The Diffusivity-Mobility Ratio Under Strong Magnetic Field in Small Gap Superlattices with Graded Structures
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THE DIFFUSIVITY-MOBILITY RATIO UNDER STRONG MAGI&TIC FIELD IN SMALL GAP SUPERLATTICES WITH GRADED STRUCTURES KAMAKHYA P.GHATAK* AND BADAL DE** *Department of Electronics and Telecommunication Engineering Faculty of Engineering and rechnology, University of Jadavpur, Calcutta 700032, India **John Brown E and C.Inc., 333 Ludlow Street, Connecticut 06902, USA.
P.O.
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ABSTRACT In this paper we have studied the Einstein relation for the diffusivity-imobiiity ratio (DMR) in small-gap superlattices (SLs) with graded structures under magnetic quantization by formulating a new dispersion law. It is found, taking InAs/ GaSb SL as an example that the DMR increases in an oscillatory way with increasing carrier degeneracy due to SdH effect. The DMR in SL. is greater than that of the constituent materials. The theoretical results are in agreement with the suggested experimental method of determining the DMR in degenerate materials having arbitrary dispersion laws. With the advent of mSE, MVCVD, FLL and other experimental techniques, the semiconductor superlattices (SLs) having various types of complex band structures have found wide applications in photciodes, photodetectors, transistors, light emitters etc./l_/. Most papers in this field are based on the assumption that the interface between the layers are sharply defined with zero thickness so as to be devoid of any interface effects; the SL potential distribution may be considered as a one-dimensional array of rectangular potential wells.The said experimental techniques may produce SLs with physical interfaces between two materials crystallographically abrupt, but the bondinq environment of the atoms adjoining this interface will change on the atomic scale. As the potential form changes from a well (barrier) to a barrier(Well), an intermediate potential region exists for the charge carriers. Thus, the influence of the finite thickness of the interface on the carrier dispersion law becomes very important since the carrier energy spectra govorn all the transport properties. it appears from the literature, that the Einstein relation for the diffusivity-mobility_r~atic (DMR) of SLs has relatively been less investigated /l_/.The connection-of the DMR with the velocity autocorrelation function / 2_/, its relation with the screening length /3_/ and the different formulations of the DMR have been studied in /4-6./ under various physical conditions. In this paper we shall study the DM4R under strong magnetic field in small-gap SLs with graded interfaces and the. constituent materials taking InAs/GaSb SL as an example. We shall also suggest an experimental method of determining the Einstein relation in degenerate materials having arbitrary dispersion. laws. The DMR can,
in
D//
(-b no/> EF)-
= (n,/-).
general,
be written as Z4_1 1
(1)
where n 0 is the electron concentration, e is the electron charge and EF is the Fermi energy in the present case. It Mat. Res. Soc. Symp. Proc. Vol. 262. ©1992 Materials Research Society
912
appears then, that, the formulation of DMR using
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