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Surface cyclotron resonance of accumulation and inversion layers in tellurium
Surface Science 58 (1976) 202-206 0 North-Holland Publishing Company
SURFACE CYCLOTRON
RESONANCE OF ACCUMULATION
AND
INVERSION LAYERS IN TELLURIUM
M. von ORTENBERG and R. SILBERMANN Physikalisches Institut der Universitiit Wiirzburg, D-87, Wiirzburg, West Germany
We present measurements of the submillimeter cyclotron resonance of electrons and holes in electric subbands on [O,O,O,l] and [ 1 ,i,O,O] tellurium surfaces [ 1,2]. As insulating layer in the applied MIS arrangement we used a Hostaphan foil of 6.3 pm thickness and a dielectric constant of E = 3.2 co. The special advantage of the MIS arrangement in comparison with the MOS device is that the influence of chemical and mechanical treatment of the surface can easily be investigated. By a special etching procedure a chemical accumulation of about 2 X 1012 e cm-2 could be generated, and the corresponding threshold voltage shifted over a range of more than 1 kV. To separate the weak surface resonance from the strong bulk cyclotron resonance lines of the substrate, we used both square wave and harmonic modulation of the electric field and detected the surface signal by phase sensitive amplification. Our experiments were performed with a continuous wave HCN molecular gas laser spectrometer described previously [3]. The magnetic field was applied parallel (Bllc) or perpendicular (Blc) to the trigonal c-axis of the samples, which were shaped as non-plane parallel slabs. Simultaneously to the optical transmission the magneto resistance of the samples was investigated and provided the necessary information to distinguish in the optical resonance spectra between occupation effects as predicted by Ando [4] and the splitting of the cyclotron resonance due to different mass parameters. The phase sensitive detection made possible to record for both inversion and accumulation layer pronounced resonance lines shown in fig. 1 for the orientation f?jI c. The recordings represent the cyclotron resonance curves for 3 11 and 337 pm wavelength radiation of the surface electron and hole in the upper and lower part, respectively. Because of the absorbing p-type substrate, the surface resonance curves exhibit a pseudo splitting originating from the cyclotron resonance absorption of free holes in the bulk material. For an optimal understanding of the experimental data we simulated the resonance curves. In the calculation we have taken account of the definite dielectric multilayer structure of the wedged MIS arrangement as schematically represented in fig. 2. The theoretical results basing on a Drude model and the experimental data are plotted for comparison in fig. 3 by broken and solid curves, respectively. The experimental situation of the gate-voltage modulation is simulated by the difference 202
M. von Ortenberg, R. Silbermann
l-
/Surface
I
I
203
cyclotron resonance
I
I
X=337(vm)
Ug=l777+~sinwtJlV) 2
~
Ugsf-555+&&sinot)lV) 2
L
I
I
0
20
40 Magnetic
I
I
80 Field,
Blk%aussl
Fig. 1. The cyclotron resonance spectra of electrons and holes in a tellurium [OOOl] surface in the upper and lower part respectively are recorded for 311 and 337 pm wavelength radiation. Besides of the common pseudo-splitting due to substrate absorption the resonance curves exhibit different line position and shape.
of the theoretical transmissions of the corresponding two surface densities Nl and N2 given by the parameters in fig. 3. To achieve a reasonable agreement with the experimental line intensity, we had to assume that only about 50% of the electric field induced charge contributes to the surface subbands. This assumption is corroborated by the Shubnikov-De Haas (SdH) results of Silbermann and Landwehr [5]. In fig. 3 this reduction is depicted by two different parameter sets for each of the lines corresponding to the capacitically determined charge density and the fit value. The mass and wr values used in the simulation are me = 0.117 mo, wr, = 4.34, m h = 0.144 mo, and arh = 4.0 for the surface electron and surface hole, respectively. The bulk concentration of the 0.5 mm thick sample is 1013 cme3. In contrast to the case of plane parallel samples, where the line position is substantially shifted by interference effects [6], for wedged samples the line position is rather unaffected. The line width, however, is increased comparatively with the line
204
M. von Ortenberg, R. Silbermann / Surface cyclotron resonance
E$i?-Wtl
/I
Fig. 2. The schematic arrangement of a wedged multilayer system depicts the complex optical boundary problem.
width of the resonant dielectric tensar component. The line shape of the electron resonance is better approximated by the constant T model (broken curves in fig. 3) than by a magnetic field dependent relaxation time of the form r h Bw0s5 as suggested by Ando (dotted curve in fig. 3) [4]. In addition to such a r dependent distortion, the line shape should exhibit at low temperatures population effects, which seem not to be present in our data. The line shape of the surface hole resonance has a less good agreement with the constant r model. We attribute this to a splitting of the resonance, which was resolved in some of our samples at high surface hole density. The resonance position of the surface electron is almost independent of the gate voltage, whereas the surface hole resonance shifts considerably to higher magnetic field intensities with increasing gate voltage. This implies an increase of the corresponding cyclotron mass of the surface hole from 0.112 to 0.18 depending on the gate voltage. For the orientation Blc the surface resonance spectra exhibit a completely different mult~ine structure. The corresponding mass parameters as function of the gate voltage are plotted in fig. 4. Both position and shift with the gate voltage of
M. von Ortenberg, R. Silbermann /Surface
I
cyclotron resonance
1
1
205
I
1
;: NI=0.78~10'*& 2 // vN2=0
1
20
I
LO Magnetic
1
1
80
60kG Field
B
Fig. 3. The theoretical resultsbasingon a constant T model (broken curves) are in better agreement with the experimental data (solid curves) than the simulation, which includes a magnetic field dependent relaxation time of the form r - B-o.5 (dotted curve). To fit the line intensity we had to assume that only about 50% of the electric field induced charge contributes to the surface subbands. The parameters indicate the two surface densities corresponding to the two peak values of the modulated gate voltage. The mass and wr values for surface electrons and holes are me = 0.117 mo, wre = 4.34, mh = 0.144 m. and Wrh = 4.0 respectively. The bulk concentration of the 0.5 mm thick substrate is 1013 cm-a.
the hole resonance can be interpreted semiquantitatively within the framework of the existing valence band models and agrees with complementary SdH measurements [5]. For the electron from the existing conduction band model, however, only one resonance line is expected [7], whereas a total of at least four different resonance positions can be identified. The mass parameter of the most dominant line deviates considerably from the value given by Button et al. [8] and Shinno et al. [7].
M. van Ortenberg, R. Silbermann /Surface
206
cyclotron resonance
0.3 -
21r m.
4
. -*-.-
-0-e
2-
1_.Electron
Hole ‘r,
0+-l-
-*-•.-•.-@i
/ Ye
l-
I
-p*_ Tellurium
Blc
X=337vm
T-2K
l
T.35Ka o-
I -lo00
I -500
I l
Gate
Voltage
500
I
l1000 v
1
Ug
Fig. 4. The different cyclotron mass values of electrons and holes in a [ 1100] demonstrate the complicated Landau level system for Blc.
tellurium
surface
References [II M. von Ortenberg PI M. von Ortenberg [31 141 I51
161 [71 [81
and R. Silbermann, Solid State Commun. 17 (1975) 617. and R. Silbermann, Intern. Conf. on Infrared Physics, Zurich, 1975. M. von Ortenberg, in: Proc. 1st Intern. Conf. on Submillimeter Waves and Their Application; in: IEE-MIT 12 (1974) 1081. T. Ando, J. Phys. Sot. Japan 38 (1975) 989. R. Silbermann, G. Landwehr, J. Bouat and J.C. Thullier, in: Proc. 2nd Intern. Conf. on Solid Surfaces, Kyoto; Japan. J. Appl. Phys. (Suppl. 2) Pt. 2 (1974) 359; R. Silbermann and G. Landwehr, Solid State Commun. 16 (1975) 1055; R. Silbermann and G. Landwehr, Surface Sci. 58 (1976) 252. M. von Ortenberg, Solid State Commun. 17 (1975) 1335. H. Shinno, R. Yoshizaki, S. Tanaka, T. Doi and H. Kamimura, J. Phys. SOC. Japan 35 (1973) 525. K.J. Button, G. Landwehr, G.G. Bradley, P. Grosse and B. Lax, Phys. Rev. Letters 23 (1969) 14.
SURFACE CYCLOTRON
RESONANCE OF ACCUMULATION
AND
INVERSION LAYERS IN TELLURIUM
M. von ORTENBERG and R. SILBERMANN Physikalisches Institut der Universitiit Wiirzburg, D-87, Wiirzburg, West Germany
We present measurements of the submillimeter cyclotron resonance of electrons and holes in electric subbands on [O,O,O,l] and [ 1 ,i,O,O] tellurium surfaces [ 1,2]. As insulating layer in the applied MIS arrangement we used a Hostaphan foil of 6.3 pm thickness and a dielectric constant of E = 3.2 co. The special advantage of the MIS arrangement in comparison with the MOS device is that the influence of chemical and mechanical treatment of the surface can easily be investigated. By a special etching procedure a chemical accumulation of about 2 X 1012 e cm-2 could be generated, and the corresponding threshold voltage shifted over a range of more than 1 kV. To separate the weak surface resonance from the strong bulk cyclotron resonance lines of the substrate, we used both square wave and harmonic modulation of the electric field and detected the surface signal by phase sensitive amplification. Our experiments were performed with a continuous wave HCN molecular gas laser spectrometer described previously [3]. The magnetic field was applied parallel (Bllc) or perpendicular (Blc) to the trigonal c-axis of the samples, which were shaped as non-plane parallel slabs. Simultaneously to the optical transmission the magneto resistance of the samples was investigated and provided the necessary information to distinguish in the optical resonance spectra between occupation effects as predicted by Ando [4] and the splitting of the cyclotron resonance due to different mass parameters. The phase sensitive detection made possible to record for both inversion and accumulation layer pronounced resonance lines shown in fig. 1 for the orientation f?jI c. The recordings represent the cyclotron resonance curves for 3 11 and 337 pm wavelength radiation of the surface electron and hole in the upper and lower part, respectively. Because of the absorbing p-type substrate, the surface resonance curves exhibit a pseudo splitting originating from the cyclotron resonance absorption of free holes in the bulk material. For an optimal understanding of the experimental data we simulated the resonance curves. In the calculation we have taken account of the definite dielectric multilayer structure of the wedged MIS arrangement as schematically represented in fig. 2. The theoretical results basing on a Drude model and the experimental data are plotted for comparison in fig. 3 by broken and solid curves, respectively. The experimental situation of the gate-voltage modulation is simulated by the difference 202
M. von Ortenberg, R. Silbermann
l-
/Surface
I
I
203
cyclotron resonance
I
I
X=337(vm)
Ug=l777+~sinwtJlV) 2
~
Ugsf-555+&&sinot)lV) 2
L
I
I
0
20
40 Magnetic
I
I
80 Field,
Blk%aussl
Fig. 1. The cyclotron resonance spectra of electrons and holes in a tellurium [OOOl] surface in the upper and lower part respectively are recorded for 311 and 337 pm wavelength radiation. Besides of the common pseudo-splitting due to substrate absorption the resonance curves exhibit different line position and shape.
of the theoretical transmissions of the corresponding two surface densities Nl and N2 given by the parameters in fig. 3. To achieve a reasonable agreement with the experimental line intensity, we had to assume that only about 50% of the electric field induced charge contributes to the surface subbands. This assumption is corroborated by the Shubnikov-De Haas (SdH) results of Silbermann and Landwehr [5]. In fig. 3 this reduction is depicted by two different parameter sets for each of the lines corresponding to the capacitically determined charge density and the fit value. The mass and wr values used in the simulation are me = 0.117 mo, wr, = 4.34, m h = 0.144 mo, and arh = 4.0 for the surface electron and surface hole, respectively. The bulk concentration of the 0.5 mm thick sample is 1013 cme3. In contrast to the case of plane parallel samples, where the line position is substantially shifted by interference effects [6], for wedged samples the line position is rather unaffected. The line width, however, is increased comparatively with the line
204
M. von Ortenberg, R. Silbermann / Surface cyclotron resonance
E$i?-Wtl
/I
Fig. 2. The schematic arrangement of a wedged multilayer system depicts the complex optical boundary problem.
width of the resonant dielectric tensar component. The line shape of the electron resonance is better approximated by the constant T model (broken curves in fig. 3) than by a magnetic field dependent relaxation time of the form r h Bw0s5 as suggested by Ando (dotted curve in fig. 3) [4]. In addition to such a r dependent distortion, the line shape should exhibit at low temperatures population effects, which seem not to be present in our data. The line shape of the surface hole resonance has a less good agreement with the constant r model. We attribute this to a splitting of the resonance, which was resolved in some of our samples at high surface hole density. The resonance position of the surface electron is almost independent of the gate voltage, whereas the surface hole resonance shifts considerably to higher magnetic field intensities with increasing gate voltage. This implies an increase of the corresponding cyclotron mass of the surface hole from 0.112 to 0.18 depending on the gate voltage. For the orientation Blc the surface resonance spectra exhibit a completely different mult~ine structure. The corresponding mass parameters as function of the gate voltage are plotted in fig. 4. Both position and shift with the gate voltage of
M. von Ortenberg, R. Silbermann /Surface
I
cyclotron resonance
1
1
205
I
1
;: NI=0.78~10'*& 2 // vN2=0
1
20
I
LO Magnetic
1
1
80
60kG Field
B
Fig. 3. The theoretical resultsbasingon a constant T model (broken curves) are in better agreement with the experimental data (solid curves) than the simulation, which includes a magnetic field dependent relaxation time of the form r - B-o.5 (dotted curve). To fit the line intensity we had to assume that only about 50% of the electric field induced charge contributes to the surface subbands. The parameters indicate the two surface densities corresponding to the two peak values of the modulated gate voltage. The mass and wr values for surface electrons and holes are me = 0.117 mo, wre = 4.34, mh = 0.144 m. and Wrh = 4.0 respectively. The bulk concentration of the 0.5 mm thick substrate is 1013 cm-a.
the hole resonance can be interpreted semiquantitatively within the framework of the existing valence band models and agrees with complementary SdH measurements [5]. For the electron from the existing conduction band model, however, only one resonance line is expected [7], whereas a total of at least four different resonance positions can be identified. The mass parameter of the most dominant line deviates considerably from the value given by Button et al. [8] and Shinno et al. [7].
M. van Ortenberg, R. Silbermann /Surface
206
cyclotron resonance
0.3 -
21r m.
4
. -*-.-
-0-e
2-
1_.Electron
Hole ‘r,
0+-l-
-*-•.-•.-@i
/ Ye
l-
I
-p*_ Tellurium
Blc
X=337vm
T-2K
l
T.35Ka o-
I -lo00
I -500
I l
Gate
Voltage
500
I
l1000 v
1
Ug
Fig. 4. The different cyclotron mass values of electrons and holes in a [ 1100] demonstrate the complicated Landau level system for Blc.
tellurium
surface
References [II M. von Ortenberg PI M. von Ortenberg [31 141 I51
161 [71 [81
and R. Silbermann, Solid State Commun. 17 (1975) 617. and R. Silbermann, Intern. Conf. on Infrared Physics, Zurich, 1975. M. von Ortenberg, in: Proc. 1st Intern. Conf. on Submillimeter Waves and Their Application; in: IEE-MIT 12 (1974) 1081. T. Ando, J. Phys. Sot. Japan 38 (1975) 989. R. Silbermann, G. Landwehr, J. Bouat and J.C. Thullier, in: Proc. 2nd Intern. Conf. on Solid Surfaces, Kyoto; Japan. J. Appl. Phys. (Suppl. 2) Pt. 2 (1974) 359; R. Silbermann and G. Landwehr, Solid State Commun. 16 (1975) 1055; R. Silbermann and G. Landwehr, Surface Sci. 58 (1976) 252. M. von Ortenberg, Solid State Commun. 17 (1975) 1335. H. Shinno, R. Yoshizaki, S. Tanaka, T. Doi and H. Kamimura, J. Phys. SOC. Japan 35 (1973) 525. K.J. Button, G. Landwehr, G.G. Bradley, P. Grosse and B. Lax, Phys. Rev. Letters 23 (1969) 14.