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Hot electron effects in gray tin at 4.2 K
Volume 41A, number 4
PHYSICS LETTERS
9 October 1972
H O T E L E C T R O N E F F E C T S I N G R A Y T I N A T 4.2 K* G. BAUER and H. KAHLERT Ludwig Boltzmann lnstitut fiir FestkriSperphysik and Institu t fiir A ngewandte Physik der Universita't Wien, A-1090 Vienna, Austria Received 30 June 1972 In a "gray" S n - G e alloy the influence of electric fields up to 140 mV/cm on the amplitudes of ShubnikovDe Haas oscillations is observed and interpreted in terms of carrier beating within the I'~ conduction band.
Ohmic conduction in gray tin has been extensively investigated and the nature of the conduction and valence bands is now well established [ 1, 2]. Temperature dependent measurements of the electrical conductivity, magnetoresistance and Hall coefficient as functions of magnetic field and doping have been used to get information on the material parameters. The results have been analyzed within the framework of the Groves-Paul band structure model [3] which assumes that there is no energy gap between the P~ conduction and valence bands. Hence, gray tin is a semimetal. It is the purpose of this letter to report the first onservation of hot electron behaviour in a semimetal. Samples have been prepared from a polycrystalline alloy of Sn + 0.75% Ge which has a transition temperature from the a(cubic) to the ~-structure of about 70°C. Therefore the preparation and the problem of contacts is much easier than for pure a-Sn. At 4.2 K our material had a carrier concentration of n = 1.7 + X 1017 cm -3. Thus only the F 8 minimum is populated and the L~ minima are unimportant for the transport properties [2]. Since at 4.2 K the usual measurements of the current density vs field strength characteristic due to the strong degeneracy yields no information on the heating of the carriers by the electric field, an alternative method was applied. The extreme sensitivity of the quantum oscillations of the magnetoresistance (Shubnikov-De Haas effect) on changes of the electron temperature [4-6] provides a useful tool for the study of hot electron properties of such a material. In order to extract the oscillations
* Work supported by the "Fonds zur F~irderung der wissenschaftlicben Forschung", Austria and the "Ludwig Boltzmann Gesellschaft", Austria.
"rE=Z,.2K
't %
10
I
I
I
20
30 ~0 50 E3 (kG) Fig. ]. Dependence of the second derivative of the resistance witb respect to the magnetic field B on B. Parameter is the applied electric field E 0 for B = 0.
from the nonoscillatory magnetoresistance a double differentiating technique has been employed. Fig. 1 shows a set of S-DH-curves for different applied electric fields. The curves clearly indicate the damping of the amplitudes with increasing electric field whereas the period of the oscillations and therefore the carrier concentration remains unchanged. The applied electric fields increased with increasing magnetic field due to the nonoscillatory component of the magnetoresistance and because of constant current conditions. Since the mobility did not change with applied electric field and the ohmic mobility was nearly temperature independent we conclude that the Dingle temperature is constant as in the case of temperature dependent ohmic measurements [ 1]. The damping of the amplitudes can therefore be interpreted by an increase of the electron temperature Te with electric field. Since the electron system is degen35l
Volume 41A, number 4
PHYSICS LETTERS
9 October 1972 +
of the electrons in the F 8 minimum of m* = 0.0255 m 0 [1], we have calculated the electron temperature as a function of electric field following a procedure given in ref. [5]. Fig. 2 shows the dependence of the electron temperature on the electric field strength. An analysis of these data in terms of relevant scattering mechanisms is in progress and will be published elsewhere.
16
TL= Z,.2 K
o
o
1c y, v
t
,A
20
AO
60 80 E (mV/cm)
100
120
140
We are indebted to Prof. K. Seeger for suggesting to investigate hot electron effects in this material. Prof. Seeger would like to express his gratitude to Prof. Busch and Dr. Yuan of the ETH, Zfirich for supplying the sample material.
Fig. 2. Dependence of the electron temperature Te on the applied electric field E.
References erate this increase in electron temperature alters the electron energy only by a very small amount and therefore the mobility, which depends on the mean electron energy, doe not change. Because of the fact that the hole mobility is more than an order of magnitude smaller than the electron mobility at this temperature and concentration [2], the influence of the holes on the SdH experiment can be neglected. Using a value of the effective mass
352
[ 1] B.L. Booth and A.W. Ewald, Phys. Rev. 168 (1968) 796. [2] C.F. Lavine and A.W. Ewald, J. Phys. Chem. Solids 32 (1971) 1121. [3] S.H. Groves and W. Paul, Phys. Rev. Lett. 11 (1963) 194. [4] R.A. Isaacson and F. Bridges, Solid State Commun. 4 (1966) 635. [5 ] H. Kahlert and G. Bauer, phys. stat. sol. (b) 46 (1971 ) 535. [6] G. Bauer and H. Kahlert, Phys. Rev. B5 (1972) 556.
PHYSICS LETTERS
9 October 1972
H O T E L E C T R O N E F F E C T S I N G R A Y T I N A T 4.2 K* G. BAUER and H. KAHLERT Ludwig Boltzmann lnstitut fiir FestkriSperphysik and Institu t fiir A ngewandte Physik der Universita't Wien, A-1090 Vienna, Austria Received 30 June 1972 In a "gray" S n - G e alloy the influence of electric fields up to 140 mV/cm on the amplitudes of ShubnikovDe Haas oscillations is observed and interpreted in terms of carrier beating within the I'~ conduction band.
Ohmic conduction in gray tin has been extensively investigated and the nature of the conduction and valence bands is now well established [ 1, 2]. Temperature dependent measurements of the electrical conductivity, magnetoresistance and Hall coefficient as functions of magnetic field and doping have been used to get information on the material parameters. The results have been analyzed within the framework of the Groves-Paul band structure model [3] which assumes that there is no energy gap between the P~ conduction and valence bands. Hence, gray tin is a semimetal. It is the purpose of this letter to report the first onservation of hot electron behaviour in a semimetal. Samples have been prepared from a polycrystalline alloy of Sn + 0.75% Ge which has a transition temperature from the a(cubic) to the ~-structure of about 70°C. Therefore the preparation and the problem of contacts is much easier than for pure a-Sn. At 4.2 K our material had a carrier concentration of n = 1.7 + X 1017 cm -3. Thus only the F 8 minimum is populated and the L~ minima are unimportant for the transport properties [2]. Since at 4.2 K the usual measurements of the current density vs field strength characteristic due to the strong degeneracy yields no information on the heating of the carriers by the electric field, an alternative method was applied. The extreme sensitivity of the quantum oscillations of the magnetoresistance (Shubnikov-De Haas effect) on changes of the electron temperature [4-6] provides a useful tool for the study of hot electron properties of such a material. In order to extract the oscillations
* Work supported by the "Fonds zur F~irderung der wissenschaftlicben Forschung", Austria and the "Ludwig Boltzmann Gesellschaft", Austria.
"rE=Z,.2K
't %
10
I
I
I
20
30 ~0 50 E3 (kG) Fig. ]. Dependence of the second derivative of the resistance witb respect to the magnetic field B on B. Parameter is the applied electric field E 0 for B = 0.
from the nonoscillatory magnetoresistance a double differentiating technique has been employed. Fig. 1 shows a set of S-DH-curves for different applied electric fields. The curves clearly indicate the damping of the amplitudes with increasing electric field whereas the period of the oscillations and therefore the carrier concentration remains unchanged. The applied electric fields increased with increasing magnetic field due to the nonoscillatory component of the magnetoresistance and because of constant current conditions. Since the mobility did not change with applied electric field and the ohmic mobility was nearly temperature independent we conclude that the Dingle temperature is constant as in the case of temperature dependent ohmic measurements [ 1]. The damping of the amplitudes can therefore be interpreted by an increase of the electron temperature Te with electric field. Since the electron system is degen35l
Volume 41A, number 4
PHYSICS LETTERS
9 October 1972 +
of the electrons in the F 8 minimum of m* = 0.0255 m 0 [1], we have calculated the electron temperature as a function of electric field following a procedure given in ref. [5]. Fig. 2 shows the dependence of the electron temperature on the electric field strength. An analysis of these data in terms of relevant scattering mechanisms is in progress and will be published elsewhere.
16
TL= Z,.2 K
o
o
1c y, v
t
,A
20
AO
60 80 E (mV/cm)
100
120
140
We are indebted to Prof. K. Seeger for suggesting to investigate hot electron effects in this material. Prof. Seeger would like to express his gratitude to Prof. Busch and Dr. Yuan of the ETH, Zfirich for supplying the sample material.
Fig. 2. Dependence of the electron temperature Te on the applied electric field E.
References erate this increase in electron temperature alters the electron energy only by a very small amount and therefore the mobility, which depends on the mean electron energy, doe not change. Because of the fact that the hole mobility is more than an order of magnitude smaller than the electron mobility at this temperature and concentration [2], the influence of the holes on the SdH experiment can be neglected. Using a value of the effective mass
352
[ 1] B.L. Booth and A.W. Ewald, Phys. Rev. 168 (1968) 796. [2] C.F. Lavine and A.W. Ewald, J. Phys. Chem. Solids 32 (1971) 1121. [3] S.H. Groves and W. Paul, Phys. Rev. Lett. 11 (1963) 194. [4] R.A. Isaacson and F. Bridges, Solid State Commun. 4 (1966) 635. [5 ] H. Kahlert and G. Bauer, phys. stat. sol. (b) 46 (1971 ) 535. [6] G. Bauer and H. Kahlert, Phys. Rev. B5 (1972) 556.