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Frequency dependent effective masses in Si inversion layers at metallic densities
Surface Science 58 (1976) 185-186 0 North-Holland Publishing Company
FREQUENCY
DEPENDENT EFFECTIVE MASSES IN Si INVERSION LAYERS
AT METALLIC DENSITIES
T.A. KENNEDY
l, R.J.
Naval Research Laboratory,
WAGNER and B.D. McCOMBE Washington, DC 20375,
USA
and D.C. TSUI Bell Laboratories, Murray Hill, New Jersey 079 74, USA
Cyclotron resonance studies [ 1] of the two-dimensional electron gas (2 DEG) realized on semiconductor surfaces are providing a wealth of information complementary to that obtained from transport studies. We report here our studies of the frequency dependence of cyclotron resonance (CR) in (lOO)Si MOSFET’s from 11.2 to 52.4 cm- 1 at high electron densities. The experiments were performed with an optically-pumped far-infrared (FIR) laser on samples with mobilities of 6500 and 4800 cm*/V sec. By coherently switching the MOSFET gate with alternate laser pulses, it is possible to record the transmission changes associated exclusively with the 2 DEG. Lineshape distortions owing to multiple internal reflections in plane parallel Si substrates were eliminated by using wedged substrates. Additional distortions at long wavelength owing to partial circular polarization of the coherent radiation by light pipe optics were eliminated by placing a linear polarizer immediately in front of the sample. Our studies of the CR linewidth over a wide frequency range at fixed electron density show a scattering rate l/7 which depends on magnetic field to the one-half power when w,~ > 2. This field dependent scattering is also evident in a particular cyclotron resonance line as a broadening to the high field side. The data has been analyzed by using the susceptibility calculated by Chiu et al. [2] and a scattering rate l/7 = yB1/* for wc~ > 2 as predicted by Ando and Uemura [3] for the high field, short range scattering limit. For w,~ < 2, the data are best fit with 7 = const. Ando and Uemura also predict that the CR scattering rate is related to the dc mobility scattering rate by y* = 2e/(nm*cTd,). In our two samples the y’s calculated from the above expression using measured values of rdc are 30% greater than those obtained from cyclotron resonance. With the lineshape and scattering rate in this system understood, it is possible to * NRC-NRL
Resident Research Associate. 185
186
T.A. Kennedy et al. /Frequency
dependent effective
masses in Si inversion layers
extract effective masses from the data. Theoretical analysis by Ando [3] shows that the short range scattering should not give rise to any direct mass renormalization. Fitting the data gives effective masses which vary from 0.193 m,, at 52.4 cm-’ to 0.220 m0 at 11.2 cm- 1 at electron density n = 1.5 X 101* cm- * for the higher mobility sample. While at the higher frequencies the effective mass is density independent for 7 X 1011
References [l]
[2]
[ 31
[4] (51 [6] [7] [8]
J.F. Koch, Surface Sci. 58 (1976) 104; J.F. Koch, in: Festkorperprobleme (Advances in Solid State Physics), Vol. 15, Ed. H.J. Queisser (Pergamon/Vieweg, Braunschweig, 1975) p. 79. K.W. Chiu, T.K. Lee and J.J. Quinn, Surface Sci. 58 (1976) 182. T. Ando and Y. Uemura, in: Proc. 12th Intern. Conf. on the Physics of Semiconductors, Stuttgart, 1974 (Teubner, Stuttgart, 1974) p. 724; T. Ando, J. Phys. Sot. Japan 38 (1975) 989. J.L. Smith and P.J. Stiles, Phys. Rev. Letters 29 (1972) 102. W. Kohn, Phys. Rev. 123 (1961) 1242. C.S. Ting, T.K. Lee and J.J. Quinn, Phys. Rev. Letters 34 (1975) 870. B. Vinter, Phys. Rev. Letters 35 (1975) 1044. T.A. Kennedy, R.J. Wagner, B.D. McCombe and D.C. Tsui, Phys. Rev. Letters 35 (1975)
1031.
FREQUENCY
DEPENDENT EFFECTIVE MASSES IN Si INVERSION LAYERS
AT METALLIC DENSITIES
T.A. KENNEDY
l, R.J.
Naval Research Laboratory,
WAGNER and B.D. McCOMBE Washington, DC 20375,
USA
and D.C. TSUI Bell Laboratories, Murray Hill, New Jersey 079 74, USA
Cyclotron resonance studies [ 1] of the two-dimensional electron gas (2 DEG) realized on semiconductor surfaces are providing a wealth of information complementary to that obtained from transport studies. We report here our studies of the frequency dependence of cyclotron resonance (CR) in (lOO)Si MOSFET’s from 11.2 to 52.4 cm- 1 at high electron densities. The experiments were performed with an optically-pumped far-infrared (FIR) laser on samples with mobilities of 6500 and 4800 cm*/V sec. By coherently switching the MOSFET gate with alternate laser pulses, it is possible to record the transmission changes associated exclusively with the 2 DEG. Lineshape distortions owing to multiple internal reflections in plane parallel Si substrates were eliminated by using wedged substrates. Additional distortions at long wavelength owing to partial circular polarization of the coherent radiation by light pipe optics were eliminated by placing a linear polarizer immediately in front of the sample. Our studies of the CR linewidth over a wide frequency range at fixed electron density show a scattering rate l/7 which depends on magnetic field to the one-half power when w,~ > 2. This field dependent scattering is also evident in a particular cyclotron resonance line as a broadening to the high field side. The data has been analyzed by using the susceptibility calculated by Chiu et al. [2] and a scattering rate l/7 = yB1/* for wc~ > 2 as predicted by Ando and Uemura [3] for the high field, short range scattering limit. For w,~ < 2, the data are best fit with 7 = const. Ando and Uemura also predict that the CR scattering rate is related to the dc mobility scattering rate by y* = 2e/(nm*cTd,). In our two samples the y’s calculated from the above expression using measured values of rdc are 30% greater than those obtained from cyclotron resonance. With the lineshape and scattering rate in this system understood, it is possible to * NRC-NRL
Resident Research Associate. 185
186
T.A. Kennedy et al. /Frequency
dependent effective
masses in Si inversion layers
extract effective masses from the data. Theoretical analysis by Ando [3] shows that the short range scattering should not give rise to any direct mass renormalization. Fitting the data gives effective masses which vary from 0.193 m,, at 52.4 cm-’ to 0.220 m0 at 11.2 cm- 1 at electron density n = 1.5 X 101* cm- * for the higher mobility sample. While at the higher frequencies the effective mass is density independent for 7 X 1011
References [l]
[2]
[ 31
[4] (51 [6] [7] [8]
J.F. Koch, Surface Sci. 58 (1976) 104; J.F. Koch, in: Festkorperprobleme (Advances in Solid State Physics), Vol. 15, Ed. H.J. Queisser (Pergamon/Vieweg, Braunschweig, 1975) p. 79. K.W. Chiu, T.K. Lee and J.J. Quinn, Surface Sci. 58 (1976) 182. T. Ando and Y. Uemura, in: Proc. 12th Intern. Conf. on the Physics of Semiconductors, Stuttgart, 1974 (Teubner, Stuttgart, 1974) p. 724; T. Ando, J. Phys. Sot. Japan 38 (1975) 989. J.L. Smith and P.J. Stiles, Phys. Rev. Letters 29 (1972) 102. W. Kohn, Phys. Rev. 123 (1961) 1242. C.S. Ting, T.K. Lee and J.J. Quinn, Phys. Rev. Letters 34 (1975) 870. B. Vinter, Phys. Rev. Letters 35 (1975) 1044. T.A. Kennedy, R.J. Wagner, B.D. McCombe and D.C. Tsui, Phys. Rev. Letters 35 (1975)
1031.