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Far-infrared magneto-spectroscopy of photo-excited carriers in tellurium
Solid State Communications, Vol. 33, pp. 199—201. Pergamon Press Ltd. 1980. Printed in Great Britain. FAR-INFRARED MAGNETO-SPECTROSCOPY OF PHOTO-EXCITED CARRIERS IN TELLURIUM Y. Nisida,* M. von Ortenberg and W. Weber Physikalisches Institut der Universität Wurzburg, Rontgenring 8, D-8700 Wurzburg, West Germany (Received 17 Sep ~ember1979 by Y. Toyozawa) The FIR transmission spectra of photo-carriers have been studied in undoped tellurium to obtain information on the conduction band, using 337pm radiation. As a result, the electron cyclotron resonance is too broad to be separated clearly from the hole one. The electron cyclotron mass is concluded to be 0.11 ±0.02m0 for both B II C and B I C. A subsidiary peak is observed in a low field region, which is ascribed to a donor state with the binding energy of 2.6meV. 1. INTRODUCTION TELLURIUM is always a p-type semiconductor whose valence bands have been mvestigated intensively by magneto-transport and magneto-optical experiments [1—3].Despite repeated efforts of chemical doping, no n-type tellurium could be obtained. Consequently the experimental information on the conduction band is rather poor. Theoretically the extrema of the conduction band are located on the c-axis near the H point of the Brillouin zone, and the complicated splitting of the Landau levels due to a k-linear term is predicted [4]. By the interband magneto-absorption, the band parameters of the conduction band are obtained experimentally, but the result is not independent of the knowledge of the valence band [4, 5]. The objective of the present study is to derive a direct information of the conduction band from observation of the cyclotron resonance of electrons generatedby interband excitation. Other methods to populate the conduction band were previously attempted. One is the thermal excitation at high temperature [61. Since the conduction band of tellurium is not simply parabolic, the cyclotron resonance spectrum is expected to change with ternperature, due to unequal spacing of Landau levels. Also high temperature involves a considerable decrease in mobility, so that the cyclotron resonance is less resolved, The second method is to employ a surface inversion layer in MIS structure. The confmement of electrons to the surface thin layer brings about additional quantization within the surface potential [7, 8]. The present method, the photo-excitation, has the advantage that high temperature and additional quantizing effects can be avoided, but inevitably results in the disadvantage
*
Alexander von Humboldt fellow. Present Address: Engineering Science, Osaka University, Machikaneyama 1-1, 560, Toyonaka, Osaka, Japan. 199
that both electrons and holes are generated simultaneously. Assuming the photo-hole resonances are the same as the bulk ones we can identify the photoelectron resonances. It is interestmg to compare the electron th d resonance spectra observed with various me o
5~
2. EXPERIMENTAL ARRANGEMENTS The experimental system for observing the cyclotron resonance of photo-carriers is similar to that of [9]. The sample was mounted in the center of 12 T magnet, in the manner of Fig. 2(b) of the above reference. The exciting interband radiation was guided to the sample through glass-fibers from a halogen lamp. The conventional HCN laser was used as FIR source. The sample was directly immersed in liquid helium to prevent from heating as much as possible. Three kinds of FIR spectra were observed for different purposes. (1) The direct transmission of the sample without the exciting radiation was detected to find the bulk-hole cyclotron resonance. (2) The differential absorption synchronized with the chopped exciting radiation was recorded to fmd the resonance absorption associated with photoelectrons and -holes. This spectrum is called the optical modulation. (3) The differential absorption correlating to application of a square-wave current across the sample without the exciting radiation was observed. The current modulation induces a change in hole distribution by the hot-hole effects and the impact ionization of bound holes, but no change in unoccupied conduction band. This spectrum indicates the absorption of holes in nonthermal equilibrium and is called the power modulation. Comparison of the spectra (2) and (3) is useful to distinguish the absorption of photo-electrons from that of photo-holes. The samples were carefully prepared by standard techniques for tellurium from different, undoped crystals [1]. The hole concentration of the 3. samples was of the order of 10i3 cm
200
PHOTO-EXCITED CARRIERS IN TELLURIUM
~a C .9 C U, 0.05 C
Powe
a
L~
lation I
Vol. 33, No. 2
~2Bc a 0.01
C 0 C, U E 0 C
2’ 00005
Optica
9
E
~
C U,
1 ~337pm
T’2~
0______________________ 2 4 Magnetic Field BlTesta)
6
C
a C
X3
.2
1’~ C
0
2
Fig. 2. The spectra of the direct transmission (lower) and the optical modulation (upper) of the sample prepared from another crystal. The optical modulation spectrum exhibits a broad hump at around 0.63 T, which does not appear in Fig. 1. This additional absorption may possibly be associated to a donor impurity with the binding energy 2.6meV.
6 Magnetic
Field
BITesla)
Fig. 1. The spectra of the direct transmission, optical and power modulation of undoped tellurium (B II C) are shown in the lower, middle and upper part, respectively. In the direct transmission, the bulk-hole resonance and impurity absorption appear at around 3.6 and 2.4 T, respectively. In the optical and power modulation, the ordinate denotes the decrease of transmitted radiation intensity and thus the increases of absorption.
I
I
Ui
1~ C U, 0 is
HW 1e43#4 XU337~Jm T~2K
Dir.Tr/100
2
8
1.
6 Magnetic Field B(Iesta)
8
10
12
Fig. 3. The spectra of the optical modulation (solid curve) and the direct transmission (broken curve) for the orientation B I C. The notation of the transmission minima is after the paper of Dreybrodt er al., Solid State Commun. 8, 1021 (1970).
Vol.33, No.2
PHOTO-EXCITED CARRIERS IN TELLURIUM
3. EXPERIMENTAL RESULTS AND DISCUSSIONS Figure 1 shows the observed spectra for the magnetic field orientation of B II C. The direct transmission spectrum in the lower part exhibits a dominant dip of the hole cyclotron resonance at about 3.6 T and a weak resonance of residual acceptor impurities at about 2.4 T. This spectrum is regarded as reference for other kinds of modulation spectra, because the transmitted radiation intensity is always affected by the bulk-hole absorption. The upper part of Fig. 1 denotes the power modulation spectra for two values of current. The square-wave current produces the heat of 3.6 and 6.2 mJ per pulse for the two curves (300 and 500 mW in average power, respectively). The remarkable increase of absorption occurs at higher magnetic field of the bulk-hole resonance. This result gives the relation between the shift of the resonance energy and the deviation from the thermal equilibrium distribution of holes. The middle part shows the optical modulation spectra for three different intensities of the exciting radiation. For the following interpretation it is of essential importance that the photo-excited carriers are uniformly distributed in the sample of 1 mm thick, because otherwise interference effects would seriously obscure the spectra. This assumption is well supported by the results of [10] and [11]. A broad resonance is modulated by the bulkhole resonance and its peak is slightly shifted to lower magnetic field intensity from the bulk resonance. It is natural to conclude that the broad resonance curve consists of a superposition of two resonances of photoelectrons and -holes, and the two resonances almost coincide. Excitonic effects should be negligible because of the small binding energy (0.69 meV) [4] and the short life-time. From the dip of the direct transmission spectrum and the peak of the normalized curve of the optical modulation spectrum, we obtain the cyclotron mass of holes, m~= 0.llm0 and of electrons, m~= (0.11 ±0.02)m0, respectively, for B C. This electron mass is consistent with the previous results [4—8]. Figure 2 shows the similar spectra of the sample prepared from another crystal. The difference in the optical modulation spectrum is a hump at about 0.63 T, which is not found in Fig. 1. This low-field absorption does not appear in the direct transmission and its appearance depends on the source of samples. Therefore, we conclude that the new resonance must be related to a transition of the electron from an unknown impurity state. Since the intensity of the acceptor levels in tellurium is extremely sensitive on the origin of the sample material, as pointed out by von Klitzing [121, the same situation is expected to hold for the donor state. Based on the assumption that a transition from the impurity ground state into the second Landau level
201
is responsible to this absorption, the binding energy of the donor ground state is estimated to be of the order of EB 2.6meV. For the complementary orientation B I C, the spectra of the optical modulation and direct transmission are shown in Fig. 3. Both spectra exhibit a multi-line structure, because the lower symmetry leads to more allowed transitions. The position of the well-known hole absorption lines, H3 to H6, are indicated. The two small high-field peaks seem to be correlated with the H5 and H6 transitions of optically excited holes. The dominant broad inain line centered at about 3.6 T, however, should be a superposition of both electron and H3, H4-hole resonances. Due to the large halfwidth of these transitions of the excited carriers there is no way for separating them into components. From the resulting peak position, however, we can conclude, that the electron cyclotron mass is within the limits of me = (0.11 ± 0.02)m0. This value agrees quite well with the results of cyclotron resonance of thermally excited electrons and of electrons in inversion layers [6, 8] In summary the FIR-transmission spectra of charge carriers excited by the interband radiation in tellurium can be explained by the cyclotron resonance of free electrons and holes, and a transition from a bound state associated with the conduction band. Acknowledgement The work was supported by the Alexander von Humboldt Foundation for one of the authors (Y.N.). He expresses his sincere gratitude to Professor G. Landwehr for many courtesies during his stay in the Institute in Wilrzburg. —
REFERENCES 1. 2. 3. 4. ~•
6. 7. 8. 9. 10. 11. 12.
M. von Ortenberg & K.J. Button, Phys. Rev. B6, 2100 (1972). M. von Ortenberg & K.J. Button,Phys. Rev. B16, 2618 (1977). E. Braun & L.J. Neuringer, Proc. 10th mt. Conf Phys. Semicond., p. 352. Cambridge (1970). H. Shinno, R. Yoshizaki, S. Tanaka, T. Doi & H. Kamimura.J. Phys. Soc. Japan 35. 525 (1973). J. Blinowski, G. Rebmann, G. Rigaux & J. Mycielski,J. Phys. 38, 1139 (1977). K.J. Button, G. Landwehr, G.G. Bradley, P. Grosse & B. Lax, Phys. Rev. Lett. 23, 14 (1969). M. von Ortenberg & R. Silbermann, Solid State Commun. 17, 617 (1975). M. von Ortenberg & R. Silbermann, Surf Sci. 58, 202 (1976). Y. Nisida, K. Muro & U. Kawata, Infrared Phys. 16,207 (1976). G. Guthmann, G. Hermann & J.M. Thuillier, Phys. Status Soildi (a) 3,365 H. Kranz, Unpublished thesis,(1970). Wurzburg Univ. (1971). K. von Klitzing, Unpublished thesis, Wurzburg Univ. (1977).
*
Alexander von Humboldt fellow. Present Address: Engineering Science, Osaka University, Machikaneyama 1-1, 560, Toyonaka, Osaka, Japan. 199
that both electrons and holes are generated simultaneously. Assuming the photo-hole resonances are the same as the bulk ones we can identify the photoelectron resonances. It is interestmg to compare the electron th d resonance spectra observed with various me o
5~
2. EXPERIMENTAL ARRANGEMENTS The experimental system for observing the cyclotron resonance of photo-carriers is similar to that of [9]. The sample was mounted in the center of 12 T magnet, in the manner of Fig. 2(b) of the above reference. The exciting interband radiation was guided to the sample through glass-fibers from a halogen lamp. The conventional HCN laser was used as FIR source. The sample was directly immersed in liquid helium to prevent from heating as much as possible. Three kinds of FIR spectra were observed for different purposes. (1) The direct transmission of the sample without the exciting radiation was detected to find the bulk-hole cyclotron resonance. (2) The differential absorption synchronized with the chopped exciting radiation was recorded to fmd the resonance absorption associated with photoelectrons and -holes. This spectrum is called the optical modulation. (3) The differential absorption correlating to application of a square-wave current across the sample without the exciting radiation was observed. The current modulation induces a change in hole distribution by the hot-hole effects and the impact ionization of bound holes, but no change in unoccupied conduction band. This spectrum indicates the absorption of holes in nonthermal equilibrium and is called the power modulation. Comparison of the spectra (2) and (3) is useful to distinguish the absorption of photo-electrons from that of photo-holes. The samples were carefully prepared by standard techniques for tellurium from different, undoped crystals [1]. The hole concentration of the 3. samples was of the order of 10i3 cm
200
PHOTO-EXCITED CARRIERS IN TELLURIUM
~a C .9 C U, 0.05 C
Powe
a
L~
lation I
Vol. 33, No. 2
~2Bc a 0.01
C 0 C, U E 0 C
2’ 00005
Optica
9
E
~
C U,
1 ~337pm
T’2~
0______________________ 2 4 Magnetic Field BlTesta)
6
C
a C
X3
.2
1’~ C
0
2
Fig. 2. The spectra of the direct transmission (lower) and the optical modulation (upper) of the sample prepared from another crystal. The optical modulation spectrum exhibits a broad hump at around 0.63 T, which does not appear in Fig. 1. This additional absorption may possibly be associated to a donor impurity with the binding energy 2.6meV.
6 Magnetic
Field
BITesla)
Fig. 1. The spectra of the direct transmission, optical and power modulation of undoped tellurium (B II C) are shown in the lower, middle and upper part, respectively. In the direct transmission, the bulk-hole resonance and impurity absorption appear at around 3.6 and 2.4 T, respectively. In the optical and power modulation, the ordinate denotes the decrease of transmitted radiation intensity and thus the increases of absorption.
I
I
Ui
1~ C U, 0 is
HW 1e43#4 XU337~Jm T~2K
Dir.Tr/100
2
8
1.
6 Magnetic Field B(Iesta)
8
10
12
Fig. 3. The spectra of the optical modulation (solid curve) and the direct transmission (broken curve) for the orientation B I C. The notation of the transmission minima is after the paper of Dreybrodt er al., Solid State Commun. 8, 1021 (1970).
Vol.33, No.2
PHOTO-EXCITED CARRIERS IN TELLURIUM
3. EXPERIMENTAL RESULTS AND DISCUSSIONS Figure 1 shows the observed spectra for the magnetic field orientation of B II C. The direct transmission spectrum in the lower part exhibits a dominant dip of the hole cyclotron resonance at about 3.6 T and a weak resonance of residual acceptor impurities at about 2.4 T. This spectrum is regarded as reference for other kinds of modulation spectra, because the transmitted radiation intensity is always affected by the bulk-hole absorption. The upper part of Fig. 1 denotes the power modulation spectra for two values of current. The square-wave current produces the heat of 3.6 and 6.2 mJ per pulse for the two curves (300 and 500 mW in average power, respectively). The remarkable increase of absorption occurs at higher magnetic field of the bulk-hole resonance. This result gives the relation between the shift of the resonance energy and the deviation from the thermal equilibrium distribution of holes. The middle part shows the optical modulation spectra for three different intensities of the exciting radiation. For the following interpretation it is of essential importance that the photo-excited carriers are uniformly distributed in the sample of 1 mm thick, because otherwise interference effects would seriously obscure the spectra. This assumption is well supported by the results of [10] and [11]. A broad resonance is modulated by the bulkhole resonance and its peak is slightly shifted to lower magnetic field intensity from the bulk resonance. It is natural to conclude that the broad resonance curve consists of a superposition of two resonances of photoelectrons and -holes, and the two resonances almost coincide. Excitonic effects should be negligible because of the small binding energy (0.69 meV) [4] and the short life-time. From the dip of the direct transmission spectrum and the peak of the normalized curve of the optical modulation spectrum, we obtain the cyclotron mass of holes, m~= 0.llm0 and of electrons, m~= (0.11 ±0.02)m0, respectively, for B C. This electron mass is consistent with the previous results [4—8]. Figure 2 shows the similar spectra of the sample prepared from another crystal. The difference in the optical modulation spectrum is a hump at about 0.63 T, which is not found in Fig. 1. This low-field absorption does not appear in the direct transmission and its appearance depends on the source of samples. Therefore, we conclude that the new resonance must be related to a transition of the electron from an unknown impurity state. Since the intensity of the acceptor levels in tellurium is extremely sensitive on the origin of the sample material, as pointed out by von Klitzing [121, the same situation is expected to hold for the donor state. Based on the assumption that a transition from the impurity ground state into the second Landau level
201
is responsible to this absorption, the binding energy of the donor ground state is estimated to be of the order of EB 2.6meV. For the complementary orientation B I C, the spectra of the optical modulation and direct transmission are shown in Fig. 3. Both spectra exhibit a multi-line structure, because the lower symmetry leads to more allowed transitions. The position of the well-known hole absorption lines, H3 to H6, are indicated. The two small high-field peaks seem to be correlated with the H5 and H6 transitions of optically excited holes. The dominant broad inain line centered at about 3.6 T, however, should be a superposition of both electron and H3, H4-hole resonances. Due to the large halfwidth of these transitions of the excited carriers there is no way for separating them into components. From the resulting peak position, however, we can conclude, that the electron cyclotron mass is within the limits of me = (0.11 ± 0.02)m0. This value agrees quite well with the results of cyclotron resonance of thermally excited electrons and of electrons in inversion layers [6, 8] In summary the FIR-transmission spectra of charge carriers excited by the interband radiation in tellurium can be explained by the cyclotron resonance of free electrons and holes, and a transition from a bound state associated with the conduction band. Acknowledgement The work was supported by the Alexander von Humboldt Foundation for one of the authors (Y.N.). He expresses his sincere gratitude to Professor G. Landwehr for many courtesies during his stay in the Institute in Wilrzburg. —
REFERENCES 1. 2. 3. 4. ~•
6. 7. 8. 9. 10. 11. 12.
M. von Ortenberg & K.J. Button, Phys. Rev. B6, 2100 (1972). M. von Ortenberg & K.J. Button,Phys. Rev. B16, 2618 (1977). E. Braun & L.J. Neuringer, Proc. 10th mt. Conf Phys. Semicond., p. 352. Cambridge (1970). H. Shinno, R. Yoshizaki, S. Tanaka, T. Doi & H. Kamimura.J. Phys. Soc. Japan 35. 525 (1973). J. Blinowski, G. Rebmann, G. Rigaux & J. Mycielski,J. Phys. 38, 1139 (1977). K.J. Button, G. Landwehr, G.G. Bradley, P. Grosse & B. Lax, Phys. Rev. Lett. 23, 14 (1969). M. von Ortenberg & R. Silbermann, Solid State Commun. 17, 617 (1975). M. von Ortenberg & R. Silbermann, Surf Sci. 58, 202 (1976). Y. Nisida, K. Muro & U. Kawata, Infrared Phys. 16,207 (1976). G. Guthmann, G. Hermann & J.M. Thuillier, Phys. Status Soildi (a) 3,365 H. Kranz, Unpublished thesis,(1970). Wurzburg Univ. (1971). K. von Klitzing, Unpublished thesis, Wurzburg Univ. (1977).