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Cyclotron resonance of electrons in 6H-SiC in high magnetic fields up to 50 T
Physica B 246—247 (1998) 270—273
Cyclotron resonance of electrons in 6H-SiC in high magnetic fields up to 50 T M. Goiran!,*, F. Engelbrecht", F. Yang!, W. Knap#, S. Huant$, N. Negre!, R. Barbaste!, J. Leotin!, R. Helbig", S. Askenazy! ! Service National des Champs Magne& tiques Pulse& s, LPMC, Complexe Scientifique de Rangueil, INSA, 31077 Toulouse, Cedex, France " Institute of Applied Physics, University Erlangen-Nu( rnberg, Staudtstr. 7, 91058 Erlangen, Germany # GES-USTL, Place Euge% ne Bataillon-34000 Montpellier, France $ Grenoble High Magnetic Field Laboratory, MPI-FKF and CNRS, BP 166, 38042 Grenoble, France
Abstract Cyclotron resonance in a bulk single crystal of n-type 6H-SiC was studied in magnetic fields up to 50 T. The measurements were carried out in three directions of the magnetic field with respect to the crystallographic axes. In the case of the magnetic field parallel to the c-axis the cyclotron mass equal to (0.45$0.02)m was found, which is in 0 agreement with theoretical predictions and experimental results obtained for epitaxial layers at low magnetic fields reported in the literature. The spectra obtained for the magnetic field perpendicular and parallel to the c-axis differ essentially. The observed dependence of the shape of a spectrum on a mutual direction of the magnetic field and the c-axis is attributed to an anisotropy of the effective mass tensor in the C—M—K plane of the Brillouin zone. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: 6H-SiC; Cyclotron resonance; Electronic effective masses; Anisotropy
1. Introduction The need for semiconductor devices at high temperatures, high power and high frequency results in a rapidly growing interest in the wide band-gap semiconductor SiC [1]. In particular, many authors studied the dispersion relation of the conduction band minimum of 6H-SiC both theoretically and by different experimental techniques. All * Corresponding author. Tel.: 33 6155 99 64; fax: 33 (0)5 61 55 99 50; e-mail: [email protected].
recent calculations of the band structure of 6H-SiC predict the position of the minimum of the conduction band along the M—¸ direction of the Brillouin zone, an anisotropic effective mass tensor with three independent components and a “camel’s back” shape [2] of the dispersion curve of the conduction band minimum along the M—L direction [3—7]. Reported values of components of the effective mass tensor in 6H-SiC were obtained by different experimental techniques: plasma reflectivity [8], Raman scattering [9], Faraday rotation [10], analysis of intra-center shallow donor absorption
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spectra [11,12] and optically detected cyclotron resonance (ODCR) [13]. However, the experimental and theoretical values of the effective mass exhibit a large scatter and do not provide a consistent picture of the conduction band structure [14]. Recently, it was shown by an analysis of intrashallow donor transition spectra in 6H-SiC in high magnetic fields that the effective mass tensor of 6HSiC has three independent components [14]. In this work, we report on the cyclotron resonance (CR) experiments carried out on bulk 6H-SiC crystals in high magnetic fields. The results give additional insight into the problem of the effective mass anisotropy in this material.
2. Experiment The samples used in this experiment were cut from unintentionally nitrogen-doped n-type 6HSiC single crystals grown by a modified Lely sublimation technique at the Siemens Research and Development Center in Erlangen [15,16]. The room-temperature free carrier concentration of the samples studied were in the range 2.0]1016—6.0] 1017 cm~3 and a maximum mobility of about k"800 cm2/V s, as determined by the Hall effect measurements. The magneto-transmission experiments were performed in the Faraday configuration with a far infrared spectrometer based on 40 and 60 T quasistatic pulsed magnets with a typical duration time of 1.3 and 0.5 s, respectively. The excitation energies were generated by a far infrared cavity optically pumped by a CO laser. The mag2 neto-transmission spectra were recorded at excitation energies from 3 to 10 meV. The magnetic field was determined with an accuracy of 2%. In order to optimize both the conduction band population and the free carrier mobility the temperature of the sample was set at ¹"200 K. The measurements were performed in three directions of the magnetic field: BDDc,BDD(1 1 0 0) and BDD(1 1 2 0) (Fig. 1).
3. Results and discussion In Fig. 2 the cyclotron resonance absorption spectra for BDDc are displayed for different excitation
Fig. 1. Brillouin zone of 6H-SiC with points of high symmetry in k-space and the directions corresponding to the three main crystallographic axes in the real space.
Fig. 2. Magneto-transmission spectra due to electron CR-absorption in the configuration BDDc (¹"200 K). The continuous lines are obtained by a fitting procedure described in the text.
energies. The continuous curves show the results of fitting the experimental data with the classical Drude formula for the cyclotron resonance absorption taking into account both circular polarizations. Due to a low electron mobility the absorption peaks are very broad with a line width of the order of 30 T. A good fit of the experimental data was obtained with the mobility k"800 cm2/V s, which agrees well with the values obtained from transport measurements [17].
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M. Goiran et al. / Physica B 246—247 (1998) 270—273
Fig. 3. Excitation energy versus resonant magnetic field according to Fig. 2. The linear extrapolation of the data gives a cyclotron effective mass m*"0.45 ($0.02)m . For a comparison the value from ODCR measurements [13] at low energy is shown. 0
Fig. 3 shows the relation between the excitation energy and the resonant magnetic field, as determined by the fitting procedure. A linear dependence of the excitation energy on the magnetic field shows that the contributing conduction bands are parabolic. The CR effective mass extracted from Fig. 3 is equal to (0.45$0.02)m . This is in good 0 agreement with the value of 0.42, deduced from ODCR experiments by Son et al., and predictions of band structure calculations [7]. In general, for an anisotropic mass in the M—C—¸ plane, when the magnetic field is perpendicular to the c-axis, three absorption peaks are expected which correspond to three different cyclotron masses. For high symmetry directions like (1 1 0 0) or (1 1 2 0), two cyclotron resonance energies are degenerated. For BDD(1 1 0 0) and for an excitation energy of 4.03 meV a broad peak occurs in the transmission spectrum with a minimum around 35 T. We do not assign any particular cyclotron mass to this minimum as one can suppose that, owing to the multivalley structure of the conduction band, it might result from the superposition of more than one CR. Due to the low carrier mobility, it was not possible
to clearly resolve the nature of this absorption peak and thus to determine how many cyclotron masses are involved. The only conclusion that can be deduced from this result, is that any resonance involved in the spectrum corresponds to a cyclotron mass more than two times heavier than that found for BDDc. For BDD(1 1 2 0), no transmission minimum up to 50 T was detected in the above-cited excitation energy range. This is probably due to a high value of the corresponding components of the effective mass tensor that shifts the CR to higher magnetic fields and reduces the mobility (broadening of the CR line). In conclusion, the CR measurements clearly indicate a high anisotropy of the effective mass in the conduction band minimum of 6H-SiC. The value of the effective mass in the case of the magnetic field parallel to the c-axis was determined to be (0.45$0.02)m . For the magnetic field perpendicu0 lar to the c-axis the cyclotron resonance masses are at least two times higher. The results show also necessity of further experiments in higher magnetic fields to clarify the problem of the 6H-SiC conduction band structure.
M. Goiran et al. / Physica B 246—247 (1998) 270—273
Acknowledgements The authors thank Dr. Stein of the Siemens Research Laboratories in Erlangen for supplying the samples. This work was supported in part by the Deutsche Forschungsgemeinschaft within Sonderforschungsbereich 292.
References [1] S. Nakashima, H. Matsunami, S. Yoshida, H. Harima, (Eds.), Proc. 6th Int. Conf. on Silicon Carbide and Related Materials, Kyoto, Conf. Ser. vol.142, Bristol, Institute of Physics Publishing, 1995. [2] P. Lawaetz, Solid State Commun. 16 (1975) 65. [3] K. Karch, G. Wellenhofer, P. Pavone, U. Ro¨{ler, D. Strauch, in: D.J. Lockwood (Ed.), Proc. 22nd Int. Conf. Phys. Semicond., World Scientific, Singapore, 1994, p. 401. [4] P. Kaeckell, B. Wenzien, F. Bechstedt, Phys. Rev. B 50 (1994) 10761. [5] W.R.L. Lambrecht, in: C.H. Carter et al. (Eds.), Diamond, SiC and Nitride Wide Bandgap Semiconductors, Mat. Res. Symp. Proc., vol. 339, Pittsburgh, 1994, p. 565.
273
[6] W.H. Backes, P.A. Bobbert, W. van Haeringen, Phys. Rev. B 49 (1994) 7564. [7] G. Wellenhofer, Ph.D. Thesis, University of Regensburg, 1997. [8] A.V. Mel’nichuk, Y.A. Pasechnik, Sov. Phys. Solid State 34 (1992) 227. [9] H. Harima, S. Nakashima, T. Uemura, J. Appl. Phys. 78 (1995) 1996. [10] B. Ellis, T.S. Moss, Proc. Roy. Soc. London Ser. A 299 (1967) 383. [11] O.V. Vakulenko, O.A. Guseva, Sov. Phys. Semicond. 15 (1981) 886. [12] W. Suttrop, G. Pensl, W.J. Choyke, R.A. Stein, S. Leibenzeder, J. Appl. Phys. 72 (1992) 3708. [13] N.T. Son, O. Kordina, A.O. Konstantinov, W.M. Chen, E. Sorman, B. Monemar, E. Janzen, Appl. Phys. Lett. 65 (1994) 3209. [14] F. Engelbrecht, S. Huant, R. Helbig, Phys. Rev. B 52 (1995) 11008. [15] G. Ziegler, P. Lanig, D. Theis, C. Weyrich, IEEE Trans. Electron. Dev. 30 (1983) 277. [16] R.A. Stein, P. Lanig, S. Leibenzeder, Mater. Sci. Eng. B 11 (1922) 55. [17] M. Schadt, G. Pensl, R.P. Devaty, W.J. Choyke, R. Stein, D. Stephani, Appl. Phys. Lett. 65 (1994) 3120.
Cyclotron resonance of electrons in 6H-SiC in high magnetic fields up to 50 T M. Goiran!,*, F. Engelbrecht", F. Yang!, W. Knap#, S. Huant$, N. Negre!, R. Barbaste!, J. Leotin!, R. Helbig", S. Askenazy! ! Service National des Champs Magne& tiques Pulse& s, LPMC, Complexe Scientifique de Rangueil, INSA, 31077 Toulouse, Cedex, France " Institute of Applied Physics, University Erlangen-Nu( rnberg, Staudtstr. 7, 91058 Erlangen, Germany # GES-USTL, Place Euge% ne Bataillon-34000 Montpellier, France $ Grenoble High Magnetic Field Laboratory, MPI-FKF and CNRS, BP 166, 38042 Grenoble, France
Abstract Cyclotron resonance in a bulk single crystal of n-type 6H-SiC was studied in magnetic fields up to 50 T. The measurements were carried out in three directions of the magnetic field with respect to the crystallographic axes. In the case of the magnetic field parallel to the c-axis the cyclotron mass equal to (0.45$0.02)m was found, which is in 0 agreement with theoretical predictions and experimental results obtained for epitaxial layers at low magnetic fields reported in the literature. The spectra obtained for the magnetic field perpendicular and parallel to the c-axis differ essentially. The observed dependence of the shape of a spectrum on a mutual direction of the magnetic field and the c-axis is attributed to an anisotropy of the effective mass tensor in the C—M—K plane of the Brillouin zone. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: 6H-SiC; Cyclotron resonance; Electronic effective masses; Anisotropy
1. Introduction The need for semiconductor devices at high temperatures, high power and high frequency results in a rapidly growing interest in the wide band-gap semiconductor SiC [1]. In particular, many authors studied the dispersion relation of the conduction band minimum of 6H-SiC both theoretically and by different experimental techniques. All * Corresponding author. Tel.: 33 6155 99 64; fax: 33 (0)5 61 55 99 50; e-mail: [email protected].
recent calculations of the band structure of 6H-SiC predict the position of the minimum of the conduction band along the M—¸ direction of the Brillouin zone, an anisotropic effective mass tensor with three independent components and a “camel’s back” shape [2] of the dispersion curve of the conduction band minimum along the M—L direction [3—7]. Reported values of components of the effective mass tensor in 6H-SiC were obtained by different experimental techniques: plasma reflectivity [8], Raman scattering [9], Faraday rotation [10], analysis of intra-center shallow donor absorption
0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 9 1 3 - 7
M. Goiran et al. / Physica B 246—247 (1998) 270—273
271
spectra [11,12] and optically detected cyclotron resonance (ODCR) [13]. However, the experimental and theoretical values of the effective mass exhibit a large scatter and do not provide a consistent picture of the conduction band structure [14]. Recently, it was shown by an analysis of intrashallow donor transition spectra in 6H-SiC in high magnetic fields that the effective mass tensor of 6HSiC has three independent components [14]. In this work, we report on the cyclotron resonance (CR) experiments carried out on bulk 6H-SiC crystals in high magnetic fields. The results give additional insight into the problem of the effective mass anisotropy in this material.
2. Experiment The samples used in this experiment were cut from unintentionally nitrogen-doped n-type 6HSiC single crystals grown by a modified Lely sublimation technique at the Siemens Research and Development Center in Erlangen [15,16]. The room-temperature free carrier concentration of the samples studied were in the range 2.0]1016—6.0] 1017 cm~3 and a maximum mobility of about k"800 cm2/V s, as determined by the Hall effect measurements. The magneto-transmission experiments were performed in the Faraday configuration with a far infrared spectrometer based on 40 and 60 T quasistatic pulsed magnets with a typical duration time of 1.3 and 0.5 s, respectively. The excitation energies were generated by a far infrared cavity optically pumped by a CO laser. The mag2 neto-transmission spectra were recorded at excitation energies from 3 to 10 meV. The magnetic field was determined with an accuracy of 2%. In order to optimize both the conduction band population and the free carrier mobility the temperature of the sample was set at ¹"200 K. The measurements were performed in three directions of the magnetic field: BDDc,BDD(1 1 0 0) and BDD(1 1 2 0) (Fig. 1).
3. Results and discussion In Fig. 2 the cyclotron resonance absorption spectra for BDDc are displayed for different excitation
Fig. 1. Brillouin zone of 6H-SiC with points of high symmetry in k-space and the directions corresponding to the three main crystallographic axes in the real space.
Fig. 2. Magneto-transmission spectra due to electron CR-absorption in the configuration BDDc (¹"200 K). The continuous lines are obtained by a fitting procedure described in the text.
energies. The continuous curves show the results of fitting the experimental data with the classical Drude formula for the cyclotron resonance absorption taking into account both circular polarizations. Due to a low electron mobility the absorption peaks are very broad with a line width of the order of 30 T. A good fit of the experimental data was obtained with the mobility k"800 cm2/V s, which agrees well with the values obtained from transport measurements [17].
272
M. Goiran et al. / Physica B 246—247 (1998) 270—273
Fig. 3. Excitation energy versus resonant magnetic field according to Fig. 2. The linear extrapolation of the data gives a cyclotron effective mass m*"0.45 ($0.02)m . For a comparison the value from ODCR measurements [13] at low energy is shown. 0
Fig. 3 shows the relation between the excitation energy and the resonant magnetic field, as determined by the fitting procedure. A linear dependence of the excitation energy on the magnetic field shows that the contributing conduction bands are parabolic. The CR effective mass extracted from Fig. 3 is equal to (0.45$0.02)m . This is in good 0 agreement with the value of 0.42, deduced from ODCR experiments by Son et al., and predictions of band structure calculations [7]. In general, for an anisotropic mass in the M—C—¸ plane, when the magnetic field is perpendicular to the c-axis, three absorption peaks are expected which correspond to three different cyclotron masses. For high symmetry directions like (1 1 0 0) or (1 1 2 0), two cyclotron resonance energies are degenerated. For BDD(1 1 0 0) and for an excitation energy of 4.03 meV a broad peak occurs in the transmission spectrum with a minimum around 35 T. We do not assign any particular cyclotron mass to this minimum as one can suppose that, owing to the multivalley structure of the conduction band, it might result from the superposition of more than one CR. Due to the low carrier mobility, it was not possible
to clearly resolve the nature of this absorption peak and thus to determine how many cyclotron masses are involved. The only conclusion that can be deduced from this result, is that any resonance involved in the spectrum corresponds to a cyclotron mass more than two times heavier than that found for BDDc. For BDD(1 1 2 0), no transmission minimum up to 50 T was detected in the above-cited excitation energy range. This is probably due to a high value of the corresponding components of the effective mass tensor that shifts the CR to higher magnetic fields and reduces the mobility (broadening of the CR line). In conclusion, the CR measurements clearly indicate a high anisotropy of the effective mass in the conduction band minimum of 6H-SiC. The value of the effective mass in the case of the magnetic field parallel to the c-axis was determined to be (0.45$0.02)m . For the magnetic field perpendicu0 lar to the c-axis the cyclotron resonance masses are at least two times higher. The results show also necessity of further experiments in higher magnetic fields to clarify the problem of the 6H-SiC conduction band structure.
M. Goiran et al. / Physica B 246—247 (1998) 270—273
Acknowledgements The authors thank Dr. Stein of the Siemens Research Laboratories in Erlangen for supplying the samples. This work was supported in part by the Deutsche Forschungsgemeinschaft within Sonderforschungsbereich 292.
References [1] S. Nakashima, H. Matsunami, S. Yoshida, H. Harima, (Eds.), Proc. 6th Int. Conf. on Silicon Carbide and Related Materials, Kyoto, Conf. Ser. vol.142, Bristol, Institute of Physics Publishing, 1995. [2] P. Lawaetz, Solid State Commun. 16 (1975) 65. [3] K. Karch, G. Wellenhofer, P. Pavone, U. Ro¨{ler, D. Strauch, in: D.J. Lockwood (Ed.), Proc. 22nd Int. Conf. Phys. Semicond., World Scientific, Singapore, 1994, p. 401. [4] P. Kaeckell, B. Wenzien, F. Bechstedt, Phys. Rev. B 50 (1994) 10761. [5] W.R.L. Lambrecht, in: C.H. Carter et al. (Eds.), Diamond, SiC and Nitride Wide Bandgap Semiconductors, Mat. Res. Symp. Proc., vol. 339, Pittsburgh, 1994, p. 565.
273
[6] W.H. Backes, P.A. Bobbert, W. van Haeringen, Phys. Rev. B 49 (1994) 7564. [7] G. Wellenhofer, Ph.D. Thesis, University of Regensburg, 1997. [8] A.V. Mel’nichuk, Y.A. Pasechnik, Sov. Phys. Solid State 34 (1992) 227. [9] H. Harima, S. Nakashima, T. Uemura, J. Appl. Phys. 78 (1995) 1996. [10] B. Ellis, T.S. Moss, Proc. Roy. Soc. London Ser. A 299 (1967) 383. [11] O.V. Vakulenko, O.A. Guseva, Sov. Phys. Semicond. 15 (1981) 886. [12] W. Suttrop, G. Pensl, W.J. Choyke, R.A. Stein, S. Leibenzeder, J. Appl. Phys. 72 (1992) 3708. [13] N.T. Son, O. Kordina, A.O. Konstantinov, W.M. Chen, E. Sorman, B. Monemar, E. Janzen, Appl. Phys. Lett. 65 (1994) 3209. [14] F. Engelbrecht, S. Huant, R. Helbig, Phys. Rev. B 52 (1995) 11008. [15] G. Ziegler, P. Lanig, D. Theis, C. Weyrich, IEEE Trans. Electron. Dev. 30 (1983) 277. [16] R.A. Stein, P. Lanig, S. Leibenzeder, Mater. Sci. Eng. B 11 (1922) 55. [17] M. Schadt, G. Pensl, R.P. Devaty, W.J. Choyke, R. Stein, D. Stephani, Appl. Phys. Lett. 65 (1994) 3120.