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Cyclotron resonance in strongly compensated n-InSb
Volume
42A, number
4
PHYSICS
CYCLOTRON
RESONANCE
LETTERS
18 December
IN STRONGLY
COMPENSATED
1972
n-InSb
V.T. POTAPOV, V.A. POPOV, V.A. STRAKHOV and 1.1. CHUSOV Institute of Radio Engineen’ng and Electronics, Moscow, USSR Received
15 November
1972
Cyclotron resonance (CR) of free electrons has been observed in a single crystal of n-InSb with the compensation ratio ND/NA > 0.99 at a radiation frequency of 300 GHz in the temperature range 5 to 72” K.
In pure uncompensated samples of n-InSb with ND > 1d4 cme3 comparatively high concentrations of free electrons (even at liquid-helium temperatures) prevent one from observing CR in the milimeter range because the condition w > wP, where w is the frequency of radiation, wp the plasma frequency, is not satisfied. On the other hand, in strongly compensated samples of n-Mb with ND -NA < 1013 cmp3 (SO that w > wp) the momentum relaxation time 7 obtained from the dc measurements of the conductivity u and Hall coefficient R gives at liquid-helium temperatures we = 0.1 and it seems that it is impossible to observe CR for plane-polarized radiation. However, in [l] it was shown that 7 obtained as mentioned above gives no correct values of the momentum relaxation time because of the strong influence of the large scale inhomogeneities on u, rather than on R. The true values of 7 can be obtained, for example, from measurements of the Faraday effect [l] and such measurements showed a possibility of observing CR in the millimeter range. We have observed CR in strongly compensated n-InSb at a wavelength X = 1 mm in the temperature range T = 9 to 72” K. Experimentally we measured the transmission of plane-polarized radiation through a sample of n-InSb with ND- NA = 1.4 X 1013 cmp3 and a mobility /L= 1.6 X lo5 cm2V-1 set-1 (obtained from the dc measurements of o and R) at 30” K. The sample covered completely the cross-section area of a wavequide placed into the portable helium cryostat. The sample temperature was varied by evaporating the liquid helium and measured by an “Allen-Bradley” resistance. As a source of radiation we used a conventional backward-wave tube with h = 0.9 to 1.O mm. The radiation power incident upon the sample didn’t exceed 10d5 W. Another crystal of n-InSb located out-
side the magnetic field and held at a temperature of 4.2”K served as a detector of the transmitted radiation. To control the radiation power absorption in the sample the response (voltage) was also measured. Curves in fig. 1 show the transmission P in relative units versus the applied static magnetic field H at 72°K (1);41.5”K(2); 26”K(3); 5.5”K(4). At T> 9°K curve P(H) has a distinctive minimum at H,. This minimum 2.t
4
. .
/ l
.
LS
/
.
’
ca
0.S
1000
2ooo
kJ(,=
Fig. 1.
285
I:&!. 7.
shifts to higher magnetic fields with increasing temperature. The temperature dependence of/f,,, is shown in fig. 2 and explained by the fact that in our experiments wr E v(T) is larger than unity but not too much so that the CR frequency tie,,, = rH,,,/nr*r*(where P./I/ ’ are the electron charge and effective mass, respectively,. (’ = 3 X IO’” cm set 1) which is given in an elementary model by i Ocn3 = L3J’rJGJ
-:---
--( I t ,I j/v.
(1)
is temperature dependent. This means in particular that determining n7* requires a knowledge of r( T) and vice versa, The estimate of T from ( I ) showed that the behaviour 7(T) qualitatively reproduced that obtained from the measurements of the Faraday effect, the difference from the latter being not more than a factor two times in magnitude. At T < 9°K the transmission increases monotonically with increasing H and the behaviour f’(H) is practically quadratic (curve 4 in fig. I ). This indicates w-r < I to be valid at these temperatures. It is evident that the heating of the electrons by say, a static electric field E increases r (because the electron scattering is due to ionized impurities) and makes it possible to observe CR at lattice temperatures less than 9)“K. This is confirmed by the curve 5 in fig. I measured at T = 5.S”K. E = 0.65 V cm I The position of the
286
curve minimum corresponds to an effective electron temperature T, = 18°K. The value of the effective mass determined at 70°K. where the influence ofinhomogeneities is negligible, happened to be equal to 777* = (0.0145 + 0.0015)n70 which is consistent with the results of [I?1, Fig. 3 shows the transmission and the response from the sample measured at T = 18°K as a functions of H. One can see a good correlation between the positions of the response maximum and the transmission minimum. The authors are indebted to Professor Yu.V. Gulyaev and Dr. V.I. Trifonov for helpful discussions.
1 I j V.T. Potapov
et al., 1.1~. Tckh.
Poluprov..
121 E.D. I’alik et ;rl., Phys. Rev. 122 (1961)475.
6 (1972) 1227
42A, number
4
PHYSICS
CYCLOTRON
RESONANCE
LETTERS
18 December
IN STRONGLY
COMPENSATED
1972
n-InSb
V.T. POTAPOV, V.A. POPOV, V.A. STRAKHOV and 1.1. CHUSOV Institute of Radio Engineen’ng and Electronics, Moscow, USSR Received
15 November
1972
Cyclotron resonance (CR) of free electrons has been observed in a single crystal of n-InSb with the compensation ratio ND/NA > 0.99 at a radiation frequency of 300 GHz in the temperature range 5 to 72” K.
In pure uncompensated samples of n-InSb with ND > 1d4 cme3 comparatively high concentrations of free electrons (even at liquid-helium temperatures) prevent one from observing CR in the milimeter range because the condition w > wP, where w is the frequency of radiation, wp the plasma frequency, is not satisfied. On the other hand, in strongly compensated samples of n-Mb with ND -NA < 1013 cmp3 (SO that w > wp) the momentum relaxation time 7 obtained from the dc measurements of the conductivity u and Hall coefficient R gives at liquid-helium temperatures we = 0.1 and it seems that it is impossible to observe CR for plane-polarized radiation. However, in [l] it was shown that 7 obtained as mentioned above gives no correct values of the momentum relaxation time because of the strong influence of the large scale inhomogeneities on u, rather than on R. The true values of 7 can be obtained, for example, from measurements of the Faraday effect [l] and such measurements showed a possibility of observing CR in the millimeter range. We have observed CR in strongly compensated n-InSb at a wavelength X = 1 mm in the temperature range T = 9 to 72” K. Experimentally we measured the transmission of plane-polarized radiation through a sample of n-InSb with ND- NA = 1.4 X 1013 cmp3 and a mobility /L= 1.6 X lo5 cm2V-1 set-1 (obtained from the dc measurements of o and R) at 30” K. The sample covered completely the cross-section area of a wavequide placed into the portable helium cryostat. The sample temperature was varied by evaporating the liquid helium and measured by an “Allen-Bradley” resistance. As a source of radiation we used a conventional backward-wave tube with h = 0.9 to 1.O mm. The radiation power incident upon the sample didn’t exceed 10d5 W. Another crystal of n-InSb located out-
side the magnetic field and held at a temperature of 4.2”K served as a detector of the transmitted radiation. To control the radiation power absorption in the sample the response (voltage) was also measured. Curves in fig. 1 show the transmission P in relative units versus the applied static magnetic field H at 72°K (1);41.5”K(2); 26”K(3); 5.5”K(4). At T> 9°K curve P(H) has a distinctive minimum at H,. This minimum 2.t
4
. .
/ l
.
LS
/
.
’
ca
0.S
1000
2ooo
kJ(,=
Fig. 1.
285
I:&!. 7.
shifts to higher magnetic fields with increasing temperature. The temperature dependence of/f,,, is shown in fig. 2 and explained by the fact that in our experiments wr E v(T) is larger than unity but not too much so that the CR frequency tie,,, = rH,,,/nr*r*(where P./I/ ’ are the electron charge and effective mass, respectively,. (’ = 3 X IO’” cm set 1) which is given in an elementary model by i Ocn3 = L3J’rJGJ
-:---
--( I t ,I j/v.
(1)
is temperature dependent. This means in particular that determining n7* requires a knowledge of r( T) and vice versa, The estimate of T from ( I ) showed that the behaviour 7(T) qualitatively reproduced that obtained from the measurements of the Faraday effect, the difference from the latter being not more than a factor two times in magnitude. At T < 9°K the transmission increases monotonically with increasing H and the behaviour f’(H) is practically quadratic (curve 4 in fig. I ). This indicates w-r < I to be valid at these temperatures. It is evident that the heating of the electrons by say, a static electric field E increases r (because the electron scattering is due to ionized impurities) and makes it possible to observe CR at lattice temperatures less than 9)“K. This is confirmed by the curve 5 in fig. I measured at T = 5.S”K. E = 0.65 V cm I The position of the
286
curve minimum corresponds to an effective electron temperature T, = 18°K. The value of the effective mass determined at 70°K. where the influence ofinhomogeneities is negligible, happened to be equal to 777* = (0.0145 + 0.0015)n70 which is consistent with the results of [I?1, Fig. 3 shows the transmission and the response from the sample measured at T = 18°K as a functions of H. One can see a good correlation between the positions of the response maximum and the transmission minimum. The authors are indebted to Professor Yu.V. Gulyaev and Dr. V.I. Trifonov for helpful discussions.
1 I j V.T. Potapov
et al., 1.1~. Tckh.
Poluprov..
121 E.D. I’alik et ;rl., Phys. Rev. 122 (1961)475.
6 (1972) 1227