The Burstein-Moss Shift in Quantum Dots of III-V, II-VI and IV-VI Semiconductors Under Parallel Magnetic Field
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such
as magneto
size
quantized
systems
and quantum
dots (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] . In the former case the motion of the carriers are quantized in the three perpendicular directions in the wave-vector space and the carriers can only move due to broadening. In quantum dots, the freedom of motion of free carriers is not allowed and the density-of-states function is changed from Heaviside step function to Dirac's delta function [3]. For non-parabolic materials the absorption edge lay at much shorter wave length when it was very n-type than if it is of this effect was intrinsic and the explanation well-known[4]. Though, the Burstein-Moss shift(BMS), has been physical studied for various materials under different conditions, nevertheless it appears that the same shift in quantum confined structures has relatively been less studied [5-6]. It appears from the literature that the BMS in QDs of III-V, II-VI and IV-VI semiconductors for the more interesting case which occurs from the presence of a parallel
673 Mat. Res. Soc. Symp. Proc. Vol. 484 ©1998 Materials Research Society
magnetic field on the basis of newly formulated carrier dispersion laws. These materials find extensive applications in the fields of materials science and technology[7] . In this paper we shall study the doping and thickness dependences of Cds and CdTe as examples in the BMS taking QDs InSb, presence a parallel magnetic field. Theoretical Background The carrier energy spectra in bulk specimens of III-V, be can, respectively, semiconductors and IV-VI II-VI expressed [8] 2 4 (1) p2 E = ac'v p2-bc,v (2) E = A Cv k S +BCV k z + CCv k s (3 a' 2v,c Py p +4-a -aa' c~ pv2/#C +a Eqa 2c,v cv 2v,c c,v c, v) 2+a2cv E=c, b c,v =aa 2c,v' v=h 2 /2m,,
where ac,v =h 2/2m c,v , B Ac,=h 2 /2mc, v' ,
a=l/E g is
C
constants of conduction or valence bands, 2 2 ai 2 p 1 a.ic,v 2+a 0c,v= =a I c,v px2+a 2 c,v pya3 c,v Pz a'2v'c = (2m'2v'c ) -and
3,
and
the
other
the
splitting
v -1, l2 =2i ;(2m.Ic,v )1 i=1,2
notations
have
been
defined in [8]. In the presence of a parallel magentic field B, along y-direction the modified carrier dispersion laws in QDs of the said materials can, respectively, be written as I CIVC
t1 c,v--aC
-a(heB/m c'v ) (Lnr/b) .t
E2
1 c'v
-
c,v,I
t21
+(e 2B 2/2m* v )< c,v+cB
-2a(e2B2/2mc'v
a(e2B2/2mc) c Iv
(h 2/2m 1 c'v ) [(Ln/b)2 +(R/c)2] )(nnr/a)2 +(e2 B2/2m 2 c'v )
+ h2/2m*2 and
c,v
E3
=t 2 c,v -at 2 c,v +a
CIVIC
-a a' h2 (Rn[/c) 2
+a
-a
3 C,V
(4)
2
+
2t 2
[2a c'v a
h 2 (R/c) 2t 2 c,v (h Rn/c) 4 a'
2 c,v
aa
C,V
e2B2-+2a
1 C,V
2
a
(5)
2
C,V
VC
h~eB2
3 C,V
(h L/b)2 + a2 cv
674
a3
c'v(h
Rn/c)
2
2 +6 a3 3
C, V
(hnn/a) 2]e 2B2 -aa'
a
2V, C
e 2B2= a4 (1/5-l/n
< 2
=
2 2
n +3/2n 4N4 )
2b
2222
b (1/3-1/2L 22) , t
h2
CV= 2
[a1 c,v (L/b)2+a2 c,v(R/c) +a3 =b 4 ( 1/5 -1/L 27r2 +3/2L 4n4)
x
2 c'v(n/a) ]
The BMS can,
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