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Submitted on 1 Jan 1978
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RECONSTRUCTION OF ENERGY SPECTRUM IN THE ALLOYS Pb1-xSnxTe UNDER HYDROSTATIC
PRESSURE
B. Akimov, R. Wadhwa, S. Chudinov
To cite this version:
B. Akimov, R. Wadhwa, S. Chudinov. RECONSTRUCTION OF ENERGY SPECTRUM IN THE
ALLOYS Pb1-xSnxTe UNDER HYDROSTATIC PRESSURE. Journal de Physique Colloques, 1978,
39 (C6), pp.C6-1077-C6-1078. �10.1051/jphyscol:19786477�. �jpa-00217958�
JOURNAL DE PHYSIQUE Colloque C6, suppkment au no 8, Tome 39, aolit 1978, page (-6-1077
RECONSTRUCTION O F ENERGY
SPECTRUM IN THE
ALLOYS Pbl-,SnXTe UNDER HYDROSTATIC PRESSURE B.A. Akimov, R.S. Wadhwa and S.M. ChudinovLow Temperature Laboratory,Physics Department, Moscow State University, USSR
Rdsum6.- Les proprigtds galvanomagndtiques des alliages Pbl-xSnxTe de type-p ont btb mesurees jus- qu'l une pression de 21 kbar pour des concentrations X = 0,18 et 0,23. L'intervalle de pression choi- si permet d'htudier le spectre energgtique direct (p<p;) et inverse (p>p;), OS pi est le point de l'inversion des bandes L. On a Btabli que sous pression la masse cyclotron et la mobilitd de Hall des porteurs libres varient en premiOre approximation de fason sym6trique par rapport au point p = pi.
Pendant le passage dans l'dtat de bande interdire nulle induit par la pression on a observd une aug- mentation considgrable du temps de relaxation. On a demontr6 que dans les alliages p-Pbl-xSnxTe la relaxation dominante des porteurs est due 2 la diffusion des trous sur les centres chargds.
Abstract.- Changes in band parameters in the alloys Pbl-xSnxTe (p-type) X = 0.18 and X = 0.23 under hydrostatic pressure have been studied in the direct (p<p;) as well as inverse (p>pi) spectral re- gions. It is established that the pressure dependence of the cyclotron mass and Hall mobility of car- riers are, to a first approximation, symmetric with respect to the point of inversion of L-bands at p = pi. A considerable rise in the relaxation time is observed during the transition to the gapless state under pressure. It is shown that scattering at charged centres is the dominating mechanism of relaxation of holes in the alloys Pbl-xSnxTe.
The electrical conductivity o
,
Hall coeffi- cient R and Shubnikov-de Haas oscillation have been studied in samples of the alloy Pbl-xSnxTe forX = 0.18 and 0.23 with hole concentration Mn 1017
c m 3 at liquid helium temperature under pressures up to 21 kbar covering a fairly wide interval cor- responding to the inverse spectrum/l-21. Typical re- sults obtained at 4.2 K for the alloy Pbo,82Sno,laTe with concentration M 1.3 x 1 0 1 7 cm-' are given
n below.
The value of hole concentration Mn as determi- ned from the Hall effect measurements in strong ma- gnetic fields -+
HI 1
<loo> remains constant within an accuracy of 2 % for the entire pressure interval.Resistivity p4.2K decreases rapidly under hydrosta- tic pressure, attains its minimum value for p - 13 kbar and then starts rising
curve
1 figure 1). Cur- ves in figure 2 shows the dependence of Hall mobili- ty of holes pH =-
cR on pressure. It is found thatP
the Fermi surface cross-section S, obtained from analysis of Shubnikov-de Haas measurements for a fixed direction of magnetic field remains constant under pressure. In particular, the minimal cross- section S111 ii momentum space for +
HI
1<111> is equal to 1.55 X IO-'~ gm2.cm2/s2. (In wave-vector space= 1.40 X 1012 cm-2). The cyclotron mass rnlll, %
determined from the same studies, at first decrea- ses with increasing pressure, passes through a mini- mum in the range of 12-13 kbar after which it in-
Fig. 1 : Pressure de endence of resistivity
R
~,.,~(1) 2nd cyclotron mass m111 at Fermi level forHI
I<111> T = 4.2 K(2) for alloy Pbo,snSno,lsTe. So- lid line 2 represents calculated values based on Kane's model.A simple 2-band model was used to describe the transformation of the energy spectrum under pres- sure. The dependence of mill K on pressure (solid cur- ve 2, figure l) and relative variation of Fermi ener- gy of holes
g(p)
/sF(0) (curve 4 figure 2) have been h calculated. A comparison of pressure dependences mx(p) and p (p) yields some information about theH
nature of scattering processes for current carriers.
For isotropic relaxation time approximation creases (curve 2, figure 1)
.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786477
uHmll X 1 3a2
T =-
.
2 a ~ + 1 , where a2 is the coefficient ofe References
anisotropy for the cyclotron mass. Assuming to be
constant, the dependence 9 (p) f ~ ( ~ ) has been calcu- / Butler,J'F' * HamanyT.C' 3 IEEE J' Quantum tron.
Q-E
(1969) 50lated and is shown in figure 2 (curve 3).
121 Melngailis,I., Kafalas,J.A., Harman,T.C., "Phy- sics of Semimetals and Narrow Gap Semiconductors"
t
Proc. Int. Conf., Dallas (1970) 407, (PergamonPress, N.Y.) 1971
Fig. 2 : Pressure dependences of relative varia- tion of Hall mobility yH(p)/y (0)(1) of the product
H P(pFJ 1/2~:(pn3/2
(dotted curve 2) of relaxation
lj,x(O~
1/2~:(o~] 3/2time T(p)/5(0) (3), of Fermi energy of holes E~(P)/ h
h 54
E (0) ( 4 ) , and reciprocal cyclotron mass m (o)/m*(p)
(31, for the alloy Pbo,stSno,lsTe for T = 4.2 K.
The dotted curve.2 on figure 2 shows the pressure dependence of the relative magnitude of the product
(my1 1/2(Eq)312, proportional to the relaxation time .ri of carriers undergoing scattering at charged centres. Close coincidence of this curve with the dependence +(p) /T
