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An experimental study on the temperature dependence of electron affinity and ionization energy at semiconductor surfaces
Surface Science 102 (1981) L54-L58 © North-Holland Publishing Company
SURFACE SCIENCE LETTERS
AN EXPERIMENTAL STUDY ON THE TEMPERATURE DEPENDENCE OF ELECTRON AFFINITY AND IONIZATION ENERGY AT SEMICONDUCTOR SURFACES W. MONCH, R. ENNINGHORST and H.J. CLEMENS Laboratorium far Festk6rperphysik der Universitdt Duisburg, D-4100 Duisburg, Germany Received 6 June 1980; accepted for publication 1 September 1980
The work function of a solid may be determined experimentally quite easy but can be calculated for simple models or specific surfaces only (see for example ref. [1]), For metals as well as semiconductors very few experimental studies were published on the temperature dependence of the work function. With respect to theoretical investigations the situation is even worse. The work function of a semiconductor may be written as ~b=Evac - EF =I - eoVs
-
Eg
(1)
+ W b ,
i.e. it is determined by the bulk band gap Eg and the bulk potential Wb = (Ec - EF)b and by the surface parameters ionization energy I = Evac - Ev and band bending eoVs = Eib --Eis. The bending of the bands adjusts such that the excess charge Qss in surface states cancels the space charge Qsc beneath the surface: Qss + Qsc = 0 .
(2)
Band bending eoVs and bulk potential Wb depend on type and level of doping while band gap Eg and ionization energy I are insensitive to these parameters for nondegenerate semiconductors [2]. In principle, the four terms of eq. (1) are temperature dependent. The variation of the band gap was measured with most semiconductors. For GaAs, the semiconductor studied in this paper, it can be expressed as Eg = 1.522
5.8 × 10-4 T 2 T+ 300 [eV],
(3)
between 0 and 973 K [3]. The bulk potential can be calculated as a function of temperature if the levels and the concentrations of the dopants are known. The band bending and its temperature dependence cannot be evaluated in general since on most semiconductor surfaces the density of surface states as a function of energy and actual temperature is very complicated and not well known. For cleaved GaAs(ll0) surfaces the situation is somewhat easier. By now, it is L54
W. Mdnch et al. /Temperature dependence o f electron affinity
L55
well established experimentally [4-8] as well as theoretically [9,10], that the bulk band gap is free of intrinsic surface states. However, cleavage produces steps with a density varying from one cleaved surface to the next. With these steps surface states and a change of the surface dipole are observed [8]. A detailed study of the temperature dependence of the work function and of the total yield spectrum in photoemission has revealed that the steps induce a narrow band of surface states 0.76 eV below the bulk conduction band edge [11 ]. This energetic position does not change with temperature [11]. Since these extrinsic surface states are of acceptor type a depletion layer forms on n-type samples beneath the surface according to eq. (2). For a nondegenerat,~ semiconductor the space charge in a depletion layer is given by asc = [2NDeeo(e0l Vs[ - kBT)] 1/2
(4)
with an error of less than 1% for eolVsl> 4 k B T . For high donor concentrations and low step densities the space charge remains constant independent of temperature since the step states remain well below the Fermi-level position. This is due to the high donor concentration which needs only small band bendings to fulfill eq. (2). According to eq. (4) the temperature dependence of the band bending in a depletion layer is given by e 0 A Vs(T) = k B AT.
(5)
This means that A Vs(T) is independent of the band bending, which varies due to the specific density of cleavage steps from sample to sample. Since for cleaved GaAs surfaces the temperature dependence of the bulk band gap, of the bulk potential, and of the band bending are known the temperature dependence of the ionization energy can be determined from measurements of the work function at different temperatures. Fig. 1 shows the contact potential differences measured at room temperature and at 100 K with six GaAs(110) surfaces cleaved from a n-type single crystal doped with 2.4 × 1018 Te atoms/cm 3. At room temperature the bulk potential amounts to I¢b = -0.013 eV. The CPD between the cleaved surfaces and a W electrode was measured by the Kelvin technique and could be determined with an accuracy of 0.1 meV, but repositioning of the probe limited the reproducibility to -+20 meV. A least square fit to the experimental points gives CPD(100 K) = (1.08 -+ 0.06) × CPD(300 K) + (90.4 -+ 11.8) [meV] . This linear relationship confirms the above given analysis..Within the limits of experimental error it follows: A¢(T) =/XCPD = (90.4 + 11.8) [meV] . The GaAs crystal used is degenerately doped. The difference in bulk potential at these temperatures was calculated as AWb = 0.7 meV. Due to the degenerate doping
W. M6nch et al. /Temperature dependence of electron affinity
L56
m,V o o
~ GaAs(1101
"
'~
~
~
i
i
I
I -500
, o
/
'
U ¢-t.O0
I
o
:6 - 300
c
_= o (21.
"5 o
-200
~
i
~
'
i
tO
__Z / 0
-100
i -200
-300
_ -400
-500
' -600 rneV-700
Contact potential difference at 300 K
Fig~ 1. Correlation of contact potential difference measured at 100 anct 300 K between six, differently stepped (110) surfaces cleaved from n-type GaAs (N = 2.4 × 1018 Te atoms/cm 3) and a W Kelvin probe.
a modified expression for the correlation between space charge and band bending has to be solved instead of eq. (4) [12]. From this analysis one obtains eoAVs = 23 meV, i.e. eq. (4) would give an underestimate. Together with the temperature change of the band gap according to eq. (3) and the experimentally determined difference in the work function it follows •(300 K) - I ( 1 0 0 K) = (4.4 -+ 11.8) [meV] . The temperature coefficient of the ionization energy of GaAs(110) surfaces thus amounts to
dl/dT = +(2.2 + 5.9) X 10 -s [eV K -1] , between room temperature and 100 K. Thus, the ionization energy is nearly independent of temperature. This result means that the electron affinity × = Evac - Ecsc increases with temperature as the band gap shrinks. This conclusion is supported by an earlier study of Bachmann [13]. From an analysis o f his experimental data and by considering the experimental results reported by Allen and Gobeli [2] he determined the tern-
If. M~nch et al. /Temperature dependence of electron affinity
L57
perature coefficient of the electron affinity for the Si(111)-7 × 7 surface as d x / d T = +(2.4 -+ 0.4) X 10 -4 [eV K - ' ] . This value again equals the absolute value of the temperature coefficient of the silicon gap in the temperature range investigated. Thus, for Si(111)-7 × 7 surfaces the ionization energy is temperature independent, too. For metals the parameter equivalent to the ionization energy of semiconductors is the work function. There are only few experimental studies on the temperature dependence of metal work function [ 1 4 - 1 7 ] . Typical values of the temperature coefficient d~/dT range from - 3 . 2 × 10 -s eV K -~ for W(310) up to +1.38 X 10 -3 eV K -1 for Cu(100) surfaces [16,14], for example. The temperature coefficient of the ionization energy of semiconductors as reported here is near the lower limit of the values found for metals. The main physical reasons for the temperature variation of metal work functions are thermal expansion and the temperature dependence of the electron-phonon coupling. Both effects were estimated to give contributions of a few k B = 8.62 × 10 -s eV K -1 with opposite sign [18]. Therefore, sign and magnitude of d¢/dT strongly depends on the specific metal considered. For metals the simple jellium model with pseudo-potential corrections was successfully used to calculate the work function [19,20] and its temperature coefficient [21] for a number of metals. The agreement with experimental values is reasonable. Up to now, calculations of the ionization energy and its temperature coefficient are lacking for semiconductors. However, the nearly vanishing temperature coefficient as observed for GaAs(110) and Si(111) surfaces is most probably caused by cancelation of thermal expansion and electron-phonon coupling effects, too. Detailed calculations would be highly desirable. This work was financially supported by the Ministerium fiir Wissenschaft und Forschung, Dtisseldorf, FRG.
References [1] J. H61zl and F.K. Schulte, in: Springer Tracts on Physics, Vol. 85, Ed. G. H6hler (Springer, 1979). [2] F.G. Alien and G.W. Gobeli, Phys. Rev. 127 (1962) 150. [3] M.B. Panish and H.C. Casey, J. Appl. Phys. 40 (1969) 163. [4] J. van Laar and J.J. Scheer, Surface Sci. 8 (1967) 343. [5] A. Huijser and J. van Laar, Surface Sci. 52 (1975) 202. [6] W. Gudat, D.E. Eastman and J.L. Freeouf, J. Vacuum Sci. Technol. 13 (1976) 250. [7] W.E. Spicer, I. Lindau, P.E. Gregory, C.M. Gerner, P. Pianetta and P.W. Chye, J. Vacuum Sci. Technol. 13 (1976) 780. [8] H.J. Clemens and W. M6nch, J. Vacuum Sci. Technol. 16 (1979). [9] J.R. Chelikowski, S.G. Louie and M.L. Cohen, Phys. Rev. B14 (1976) 4726. [10] D.J. Chadi, Phys. Rev. B18 (1978) 1800; }. Vacuum Sci. Technol. 15 (1978) 1244.
L58
W. M6nch et al. /Temperature dependence of electron affinity
[ 11 ] H.J. Clemens, Thesis, Duisburg, 1979. [12] R. Seiwatz and M. Green, J. Appl. Phys. 29 (1958) 1034. [13] R. Bachmann, Physik Kondens. Materie 8 (1968) 31. I14} E.H. Blevis and A.C. CroweU, Phys. Rev. 133 (1964) A580. [15] P. K6hler, Z. Angew. Phys. 21 (1966) 191. [16] L.W. Swanson and L.C. Crouser, Phys. Rev. 163 (1967) 622. [17] P.O. Gastland, S. Berge and B.J. Slagsvold, Physica Norvegica 7 (1973) 39. [18] C. Herring and M.H. Nichols, Rev. Mod. Phys. 21 (1949) 185. [19] N.D. Lang and W. Kohn, Phys, Rev. B3 (1971) 1215. [20] A. Kiejna and K.F. Wojciechowski, Solid State Commun. 31 (1979) 857, [21] A. Kiejna, K.F. Wojciechowski and H. Zebrowski, J. Phys, F (Metal Phys.) 9 (1979) 1361.
SURFACE SCIENCE LETTERS
AN EXPERIMENTAL STUDY ON THE TEMPERATURE DEPENDENCE OF ELECTRON AFFINITY AND IONIZATION ENERGY AT SEMICONDUCTOR SURFACES W. MONCH, R. ENNINGHORST and H.J. CLEMENS Laboratorium far Festk6rperphysik der Universitdt Duisburg, D-4100 Duisburg, Germany Received 6 June 1980; accepted for publication 1 September 1980
The work function of a solid may be determined experimentally quite easy but can be calculated for simple models or specific surfaces only (see for example ref. [1]), For metals as well as semiconductors very few experimental studies were published on the temperature dependence of the work function. With respect to theoretical investigations the situation is even worse. The work function of a semiconductor may be written as ~b=Evac - EF =I - eoVs
-
Eg
(1)
+ W b ,
i.e. it is determined by the bulk band gap Eg and the bulk potential Wb = (Ec - EF)b and by the surface parameters ionization energy I = Evac - Ev and band bending eoVs = Eib --Eis. The bending of the bands adjusts such that the excess charge Qss in surface states cancels the space charge Qsc beneath the surface: Qss + Qsc = 0 .
(2)
Band bending eoVs and bulk potential Wb depend on type and level of doping while band gap Eg and ionization energy I are insensitive to these parameters for nondegenerate semiconductors [2]. In principle, the four terms of eq. (1) are temperature dependent. The variation of the band gap was measured with most semiconductors. For GaAs, the semiconductor studied in this paper, it can be expressed as Eg = 1.522
5.8 × 10-4 T 2 T+ 300 [eV],
(3)
between 0 and 973 K [3]. The bulk potential can be calculated as a function of temperature if the levels and the concentrations of the dopants are known. The band bending and its temperature dependence cannot be evaluated in general since on most semiconductor surfaces the density of surface states as a function of energy and actual temperature is very complicated and not well known. For cleaved GaAs(ll0) surfaces the situation is somewhat easier. By now, it is L54
W. Mdnch et al. /Temperature dependence o f electron affinity
L55
well established experimentally [4-8] as well as theoretically [9,10], that the bulk band gap is free of intrinsic surface states. However, cleavage produces steps with a density varying from one cleaved surface to the next. With these steps surface states and a change of the surface dipole are observed [8]. A detailed study of the temperature dependence of the work function and of the total yield spectrum in photoemission has revealed that the steps induce a narrow band of surface states 0.76 eV below the bulk conduction band edge [11 ]. This energetic position does not change with temperature [11]. Since these extrinsic surface states are of acceptor type a depletion layer forms on n-type samples beneath the surface according to eq. (2). For a nondegenerat,~ semiconductor the space charge in a depletion layer is given by asc = [2NDeeo(e0l Vs[ - kBT)] 1/2
(4)
with an error of less than 1% for eolVsl> 4 k B T . For high donor concentrations and low step densities the space charge remains constant independent of temperature since the step states remain well below the Fermi-level position. This is due to the high donor concentration which needs only small band bendings to fulfill eq. (2). According to eq. (4) the temperature dependence of the band bending in a depletion layer is given by e 0 A Vs(T) = k B AT.
(5)
This means that A Vs(T) is independent of the band bending, which varies due to the specific density of cleavage steps from sample to sample. Since for cleaved GaAs surfaces the temperature dependence of the bulk band gap, of the bulk potential, and of the band bending are known the temperature dependence of the ionization energy can be determined from measurements of the work function at different temperatures. Fig. 1 shows the contact potential differences measured at room temperature and at 100 K with six GaAs(110) surfaces cleaved from a n-type single crystal doped with 2.4 × 1018 Te atoms/cm 3. At room temperature the bulk potential amounts to I¢b = -0.013 eV. The CPD between the cleaved surfaces and a W electrode was measured by the Kelvin technique and could be determined with an accuracy of 0.1 meV, but repositioning of the probe limited the reproducibility to -+20 meV. A least square fit to the experimental points gives CPD(100 K) = (1.08 -+ 0.06) × CPD(300 K) + (90.4 -+ 11.8) [meV] . This linear relationship confirms the above given analysis..Within the limits of experimental error it follows: A¢(T) =/XCPD = (90.4 + 11.8) [meV] . The GaAs crystal used is degenerately doped. The difference in bulk potential at these temperatures was calculated as AWb = 0.7 meV. Due to the degenerate doping
W. M6nch et al. /Temperature dependence of electron affinity
L56
m,V o o
~ GaAs(1101
"
'~
~
~
i
i
I
I -500
, o
/
'
U ¢-t.O0
I
o
:6 - 300
c
_= o (21.
"5 o
-200
~
i
~
'
i
tO
__Z / 0
-100
i -200
-300
_ -400
-500
' -600 rneV-700
Contact potential difference at 300 K
Fig~ 1. Correlation of contact potential difference measured at 100 anct 300 K between six, differently stepped (110) surfaces cleaved from n-type GaAs (N = 2.4 × 1018 Te atoms/cm 3) and a W Kelvin probe.
a modified expression for the correlation between space charge and band bending has to be solved instead of eq. (4) [12]. From this analysis one obtains eoAVs = 23 meV, i.e. eq. (4) would give an underestimate. Together with the temperature change of the band gap according to eq. (3) and the experimentally determined difference in the work function it follows •(300 K) - I ( 1 0 0 K) = (4.4 -+ 11.8) [meV] . The temperature coefficient of the ionization energy of GaAs(110) surfaces thus amounts to
dl/dT = +(2.2 + 5.9) X 10 -s [eV K -1] , between room temperature and 100 K. Thus, the ionization energy is nearly independent of temperature. This result means that the electron affinity × = Evac - Ecsc increases with temperature as the band gap shrinks. This conclusion is supported by an earlier study of Bachmann [13]. From an analysis o f his experimental data and by considering the experimental results reported by Allen and Gobeli [2] he determined the tern-
If. M~nch et al. /Temperature dependence of electron affinity
L57
perature coefficient of the electron affinity for the Si(111)-7 × 7 surface as d x / d T = +(2.4 -+ 0.4) X 10 -4 [eV K - ' ] . This value again equals the absolute value of the temperature coefficient of the silicon gap in the temperature range investigated. Thus, for Si(111)-7 × 7 surfaces the ionization energy is temperature independent, too. For metals the parameter equivalent to the ionization energy of semiconductors is the work function. There are only few experimental studies on the temperature dependence of metal work function [ 1 4 - 1 7 ] . Typical values of the temperature coefficient d~/dT range from - 3 . 2 × 10 -s eV K -~ for W(310) up to +1.38 X 10 -3 eV K -1 for Cu(100) surfaces [16,14], for example. The temperature coefficient of the ionization energy of semiconductors as reported here is near the lower limit of the values found for metals. The main physical reasons for the temperature variation of metal work functions are thermal expansion and the temperature dependence of the electron-phonon coupling. Both effects were estimated to give contributions of a few k B = 8.62 × 10 -s eV K -1 with opposite sign [18]. Therefore, sign and magnitude of d¢/dT strongly depends on the specific metal considered. For metals the simple jellium model with pseudo-potential corrections was successfully used to calculate the work function [19,20] and its temperature coefficient [21] for a number of metals. The agreement with experimental values is reasonable. Up to now, calculations of the ionization energy and its temperature coefficient are lacking for semiconductors. However, the nearly vanishing temperature coefficient as observed for GaAs(110) and Si(111) surfaces is most probably caused by cancelation of thermal expansion and electron-phonon coupling effects, too. Detailed calculations would be highly desirable. This work was financially supported by the Ministerium fiir Wissenschaft und Forschung, Dtisseldorf, FRG.
References [1] J. H61zl and F.K. Schulte, in: Springer Tracts on Physics, Vol. 85, Ed. G. H6hler (Springer, 1979). [2] F.G. Alien and G.W. Gobeli, Phys. Rev. 127 (1962) 150. [3] M.B. Panish and H.C. Casey, J. Appl. Phys. 40 (1969) 163. [4] J. van Laar and J.J. Scheer, Surface Sci. 8 (1967) 343. [5] A. Huijser and J. van Laar, Surface Sci. 52 (1975) 202. [6] W. Gudat, D.E. Eastman and J.L. Freeouf, J. Vacuum Sci. Technol. 13 (1976) 250. [7] W.E. Spicer, I. Lindau, P.E. Gregory, C.M. Gerner, P. Pianetta and P.W. Chye, J. Vacuum Sci. Technol. 13 (1976) 780. [8] H.J. Clemens and W. M6nch, J. Vacuum Sci. Technol. 16 (1979). [9] J.R. Chelikowski, S.G. Louie and M.L. Cohen, Phys. Rev. B14 (1976) 4726. [10] D.J. Chadi, Phys. Rev. B18 (1978) 1800; }. Vacuum Sci. Technol. 15 (1978) 1244.
L58
W. M6nch et al. /Temperature dependence of electron affinity
[ 11 ] H.J. Clemens, Thesis, Duisburg, 1979. [12] R. Seiwatz and M. Green, J. Appl. Phys. 29 (1958) 1034. [13] R. Bachmann, Physik Kondens. Materie 8 (1968) 31. I14} E.H. Blevis and A.C. CroweU, Phys. Rev. 133 (1964) A580. [15] P. K6hler, Z. Angew. Phys. 21 (1966) 191. [16] L.W. Swanson and L.C. Crouser, Phys. Rev. 163 (1967) 622. [17] P.O. Gastland, S. Berge and B.J. Slagsvold, Physica Norvegica 7 (1973) 39. [18] C. Herring and M.H. Nichols, Rev. Mod. Phys. 21 (1949) 185. [19] N.D. Lang and W. Kohn, Phys, Rev. B3 (1971) 1215. [20] A. Kiejna and K.F. Wojciechowski, Solid State Commun. 31 (1979) 857, [21] A. Kiejna, K.F. Wojciechowski and H. Zebrowski, J. Phys, F (Metal Phys.) 9 (1979) 1361.