig. 6, this condition persists at all temperatures measured. In the case of the heavily doped p-type crystal (sample A), fig. 3 again gives a surface potential equal to the bulk potential. For this doping level however, any space-charge layer would be so shallow that electrons could in principle escape through it without loss of energy. Therefore, curve A in fig. 3 is not incompatible with band bending. Thus, we can only speculate on the surface properties of the degenerate p-type crystal. The work function and its temperature dependence for this sample as given in fig. 6 differ from that of sample C by an amount consistent with flat bands on sample A under the assumption that the ionization energy is not affected by bulk doping level. [With NA - Nn= 3.6 x 10’ 9 cm- 3, however, such as assumption may not be validi)]. Moreover, we have observedi*) that deposition of cesium onto surfaces of sample A produces band bending that is clearly visible in energy distributions (as though escape depths were as low as 10 A). Therefore, the curve shown in fig. 3 is probably characteristic of the region at the surface. These data then indicate that negligible band bending
occurs for sample
4.2. IONIZATION
ENERGY
The ionization cording
AND
A.
ELECTRON
AFFINITY
energy t can be determined
in two independent
ways. Ac-
to fig. 1, 5 U-) = (-I% - &)S P-) + $, CT).
(3)
The surface potential can be determined from energy distributions and the work function from contact-potential difference measurements. r can also be determined directly from the width of an energy-distribution curve. Since the low-energy edge L is a measure of the work function, it is evident that t = hv - [(Ev - L) - -5 A&,,],
(4)
where (E&-L) is determined from fig. 3 (e.g., 1 eV for sample C). We subtract only half of the experimental broadening because the other half was accounted for in the determination of K, in fig. 7. Eqs. (3) and (4) do not take
ELECTRONICPROPERTIESOF
into account
the variations
599
{110)GaAs SURFACES
of surface potential
for the n-type samples. Since these variations
and work function
are systematic,
observed
they compensate
each other: in eq. (3), we add the largest 4 to the smallest (E, - E,)s and vice versa. In determining 5 from the energy distributions alone, we consider that the low-energy edge L corresponds to the smaller band bending, i.e., to the lowest value of E, shown in fig. 3 for every sample. Temperature-dependence of 5 is best measured as the change in width of the distributions for the case where the surface potential is constant and one is certain that the distribution represents the surface potential, namely, the non-degenerate p-type sample. We find that the width decreases by 30 meV upon cooling to 110°K and that this decrease is linear in temperature. According to eq. (4), 5 increases by the same amount upon cooling. We consider this temperature variation of 5 an upper limit since we cannot rule out some variation of (E, - E,), due to inhomogeneous doping. Values for c given in table 1 are averages of the values obtained by the two methods described. Both methods give for n-type material values that are smaller than for p-type material. The uncertainty introduced into the determination of 5 for n-type material by local variations of surface potential is large enough to account for these differences. However, a plot of the yield spectra for the n- and p-type samples gavels) an extrapolated cubic thresholdl) of approximately 5.50 eV for the p-type and 5.43 eV for n-type samples. Similar differences have been found by Arsen’eva-Geil and Wang7). While the cubic threshold is not an adequate absolute measure of the ionization energy2), its variation from sample to sample of the same material is a measure of A5 that is not affected in first order by inhomogeneous band bending. We conclude that the differences in ionization energy given in table 1 are real. Values for the electron affinity are given by x = 5 -E,. 4.3. SURF.~CESSTATES In general, band bending at a semiconductor surface is a manifestation of the existence of surface states whose energy levels lie in the band gap. The observed absence of band bending for {I lo} surfaces of p-type GaAs is incompatible with the presence of donor surface states. The band bending of 0.8 eV observed for n-type crystals indicates that acceptor surface states are present. Occupation of these states according to Fermi-Dirac statistics results in a negative surface charge density Z which is related to the density of surface states D,(E) by Z=--e
.Z gives rise to a space charge density
-1 1 dE.
Q,, of equal but opposite
charge which,
600
J.H.DINAN,
L.K.GALBRAITH
AND T. E.FISCHER
for depletion layers, is given by Q,, = [2sa,e (Nu - N,) k’]+ = -C,
(6)
where E and a0 are the dielectric constant and permittivity of the vacuum and ND and NA are the density of bulk donors and acceptors. The simplest surface state distribution is a band with lower edge at energy Es with the constant state density r;t, predicted by theory in two dimensions. For this case, eq. (5) can be solved to give C
=
EF
ekTD, In exp ~--
-
Es
kl”
+l.
1
D, and Es can be determined explicitly by measuring the temperature dependence of Z. According to eq. (6), this involves measuring the temperature dependence of V and therefore of the bulk and surface potentials. If the effect of deep traps is neglected, bulk potential at any temperature can be calculated by assuming that the free electron concentration at room temperature is equaf to the carrier concentration given in table 1. Because of spurious voltage drops along the n-type samples made highly resistive at low temperatures, attempts to correlate shifts in photoemission energy distribution curves with temperature dependence of surface potential were unsuccessful. According to eq. (3), however, this dependence can be determined by measuring 5 (T) and 4 (T). The linear dependence of 5 on temperature was mentioned in section 4.2. The possible existence of effects with extremely long time constants at low temperatures makes it dificult to decide with certainty whether 43(T) is given by the solid line or by the dashed line in fig. 6. If the dashed line represents thermodynamic equilibrium, then (p and Z are essentially independent of temperature and the Fermi level must lie within or quite near the edge of the surface band. An estimate of a minimum value for D, can be made if it is assumed that the Fermi level lies within the band for both n-type samples. In this case, eq. (7) becomes D, 2
(C” -
.E')/(E;
-
E;),
(8)
where the superscripts refer to the samples. Substitution of room-temperature values from table 1 into eqs. (6) and (8) gives D,z2 x 1Ol3 cm-’ eV_‘. Lack of precision in our data due to inhomogeneous doping of the samples prevents us from making a reasonable estimate of an upper limit on D,. It is also possible that the solid line in fig. 6 represents thermodynamic equilibrium. The fact that it was possible to cycle between (p2 and 4iri by illuminating the sample but that no transition from (p, to Cprwas ever ob-
ELECTRONIC
served lends support
PROPERTIES
to his alternative.
OF {llO} GaAs
SURFACES
601
If this is the case, then the data along
the solid line (and similar data taken on sample B) can be used to calculate the temperature dependence of the surface potentials. The results of such a calculation are displayed for samples E and B in fig. 8 in the form of the locations in the gap of the Fermi level in the bulk and at the surface. The band bending V and surface charge density .X calculated according to eq. (6) are shown in fig. 9. It is immediately clear that no set of values generated by
EFb
E
5.5
IIIIIII 100
Fa -
lIlI,lj
200
300
400
T (“Kf
Fig. 8. Temperature dependence of the quantities (EF-EV)S and (h-&)b for {llO} surfaces of n-type GaAs. EC and E, represent the conduction and valence band edges, EFb and EF~, the location of the Fermi level in the bulk and at the surface. The lables E and B correspond to table 1 and denote the samples with ND -NA = 2.7 x 1W7 cm-3 and 1.7 x 1016cm-3 respectively. The values shown correspond to the smallest values of band bending [largest (EF-&)s in fig. 31. The locations of EFs in the gap are calcuiated from the data shown in fig. 6 and from the measured temperature dependence of c.
temperature-independent quantities DS and E, can be found to cause eq. (7) to fit the non-monotonic curves in fig. 9. The rapid drop in _Zat low temperatures must be the result of a shift in the surface band edge toward the conduction band edge. If D, is equal to the minimum value given above, E, coincides approximately with the curve EFs for sample B in fig. 8. If, on the other hand, D, is equal to the value 4.2 x 1O’4 cm-’ eV_’ calculated for a free electron gas in two dimensions, then Es lies 1.6kT above E,, for sample Eat all temperatures. Such a temperature dependence of the positions of the
602
1.H.
DINAN,
L. K. GALBRAITH
AND T. E. FISCHER
energy levels of surface states would be much larger than any known perature induced shift in bulk band structures.
tem-
There was no evidence of photoemission out of surface states in our measurements. It was discussed earlierz) and shownlg) for the case of InP that such evidence would consist of non-zero energy distributions of photoelectrons at energies between E,, +hv and E,, +hv and also of an additive departure from a cubic yield Ycc(hv- E,)3 at low photon energies.
(b) 1.7 x Id2
100
200
300
400
T(=‘K)
Fig. 9. (a) Temperature dependence of band bending V for (1 lo} surfaces of n-type GaAs, calculated from the difference between the values for sulfate and bulk potentials shown in fig. 8. (b) Temperature dependence of the surface charge density Z calculated from the data shown in fig. 9(a). 5. Summary and conclusions Measurements of photoemission energy distributions and of contact-potential differences have been interpreted to give values for the quantities characterizing the electronic structure of clean cleaved { 1101 GaAs surfaces. No evidence for the presence of donor-like surface states was found; a band of acceptor-like states with density of at least 2 x 1Ol3 cm-’ eV_l and lower edge 0.85 eV below the conduction band edge at room temperature accounts for large upward band bending on n-type samples. The work function was
ELECTRONICPROPERTIESOF
found
to depend
on doping
{110)
GaAs
level, illumination
SURFACES
and temperature.
603
Possible
large temperature-dependence of the work function could best be interpreted in terms of an unusually large shift of the band of surface states with changing temperature. It is possible that such a shift is caused by a displacement of surface atoms with temperature as discussed by Levine and Freemanso). It must, however, be noted that the shift in surface states is continuous with temperature below 250°K and is therefore incompatible with phase transition of the surface structure at a well-defined temperature. Jonessi*sa) has calculated the spectrum of surface states on the { llO} surface of GaAs. He finds a band of surface acceptors extending from the conduction band down to a value EC-Es = 0.9 eV and a band of surface donors extending to approximately 0.2 eV above the valence band. Our results are in good agreement with his surface acceptor band but suggest that the surface donor band completely overlaps the valence band. Note added in proof Recent work (L. K. Galbraith and T. E. Fischer, 31st Physical Electronics Conference, Gaithersburg, Md., March 1971) has shown that the mechanism responsible for the large changes in work function of n-type samples shown as solid lines in fig. 6 is surface photovoltage with an extremely long time constant. The data can therefore properly be interpreted in terms of a temperature-independent spectrum of surface states. Acknowledgements The authors are indebted to Dr. R. M. Broudy who supplied them with an absolute light intensity calibration, to Dr. P. J. Viljoen, Messrs. D. Feigenbaum and M. S. Jazzar for their help in various stages of design and interpretation and to the personnel of the Department’s machine shop for their cooperative and skillful assistance. References 1) F. G. Allen and G. W. Gobeli, Phys. Rev. 127 (1962) 150. 2) T. E. Fischer, Surface Sci. 13 (1969) 30. 3) D. Haneman, J. Phys. Chem. Solids 11 (1959) 205. 4) G. W. Gobeli and F. G. Allen, Phys. Rev. 137 (1965) A245; Physics of III-V Compounds in: Semiconductors and Semimetals, Vol. 2, Eds. R. K. Willardson and A. C. Beer (Academic Press, New York, 1966) ch. 11. 5) J. van Laar and J. J. Scheer, Surface Sci. 8 (1967) 342. 6) 0. H. Hughers and P. M. White, Phys. Status Solidi 33 (1969) 309. 7) A. N. Arsen’eva-Geil and Wang Pao-K’un, Fiz. Tverd. Tela 3 (1961) 3621 [Engl. Transl. Soviet Phys.-Solid State 3 (1962) 26231;
604
8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)
J.H.DINAN,
L. K. GALBRAITH
AND T. E. FISCHER
Wang Pao K’un and A. N. Arsen’eva-Geil, Fiz. Tverd. Tela 3 (1961) 3628 [Engl. Transl. Soviet Phys-Solid State 3 (1962) 26371. A. N. Arsen’eva-Geil and A. A. Kask, Fiz. Tverd. Tela 7 (1965) 1187 [Engl. Transl. Soviet Phys-Solid State 7 (1965) 9521. J. Wojas, Phys. Status Solidi 35 (1969) 903. R. E. Weber and F. Cordes, Rev. Sci. Instr. 37 (1966) 112. A. Y. Cho and J. R. Arthur, Jr., Phys. Rev. Letters 22 (1969) 1180. M. D. Sturge, Phys. Rev. 127 (1962) 768. W. Klein, 30th Physical Electronics Conference, Milwaukee (1970). T. E. Fischer, Phys. Rev. Letters 21 (1968) 31. G. W. Gobeli and F. G. Allen, Phys. Rev. 127 (1962) 141. J. J. Scheer and J. van Laar, Phys. Letters 3 (1963) 246. T. E. Fischer, Phys. Rev. 142 (1966) 519. J. H. Dinan and T. E. Fischer, unpublished. T. E. Fischer, Helv. Phys. Acta 41 (1968) 827. J. D. Levine and S. Freeman, Phys. Rev., to be published. R. 0. Jones, Phys. Rev. Letters 20 (1968) 992. R. 0. Jones, in: The Strucutre and Chemistry of Solid Surfaces, Ed. G. A. Somorjai (Wiley, New York, 1969) p. 16.
SCIENCE 26 (1971) 587-604 8 North-Holland
ELECTRONIC
P~OPERT~S
Publishing Co.
OF CLEAN
CLEAVED
(11Oj GaAs SURFACES *
J. H. DINAN**,
L. K. GALBRAITH
and T. E. FISCHER
Beeton Center, Yale University, New Haven, Connecticut 06520, U.S.A
Received 8 December
1970; revised manuscript
received 17 February 1971
Photoelectric emission, contact potentials and surface photovoltages have been measured on clean, cleaved {llO) surfaces of n-and p-type GaAs between 77°K and 350°K. Roomtemperature work-function values depend on bulk doping and range from 4.70eY to 5.53 eV. Ionization energy is in agreement with values reported by Gobeli and Allen. P-type samples show no band bending, no surface photovoltage and small temperaturedependence of the work function. N-type samples show large band bending (0.8 eV at room temperature in the dark) that depends strongly on illumination and temperature. Surface photovoltage is due to interband transitions in the bulk. Results are interpreted in terms of a band of surface acceptors with a density of at least 2 x 1013cm-2 eV-1 at a lower band-edge which lies 0.85 eV below the conduction band edge.
1. Introduction This paper presents results of an investigation of electronic properties of clean cleaved { 1101 surfaces of GaAs. Measurements performed include photoelectric emission, contact potentials by the Kelvin method, and their variation with temperature between 370°K and 77°K as well as with illumination (surface photovoItage). Crystals with bulk doping levels ranging from 3.6 x 10” cmW3 p-type to 2.7 x lOI7 cmT3 n-type were used. The aim of the investigation was an experimental determination of those quantities needed to completely specify an energy-level diagram for the region near the surface (fig. 1). The approach was similar to that used for siliconl) by Allen and Gobeli who measured work functions 4 and photoelectric yield spectra for crystals with a wide range of bulk dopings. They equated ionization energy { with measured photoelectric threshold energy and calculated surface potential from (I&-E,), = 5 - 4. Band bending Vis given by (EF - _E,), - (_!&-I?& where bulk potential is calculated from bulk doping. From these, the charge density in surface states and, finally, information on the spectrum of surface * Supported by Night Vision Laboratory, Fort Belvoir, Va., under Contract No. DAAK 02-68-C-0232 and National Science Foundation Institutional Grant No. Gu-1658. ** Present address: Night Vision Laboratory, Fort Belvoir, Virginia 22060, U.S.A. 587
588
J. H. DINAN,
L. K. GALBRAITH
AND
T. E. FISCHER
states are obtained. Our method of determining (_!$ - I&), and t differs from that of Allen and Gobeli. Energy distributions are used in preference to yield spectra2). This method has the advantage of being free from assumptions about the optical excitation process and the significance of the threshold. Electronic properties of GaAs surfaces have been studied before. From photoelectric energy-distribution measurements on broken surfaces on n-type material, Hanemans) deduced a value of (E,-E,),=0.3 eV, which implied a band bending of about 1 eV. Gobeli and Allen4) measured contact-potentials and photoelectric yields for cleaved surfaces of two n-type crystals of nearly identical doping. They found a band bending of 0.6 eV and predicted Fermi-level clamping by a surface-state density of at least 10” cm-‘. Van
Ga As
Vacuum
Fig. 1. Energy-level diagram for the region near the (1 lo} surface on n-type GaAs. EF is the Fermi level, E, the conduction band edge, Es the lower edge of the band of surface acceptors, U,,, the asymptotic potential energy of electrons in vacuum, V the amount of band bending, D the depth of the space-charge layer, x the electron affinity, 4 the work function and r the ionization energy.
Laar and Scheer5) extended these measurements to a wider range of dopings. They observed no significant variation in spectral character or threshold and found that for non-degenerate samples A4 =A (J&&. These results are inconsistent with clamping and they estimate a surface-state density of 5 2 x x 1O’l cme2. Field-electron emission measurements by Hughes and Whites) on n-type material indicate band bending of 0.6 eV and a density of at least 2.8 x 1013 acceptors/cm2 on the { 11 l} surface. Arsen’eva-Geil, Wang and KaskT>s) and, more recently, Wojasg) have observed changes in photoelectric yield and shifts of I-V characteristics caused by additional longer-wavelength illumination that could not by itself cause photoemission. These measurements were interpreted as evidence for downward band bending on p-type material and upward band bending on n-type material.
ELECTRONIC
PROPERTIES
2. Experimental
OF (1 io}
GaAs
SURFACES
589
apparatus and procedure
All photoemission measurements and absolute work function measurements were performed in an ion-pumped stainless-steel chamber containing a photoemission retarding-potential analyzer, a cleaver and anvil, a Kelvin probe for contact-potential measurements, a cesium-ion gunlo), and a sample holder that could be rotated to face any of these elements. The CaAs samples were cut from slices obtained from the Monsanto Company. Each sample was a bar with cross section 3 mm x 8 mm and length 25 mm with a (110) direction along the length of the bar. Samples were chemically etched and mounted between sapphire slabs which provided electrical but not thermal isolation from a copper clamp. In some instances ohmic contacts were made by diffusion of indium. The copper clamp insured adequate heat transfer between sample and stainless-steel tubes through which liquid nitrogen was circulated for low-temperature measurements, A thermocouple attached to the clamp near the sample indicated a base temperature of 11Ort 10°K about 40 min after circulation had begun. A tungsten single-crystal ribbon was mounted on the rotatable holder and used to calibrate the energy analyzer and Kelvin probe.
Fig. 2.
Energy analyzer for photoemission
measurements.
Work functions were measured by vibrating a 1 mm diameter molybdenum rod first in front of the cleaved surface and then in front of the tungsten ribbon whose work function could be established to within &0.03 eV by photoelectric yield measurements. Contact potentials could be measured with an accuracy of 0.005 V. The energy analyzer (fig. 2) consists of three independent electrodes: a Co-Netic cylinder, a hemispherical collector, and a cage formed by a CoNetic back plate and a hemispherical grid. Energy sorting is done in the region between grid and collector by applying a ramp voltage to the sample and cage. This closely approximates the ideal spherical-capacitor retardingfield configuration. It was originally intended to bias the cage until the cavity defined by it and the sample was field free. However, stray light reaching the
590
J. H.DINAN,
L. K.GALBRAITH
AND T.E.
FISCHER
cage caused spurious current to the collector and necessitated an alternate mode of operation. Maintaining the cage at a constant positive potential of about three volts with respect to the sample isolated electrons emitted by the cage from those emitted by the sample. Negligible degradation of resolution occurred as a result of this modification. Magnetic fields in the analyzer were reduced to below 10 mG by enclosing the elements in the Co-Netic cylinder. All electrodes were electroplated with gold to reduce contact-potential differences. Energy distributions obtained by ac and dc electronic differentiating techniques were found to be identical; the dc technique was used for all measurements reported here. Energy resolution is limited mainly by inhomogeneity of the work function of the collector and by the bandwidth of the light and was determined from the energy distributions of the tungsten ribbon. Pressure in the vacuum chamber during cleavage and measurement was less than 5 x lo-” torr. A detailed investigation of changes in contact potential caused by illumination or by cooling was performed in a separate apparatus. The ion-pumped stainless-steel system had a base pressure of lo-” torr. A vibrating probe consisting of a 2 mm diameter quartz rod with a semi-transparent gold electrode evaporated onto one end could detect 0.2 mV changes in contact potential. Sample temperature could be measured with an accuracy of + 2 “K. No provision for absolute calibration of work functions was available in this system. 3. Experimental
results
In this section, results are presented of measurements taken on the four GaAs single crystals whose bulk doping levels are listed in table 1. The ex.perimental procedure followed for each crystal was to expose a fresh surface by cleaving, to record yield and energy-distribution curves for the sample and for the tungsten ribbon, and finally to measure contact potentials between sample and ribbon with the Kelvin probe. 3.1. PHOTOELECTRIC EMISSION Photoelectric yield spectra were similar to those reported by Gobeli and Allend). A set of energy-distribution curves all taken at room temperature at hv = 6.20 eV is shown in fig. 3. The high-energy edge of a distribution from the tungsten ribbon at the same photon energy is also shown. The latter is a resolution-broadened replica of the Fermi-Dirac distribution. The retarding voltage at which this curve is at half-maximum represents the energy E=E,+hv.
(1)
5.37 & 0.05 5.53 f 0.02
4.70 f 0.1 4.78 ItO. 0.11 -0.06
I .41 1.33
(eV)
(EF-&)b
Bulk potential
4
0.08 rtr 0.03 -0.08 rt 0.03
0.61 Ifi 0.07 0.55 j, 0.10
(eV)
(EF-&IS
Surface potential
5
0 0
0.80 i 0.07 0.78 It 0.08
Band bending
6
5.45 rt 0.07 5.45 zt 0.07
5.38 i 0.10 5.38 + 0.10
.-
Ionization energy
7
without illumination
4.03 & 0.07 4.03 & 0.07
3.95 fO.10 3.95 hO.10
_____
Electron aflinity
a
Values for carrier concentration are those supplied by Monsanto and were not remeasured. The large uncertainties given for n-type crystals represent real variations of the quantities across a surface of the sample. Band binding V and electron affinity x are calculated using the value of 1.43 eV for the band gap given in ref. 12.
C A
2.7 x 1017n 1.7 x lOian 1.0 x 1017p 3.6 x 10lg p
Work function
Carrier concentration and type (cm-s)
Sample
_-.
3
2
E B
TABLE 1
of cleaved {110) surfaces of GaAs at room temperature
1
Electronic properties
ti 8
F z
;
c 6
8
8
% 6 3 d z
Fr!
J. H.DINAN,
592
L. K.GALBRAITH
AND T. E. FISCHER
Even if the work function of the collector changes because of changing vacuum conditions, valid comparison of semiconductor energy-distribution curves is possible if the retarding-voltage scale is calibrated each time by registering
the position
of the Fermi level in accordance
with eq. (1).
The energy-distributions from the metal can also be used to estimate the energy resolution AE,,, of the apparatus. In principle, the high-energy edge of such a distribution rises from 10% to 90% of maximum within about 4kT(lOO meV at room temperature). In reality, this width is 4kT+ AE,,,. For our apparatus, the resolution was determined to be 0.1 eV while measurements were being made on samples B and E, 0.15 eV for sample A, and 0.25 eV for sample
C.
E-E,-
hv
Fig. 3. Energy distribution curves from the (110) surface of GaAs and from tungsten (only the high-energy edge is shown for W). Samples A, B, C and E are identified in table 1. Photon energy was 6.20 eV. The marks below the base line indicate the location of E, for each sample as determined from fig. 7. The limits of the variation of E, over the surface of B and E are shown. L is the low-energy edge of each curve.
Notice that the shape and the width of the energy distributions vary from one sample to the other. The distributions for samples A and C have a relatively well-defined high-energy end. Distribution C is wider than distribution A by the difference in experimental energy resolution. Despite the better experimental resolution, the distributions for the two n-type samples (B and E) are wider than distribution A and have extended high-energy tails. Notice also that the curves are displaced with respect to each other and with respect to the metal curve, and that the displacement from the metal curve is least for the degenerate p-type. An immediate conclusion is that the position of the bands at the surface depends upon bulk doping and therefore that complete clamping of the Fermi level does not occur.
ELECTRONICPROPERTIESOF
593
{110)GaAs SURFACES
3.2. EFFECTS OF ADDITIONAL ILLUMINATION ON PHOTOEMISSION Additional longer-wavelength illumination provided by either a tungstenfilament lamp or by a He-Ne laser (1 mW) had no effect on photoemission from p-type samples. For n-type samples, we observed: (1) an increase in emitted current by as much as 20x, (2) a shift of the energy-distribution curves toward lower energies, and (3) a narrowing of the distributions. Wojasg) has observed (1) and (2) and has interpreted (2) as a reduction in band bending. The lower barrier for escape of photoelectrons gives rise to (1). If the samples were not homogeneously doped, one could expect variations in band bending parallel to the surface. Such a variation would result in the unusually broad distributions mentioned in 3.1. Reduction of this component of band bending by additional illumination would give rise to (3). Variation of band bending parallel to the surface would cause similar variations in the work function, provided that the electron affinity is a well-defined material constant. 3.3. WORK FUNCTION MEASUREMENTS Values for the work function of the four samples measured at room temperature in the dark are listed in table 1. The work function of sample A was found to vary by only 0.005 eV across its surface. The uncertainty of 0.02 eV given in table 1 is the limit of accuracy as discussed in section 2. Uncertainties given for the other samples represent real variations across the surfaces and are attributed
to inhomogeneities
in doping.
3.4. EFFECTS OF ILLUMINATIONON WORK FUNCTION Illumination
had no effect on the work functions
of p-type
crystals
but
caused a decrease in the average work function as well as in the variation over the surfaces of n-type crystals. Typical changes in work function at room temperature and at 77°K are shown in fig. 4 for sample B as a function of intensity of illumination from a He-Ne laser. If x and 5 are not affected by illumination, then changes in 4 are due to changes in band bending and this effect is known as the surface photovoltage effect. The data in fig. 4 can be described by an equation of the form
Ag$=AJI=-.
Z is the light intensity,
“~71n(~)~
C(n), I0 and 12are empirical
+ 1).
parameters
giving best fit
594 to
J.H.DINAN,
L.K.GALBRAITH
AND
T.E.FISCHER
the curves. For the curves in fig. 4, values are n = 0.83 at room temperature,
&/C(A) = 1 x 1o-4 I,,, I&(A)
= 3.55 x lo-’
I,,,
IZ= 1.4at 77°K.
Imaxis the maximum available light intensity, of the order of 10” photons persecond.
0.1 I-
i
I
-6
I
-7 log,,,
I
-6
-5
,
-4
i
-3
,
-2
,
,
-1
0
Light intensity ~arbitrary)
Eig. 4. Surface photovoltage
of the (110) surface of n-type GaAs, ND-NA = 1.7 x lOle cm-a, at 77°K (curve 1) and at 294°K (curve 2). Source of illumination was a 1 mW He-Ne laser (hv = 1.96 eV). Curves are calculated from A# = V* In(CZ/Zo + 1)with parameters V* = 0.00965 eV and lo/C = 3.55 x IO-7 for T= 77”K, and V* = 0.021 eV and Jo/C = lo-* for T= 294’K.
Surface photovoltage could be due to light absorption in the bulk within a diffusion length of the space-charge layer or to absorption by carriers in surface statesll). The latter phenomenon can occur at hv < EG. Measurements have been made of surface photovoltage on sample B caused by illumination 5
5
C(~)/l,(78’10 T-----
4ci
-3-
E?
-2
1.40
I 1.42
I 1.44
I 1.46
I 1.46
I 1.50
I 1.52
I 1.54
I 1.56
hu (eV) Fig. 5.
Spectral dependence of surface photovoltage of the {I 10) surface of n-type GaAs; = 1.7 x 10x6cm-3 at 77°K and at 294°K. Values for C/IO are determined as in section 3.4. Also shown are values of the optical absorption coefficient a after Sturgelaf. ND-NA
ELECTRONICPROPERTIESOF
of various
photon
energies.
{llO} GaAs SURFACES
It was found that eq. (2) correctly
595
describes
the
results for all hv > E,. In fig. 5, surface photovoltages at photon energies near EG are shown for sample B at two temperatures. Also shown are absorption coefficients for GaAs taken from Sturge12). For hv
A (3.6xlO"pj
50
100 150 200 250 300 350 400
T (“K) Fig. 6. Temperature dependence of the work function of {110) surfaces of GaAs crystals whose bulk doping-levels are given. For sample E, $ incresaes to $1 when the sample is cooled rapidly in the dark. If the sample is illuminated while cold, 4 decreases to $2 in < 0.2 set, then decreases to &u after an additional 20 sec. Arrows show the direction of the only changes observed.
Relative temperature-dependence was measured in the more sensitive apparatus used to measure illumination-dependence. For p-type crystals, the measured temperature-dependence of C#Jcan be accounted for by the temperature-dependence of the value of < and of the location of EF in the gap in the bulk. For n-type crystals, the behavior was considerably more complicated as illustrated for sample E in fig. 6. Rapid
596
J. H.DINAN,
L. K.GALBRAJTH
AND T.E.
FISCHER
cooling (in 2 min) resulted in an increase in 4 by about 30 meV, as shown by the dashed line. When the sample was kept at low temperature, 4 drifted very slowly (50 meV/hr) toward lower values. Illumination of the sample surface with the He-Ne laser then caused 4 to drop rapidly (r-O.2 set) to the value 42 and then more slowly (r-20 set) to a value &, which was 0.15 eV below +2. Switching off the light caused the work function to return to 4Z in about 10 min, from where it drifted to higher values at less than 50 meV/hr. Such drifts may have been caused by contamination. The transition between 42 and dill was repeatable. No transition from $Z to 4i was observed. This phenomenon is very similar to that reported by Klein13) for heavily doped p-type GaAs covered with Cs-0 layers and also to that reported for cesiated annealed surfaces14) of n-type GaAs.
4. interpretation
of results
In this section, values for the quantities which characterize level diagram of fig. 1 are obtained according to the method ref. 2 with certain improvements described below. 4.1. SURFACEPOTENTIALANDBAND
the energypresented in
BENDING
If band bending occurs at a surface, care must be taken in determining surface potentials from energy distribution curves. Unequivocal interpretation of curves for n-type crystals is possible because electrons photo-excited at the surface lie higher in energy than those excited deeper in the bulk. In order to determine the surface potential from the curves shown in fig. 3, it is necessary to locate the position of the valence band edge E,, with respect to each of the distributions. It is not known a priori whether the high-energy edges of these curves are the result of interband transitions which may be direct or indirect or of transitions out of surface states. According to available band structure information, direct interband transitions from E, in GaAs occur for photon energies near 4.4 eV, which is below threshold for clean surfaces. However, energy distributions at this photon energy can be recorded if fractional monolayers of cesium are deposited onto the surface. Highenergy edges of curves taken from sample C at hv=4.43 eV and at 6.20 eV are shown in fig. 7 on a scale which would superimpose identical initial states. The use of curves taken from sample C guarantees that deformation due to band bending either normal to or parallel to the surface will be minimal. The fact that the edge of the 4.43 eV curve is abrupt and well defined and lies higher in energy than the edge of the 6.20 eV curve implies that direct interband transitions predominate in GaAs. The exact location of E, on the abscissa of fig. 7 is determined by taking into account the energy resolution
ELECTRONICPROPERTIESOF
obtained
previously.
{llO}
GaAs
597
SURFACES
at + AE,,, below the high-energy
It is located
cutoff of
the 4.43 eV curve. It is reasonable to assume that the energy separation between E, and the initial state for transitions at 6.20 eV is not distorted by the application of cesium to the crystal surface. Then, if the 6.20 eV curves for clean and cesiated surfaces are normalized to the respective yields and superimposed in such a way that the high-energy edges coincide, the location of E, with respect to the energy distribution for the clean surface has been determined. This procedure was followed for each curve in fig. 3.
-cesioted . ..clean
-1.5
-I
E-E,
-0.5
0
- hu
Fig. 7. Energy-distribution curves at hv = 4.43 eV and at 6.20 eV for clean and cesiated (110) surfaces of GaAs doped with NA = 1.7 x 1017 cm-3 (sample C). Dotted line is the distribution from the clean surface. Solid lines are high-energy portions of distributions from a cesiated surface. The high-energy edge of the distribution at hv = 4.43 eV represents direct transitions from the valence band edge and determines the origin of the abscissa. The x 10 curve for the cesiated surface and the curve for the clean surface are normalized to their respective yields.
Values for (Er-E,), determined from fig. 3 must be corrected by an amount equal to the surface photovoltage due to the light used for photoemission. At hv=6.20 eV, approximately 10” photons cm-’ set-’ were absorbed by the crystals. This is about lo4 times smaller than I,,,,, in fig. 4. Since surface photovoltage is independent of hv for hv > E, the value of A V at 10m4 in fig. 4 (0.02 eV at room temperature) is a good measure of the correction for sample B. Extrapolation of data obtained at hv= 1.96 eV to hv=6.20 eV is reasonable because surface photovoltage is due to interband transitions and the penetration depth of the light for both photon energies is less than the depth of the space-charge layer. Corrected values for surface potential are given for samples B and E in table 1. Also listed are values for the band bending V given by the difference between surface and bulk potentials. For p-type
crystals,
the bands
may bend
downward
at the surface,
in
598
J. H. DINAN.
which case electrons bulk rather
L. K. GALBRAITH
responsible
AND T. E. FISCHER
for the curves in fig. 3 might originate
than at the surface and the quantity
(EF-_!$)
determined
in the from
fig. 3 would not correspond to (E, - E,),. For sample C, however, the depth of the space-charge layer is calculated to be 1100 8, and 370 w for band bendings of 1 eV and 0.1 eV respectively. In either case the space-charge layer is deeper than the penetration depth of 6.2 eV radiation (x 100 A) and energy distribution curves can be expected to be characteristic of the surface. For sample C, (Er-E,), determined from fig. 3 is equat to (Er -Ev),, and the bands are therefore flat up to the surface. According to fig. 6, this condition persists at all temperatures measured. In the case of the heavily doped p-type crystal (sample A), fig. 3 again gives a surface potential equal to the bulk potential. For this doping level however, any space-charge layer would be so shallow that electrons could in principle escape through it without loss of energy. Therefore, curve A in fig. 3 is not incompatible with band bending. Thus, we can only speculate on the surface properties of the degenerate p-type crystal. The work function and its temperature dependence for this sample as given in fig. 6 differ from that of sample C by an amount consistent with flat bands on sample A under the assumption that the ionization energy is not affected by bulk doping level. [With NA - Nn= 3.6 x 10’ 9 cm- 3, however, such as assumption may not be validi)]. Moreover, we have observedi*) that deposition of cesium onto surfaces of sample A produces band bending that is clearly visible in energy distributions (as though escape depths were as low as 10 A). Therefore, the curve shown in fig. 3 is probably characteristic of the region at the surface. These data then indicate that negligible band bending
occurs for sample
4.2. IONIZATION
ENERGY
The ionization cording
AND
A.
ELECTRON
AFFINITY
energy t can be determined
in two independent
ways. Ac-
to fig. 1, 5 U-) = (-I% - &)S P-) + $, CT).
(3)
The surface potential can be determined from energy distributions and the work function from contact-potential difference measurements. r can also be determined directly from the width of an energy-distribution curve. Since the low-energy edge L is a measure of the work function, it is evident that t = hv - [(Ev - L) - -5 A&,,],
(4)
where (E&-L) is determined from fig. 3 (e.g., 1 eV for sample C). We subtract only half of the experimental broadening because the other half was accounted for in the determination of K, in fig. 7. Eqs. (3) and (4) do not take
ELECTRONICPROPERTIESOF
into account
the variations
599
{110)GaAs SURFACES
of surface potential
for the n-type samples. Since these variations
and work function
are systematic,
observed
they compensate
each other: in eq. (3), we add the largest 4 to the smallest (E, - E,)s and vice versa. In determining 5 from the energy distributions alone, we consider that the low-energy edge L corresponds to the smaller band bending, i.e., to the lowest value of E, shown in fig. 3 for every sample. Temperature-dependence of 5 is best measured as the change in width of the distributions for the case where the surface potential is constant and one is certain that the distribution represents the surface potential, namely, the non-degenerate p-type sample. We find that the width decreases by 30 meV upon cooling to 110°K and that this decrease is linear in temperature. According to eq. (4), 5 increases by the same amount upon cooling. We consider this temperature variation of 5 an upper limit since we cannot rule out some variation of (E, - E,), due to inhomogeneous doping. Values for c given in table 1 are averages of the values obtained by the two methods described. Both methods give for n-type material values that are smaller than for p-type material. The uncertainty introduced into the determination of 5 for n-type material by local variations of surface potential is large enough to account for these differences. However, a plot of the yield spectra for the n- and p-type samples gavels) an extrapolated cubic thresholdl) of approximately 5.50 eV for the p-type and 5.43 eV for n-type samples. Similar differences have been found by Arsen’eva-Geil and Wang7). While the cubic threshold is not an adequate absolute measure of the ionization energy2), its variation from sample to sample of the same material is a measure of A5 that is not affected in first order by inhomogeneous band bending. We conclude that the differences in ionization energy given in table 1 are real. Values for the electron affinity are given by x = 5 -E,. 4.3. SURF.~CESSTATES In general, band bending at a semiconductor surface is a manifestation of the existence of surface states whose energy levels lie in the band gap. The observed absence of band bending for {I lo} surfaces of p-type GaAs is incompatible with the presence of donor surface states. The band bending of 0.8 eV observed for n-type crystals indicates that acceptor surface states are present. Occupation of these states according to Fermi-Dirac statistics results in a negative surface charge density Z which is related to the density of surface states D,(E) by Z=--e
.Z gives rise to a space charge density
-1 1 dE.
Q,, of equal but opposite
charge which,
600
J.H.DINAN,
L.K.GALBRAITH
AND T. E.FISCHER
for depletion layers, is given by Q,, = [2sa,e (Nu - N,) k’]+ = -C,
(6)
where E and a0 are the dielectric constant and permittivity of the vacuum and ND and NA are the density of bulk donors and acceptors. The simplest surface state distribution is a band with lower edge at energy Es with the constant state density r;t, predicted by theory in two dimensions. For this case, eq. (5) can be solved to give C
=
EF
ekTD, In exp ~--
-
Es
kl”
+l.
1
D, and Es can be determined explicitly by measuring the temperature dependence of Z. According to eq. (6), this involves measuring the temperature dependence of V and therefore of the bulk and surface potentials. If the effect of deep traps is neglected, bulk potential at any temperature can be calculated by assuming that the free electron concentration at room temperature is equaf to the carrier concentration given in table 1. Because of spurious voltage drops along the n-type samples made highly resistive at low temperatures, attempts to correlate shifts in photoemission energy distribution curves with temperature dependence of surface potential were unsuccessful. According to eq. (3), however, this dependence can be determined by measuring 5 (T) and 4 (T). The linear dependence of 5 on temperature was mentioned in section 4.2. The possible existence of effects with extremely long time constants at low temperatures makes it dificult to decide with certainty whether 43(T) is given by the solid line or by the dashed line in fig. 6. If the dashed line represents thermodynamic equilibrium, then (p and Z are essentially independent of temperature and the Fermi level must lie within or quite near the edge of the surface band. An estimate of a minimum value for D, can be made if it is assumed that the Fermi level lies within the band for both n-type samples. In this case, eq. (7) becomes D, 2
(C” -
.E')/(E;
-
E;),
(8)
where the superscripts refer to the samples. Substitution of room-temperature values from table 1 into eqs. (6) and (8) gives D,z2 x 1Ol3 cm-’ eV_‘. Lack of precision in our data due to inhomogeneous doping of the samples prevents us from making a reasonable estimate of an upper limit on D,. It is also possible that the solid line in fig. 6 represents thermodynamic equilibrium. The fact that it was possible to cycle between (p2 and 4iri by illuminating the sample but that no transition from (p, to Cprwas ever ob-
ELECTRONIC
served lends support
PROPERTIES
to his alternative.
OF {llO} GaAs
SURFACES
601
If this is the case, then the data along
the solid line (and similar data taken on sample B) can be used to calculate the temperature dependence of the surface potentials. The results of such a calculation are displayed for samples E and B in fig. 8 in the form of the locations in the gap of the Fermi level in the bulk and at the surface. The band bending V and surface charge density .X calculated according to eq. (6) are shown in fig. 9. It is immediately clear that no set of values generated by
EFb
E
5.5
IIIIIII 100
Fa -
lIlI,lj
200
300
400
T (“Kf
Fig. 8. Temperature dependence of the quantities (EF-EV)S and (h-&)b for {llO} surfaces of n-type GaAs. EC and E, represent the conduction and valence band edges, EFb and EF~, the location of the Fermi level in the bulk and at the surface. The lables E and B correspond to table 1 and denote the samples with ND -NA = 2.7 x 1W7 cm-3 and 1.7 x 1016cm-3 respectively. The values shown correspond to the smallest values of band bending [largest (EF-&)s in fig. 31. The locations of EFs in the gap are calcuiated from the data shown in fig. 6 and from the measured temperature dependence of c.
temperature-independent quantities DS and E, can be found to cause eq. (7) to fit the non-monotonic curves in fig. 9. The rapid drop in _Zat low temperatures must be the result of a shift in the surface band edge toward the conduction band edge. If D, is equal to the minimum value given above, E, coincides approximately with the curve EFs for sample B in fig. 8. If, on the other hand, D, is equal to the value 4.2 x 1O’4 cm-’ eV_’ calculated for a free electron gas in two dimensions, then Es lies 1.6kT above E,, for sample Eat all temperatures. Such a temperature dependence of the positions of the
602
1.H.
DINAN,
L. K. GALBRAITH
AND T. E. FISCHER
energy levels of surface states would be much larger than any known perature induced shift in bulk band structures.
tem-
There was no evidence of photoemission out of surface states in our measurements. It was discussed earlierz) and shownlg) for the case of InP that such evidence would consist of non-zero energy distributions of photoelectrons at energies between E,, +hv and E,, +hv and also of an additive departure from a cubic yield Ycc(hv- E,)3 at low photon energies.
(b) 1.7 x Id2
100
200
300
400
T(=‘K)
Fig. 9. (a) Temperature dependence of band bending V for (1 lo} surfaces of n-type GaAs, calculated from the difference between the values for sulfate and bulk potentials shown in fig. 8. (b) Temperature dependence of the surface charge density Z calculated from the data shown in fig. 9(a). 5. Summary and conclusions Measurements of photoemission energy distributions and of contact-potential differences have been interpreted to give values for the quantities characterizing the electronic structure of clean cleaved { 1101 GaAs surfaces. No evidence for the presence of donor-like surface states was found; a band of acceptor-like states with density of at least 2 x 1Ol3 cm-’ eV_l and lower edge 0.85 eV below the conduction band edge at room temperature accounts for large upward band bending on n-type samples. The work function was
ELECTRONICPROPERTIESOF
found
to depend
on doping
{110)
GaAs
level, illumination
SURFACES
and temperature.
603
Possible
large temperature-dependence of the work function could best be interpreted in terms of an unusually large shift of the band of surface states with changing temperature. It is possible that such a shift is caused by a displacement of surface atoms with temperature as discussed by Levine and Freemanso). It must, however, be noted that the shift in surface states is continuous with temperature below 250°K and is therefore incompatible with phase transition of the surface structure at a well-defined temperature. Jonessi*sa) has calculated the spectrum of surface states on the { llO} surface of GaAs. He finds a band of surface acceptors extending from the conduction band down to a value EC-Es = 0.9 eV and a band of surface donors extending to approximately 0.2 eV above the valence band. Our results are in good agreement with his surface acceptor band but suggest that the surface donor band completely overlaps the valence band. Note added in proof Recent work (L. K. Galbraith and T. E. Fischer, 31st Physical Electronics Conference, Gaithersburg, Md., March 1971) has shown that the mechanism responsible for the large changes in work function of n-type samples shown as solid lines in fig. 6 is surface photovoltage with an extremely long time constant. The data can therefore properly be interpreted in terms of a temperature-independent spectrum of surface states. Acknowledgements The authors are indebted to Dr. R. M. Broudy who supplied them with an absolute light intensity calibration, to Dr. P. J. Viljoen, Messrs. D. Feigenbaum and M. S. Jazzar for their help in various stages of design and interpretation and to the personnel of the Department’s machine shop for their cooperative and skillful assistance. References 1) F. G. Allen and G. W. Gobeli, Phys. Rev. 127 (1962) 150. 2) T. E. Fischer, Surface Sci. 13 (1969) 30. 3) D. Haneman, J. Phys. Chem. Solids 11 (1959) 205. 4) G. W. Gobeli and F. G. Allen, Phys. Rev. 137 (1965) A245; Physics of III-V Compounds in: Semiconductors and Semimetals, Vol. 2, Eds. R. K. Willardson and A. C. Beer (Academic Press, New York, 1966) ch. 11. 5) J. van Laar and J. J. Scheer, Surface Sci. 8 (1967) 342. 6) 0. H. Hughers and P. M. White, Phys. Status Solidi 33 (1969) 309. 7) A. N. Arsen’eva-Geil and Wang Pao-K’un, Fiz. Tverd. Tela 3 (1961) 3621 [Engl. Transl. Soviet Phys.-Solid State 3 (1962) 26231;
604
8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)
J.H.DINAN,
L. K. GALBRAITH
AND T. E. FISCHER
Wang Pao K’un and A. N. Arsen’eva-Geil, Fiz. Tverd. Tela 3 (1961) 3628 [Engl. Transl. Soviet Phys-Solid State 3 (1962) 26371. A. N. Arsen’eva-Geil and A. A. Kask, Fiz. Tverd. Tela 7 (1965) 1187 [Engl. Transl. Soviet Phys-Solid State 7 (1965) 9521. J. Wojas, Phys. Status Solidi 35 (1969) 903. R. E. Weber and F. Cordes, Rev. Sci. Instr. 37 (1966) 112. A. Y. Cho and J. R. Arthur, Jr., Phys. Rev. Letters 22 (1969) 1180. M. D. Sturge, Phys. Rev. 127 (1962) 768. W. Klein, 30th Physical Electronics Conference, Milwaukee (1970). T. E. Fischer, Phys. Rev. Letters 21 (1968) 31. G. W. Gobeli and F. G. Allen, Phys. Rev. 127 (1962) 141. J. J. Scheer and J. van Laar, Phys. Letters 3 (1963) 246. T. E. Fischer, Phys. Rev. 142 (1966) 519. J. H. Dinan and T. E. Fischer, unpublished. T. E. Fischer, Helv. Phys. Acta 41 (1968) 827. J. D. Levine and S. Freeman, Phys. Rev., to be published. R. 0. Jones, Phys. Rev. Letters 20 (1968) 992. R. 0. Jones, in: The Strucutre and Chemistry of Solid Surfaces, Ed. G. A. Somorjai (Wiley, New York, 1969) p. 16.