On The Photoemission From Quantum Confined Compound Semiconductors
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ON THE PHOTOEMISSION FROM QUANTUM CONFINED COMPOUND SEMICONDUCTORS Kamakhya P. Ghatak* and B. De** *
Department of Electronics and Jadavpur, Calcutta 700032, India
Telecommunication
Engineering,
** Department
University
of Electrical Engineering, John Browne and Cinc, 333 Ludlow P. 0. Box 1422, Stamford, Connecticut 06902, USA
of
Street,
Abstract In this paper, we have studied the photoemission from quantum wells (QWs), quantum well wires (QWWs) and quantum dots (QDs) of degenerate Kane-type semiconductors, on the basis of a newly derived electron dispersion law considering all types of anisotropies within the framework of k.p formalism. It is found, taking n-Cd 3 As 2 as an example, that the photoemission increases with increasing photon energy in a ladder-like manner and also exhibits oscillatory dependences with changing electron concentration and with film thickness, for all types of quantum confinement. The photoemission current density is greatest in QDs and least in QWWs. In addition, the theoretical results are in agreement with the experimental observation as reported elsewhere. With the advent of MBE, MOCVD, FLL and other experimental techniques, low-dimensional structures having quantum confinements of one, two, and three dimensions, such as, QWs, QWWs, and QDs have, in the last few years, attracted much attention not only for their potential in uncovering new phenomena in material science, but also for their interesting device applications [1,2]. In this paper, we shall study the photoemission from QWs, QWWs and QDs of quantum confined compound semiconductors on the basis of a newly derived electron dispersion law considering the anisotropic crystal potential, anisotropic effective electron masses and the spin-orbit splitting parameters of the valence bands. We shall investigate the doping, thickness, and the incident photon energy dependences of such photoemission from such quantum confined compound semiconductors, taking n-Cd 3 As 2 as an example. The generalized electron dispersion law in compound semiconductors can be expressed, considering all types of anisotropies of the energy band parameters, with the same notations of [3], as U(E)
The modified written as
electron
= ks25
energy
2
+ V(e) kz
spectra
in QWs,
2 2 x + ky
U(E) = (nxlr/dx) U(E) = (nxlr/dx)
and U(e) where n , rcspectivel;',
=
(nxlr/dx)
2
2
(!)
+ V(E)k
+ (nylr/dy) 2
2
QWWs and
QDs can,
2
be (2)
z
+ V(E) kz
+ (nnny/dy) + V(e) (irnz/dz)
respectively,
(3) 2
(4)
ny and nz are size quantum numbers along x, y and z directions and dx, dy and dz are the thicknesses along the x, y and z axes,
Mat. Res. Soc. Symp. Proc. Vol. 228. (01992 Materials Research Society
238
respectively. written as
The electron
no=
concentration
in
A,
ny= I
nxmax Z nx=l
no = ( 2 /dxdydz)
(5)
[A2 +B?]
nymax I ny=i
i=l and Fermi 2, vr energy, = 2(kBT)2 r[l-21 2r]0( respective
=
[(U (eF) - (nmx/dx)
(7)
S BI = VrLAi], r=i
2rr/dEF2r,
2
(6)
nzmax I nz=i
[U(EF) - (Cnxr/dx)2 ] /, V(_E
A2
be
nym ax
Z
= ( T"X I n
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