Ijetcas14 306 by iasir journals

I. Q. Taha et al., International Journal of Emerging Technologies in Computational and Applied Sciences, 8(1), March-May, 2014, pp. 01-12

C A t   i e

iE  A t  G  t   dt 

 0

  1

n l

nmlk

 2i int   L

  

nm

 i L   2 L

  

l k

i E  E  Z i   C  2  L  L  n  m  2 l 2 k t  VA e  A  e i  n  m  2 l  2 k     E   E A Z   L n  m  2l  2k   i C  2 L 



WA e i e



(10)



i E   E A  Z  L  1 n  m  2 l  2 k i   C  2  L  t

E   E A Z   L  1  n  m  2l  2k   i C  2 L  



i E   E A  Z  L 1 n  m  2 l  2 k i   C  2  L  t

   E   E A Z   L 1  n  m  2l  2k   i C  2 L    However, if the perturbation is time dependent harmonic one, then the system levels generated from WA e i e



 

E A ( Z) will

be E A Z  nL , with L  L and n  0,1,2,...... . Some of these levels are thrown above Fermi level and the others below the conduction band bottom position. So they may do not effectively take parts in the resonance charge exchange process. Accordingly, all the terms in eq. (10) are neglected except for n  m  l  k  1 , so eq. (10) can be written as,  VA   C A t   e i E  E A  Z t    E   E A Z  i C  2 L   WA e iiL t WA e iiL t    (11) E   E A Z  L   i C  2 L  E   E A Z  L   i C  2 L  The adatom’s occupation level can be given by [21],

nA 

2 1 C A  E  E  dE    

(12)

Substituting eq. (11) in eq. (12), we get the following expression, nA 

 C dE 1 1  L dE    E  E A Z 2   C  2 L 2   E  E A Z   L 2   C  2 L 2



1  L dE   E  E A Z   L 2   C  2 L 2



 int e i iL t dE 1   E  E A Z   i C  2 L E  E A Z   L   i C  2 L 



 int e i iL t dE 1   E  E A Z   i C  2 L E  E A Z   L   i C  2 L 



 int e i iL t dE 1   E  E A Z   i C  2 L E  E A Z   L   i C  2 L 



 int e i iL t dE 1   E  E A Z   i C  2 L E  E A Z   L   i C  2 L 



1  L e 2i  2iL t dE         E  E A Z  L  i  C  2 L E  E A Z   L   i C  2 L 



1  L e 2i 2iL t dE   E  E A Z   L   i C  2 L E  E A Z   L   i C  2 L 

(13)

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