On the Thermoelectric Power in Ultrathin Films of A 3 II B 2 V Semiconductors Under Magnetic Quantization
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ON THE THERMOELECTRIC POWER IN ULTRATHIN FILMS OF A3 1B 2 V SEMICONDUCTORS UNDER MAGNETIC QUANTIZATION KAMAKHYA P.
GHATAK* AND BADAL DE**
*DEPARTMENT OF ELECTRONICS AND TELECOMMUNICATION ENGINEERING, UNIVERSITY OF JADAVPUR, CALCUTTA-700032, INDIA **DEPARTMENT OF ELECTRICAL ENGINEERING, JOHN BROWN E AND CINC., 333 LUDLOW STREET, P.O. BOX-1422, CONNECTICUT-06902, U.S.A.
ABSTRACT An attempt is made to study the thermoelectric power in ultrathin films of A3 Bý semiconductors under magnetic quantization by including all types o1 anisotropies in the energy spectrum within the domain of k.p theory, and taking n-Cd3As2 as an example. It is found that, the magneto-ther-
mopower decreases with increasing surface electron concentration and also changes in an oscillatory manner with film thickness respectively. The theoretical results are in agreement with the experimental observations as reported elsewhe re.
The remarkable developments in FLL and new epitaxial technologies of M3 and 16CVD have generated significant possibilities of fabricating various types of low-dimensional structures likes quantum wells, quantum wire and quantum dots /rh 7. Though considerable work has already been done, neverTheTess it appears from, the literatqre that the thermoelectrio power in
ultrathin films of A3?
B 2 semiconductors under
magnetic quantization has yet to be studied. The discoVery of QMI has brought interest to the study of the thermoelectric power in semiconductor heterostructures. In this paper we shall study the thermoelectric power un4er strong magnetic quantization in ultrathin films of A 3 B2 semiconductors on the basis of a newly derived electron Inergy spectrum considering the anisotropic crystal potential, anisotropic effective electron masses and the anisotropic spin-orbit splitting parameters of the valence bands. In what follows, this is done by taking n-Cd3 As 2 as an example. The generalized electron energy spectrum in A B2 semiconductors including all types of anisotropies in 1he energy band can be written /-2 7as
U (C)
= ks 2 +
(V )kz
2
where the notations are defined in /-2 7. The modified electron energy spectrum for the present case can be expressed as V() = D÷ (n,) + f 2 (F') (tr/do)2
(2)
where D.(n,E) = /"(2eH)
(n+4) fl (C) + bO (z
*+g
Mat. Res. Soc. Symp. Proc. Vol. 234. 01991 Materials Research Society
+
56
(41 2
(34
+
2 ) 79 e is
the electron charge,
H is the qua-
ntizing magnetic field along Z-direction, n and t are Fespectively the magnetic and size quantum numbers, bo=/TeHh,_ .,.) +(Eg + 7 /-6 mo (2, + (2/3)4,7F,E is the electoin energy in
the presence of magneto-size quantization
as measured from
the edge of the conduction band in the absence of any quantization and do is the thickness of the ultrathin films. Using (2) the surface electron concentration can be written as nmaX t ma n
= (eB/h) E
(n,t,IF)
A1
(3)
n=0 t=l where A1 (n,t,.F) = apl/p 2 , a = exp (c), B•
is
(1)
the Fermi energy in + Cos p_7,
C = (kBT)-
the present case,
, P1 = /-a
p = q/kýT, q is
the Landa
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