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Character of surface states at InSb surfaces
Surface Science @ North-llolland
CHARACTER
86 (1979) 794k802 Publishing Company
OF SURFACE STATES AT InSb SURFACES
T‘he structural and electronic properties of real (oxidised) and 01 clean InSb( I IO) surtacc\ ‘ire investigated by I
1. Introduction As was shown nlination
thcorctically
of LIperiodic
tial, and the wsvefunction ity. causing under certain crties
01‘ the surface
[l-4]
crystal
states
and cotifirnied
at the surface
taken
experimentally
IS,6 I. the tcr-
3s a discontinuity
in the potcn-
and its derivation, were matched across the discoiitin~lconditions electronic states. the surface states. The prop-
of surface at017lS to the p!-opt‘rtics of the electronic bulk states, which are tletcrmined by the pcriodicity of tllc cryst:!l lattice. In addition to these intrinsic surface statcs. cliffcI-enI nieclianisiiis Ilave been proposed for the physical origin of’ extrinsic s~~rl’acc states. The electIon OI- hole levels muy 12~‘associated with impurities, adsorbed spcc,ics. structural defects or tiixorder in the surface, ()I- with bulk electronic states in the surface space chatgc: layer. Various spectroscopy techniques have been used to examine the cIcctroniC stluctmt‘ of scmiconcluctor sut-fiiccs, i.c. to probe occupied and rinoccupied levels or distributions of surface states. Nevertheless, the physical undcrstandi~~g 01‘ the 5111 t‘acc states in most cxxs is still unsntislhctory. Thet-ei’ot-c. I‘urthcr insight into the propet-ties of thcsc states is highly desirable. The structural and electrical propel-ties of real (oxidized) and ofclea:~ InSb( I 10) surkiczs arc investigated by IIIIlX.ED and by nic;isurenicIIts 01‘ intcgrd field Ct‘lCct StIIIilgly
17.8 1 alid on the reconstruction
depend
on
the ai-rangenlet~t
of the surl‘ace [9,l 01, sitnilarly
E W. Kreutz et al. /Surface
states at InSb surfaces
195
and of differential field effect. Illumination with photons, variation of temperature, and external fields allow studies not only within the depletion region but also under strong accumulation and inversion. The procedure of sample preparation allows US to study the influence of the surface structure as well as of one- and two-dimensional surface defects on the surface properties. It is possible to discern different groups of states in the measured term spectra of fast surface states by their different responses to physical and chemical influences. From the correlations between structural and electrical properties we have tried to discuss the nature of the surface states involved.
2. Experimental
The samples were cut from InSb single crystals (M.C.P. Ltd., Alperton Wembley, Middlesex), grown in the [21 1] direction with a Bridgman technique. The specimens were prepared by grinding with papers of different roughness, by mechanical polishing wit Sic powder in distilled water and then by polish etching for 3 --6 s in CP4A [ 111. The etching was stopped by flooding with distilled water. The specimens investigated were rectangular parallelepipeds with the large sample faces either for the real surfaces of any crystallographic orientation or for the clean surfaces of a (1 10) plane oriented to within lo by the Laue X-ray backscattering method. Electrical contacts for current measurements and as potential probes were made by silver paint, by pressing tungsten or stainless steal wires to the specimens. The oxidation stage of the surface oxide [ 121 inevitably present on the real surfaces was altered by etching in HF. by treatment in methylalcohol and by storage in laboratory air or vacuum subsequently to the prior etchvnt in CP4A. The charge distribution within the surface was changed by X-ray irradiation, by illumination with light and by external electric fields. The clean (1 IO) surfaces were obtained by cleaving under UHV conditions using grooves on top and bottom for cleavage by means of the double wedge technique. Each cleavage resulted in a (1 10) surface of mirrorlike finish with a very low number of tear marks and of crystallographic irregularities. Cleavage procedure and temperature treatment have been used to. influence the surface structure and the surface charge, respectively. Integral and differential ac field effect measurements were performed with a convetional circuit minimizing the effect of the displacement current [ 131. The alternating voltage was capacitively applied either to the real surfaces by an Au electrode over a hostaphan sheet or to the clean surfaces by an Al electrode evaporated on an Al,03 base with vacuum as dielectric medium. The sample configuration and the electronic equipment have been described [ 14,151. The electrical conductivity and the Hall coefficient were additionally measured with an experimental arrangement reported elsewhere [ 161 in order to get a relationship between surface and bulk transport properties.
796
E. W. Kreutz et al. /Surface
states at InSb surfaces
3. Results The RHEED patterns of the real surfaces show streaks and rings which were separately used for determination of the surface unit mesh dimensions. Independent of the surface treatment, the analysis of the streak pattern yields a lattice constant a = 6.53 .& [12] in reasonable agreement with that (a = 6.47 A) of InSb. Dependent on surface treatments, the analysis of the ring systems shows the existence of polycrystalline InSb and of various oxides of the underlying 111-V compound [12]. The RHEED diagram of the cleaved InSb(ll0) surface consists of a series of streaks perpendicular to the shadow edge of the crystal as well as Kikuchi lines and bands originating from the cubic zinc blende structure of the InSb lattice. The temperature treatment has no extraordinary influence on the RHEED patterns. The surface treatment governs for the real surfaces the location of the minimum of the field effect curve. Immediately after CP4A etchant the minimum is observed for n(p)-type specimens with oxidized surfaces at negative (positive) voltages in agreement with the observations of other authors [ 14,17-2 11. After etching in HF the minimum for p-type samples is located at a higher positive voltage than for CP4A etchant [21]. Independent of bulk doping the minimum shifts to higher positive voltages with storage time in laboratory air in combination with a decrease of the Hall coefficient [22]. Any change of the surface charge ~ for example, by a procedure described in section 2 --- shifts the field effect curve in the direction determined by the sign of the change [20,22]. The cleaved InSb(ll0) surfaces of p-type specimens exhibit the minimum of the field effect curve at low positive voltages [ 151. Heating in UHV at temperatures far below the melting point causes a shift of the minimum to higher positive voltages
[ISI. Following the procedure described by other authors [ 141 from measurements of integral and differential field effect the N,,(E) term spectra of fast surface states were provided by electronic computation and plotting [ 14,151. The N,,(E) distributions are plotted in figs. 1 to 3. Independent of surface preparation and of surface treatment the real and clean surfaces generally show throughout the energy gap a continuous distribution ofsurface states with a minimum near the middle of the gap (figs. I and 2). There is always a steep increase of N&J towards the band edges (figs. 1 and 2). At the valence band edge the density is higher than at the conduction band edge. The fast surface state density per energy interval depends on the surface preparation and on the surface treatment (fig. I), for example, the density of the HF etched surface is far higher than for the CP4A etched ones. Any change of the surface charge as accomplished by X-ray irradiation or illumination with photons has no influence on the N,,(E) distributions [ 141. Sometimes more or less pronounced and detailed structures (figs. 2 and 3) are superposed to the continuous N,,(E) governed by the chemical state of the investi-
797
E. W. Kreutz et al. / Surface states at InSb surfaces
Fig. 1. Fast surface state density per energy with real surfaces at T = 79 K after various etchant.
interval surface
for a p-type sample @ - lo-t3 treatments: (0) CP4A etchant;
cmm3) (0) HI:
gated surfaces. The maximum present in the upper gap region inN&‘) of the cleaved surfaces (fig. 2) vanishes during heating in UHV without changing the observed continuous distribution of fast surface states (fig. 2). Heating of real surfaces in vacuum at temperatures near the melting point produces for example a peaking structure in
-5
0 Ed
'-'15clg +lO
+5 -
0
"s
l:ig. 2. Fast surface state density per energy interval at T= 100 K for cleaved faces of a p-type sample @ - 4 X 1014 cmm3) at various stages of temperature before heating; (A) after heating at T = 100°C; (o) after heating at T = 350°C.
InSb(ll0) treatment:
sur(0)
798
C: W. Krcutz
0,172
ct al. /Surface
0,176
0.180
states at lr1S11 surjhws
0.181
0.188
0.192
-EC-EIeVl I:ig. 3. I:ast
surface 10”
sample (I-, T=
450°C:
hand scale)
state density cmm3) with
(0) 56 h heating; obtained
from
per cncrgy interval
(left
real surfaces after CP4A (,j)
hand scale) at 7’:
etchant 11s;I function
173 h: (,l) 260 II. Concentration
the tcmpcraturc
dcpcndcncc ot llall
of thermal
79 K t‘or ;I ptypc ~11hcatinp time at clcccptor\ (ri$t
cocf t’icicnt and electrical
cow
ductivity.
the N,,(fz’) term spectt-a in the lower gap region (fig. 3) with a shift uftlte peak to the valence band edge with increasing duration of the heating (fig. 3). The co~~ccntration of thermally induced acceptors as well as their activation energy, both tlte quantities derived from measurements of the temperature dependence ofclectrical conductivity and of Hall coefficient performed simultaneously to the field effect measurements, are also given in fig. 3.
4. Discussion The thickness dependence of the electrical conductivity and of the Ilalt cocflicient as well as magneto-surface experiments for InSb single-crystal specimens with real surfaces have been successfully interpreted in terms of the two-conductotthree-band model [ 16,22]_ The experimental data are in general agreement witlt the theoretical calculations under the assumption of completely diffuse surface scattering, i.e. w = 0, where w is the probability for specular reflection of carriers on the surface. The model and the assumpGons on which it is mainly based are justified by the quantitative agreement between the concentrations and tnobililies obtained for the bulk and those of other authors. Thus, the theoretical calculations necessary for the analysis of the field effect data (section 3) for I-eal surfaces also have been done under assumption of contpletcly diffuse surfHce scattering, in or-det to derive Ihe N,,(E) term spectra (fig. 1). Allowing par-tially specular sum-I‘accscattering, i.e. w # 0, results qualitatively in the same N,,(f:‘) distribution (fig. I ), only
1:: W. Kreutz
et al. /Surface
states at InSb surfaces
799
the density of fast surface states is altered quantitatively near the band edges. On the other hand, the numerical evaluations for the analysis of the field effect measurements (section 3) on the clean surfaces have been performed mainly assuming totally specular reflection (~3 = 1). Depending on the surface roughness in an atomic scale as induced by the cleaving procedure, an admixture of diffuse surface scattering has to be considered for the clean InSb( 110) surface. For strong accumulation or inversion, the carriers in the surface charge layer may be degenerate. In this case the Boltzmann equations for the theoretical computations have to be replaced by more complex relations based on the Fermi-Dirac statistics [23] giving a slower change of surface state densities with external voltage. A quantitative trealmerit including degenerate conditions yields only in a higher absolute density of fast surface states without changing the general shape of the Ars,(E) distribution [34j. For strong band bending quantization effects [X,26] may become significant for carrier-s attracted to the surface. Following the theoretical calculations [27,X] and experimental investigations [29,30] of other authors, quantization effects may be neglected because the swing of the energy bands by the applied external electric fields is too low for a’ measurable population of the quantized subbands. Taking into account these restricting factors, the derived N,,(E) spectra are accurate within the limits of the lack in the detailed knowledge about the surface mobilities in the range investigated. Nevertheless, the shape of the distributions of the fast surface states probably seems to be a real feature of the real and clean InSb surfaces, because all the sur-faces investigated show independent of surface preparation this continuous distribution (figs. I and 2, ref. [ 141). The nature of the continuous N,,(E) distributions will be discussed in an extended way based on the consider-ations of other authors [31,32] in terms that the wave functions of the surface states split off from the bulk bands. The In and Sb wave functions of surface states split off from the valence band might be expected to he energetically within the valence band or in the lower gap region. If these states remain below the Fermi ener-gy, they retain their initial electronic charge causing no band bending. The Sb wave function of surface states split off fr-om the conduction band, assumingly should be located in the energy gap near the valence band maximum, resulting in band bending by the captured negative charge if they are located below the Fermi energy. The ln wave function of surface states should lie in the energy gap near the conduction band minimum and remain neutral if they are located above the Fermi energy. Bccausc of the Sb electron affinity, the net charge of the fast surface state system is negative as a result of the Sb electronic state perturbed out of the conduction band, possibly causing an electron transfer from the bulk to this level. This picture is in qualitative agreement with the gencr-ally accepted model of surface states on clean InSb( 1 10) surfaces, showing the existence of Sb der-ived occupied states within the valence band region and of In der-ived unoccupied states within the conduction band region [33--351. As a consequence, the density of fast surface states has to be correlated to the total density of Sb on regular sites of the dift’erent lattices present within the surface region
800
E. W. Kreutz et al. /Surface
states at InSb surfaces
[12,31]. The field effect measurements on real surfaces (section 3) confirm this hypothesis. The density of fast surface states is higher after an etchant in HF (section 3) than after an etchant in CP4A (fig. 1). During etching HF attacks preferred the In atoms in the InSb surfaces leaving a Sb rich surface as evidenced from RHEED measurements (section 3), indicating the existence of polycrystalline Sb and of polycrystalline Sb oxides within the real surfaces [ 121. The clean InSb( 1 10) surfaces exhibit a lower density of surfaces states (fig. 2) than the real surfaces (fig. 1) because of the lower Sb concentration within the surface. Accordingly, the degree of p-type character should be proportional to the total probability density of the wave functions of the Sb species near the surface [ 12,3 l] as supported by field effect measurements (section 3). After etching in HF the accumulation is stronger for p-type specimens (section 3) in comparison to CP4A etching and the clean InSb(ll0) surfaces of p-type specimens show immediately after cleaving depletion layers. The levels split off from the bulk energy bands may degenerate into continuous distributions by different physical mechanisms. With a known or postulated distribution of states in the k-state (k wave vector), the energy distribution of states N(E) may be calculated with the f?‘(k) function. Using an effective mass approximation a continuation of nonlocalized systems to systems with localized states has been tried in the isotropic case [32] to get results with a constant density of states in the K-space (k = X), i.e. any localization is of equal probability. Large fluctuations of the potential or a large scatter of boundary conditions result in such a spread of states in the K-space causing a scatter of a number of volume states into the forbidden gap. Theoretical calculations with the simplest two-band approximation [32] give symmetricalN(E) distributions with a minimum in the middle of the energy gap and with maxima towards the band edges. Taking into account different effective masses, non-isotropic E(k) functions, and more than two bands yields nonsymmetrical N(E) spectra with a higher density of surface states near the valence band edge as observed for the InSb surfaces (fig. 1 and 3, ref. [ 141). As can be seen from RHEED measurements (section 3), polycrystalline InSb, Sb, and Sb oxides al-c present [ 121 on the real InSb surfaces. The barrier heights as well as the distortions of the structure near the grain boundaries assumingly result in fluctuations of the surface potential and of the boundary conditions necessary for generating the N,,(E) distributions. Because of the absence of the polycrystalline layers on the cleaved InSb(ll0) surfaces, the real surfaces consequently show a higher density of fast surface states (fig. 1) than the cleaved ones (fig. 2). The density of fast surface states on the cleaved surfaces is governed by their defect state, which probably is lower than the one of the real surfaces. The N,,(E) distribution in the middle of the energy gap is flattened with decreasing defect concentration in the surface region resulting by band .splitting in the general accepted picture [32--351 of the two groups of surface states on the ideal InSb( 110) surface. Perhaps these groups of surface states are tailing into the gap giving the surface states within the gap, which might be effected by the reconstruction of the surface.
E. W. Kreutz et al. /Surface
states at InSb surfaces
801
In addition to these intrinsic states, extrinsic states are observed in the measured surface states spectra (figs. 2 and 3). The maximum in N,,(E) of the cleaved surface (fig. 2) is attributed to a surface defect. Further investigations have to clarify its nature - point defects like empty sites and single atoms on top of the surface or line defects like atomic steps and domain boundaries of superstructures. The reconstruction of InSb( 110) surface might be excluded, because theoretical calculations of surface state spectra incorporating relaxation effects [8] show only a shift of the surface state distribution involved but no vanishing peaking structure at a certain energy with rearrangement. Similarly the peak in N&6’) of the heated real surface (fig. 3) is correlated to a thermally induced acceptor that bulk point defects near surfaces contribute also to the N,,(Z$ distributions analogous to the observed subsurface states [3 l] within the space charge layer.
5. Conclusion
The streak/spot patterns in all the RHEED diagrams of the real and clean InSb surfaces originate from the cubic zinc blende structure of the InSb lattice. With respect to surface treatments the analysis of the ring systems exhibit the existence of a surface layer of polycrystalline InSb and of various oxides of the underlying III--V compound. The general shape of the surface state density per energy interval consist out of a continuous distribution across the whole energy gap and within the energy bands showing peaking structures at certain values of the surface potential. The energy levels of the intrinsic surface states splitt off from the bulk bands degenerate to a distribution by bond distortions and rearrangement of the chemical environment within the surface region. The extrinsic states are correlated with the roughness of the surface and with the defects in the surface or in the space charge layer.
Acknowledgement
The authors wish to acknowledge much support by Professor Dr. W. Waidelich. They like to thank Professor Dr. H. Pagnia for valuable discussions. They are very grateful to Mrs. D. Hoppe cooperating in typing the manuscript.
References [l] I. Tamm, 2. Physik 76 (1932) 849. [2] W. Shockley, Phys. Rev. 56 (1939) 317. [3] J. Koutccky and M. Tom&k, Phys. Rev. 120 (1960)
1212.
802
If. W. Kreutz et al. /Surface
states at IILVJ surfaces
(4 ] M. Steslickn and K.1:. b’ojciechowski, Physica 32 (1966) 1274. (51 M. llenzler, Surface Sci. 25 (197 1) 650. [6] W. M6ncl1, l.cstkdrperproblel71c 13 (1973) 241. [7] K.C. Pandcy and J.C. Phillips, Phys. Rev. Bl3 (1976) 750. [S] J.R; Chclikowsky, S.G. Louie and M.L. Cohen, Phys. Rev. 1314 (1976) 4724. [9] G. Chivrotti and S. Nannarone, Phys. Rev. Letters 37 (1976) 934. [IO] J.A. Appclbaum, G.A. Baraff and 1I.R. Ilamann, Phys. Rev. 1314 (1976) 588. [ 11 1A.l‘. Hogenschut~, itzpraxis fdr Halblcitcr (Hanrur, Munchcn, 1976). [ 121 1c.W. Kreutz, Japan. J. Appl. Phys. Suppl. 2, Part 2 (1974) 445. 1131 G.G.F. Low, Proc. Phys. Sot. (London) 1368 (1955) 1154. [ 141 E.W. Krcutr and P. Schroll, Surface Sci. 37 (1973) 410. [ I5 1 I<. Rickus, Thesis, TH Darmstadt. [ 16 I E.W. Kreut7 and 13. Waack, Phys. Status Solidi (a) 25 ( 1974) 751. [ 17 I J.L. I)avis, Surface Sci. 2 (1964) 33. [ ISI tl.R. Iluff, S. Kawaji and t1.C. Gates, Surfarc Sci. 5 (1966) 399. [ 191 H.R. Iluff, S. Kawaji and 1I.C. <;atos, Surface Sci. 12 (I 968) 53. [ZO] H. I’agnia, Phys. Status Solidi 34 (1969) 121. [21 ] 1C.W. Kreutl, Z. Physik 27 ( 1969) 244. [221 l<.W. Kreutz. Phys. Status Solidi (a) 40 (1977) 415. 1231 II. Seiwatz and M.
CHARACTER
86 (1979) 794k802 Publishing Company
OF SURFACE STATES AT InSb SURFACES
T‘he structural and electronic properties of real (oxidised) and 01 clean InSb( I IO) surtacc\ ‘ire investigated by I
1. Introduction As was shown nlination
thcorctically
of LIperiodic
tial, and the wsvefunction ity. causing under certain crties
01‘ the surface
[l-4]
crystal
states
and cotifirnied
at the surface
taken
experimentally
IS,6 I. the tcr-
3s a discontinuity
in the potcn-
and its derivation, were matched across the discoiitin~lconditions electronic states. the surface states. The prop-
of surface at017lS to the p!-opt‘rtics of the electronic bulk states, which are tletcrmined by the pcriodicity of tllc cryst:!l lattice. In addition to these intrinsic surface statcs. cliffcI-enI nieclianisiiis Ilave been proposed for the physical origin of’ extrinsic s~~rl’acc states. The electIon OI- hole levels muy 12~‘associated with impurities, adsorbed spcc,ics. structural defects or tiixorder in the surface, ()I- with bulk electronic states in the surface space chatgc: layer. Various spectroscopy techniques have been used to examine the cIcctroniC stluctmt‘ of scmiconcluctor sut-fiiccs, i.c. to probe occupied and rinoccupied levels or distributions of surface states. Nevertheless, the physical undcrstandi~~g 01‘ the 5111 t‘acc states in most cxxs is still unsntislhctory. Thet-ei’ot-c. I‘urthcr insight into the propet-ties of thcsc states is highly desirable. The structural and electrical propel-ties of real (oxidized) and ofclea:~ InSb( I 10) surkiczs arc investigated by IIIIlX.ED and by nic;isurenicIIts 01‘ intcgrd field Ct‘lCct StIIIilgly
17.8 1 alid on the reconstruction
depend
on
the ai-rangenlet~t
of the surl‘ace [9,l 01, sitnilarly
E W. Kreutz et al. /Surface
states at InSb surfaces
195
and of differential field effect. Illumination with photons, variation of temperature, and external fields allow studies not only within the depletion region but also under strong accumulation and inversion. The procedure of sample preparation allows US to study the influence of the surface structure as well as of one- and two-dimensional surface defects on the surface properties. It is possible to discern different groups of states in the measured term spectra of fast surface states by their different responses to physical and chemical influences. From the correlations between structural and electrical properties we have tried to discuss the nature of the surface states involved.
2. Experimental
The samples were cut from InSb single crystals (M.C.P. Ltd., Alperton Wembley, Middlesex), grown in the [21 1] direction with a Bridgman technique. The specimens were prepared by grinding with papers of different roughness, by mechanical polishing wit Sic powder in distilled water and then by polish etching for 3 --6 s in CP4A [ 111. The etching was stopped by flooding with distilled water. The specimens investigated were rectangular parallelepipeds with the large sample faces either for the real surfaces of any crystallographic orientation or for the clean surfaces of a (1 10) plane oriented to within lo by the Laue X-ray backscattering method. Electrical contacts for current measurements and as potential probes were made by silver paint, by pressing tungsten or stainless steal wires to the specimens. The oxidation stage of the surface oxide [ 121 inevitably present on the real surfaces was altered by etching in HF. by treatment in methylalcohol and by storage in laboratory air or vacuum subsequently to the prior etchvnt in CP4A. The charge distribution within the surface was changed by X-ray irradiation, by illumination with light and by external electric fields. The clean (1 IO) surfaces were obtained by cleaving under UHV conditions using grooves on top and bottom for cleavage by means of the double wedge technique. Each cleavage resulted in a (1 10) surface of mirrorlike finish with a very low number of tear marks and of crystallographic irregularities. Cleavage procedure and temperature treatment have been used to. influence the surface structure and the surface charge, respectively. Integral and differential ac field effect measurements were performed with a convetional circuit minimizing the effect of the displacement current [ 131. The alternating voltage was capacitively applied either to the real surfaces by an Au electrode over a hostaphan sheet or to the clean surfaces by an Al electrode evaporated on an Al,03 base with vacuum as dielectric medium. The sample configuration and the electronic equipment have been described [ 14,151. The electrical conductivity and the Hall coefficient were additionally measured with an experimental arrangement reported elsewhere [ 161 in order to get a relationship between surface and bulk transport properties.
796
E. W. Kreutz et al. /Surface
states at InSb surfaces
3. Results The RHEED patterns of the real surfaces show streaks and rings which were separately used for determination of the surface unit mesh dimensions. Independent of the surface treatment, the analysis of the streak pattern yields a lattice constant a = 6.53 .& [12] in reasonable agreement with that (a = 6.47 A) of InSb. Dependent on surface treatments, the analysis of the ring systems shows the existence of polycrystalline InSb and of various oxides of the underlying 111-V compound [12]. The RHEED diagram of the cleaved InSb(ll0) surface consists of a series of streaks perpendicular to the shadow edge of the crystal as well as Kikuchi lines and bands originating from the cubic zinc blende structure of the InSb lattice. The temperature treatment has no extraordinary influence on the RHEED patterns. The surface treatment governs for the real surfaces the location of the minimum of the field effect curve. Immediately after CP4A etchant the minimum is observed for n(p)-type specimens with oxidized surfaces at negative (positive) voltages in agreement with the observations of other authors [ 14,17-2 11. After etching in HF the minimum for p-type samples is located at a higher positive voltage than for CP4A etchant [21]. Independent of bulk doping the minimum shifts to higher positive voltages with storage time in laboratory air in combination with a decrease of the Hall coefficient [22]. Any change of the surface charge ~ for example, by a procedure described in section 2 --- shifts the field effect curve in the direction determined by the sign of the change [20,22]. The cleaved InSb(ll0) surfaces of p-type specimens exhibit the minimum of the field effect curve at low positive voltages [ 151. Heating in UHV at temperatures far below the melting point causes a shift of the minimum to higher positive voltages
[ISI. Following the procedure described by other authors [ 141 from measurements of integral and differential field effect the N,,(E) term spectra of fast surface states were provided by electronic computation and plotting [ 14,151. The N,,(E) distributions are plotted in figs. 1 to 3. Independent of surface preparation and of surface treatment the real and clean surfaces generally show throughout the energy gap a continuous distribution ofsurface states with a minimum near the middle of the gap (figs. I and 2). There is always a steep increase of N&J towards the band edges (figs. 1 and 2). At the valence band edge the density is higher than at the conduction band edge. The fast surface state density per energy interval depends on the surface preparation and on the surface treatment (fig. I), for example, the density of the HF etched surface is far higher than for the CP4A etched ones. Any change of the surface charge as accomplished by X-ray irradiation or illumination with photons has no influence on the N,,(E) distributions [ 141. Sometimes more or less pronounced and detailed structures (figs. 2 and 3) are superposed to the continuous N,,(E) governed by the chemical state of the investi-
797
E. W. Kreutz et al. / Surface states at InSb surfaces
Fig. 1. Fast surface state density per energy with real surfaces at T = 79 K after various etchant.
interval surface
for a p-type sample @ - lo-t3 treatments: (0) CP4A etchant;
cmm3) (0) HI:
gated surfaces. The maximum present in the upper gap region inN&‘) of the cleaved surfaces (fig. 2) vanishes during heating in UHV without changing the observed continuous distribution of fast surface states (fig. 2). Heating of real surfaces in vacuum at temperatures near the melting point produces for example a peaking structure in
-5
0 Ed
'-'15clg +lO
+5 -
0
"s
l:ig. 2. Fast surface state density per energy interval at T= 100 K for cleaved faces of a p-type sample @ - 4 X 1014 cmm3) at various stages of temperature before heating; (A) after heating at T = 100°C; (o) after heating at T = 350°C.
InSb(ll0) treatment:
sur(0)
798
C: W. Krcutz
0,172
ct al. /Surface
0,176
0.180
states at lr1S11 surjhws
0.181
0.188
0.192
-EC-EIeVl I:ig. 3. I:ast
surface 10”
sample (I-, T=
450°C:
hand scale)
state density cmm3) with
(0) 56 h heating; obtained
from
per cncrgy interval
(left
real surfaces after CP4A (,j)
hand scale) at 7’:
etchant 11s;I function
173 h: (,l) 260 II. Concentration
the tcmpcraturc
dcpcndcncc ot llall
of thermal
79 K t‘or ;I ptypc ~11hcatinp time at clcccptor\ (ri$t
cocf t’icicnt and electrical
cow
ductivity.
the N,,(fz’) term spectt-a in the lower gap region (fig. 3) with a shift uftlte peak to the valence band edge with increasing duration of the heating (fig. 3). The co~~ccntration of thermally induced acceptors as well as their activation energy, both tlte quantities derived from measurements of the temperature dependence ofclectrical conductivity and of Hall coefficient performed simultaneously to the field effect measurements, are also given in fig. 3.
4. Discussion The thickness dependence of the electrical conductivity and of the Ilalt cocflicient as well as magneto-surface experiments for InSb single-crystal specimens with real surfaces have been successfully interpreted in terms of the two-conductotthree-band model [ 16,22]_ The experimental data are in general agreement witlt the theoretical calculations under the assumption of completely diffuse surface scattering, i.e. w = 0, where w is the probability for specular reflection of carriers on the surface. The model and the assumpGons on which it is mainly based are justified by the quantitative agreement between the concentrations and tnobililies obtained for the bulk and those of other authors. Thus, the theoretical calculations necessary for the analysis of the field effect data (section 3) for I-eal surfaces also have been done under assumption of contpletcly diffuse surfHce scattering, in or-det to derive Ihe N,,(E) term spectra (fig. 1). Allowing par-tially specular sum-I‘accscattering, i.e. w # 0, results qualitatively in the same N,,(f:‘) distribution (fig. I ), only
1:: W. Kreutz
et al. /Surface
states at InSb surfaces
799
the density of fast surface states is altered quantitatively near the band edges. On the other hand, the numerical evaluations for the analysis of the field effect measurements (section 3) on the clean surfaces have been performed mainly assuming totally specular reflection (~3 = 1). Depending on the surface roughness in an atomic scale as induced by the cleaving procedure, an admixture of diffuse surface scattering has to be considered for the clean InSb( 110) surface. For strong accumulation or inversion, the carriers in the surface charge layer may be degenerate. In this case the Boltzmann equations for the theoretical computations have to be replaced by more complex relations based on the Fermi-Dirac statistics [23] giving a slower change of surface state densities with external voltage. A quantitative trealmerit including degenerate conditions yields only in a higher absolute density of fast surface states without changing the general shape of the Ars,(E) distribution [34j. For strong band bending quantization effects [X,26] may become significant for carrier-s attracted to the surface. Following the theoretical calculations [27,X] and experimental investigations [29,30] of other authors, quantization effects may be neglected because the swing of the energy bands by the applied external electric fields is too low for a’ measurable population of the quantized subbands. Taking into account these restricting factors, the derived N,,(E) spectra are accurate within the limits of the lack in the detailed knowledge about the surface mobilities in the range investigated. Nevertheless, the shape of the distributions of the fast surface states probably seems to be a real feature of the real and clean InSb surfaces, because all the sur-faces investigated show independent of surface preparation this continuous distribution (figs. I and 2, ref. [ 141). The nature of the continuous N,,(E) distributions will be discussed in an extended way based on the consider-ations of other authors [31,32] in terms that the wave functions of the surface states split off from the bulk bands. The In and Sb wave functions of surface states split off from the valence band might be expected to he energetically within the valence band or in the lower gap region. If these states remain below the Fermi ener-gy, they retain their initial electronic charge causing no band bending. The Sb wave function of surface states split off fr-om the conduction band, assumingly should be located in the energy gap near the valence band maximum, resulting in band bending by the captured negative charge if they are located below the Fermi energy. The ln wave function of surface states should lie in the energy gap near the conduction band minimum and remain neutral if they are located above the Fermi energy. Bccausc of the Sb electron affinity, the net charge of the fast surface state system is negative as a result of the Sb electronic state perturbed out of the conduction band, possibly causing an electron transfer from the bulk to this level. This picture is in qualitative agreement with the gencr-ally accepted model of surface states on clean InSb( 1 10) surfaces, showing the existence of Sb der-ived occupied states within the valence band region and of In der-ived unoccupied states within the conduction band region [33--351. As a consequence, the density of fast surface states has to be correlated to the total density of Sb on regular sites of the dift’erent lattices present within the surface region
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[12,31]. The field effect measurements on real surfaces (section 3) confirm this hypothesis. The density of fast surface states is higher after an etchant in HF (section 3) than after an etchant in CP4A (fig. 1). During etching HF attacks preferred the In atoms in the InSb surfaces leaving a Sb rich surface as evidenced from RHEED measurements (section 3), indicating the existence of polycrystalline Sb and of polycrystalline Sb oxides within the real surfaces [ 121. The clean InSb( 1 10) surfaces exhibit a lower density of surfaces states (fig. 2) than the real surfaces (fig. 1) because of the lower Sb concentration within the surface. Accordingly, the degree of p-type character should be proportional to the total probability density of the wave functions of the Sb species near the surface [ 12,3 l] as supported by field effect measurements (section 3). After etching in HF the accumulation is stronger for p-type specimens (section 3) in comparison to CP4A etching and the clean InSb(ll0) surfaces of p-type specimens show immediately after cleaving depletion layers. The levels split off from the bulk energy bands may degenerate into continuous distributions by different physical mechanisms. With a known or postulated distribution of states in the k-state (k wave vector), the energy distribution of states N(E) may be calculated with the f?‘(k) function. Using an effective mass approximation a continuation of nonlocalized systems to systems with localized states has been tried in the isotropic case [32] to get results with a constant density of states in the K-space (k = X), i.e. any localization is of equal probability. Large fluctuations of the potential or a large scatter of boundary conditions result in such a spread of states in the K-space causing a scatter of a number of volume states into the forbidden gap. Theoretical calculations with the simplest two-band approximation [32] give symmetricalN(E) distributions with a minimum in the middle of the energy gap and with maxima towards the band edges. Taking into account different effective masses, non-isotropic E(k) functions, and more than two bands yields nonsymmetrical N(E) spectra with a higher density of surface states near the valence band edge as observed for the InSb surfaces (fig. 1 and 3, ref. [ 141). As can be seen from RHEED measurements (section 3), polycrystalline InSb, Sb, and Sb oxides al-c present [ 121 on the real InSb surfaces. The barrier heights as well as the distortions of the structure near the grain boundaries assumingly result in fluctuations of the surface potential and of the boundary conditions necessary for generating the N,,(E) distributions. Because of the absence of the polycrystalline layers on the cleaved InSb(ll0) surfaces, the real surfaces consequently show a higher density of fast surface states (fig. 1) than the cleaved ones (fig. 2). The density of fast surface states on the cleaved surfaces is governed by their defect state, which probably is lower than the one of the real surfaces. The N,,(E) distribution in the middle of the energy gap is flattened with decreasing defect concentration in the surface region resulting by band .splitting in the general accepted picture [32--351 of the two groups of surface states on the ideal InSb( 110) surface. Perhaps these groups of surface states are tailing into the gap giving the surface states within the gap, which might be effected by the reconstruction of the surface.
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In addition to these intrinsic states, extrinsic states are observed in the measured surface states spectra (figs. 2 and 3). The maximum in N,,(E) of the cleaved surface (fig. 2) is attributed to a surface defect. Further investigations have to clarify its nature - point defects like empty sites and single atoms on top of the surface or line defects like atomic steps and domain boundaries of superstructures. The reconstruction of InSb( 110) surface might be excluded, because theoretical calculations of surface state spectra incorporating relaxation effects [8] show only a shift of the surface state distribution involved but no vanishing peaking structure at a certain energy with rearrangement. Similarly the peak in N&6’) of the heated real surface (fig. 3) is correlated to a thermally induced acceptor that bulk point defects near surfaces contribute also to the N,,(Z$ distributions analogous to the observed subsurface states [3 l] within the space charge layer.
5. Conclusion
The streak/spot patterns in all the RHEED diagrams of the real and clean InSb surfaces originate from the cubic zinc blende structure of the InSb lattice. With respect to surface treatments the analysis of the ring systems exhibit the existence of a surface layer of polycrystalline InSb and of various oxides of the underlying III--V compound. The general shape of the surface state density per energy interval consist out of a continuous distribution across the whole energy gap and within the energy bands showing peaking structures at certain values of the surface potential. The energy levels of the intrinsic surface states splitt off from the bulk bands degenerate to a distribution by bond distortions and rearrangement of the chemical environment within the surface region. The extrinsic states are correlated with the roughness of the surface and with the defects in the surface or in the space charge layer.
Acknowledgement
The authors wish to acknowledge much support by Professor Dr. W. Waidelich. They like to thank Professor Dr. H. Pagnia for valuable discussions. They are very grateful to Mrs. D. Hoppe cooperating in typing the manuscript.
References [l] I. Tamm, 2. Physik 76 (1932) 849. [2] W. Shockley, Phys. Rev. 56 (1939) 317. [3] J. Koutccky and M. Tom&k, Phys. Rev. 120 (1960)
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