modeling in semiconductor spintronics, s. k. saikin, y. v. pershin
TRANSCRIPT
Modeling in Semiconductor Spintronics, S. K. Saikin, Y. V. Pershin,
V. L. Privman, Sci. Trans. Kazan State Univ. 147, 97-115
(2005)
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Modeling in Semiconductor Spintronics, S. K. Saikin, Yu. V. Pershin and V. L. Privman, Sci. Trans. Kazan State Univ. 147, 97-115 (2005)
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α # β # # Mαβ ! + # , ! - * './)
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Summary
S.K. Saikin, Yu.V. Pershin, V.L. Privman. Modeling in semiconductor spintronics.
In this paper we review theoretical methods utilized to investigate spin dynamics in semi- conductor structures. In particular, we consider drift-diffusion, kinetic transport equation and Monte-Carlo simulation approaches applied for spin transport modelling. Several examples of applications of these modelling techniques are presented.
(URL: http://public.itrs.net/Files/2003ITRS/Home2003.htm)
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! "# $ % % & ' ()* +, -. .* /$ ! " 0 0# % * " " / . # * 0# % (1, 0 / # .. . ! . " # #* " .% &23456789 :35;<= >996?? 26=<@A' B # # 0 . C % $ D % E ()F, G * 0 ! #* . " $ ! 0 / . " . $ B " " # % ())1+,* 0# ! # # H $ 0 # % ! (+I* +J, - #. $
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Modeling in Semiconductor Spintronics, S. K. Saikin, Yu. V. Pershin and V. L. Privman, Sci. Trans. Kazan State Univ. 147, 97-115 (2005)
2 σ · B, 3)4
# g∗ ,, g ", ! σ " ! & + ( 3)4 - # ' " # ! % - $ ,- ' # ( " $ # ! $ " # 3 " 4! % 5 " # % ! # - 5 6& ! &" # ! " ! # # # $- 7 " ,, 8 ' 9
HSO =
2
4m2c2
1 (& & 7 & & #.3 .8 45% / ' ' ( ! + * & 9 & 6 ( (( '& , +0
e ∂n↑(↓)
σ↑(↓) = en↑(↓)µ, :
+ , --- " - ./ n * " %&&( 0 " " 1 )) " 2 !) , , -- -- Di Ni τi 34$ $ -- 4) " %&5( . ! ) # 4) * " " $ "), 6 , ) $ %&5(
!"# $%&! ' (")* !* *! %! n&"+ ,"&'%- *% &,# !"# $%&# % &*.& ! *!% ! &'% x = x0 ,/".& ! ""! &0-"1 x = 0 1 -&!, !2( $%&'%( &&3 !- ")1 "!"," &'%,1 "#, ! &'% x0 = −10 1 %"% 0*%) %"&# x
" '# %)&") ,- N2 4τ1 = τ2 D1 = D2 !' N2 !& % ! "&". && !- ") !5 &0-" &&3 !- ") *'&, " $%&- && !5 (" )# 6789 %" "" 2&*%&- -
!" # ! $%&'$(& ) # * + + ! # , * ! + α β (- % . # ! ! / * + ( 0 ! + # 1 +
ρσ = 1
(x,y),(x′,y′)dx ′dy′,
(x,y),(x′,y′) #
(x′, y′) P(x, y, t) $ % $ & # !! ' ! ! (x, y) !! ! t !! # ( ) " ( *( ! ' ! $ + " ) , (x′, y′) (x, y) " ! P′
(x,y),(x′,y′) , )( ) $
- " .!" !!, ! # , ! . ! (x′, y′) (x, y) $ / . ! ! ( ! (" !# $ 0 " ! " ! # , , ) $ 1 " a ) # " # " 234
P′ (x,y),(x′,y′) = P + P⊥ (cos− 1) + a×P sin, 3
: ) " # !. !*, ,* " ! , 0!$ ; !. " ! 23<4" ! ( # 23=" 3>4 ? 239" =4" " ( # . $ @! " ! # ! " ! 2<4$ ? )! ! ) # # ( # , ! . ) # !$ ; " ,* , ," ! ! # # 1/2 ) , $ & . !. #" ! #$ ? * ! , !$
A ! ! ( # ( ) ( ( !(" ! ! ! # ! " $ % ! !. " ! # ? 2=" 394$ ? . ) #
α # β # # Mαβ ! + # , ! - * './)
Ws′s(R,k, t) =
∫ ψ∗(R−r/2, s′)ψ(R + r/2, s) exp (−ikr) d2r, (
ψ(r, s) & ! * & * ( 0 0! 1 2 $ $ 3 σα 4 I ')
W = 1
∂W
∂t +
1
2
{ vj ,
∂W
∂xj
+ ikj [vj ,W ] = StW, /
vj = ∂H/∂pj 2 [A,B] {A,B} # $ 4 '( ./)! * $ & StW 4% ! 8 2 2 4 , 2 # '. .5)!
9 4% # # $ , './)! * $2 $ %4 '.) '( .()! : 2 4# # 4 '.5 ;)!
! " # !
$ # % & # '' ()*+)*,*-./.01* +/).023*,4! 5 '' ! $ # # 6 #! 7 # ! $ 6 (,/8+30-9 .08*4 " ! " 6: 6 6 # ! ; ' ' # # ! ! <!
= # ( # >?@A >?BA4 # ! C # ( 4 # 6 # ! " 6# # '! $ i#
ρi(t+ δt) = exp
F #
Pα = ∑
i
I dV ! J (DD4 (DH4 # ' >?GA
Pα =
∑ i
5 ( ' ) -"1$ 8 9):* -"1* , 0#$ 5 ) , $
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Summary
S.K. Saikin, Yu.V. Pershin, V.L. Privman. Modeling in semiconductor spintronics.
In this paper we review theoretical methods utilized to investigate spin dynamics in semi- conductor structures. In particular, we consider drift-diffusion, kinetic transport equation and Monte-Carlo simulation approaches applied for spin transport modelling. Several examples of applications of these modelling techniques are presented.
(URL: http://public.itrs.net/Files/2003ITRS/Home2003.htm)
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