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Surface Debye temperature of Si(001) surfaces measured by HEED
Surl’ace Scicncc 67 (1977) 0 North-Holland
Publishing
358-361 Company
LETTERS TO TllE EDITOR SURFACE DEBYE TEMPERATURE BY HEED Received 23 March 1976; manuscript
OF Si(OO1) SURFACES MEASURED
received in tinal t‘orm 26 May 1977
Changes in the bonds between atoms near the surface of a crystal, compared with the bulk (i.e. a smaller number of nearest neighbours) lead to the expectation that the mean-square displacement of the surface atoms and, consequently, their Debye temperature should be different from that of the bulk. This has been observed in recent LEED experiments [ 11. By performing a high-energy electron diffraction experiment (HEED) and measuring the temperature dependence of the diffracted beam intensities it is possible to derive the mean-sqaure displacement 2 of the atoms near the surface using the dynamical theory of scattering. Single crystals of antimony doped Si (1 Q cm) were used. The error in the orientation of the polished Si(OO1) surface was less than 15’. The surfaces were etched in HF and covered with a layer of iodine [2]. The crystals were then heated in situ to 1100°C for 2 min, when the iodine desorbs leaving a clean Si(OO1) surface with a 2 X 1 superstructure. HEED experiments were performed at electron energies of 10 keV and at glancing incidence. The electron diffraction apparatus [3] was equipped with a retarding field analyser which allows energy analysis of the diffracted electrons. The experiments were carried out at a pressure of 5 X lo-” Torr. In order to measure the temperature dependence of the elastically scattered intensities of the reflections (004) and (008), the crystal was first heated to 900°C. After switching off the heater the intensities were recorded as a function of temperature. The temperature was measured at the thermal radiation shield around the crystal by a PtlO%Rh-Pt thermocouple, the reading of which had been correlated to the crystal temperature by an optical pyrometer. The direction of incidence was chosen in such a way that the best possible approximation to the “two-beam” case was realized, i.e. the reflection to be measured was strongly excited and the azimuth was adjusted so that additional reflections were practically not excited. The azimuths thus chosen were [130] for the reflection (004) and 22” from [ 1 lo] towards [OlO] for the reflection (008). The results are shown in fig. 1. The measurements are interpreted according to Bethe’s dynamical diffraction theory [4,5] using (0, 0, h) reciprocal lattice vectors only (systematic many-beam case). Temperature dependent Fourier coefficients were used for the crystal poten-
K. Britze,
(;. Mgw-l:%mer~
1 Surface Lkbvc
tcnlpcraturcs
I001 1
of Si(OOI)
359
surfaces
0 crystal 0 crystal
II
A crystal
IV
I
1.0 0.8 ~,=513K a
0.6
Q,=L30K
0.24 0
200
600
LOO
800
TPCI
ocrystal
I
crystal
II
rcrystal
IV
b
200
0
600
LOO
l:ig. 1. Intensity of elastically scattered electrons (b) reflections as a function of temperature for a
(arbitrary
units)
800
TPCI
for the (004)
(a) and (008)
Si(OO1)surface.
tial
40) = 4 ew-Mb),
where Mh = 27-r*~2 Ih I* .
a(T) is the mean-square displacement of the atoms at the temperature direction of h [6]. The result of the Debye model is [7]
Tin
the
where
kB is Boltzmann’s ture.
constant,
MAt is the atomic mass and eD is the Debye tempera-
Calculated curves using the Debye temperature for the bulk (543 K) and theoretical CLKVCS that were fitted to the measurements by adjusting the value of the Debye tcmperaturc arc also shown in fig. 1 together with the experimental values. It has to be noted that these theoretical curves deviate from the kinematical temperature factor exp(-2Mh) and have the approximate form exp(-2.5&) and cxp(--2.%f~) for the reflections ( 0, 0,4) and (O,O, 8) respectively. The temperature dependence of the intensity of the (004) reflection is best described by a Debye temperature of 430 K. A Debye temperature of 475 K is obtained from the temperature dependence of the (008) reflection. The difference between these effective Debye temperatures can be explained by the different bulk and surface contributions resulting from the differences in the penetration depth of the electrons for the two angles of incidence. For the (008) reflection the fitted curve is satisfactory only in the region between 0 and 600°C. For higher temperatures the measured values lie below the calculated values. Presumably this is a consequence of the anharmonicity of the vibrations at the surface. The mean-square displacement in the direction normal to the (001) surface that corresponds to the values obtained for the Debye temperatures is greater than in the bulk by a factor of 1.6 and 1.3 respectively. Model calculations [3] have shown that the penetration depth of the electrons is approx. 15 A in the case of the (004) reflection and 33 A for the (008) reflection. The contribution of the bulk is thus greater for the (008) reflection. The meansquare displacement of the surface atoms normal to the (001) surface is probably considerably greater than even that obtained for the (004) reflection. In LEED experiments on Si(OO1) surfaces [I] a decrease in the Debye temperature was also observed, however this result was obtained using kinematical scattering theory, which certainly is not adequate. Colelfa et al. [8] have determined the mean-sqauare displacement normal to the surface of Si(ll1). Using HEED they obtained a value which was greater than in the bulk by a factor of 1.4. Independently, Nesterenko and Borodkin [9] dete~ined the mean-sqaure dispiacement at Si(ll1) surfaces by LEED, obtaining a factor of approximately 1.4. These values are in rather good agreement with the results of this work for Si(OO1) surfaces. The support of this work by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. We also thank Dr. H. Koschmieder for helpful discussions.
K. Britze, G. Mcycr-Ehmsen
/ Surface DebJv temperatures
ofSi(OO1) surfaces
References [I] A. lgnatiev and F. Jona, Surface Sci. 42 (1974) 605. [2J R. Lieberman and D.L. Klein, J. Electrochcm. Sot. 113 (1966) 956. [ 3 1 K. Britze and G. Meyer-Ehmsen, to be published. [4] H.A. Bethe, Ann. Physik 87 (1928) 55. [5] A.R. Moon, Z. Naturforsch. 27a (1972) 390. [6] K. Kambe, Z. Naturforsch. 203 (1965) 1730. [7] P. Debye, Ann. Physik43 (1914) 49. [S] R. Colella, B.W. Batterman and J.F. Menadue, ActaCryst. A29 (1973) 151. [9] B.A. Nesterneko and A.D. Borodkin, Soviet Phys. Solid State, 12 (1971) 1621.
361
Publishing
358-361 Company
LETTERS TO TllE EDITOR SURFACE DEBYE TEMPERATURE BY HEED Received 23 March 1976; manuscript
OF Si(OO1) SURFACES MEASURED
received in tinal t‘orm 26 May 1977
Changes in the bonds between atoms near the surface of a crystal, compared with the bulk (i.e. a smaller number of nearest neighbours) lead to the expectation that the mean-square displacement of the surface atoms and, consequently, their Debye temperature should be different from that of the bulk. This has been observed in recent LEED experiments [ 11. By performing a high-energy electron diffraction experiment (HEED) and measuring the temperature dependence of the diffracted beam intensities it is possible to derive the mean-sqaure displacement 2 of the atoms near the surface using the dynamical theory of scattering. Single crystals of antimony doped Si (1 Q cm) were used. The error in the orientation of the polished Si(OO1) surface was less than 15’. The surfaces were etched in HF and covered with a layer of iodine [2]. The crystals were then heated in situ to 1100°C for 2 min, when the iodine desorbs leaving a clean Si(OO1) surface with a 2 X 1 superstructure. HEED experiments were performed at electron energies of 10 keV and at glancing incidence. The electron diffraction apparatus [3] was equipped with a retarding field analyser which allows energy analysis of the diffracted electrons. The experiments were carried out at a pressure of 5 X lo-” Torr. In order to measure the temperature dependence of the elastically scattered intensities of the reflections (004) and (008), the crystal was first heated to 900°C. After switching off the heater the intensities were recorded as a function of temperature. The temperature was measured at the thermal radiation shield around the crystal by a PtlO%Rh-Pt thermocouple, the reading of which had been correlated to the crystal temperature by an optical pyrometer. The direction of incidence was chosen in such a way that the best possible approximation to the “two-beam” case was realized, i.e. the reflection to be measured was strongly excited and the azimuth was adjusted so that additional reflections were practically not excited. The azimuths thus chosen were [130] for the reflection (004) and 22” from [ 1 lo] towards [OlO] for the reflection (008). The results are shown in fig. 1. The measurements are interpreted according to Bethe’s dynamical diffraction theory [4,5] using (0, 0, h) reciprocal lattice vectors only (systematic many-beam case). Temperature dependent Fourier coefficients were used for the crystal poten-
K. Britze,
(;. Mgw-l:%mer~
1 Surface Lkbvc
tcnlpcraturcs
I001 1
of Si(OOI)
359
surfaces
0 crystal 0 crystal
II
A crystal
IV
I
1.0 0.8 ~,=513K a
0.6
Q,=L30K
0.24 0
200
600
LOO
800
TPCI
ocrystal
I
crystal
II
rcrystal
IV
b
200
0
600
LOO
l:ig. 1. Intensity of elastically scattered electrons (b) reflections as a function of temperature for a
(arbitrary
units)
800
TPCI
for the (004)
(a) and (008)
Si(OO1)surface.
tial
40) = 4 ew-Mb),
where Mh = 27-r*~2 Ih I* .
a(T) is the mean-square displacement of the atoms at the temperature direction of h [6]. The result of the Debye model is [7]
Tin
the
where
kB is Boltzmann’s ture.
constant,
MAt is the atomic mass and eD is the Debye tempera-
Calculated curves using the Debye temperature for the bulk (543 K) and theoretical CLKVCS that were fitted to the measurements by adjusting the value of the Debye tcmperaturc arc also shown in fig. 1 together with the experimental values. It has to be noted that these theoretical curves deviate from the kinematical temperature factor exp(-2Mh) and have the approximate form exp(-2.5&) and cxp(--2.%f~) for the reflections ( 0, 0,4) and (O,O, 8) respectively. The temperature dependence of the intensity of the (004) reflection is best described by a Debye temperature of 430 K. A Debye temperature of 475 K is obtained from the temperature dependence of the (008) reflection. The difference between these effective Debye temperatures can be explained by the different bulk and surface contributions resulting from the differences in the penetration depth of the electrons for the two angles of incidence. For the (008) reflection the fitted curve is satisfactory only in the region between 0 and 600°C. For higher temperatures the measured values lie below the calculated values. Presumably this is a consequence of the anharmonicity of the vibrations at the surface. The mean-square displacement in the direction normal to the (001) surface that corresponds to the values obtained for the Debye temperatures is greater than in the bulk by a factor of 1.6 and 1.3 respectively. Model calculations [3] have shown that the penetration depth of the electrons is approx. 15 A in the case of the (004) reflection and 33 A for the (008) reflection. The contribution of the bulk is thus greater for the (008) reflection. The meansquare displacement of the surface atoms normal to the (001) surface is probably considerably greater than even that obtained for the (004) reflection. In LEED experiments on Si(OO1) surfaces [I] a decrease in the Debye temperature was also observed, however this result was obtained using kinematical scattering theory, which certainly is not adequate. Colelfa et al. [8] have determined the mean-sqauare displacement normal to the surface of Si(ll1). Using HEED they obtained a value which was greater than in the bulk by a factor of 1.4. Independently, Nesterenko and Borodkin [9] dete~ined the mean-sqaure dispiacement at Si(ll1) surfaces by LEED, obtaining a factor of approximately 1.4. These values are in rather good agreement with the results of this work for Si(OO1) surfaces. The support of this work by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. We also thank Dr. H. Koschmieder for helpful discussions.
K. Britze, G. Mcycr-Ehmsen
/ Surface DebJv temperatures
ofSi(OO1) surfaces
References [I] A. lgnatiev and F. Jona, Surface Sci. 42 (1974) 605. [2J R. Lieberman and D.L. Klein, J. Electrochcm. Sot. 113 (1966) 956. [ 3 1 K. Britze and G. Meyer-Ehmsen, to be published. [4] H.A. Bethe, Ann. Physik 87 (1928) 55. [5] A.R. Moon, Z. Naturforsch. 27a (1972) 390. [6] K. Kambe, Z. Naturforsch. 203 (1965) 1730. [7] P. Debye, Ann. Physik43 (1914) 49. [S] R. Colella, B.W. Batterman and J.F. Menadue, ActaCryst. A29 (1973) 151. [9] B.A. Nesterneko and A.D. Borodkin, Soviet Phys. Solid State, 12 (1971) 1621.
361