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Far-infrared reflection spectra of HgSe
Pergamon Press.
Solid State Communications,Vol. 16, pp. 743-745, 1975.
Printed in Great Britain
FAR-INFRARED REFLECTION SPECTRA OF HgSe A. Manabe and A. Mitsuishi Department of Applied Physics, Osaka University, Suita, Osaka, Japan (Received 30 September 1974 by H. Kawamura)
Reflectivity of HgSe (N = 2.0 X 1018-4.2 X 1017cm-3) was measured in the spectral region from 2-100~ at temperatures between 95 and 300 K. The frequency of the transverse optical phonon at = 132 f 2 cm-’ was determined from Kramers-Kronig analysis. The w+ mode of the plasmonLO phonon coupled modes is shown to depend anomalously on temperature. Two extra bands of unknown origin were also observed at about 110 and 120 cm-’ .
RECENTLY infrared reflection spectra of zero-gap semiconductors have attracted considerable attention in connection with the interaction of electronic interband transitions and lattice vibrations. In the family of mercury chalcogenides, HgTe has been investigated in detail by Grynberg et al.’ Up to now, however, only limited information on the infrared properties of HgSe has been available. The earlier works on the infrared reflection spectra of HgSe were that of Wright et al.2 and of Volkov et al.3 in the region of the plasma oscillation of free carriers.
were made immediately after the galvanomagnetic measurements. For reflectivity measurements the surface was polished to an optical finish and was etched in a polishing etchant to remove work damage. The reflectivity was measured relative to an evaporated aluminium standard mirror using a vacuum grating spectrometer for the spectral range of 20-100~ and a prism-grating double monochrometer in 2-20 pm.
WAVENUMBER
( cm-’ )
80 - NQ 25-l
In this note, we report preliminary results of the reflection measurements of HgSe in the region of plasmon-LO phonon coupling at temperature between 95 and 300 K. Large-grained samples (10 X 20 X 1.5 mm’) were cut from ingots prepared from the elements (99.999% purity) by the Bridgeman method. Some samples were annealed in selenium vapor at 240°C for several weeks to reduce the carrier concentration. The Hall coefficient and the conductivity of these samples were measured by Vander Paw method and showed concentrations of n-type carriers ranging from 2.0 X 10” to 5.9 X 101’cm-3 with almost constant mobility of 1.5 X 104cm2V-’ set-’ at 300 K and from 2.0 X 10’s to 4.2 X 10’7cm-3 with 5.5 X 104cm2V-’ set-’ at 95 K. The optical measurements
-0
20
40 WAVELENGTH
60
60
100
(pm)
FIG. 1. The reflectivity spectra of HgSe with various carrier concentrations: 95 K,---120K, ___________ 3OOK. 743
FAR-INFRARED
744
WAVENUMBER 200
500 1 -
REFLECTION
SPECTRA OF HgSe
Vol. 16, No. 6
(cm-‘) 100
i,
60 WAVELENGTH
60
100
t
I
1
I
3
4
5
6
( N / m* )‘A
120
(Ym)
FIG. 2. Imaginary part e2 of the dielectric constant and Im (- l/e) obtained from Kramers-Kronig analysis of experimental reflectivity for sample No.251: -----95K,-------300K.
Figure 1 shows the typical results of the reflection measurements. The characteristics of these spectra will be ascribed firstly to the plasmon-LO phonon coupling. There seem, however, anomalous behaviors of two types. One is a strong temperature dependent shift of the high-frequency minimum due to the plasmon like w+ mode. The minimum of the sample No. 26 at 95 K, for example, appears at lower frequency than that of No. 25-l at 300 K being contrary to the expectation from their carrier concentrations. The other anomaly observed is two extra minima at the lower frequency side of the phonon like w-mode around 80pm, which are clearly shown at lower temperature. To obtain the frequencies of the oscillators which contribute to the spectra, Kramers-Kronig analysis was performed. The resulting imaginary part e2 of the dielectric constant E and imaginary part of (- l/e) are shown in Fig. 2 for the case of sample No. 25-l.
FIG. 3. Plots of frequencies of longitudinal and transverse modes vs (N/m*)). Lines are calculated frequencies of plasmon-LO phonon coupled modes using values of at = 132 cm-‘, E,, = 25.6 and adjustable parameter e,.
value of ut is almost independent on temperature and on carrier concentration within an experimental error. The frequencies of TO phonon of fl-HgS 5 and HgTel are reported as 177 and 117 cm-’ respectively. These values at of mercury chalcogenides satisfy well the simple relation at a M-’ as is the case for other II-VI compounds with zinc-blende structure6, where M is the reduced mass of the elements. Maxima of the Im (- l/e) curve are connected with oscillators having longitudinal polarization character. Two principal maxima are considered to correspond to the frequencies of the plasmon-LO phonon coupled modes which can be given by the well-known formula, 2w’I = w; + o:t
[(wi + w:)’ -40;w:+
(1)
with 2
UP
Maxima in the e2 -spectrum correspond to the frequency of transverse oscillators. The frequency of the transverse optical phonon at of HgSe is determined as 132 + 2 cm- ’ from a strong peak in e2 curve. The
1
7 xlOgcm - %
_
4rNe*
_-
E==%
(4
2=
fo
tea
0:
>
where wp and o1 are frequencies of plasmon and LO phonon respectively and E, and e. are the optical and static dielectric constant respectively. The values
Vol. 16, No. 6
FAR-INFRARED REFLECTION SPECTRA OF HgSe
of electron effective mass m, are calculated for our samples taking account of the Kane-type non-parabolicity of the Fs conduction band and the temperature dependency of the energy gap (Fe - I’a) and interbandmomentum-matrix element reported by Lehocsky et al.’ In Fig. 3, frequencies of longitudinal oscillators obtained from Im (- l/e) curves are plotted against the root of N/m*, where m.* = m,/m,, is the electron effective mass ratio. The mode frequencies o, and w_ are calculated using equation (1) in which tit is taken as 132 cm-’ and co is tentatively fuced to the value 25.6 reported by Kir’iashkina et al.* The optical dielectric constant e- is chosen as adjustable parameter in order to fit the calculated frequencies with experimental values. As is shown in Fig. 3, we obtain the value E, = 12 which agrees with the data of o+ mode for the highest carrier concentration. This value is coincident with that reported by Wright et al.2 However, larger and temperature dependent values E, = 17 (300 K) and 21 (95 K) are required to explain w, modes at lower carrier concentrations. This fact suggests that the o+ is screened by the optical dielectric constant which has the frequency and temperature dependent contribution. The most probable origin of this extra contribution will be the interband transition between the degenerated Fs valence and Fs conduction band which was studied theoretically by Broermang and experimentally by Grynberg et al.’ in HgTe.
745
Two extra minima which are observed at the lower frequency side of the reflection spectra are connected with two oscillators having both polarization character, longitudinal and transverse, as shown in Fig. 2 and Fig. 3. They are clearly observed at lower temperature and lower carrier concentration. Their frequencies are shifted to higher frequency with decreasing temperature but do not depend on the carrier concentration. One similar mode has been observed in the case of HgTe.l It was suggested that a gap mode of high density Hg substituted to Te or solid solution of Hg, Te in HgTe will be a possible origin of the mode. A large number of complex defects such as Hg, Se may be a possible origin of these modes in HgSe. Further measurements of the reflection spectra at lower temperature and lower carrier concentration would be necessary to clarify the behavior of the plasmon-lO phonon coupled modes and the origin of the two extra modes.
Acknowledgement - The authors wish to thank Mr.
K. Kumazaki of Hokkaido Institute of Technology for his helpful comments in preparing the materials.
REFERENCES 1.
GRYNBERG M., LE TOULLEC R. and BALKANSKI M., Phys. Rev. B9,5 17 (1974).
2.
WRIGHT G.B., STRAUSS A.J. and HARMAN T.C., Phys. Rev. 125,1534 (1962).
3.
VOLKOV V.V., VOLKOVA L.V. and KIREEV P.S.,Sov. Phys.-Semicond. 4, 1230 (1971).
4.
WAREKOIS E.P., LAVINE M.C., MARIANO A.N. and GATOS H.C., J. Appl. Phys. 33,690
5.
RICCIUS H.D. and SIEMSEN K.J., J. Chem. Phys. 52,409O (1970).
6.
MANABE A., MITSUISHI A. and YOSHINAGA H.,Jupan J. Appl. Phys. 6,593 (1967).
7.
LEHOCZKY S.L., BROERMAN J.G., NELSON D.A. and WHITSETT C.R., Phys. Rev. B9, 1598 (1974).
8.
KIR‘IASHKINA Z.I., POPOV F.M., BILENKO D.N. and KIR’IASHKINA V.I., Sov. Phys.-Tech. Phys. 2,69 (1957).
9.
BROERMAN J.G., Phys. Rev. BS, 397 (1972).
(1962).
Solid State Communications,Vol. 16, pp. 743-745, 1975.
Printed in Great Britain
FAR-INFRARED REFLECTION SPECTRA OF HgSe A. Manabe and A. Mitsuishi Department of Applied Physics, Osaka University, Suita, Osaka, Japan (Received 30 September 1974 by H. Kawamura)
Reflectivity of HgSe (N = 2.0 X 1018-4.2 X 1017cm-3) was measured in the spectral region from 2-100~ at temperatures between 95 and 300 K. The frequency of the transverse optical phonon at = 132 f 2 cm-’ was determined from Kramers-Kronig analysis. The w+ mode of the plasmonLO phonon coupled modes is shown to depend anomalously on temperature. Two extra bands of unknown origin were also observed at about 110 and 120 cm-’ .
RECENTLY infrared reflection spectra of zero-gap semiconductors have attracted considerable attention in connection with the interaction of electronic interband transitions and lattice vibrations. In the family of mercury chalcogenides, HgTe has been investigated in detail by Grynberg et al.’ Up to now, however, only limited information on the infrared properties of HgSe has been available. The earlier works on the infrared reflection spectra of HgSe were that of Wright et al.2 and of Volkov et al.3 in the region of the plasma oscillation of free carriers.
were made immediately after the galvanomagnetic measurements. For reflectivity measurements the surface was polished to an optical finish and was etched in a polishing etchant to remove work damage. The reflectivity was measured relative to an evaporated aluminium standard mirror using a vacuum grating spectrometer for the spectral range of 20-100~ and a prism-grating double monochrometer in 2-20 pm.
WAVENUMBER
( cm-’ )
80 - NQ 25-l
In this note, we report preliminary results of the reflection measurements of HgSe in the region of plasmon-LO phonon coupling at temperature between 95 and 300 K. Large-grained samples (10 X 20 X 1.5 mm’) were cut from ingots prepared from the elements (99.999% purity) by the Bridgeman method. Some samples were annealed in selenium vapor at 240°C for several weeks to reduce the carrier concentration. The Hall coefficient and the conductivity of these samples were measured by Vander Paw method and showed concentrations of n-type carriers ranging from 2.0 X 10” to 5.9 X 101’cm-3 with almost constant mobility of 1.5 X 104cm2V-’ set-’ at 300 K and from 2.0 X 10’s to 4.2 X 10’7cm-3 with 5.5 X 104cm2V-’ set-’ at 95 K. The optical measurements
-0
20
40 WAVELENGTH
60
60
100
(pm)
FIG. 1. The reflectivity spectra of HgSe with various carrier concentrations: 95 K,---120K, ___________ 3OOK. 743
FAR-INFRARED
744
WAVENUMBER 200
500 1 -
REFLECTION
SPECTRA OF HgSe
Vol. 16, No. 6
(cm-‘) 100
i,
60 WAVELENGTH
60
100
t
I
1
I
3
4
5
6
( N / m* )‘A
120
(Ym)
FIG. 2. Imaginary part e2 of the dielectric constant and Im (- l/e) obtained from Kramers-Kronig analysis of experimental reflectivity for sample No.251: -----95K,-------300K.
Figure 1 shows the typical results of the reflection measurements. The characteristics of these spectra will be ascribed firstly to the plasmon-LO phonon coupling. There seem, however, anomalous behaviors of two types. One is a strong temperature dependent shift of the high-frequency minimum due to the plasmon like w+ mode. The minimum of the sample No. 26 at 95 K, for example, appears at lower frequency than that of No. 25-l at 300 K being contrary to the expectation from their carrier concentrations. The other anomaly observed is two extra minima at the lower frequency side of the phonon like w-mode around 80pm, which are clearly shown at lower temperature. To obtain the frequencies of the oscillators which contribute to the spectra, Kramers-Kronig analysis was performed. The resulting imaginary part e2 of the dielectric constant E and imaginary part of (- l/e) are shown in Fig. 2 for the case of sample No. 25-l.
FIG. 3. Plots of frequencies of longitudinal and transverse modes vs (N/m*)). Lines are calculated frequencies of plasmon-LO phonon coupled modes using values of at = 132 cm-‘, E,, = 25.6 and adjustable parameter e,.
value of ut is almost independent on temperature and on carrier concentration within an experimental error. The frequencies of TO phonon of fl-HgS 5 and HgTel are reported as 177 and 117 cm-’ respectively. These values at of mercury chalcogenides satisfy well the simple relation at a M-’ as is the case for other II-VI compounds with zinc-blende structure6, where M is the reduced mass of the elements. Maxima of the Im (- l/e) curve are connected with oscillators having longitudinal polarization character. Two principal maxima are considered to correspond to the frequencies of the plasmon-LO phonon coupled modes which can be given by the well-known formula, 2w’I = w; + o:t
[(wi + w:)’ -40;w:+
(1)
with 2
UP
Maxima in the e2 -spectrum correspond to the frequency of transverse oscillators. The frequency of the transverse optical phonon at of HgSe is determined as 132 + 2 cm- ’ from a strong peak in e2 curve. The
1
7 xlOgcm - %
_
4rNe*
_-
E==%
(4
2=
fo
tea
0:
>
where wp and o1 are frequencies of plasmon and LO phonon respectively and E, and e. are the optical and static dielectric constant respectively. The values
Vol. 16, No. 6
FAR-INFRARED REFLECTION SPECTRA OF HgSe
of electron effective mass m, are calculated for our samples taking account of the Kane-type non-parabolicity of the Fs conduction band and the temperature dependency of the energy gap (Fe - I’a) and interbandmomentum-matrix element reported by Lehocsky et al.’ In Fig. 3, frequencies of longitudinal oscillators obtained from Im (- l/e) curves are plotted against the root of N/m*, where m.* = m,/m,, is the electron effective mass ratio. The mode frequencies o, and w_ are calculated using equation (1) in which tit is taken as 132 cm-’ and co is tentatively fuced to the value 25.6 reported by Kir’iashkina et al.* The optical dielectric constant e- is chosen as adjustable parameter in order to fit the calculated frequencies with experimental values. As is shown in Fig. 3, we obtain the value E, = 12 which agrees with the data of o+ mode for the highest carrier concentration. This value is coincident with that reported by Wright et al.2 However, larger and temperature dependent values E, = 17 (300 K) and 21 (95 K) are required to explain w, modes at lower carrier concentrations. This fact suggests that the o+ is screened by the optical dielectric constant which has the frequency and temperature dependent contribution. The most probable origin of this extra contribution will be the interband transition between the degenerated Fs valence and Fs conduction band which was studied theoretically by Broermang and experimentally by Grynberg et al.’ in HgTe.
745
Two extra minima which are observed at the lower frequency side of the reflection spectra are connected with two oscillators having both polarization character, longitudinal and transverse, as shown in Fig. 2 and Fig. 3. They are clearly observed at lower temperature and lower carrier concentration. Their frequencies are shifted to higher frequency with decreasing temperature but do not depend on the carrier concentration. One similar mode has been observed in the case of HgTe.l It was suggested that a gap mode of high density Hg substituted to Te or solid solution of Hg, Te in HgTe will be a possible origin of the mode. A large number of complex defects such as Hg, Se may be a possible origin of these modes in HgSe. Further measurements of the reflection spectra at lower temperature and lower carrier concentration would be necessary to clarify the behavior of the plasmon-lO phonon coupled modes and the origin of the two extra modes.
Acknowledgement - The authors wish to thank Mr.
K. Kumazaki of Hokkaido Institute of Technology for his helpful comments in preparing the materials.
REFERENCES 1.
GRYNBERG M., LE TOULLEC R. and BALKANSKI M., Phys. Rev. B9,5 17 (1974).
2.
WRIGHT G.B., STRAUSS A.J. and HARMAN T.C., Phys. Rev. 125,1534 (1962).
3.
VOLKOV V.V., VOLKOVA L.V. and KIREEV P.S.,Sov. Phys.-Semicond. 4, 1230 (1971).
4.
WAREKOIS E.P., LAVINE M.C., MARIANO A.N. and GATOS H.C., J. Appl. Phys. 33,690
5.
RICCIUS H.D. and SIEMSEN K.J., J. Chem. Phys. 52,409O (1970).
6.
MANABE A., MITSUISHI A. and YOSHINAGA H.,Jupan J. Appl. Phys. 6,593 (1967).
7.
LEHOCZKY S.L., BROERMAN J.G., NELSON D.A. and WHITSETT C.R., Phys. Rev. B9, 1598 (1974).
8.
KIR‘IASHKINA Z.I., POPOV F.M., BILENKO D.N. and KIR’IASHKINA V.I., Sov. Phys.-Tech. Phys. 2,69 (1957).
9.
BROERMAN J.G., Phys. Rev. BS, 397 (1972).
(1962).