Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc15786/doc.pdf Дата изменения: Tue Oct 30 14:51:38 2007 Дата индексирования: Mon Oct 1 20:41:45 2012 Кодировка:

, .., .., .. () - , . , , , . . , , . . Simulation of charge dynamics in a dielectric target during irradiation by an electron beam Eugene A. Cheremukhin, Eugene A. Grachev, Nikolay N. Negulyaev (Moscow) On the basis of Monte Carlo simulation model of an electron scattering in a solid distribution of a charge produced during exposure is presented in the paper. There is shown that using a model of generation of secondary electrons adequately estimates positive charge as well as negative one. The modeling of dynamics of produced charge to behavior state is presented. Special computational algorithm was developed to solve a system of equations that describes charge relaxation in three-dimensional case. The examples are given.

253


, . , , . , , , [1]. , . , , ( , ) . , , , , . [2-4] (. 1).

.1 (--). 254


.. . -- -10, 2002, .253-255

, , . 1. , - [5,6]. 5 [6]: Z 2/3 d Z ( Z + 1)e 4 (1 - cos + 2 )- 2 , = 3.43 10-3 = E d 4E 2 E ­ (), - . « » ( 2 ) (Evans) [5]: 1 dE e 4 1 = 2 Z 2 + d (1 - )2 E E = E , - . . , (Joy, Lou) [6]: N 2e 4 N a el Z i 1.166( E + 0.85J i ) dE , =- Ci A ln ds E Ji i i =1 Nel ­ , Ji - , Zi - i- , - (/3), Ai ­ i- (/).
255


, , [6]: dE dE dE , = - ds total ds Bethe ds Evans

dE ds

=
Evans


i =1

N

el

1/ 2

Ni Z

i





c

dE E d

d , Ni ­
Evans

i- , ­ ( 0.001). 2. , 2- ­ (C582) 500, - 100, ( ­ SiO2) (. 1). , , , . . 2 20 .

. 2. (). , 100 ().

(.3).
256


.. . -- -10, 2002, .253-257

. 3. .

3.

. 4.

, . , , , « » [2-4] . . , , : r 1 = - ec( r ) / 0 2 = 0
1, x
2 x=±

=0 =0 2 z =0
z=+

1, y

2 y=±

=0 =
z=L-0

1

z=0



z

z

z=L+0



1 ­ 1 (. 4); 2 ­ 257


2; L ­ ; ­ ; 0 ­ r ; ( r ) ­ . [7]. . 5 ( .2). (0.5 ) (5, 10, 15 20 ) ­ . , ­ 25-100 /2.

. 5. () ().

, , , , , [8]. 4. () [9]. : 1) ; 2) , 3) , 4) , 5) 258


.. . -- -10, 2002, .253-259

. - , . , , . , , , . , , ­ (. 1). - , - ( ), . , Mn, Mp . S(E), ,
S(E) =
m =1



M

n

N m ( - m )

Nm ­ Em. , , [9]:
t t n f + p + f
M

ni = G - n f p f + i =1
n

M


j =1
p

p

pj -

n f +




Mn

ni
i =1

rr p f + nkT n f - n(n f ) (1) e

M


j =1

p

p j = G -n f p f +

M


j =1

pj -

n f +

Mn

ni
i =1

kT rr p f + p p f + p( p f ) (2) e

259


ni n = k3n f ( N i - ni ) - i - p f ni , i = 1,..., Mn t i p
j

(3) (4)

t

pj = k3 p f ( Pj - p j ) - - n f p j , j = 1,..., M



p

j

= -

e p + 0 f

M



p

pj -nf -

j =1


i =1

M

n

ni

(5),

nf, pf ­ n p; G ­ ; ni, pj ­ ; Ni, Pj ­ i- j­ i i ; , ' - ; k3, k3' ­ ; - ; - ; 0 - ; T ­ ; e ­ ; k ­ ; L ­ . (1)-(5) :
n
f x, y =± z =0

=n

f0

n f e z - kT n f z p f e z + kT p f z

=0
z = L-0

p

f x, y =± z =0

=p

f0

=0
z = L-0




(6)



z =0

=0
x=±

/ z
= / y
y =±

z =L-0 z =+

= / z

z =L+0

/ x

= / z

=0

(7),

nf0, pf0 - . :

260


.. . -- -10, 2002, .253-261

n

f t =0 f t =0

r = n f 0 + gn (r ) r = p f 0 + g p (r )

ni p

t =0 j t =0

= ni0 , = p j0 ,

i = 1,...,M

p

j = 1,...,M p
n

(8),

ni0, pj0 - i- j- ; r r g n ( r ) , g p ( r ) - . . , (1)-(5) (6)-(7) (8) . , , , . tm, , , . (1)-(5) [7]. , , (5). tm, [tm, tm+ tm] . (1)-(4) [7]. [tm, tm+ tm] (1)-(4) X, ­ Y, ­ Z. . . 6, 7 . , . , .2, .. , 100 500. 20 .
261


. 6. . 1 ­ ; 2 ­ ; 3 ­ . : n = 10-8 2/(*); p = 10-10 2/(*); = 10-4 ; L = 0.5 ; Nt = 1021 -3; = 10-16 3/; ' = 0. n/p << 1, . , , .

262


.. . -- -10, 2002, .253-263

. 7. . 1 ­ ; 2 ­ ; 3 ­ . : n = 10-8 2/(*); p = 10-10 2/(*); = 10-4 ; L = 0.5 ; Nt = 1021 -3; = 10-13 3/; ' = 0. , , ( ), , , .

. - , . , -. , .
263


. , , . . 1. H.Itoh, K.Nakamura "Charging effects on trilevel resist and metal layer in electron-beam lithography" // J.Vac.Sci.Technol.B 9(6), 1991. 2. J.Cazaux "Some considerations on the electric field induced in insulators" // J.Appl.Phys., 59(5), 1986. 3. D.Melchinger, S.Hofmann "Dynamic double layer model: description of time dependent charging phenomena in insulators under electron beam irradiation" // J.Appl.Phys, 78(10), 1995. 4. H.Chen, H.Gong, C.R.Ong "Determination of charge distribution volume in electron irradiated insulators by scanning electron microscope" // J.Appl.Phys.78(6),1995. 5. .. « » // .:, 1990. 6. D.C.Joy "Monte Carlo Modeling for Electron Microscopy and Microanalysis" // Oxford University Press, 1995. 7. .. , .. . , ., , 1989. 8. M.Kotera and H.Suga "A simulation of keV electron scattering in a charged-up specimen" // J.Appl.Phys. 63(2), 1988 9. .. , .. . . ., , 1991.

264