v, . hυ>>EG, . . . , :
, (4.3)
υ , . = 2π/λ ~ 105 -1, υ 108 -1. = 0 (4.3) :
= υ, (4.4)
. (4.4) . , , , . , , . , , , , .
, ( ) . , (<100 ). , , . , . 1 , .. . , , . , , , 80 % .
4.1.3
, (, ). (t10-11 ¸10-13 ), (t10-8¸10-9) , (.4.1,). fu fc, , , (4.2), :
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, (4.3.)
. (4.3.)
- .
, .. . , .
. , n V : V×dNn /dt = (A+BNn ), (4.4)
Nn - . , . - , ..: Nn = 2/[exp(hn/kT) 1]. (4.5)
dNn /dt = 0, (4.4) :
/ = - Nn (4.6)
2 1 . 2 1. , - (4.2), , , .. :
. (4.7)
, 2 1, ..:
= 0 f(2)[1 - f(1)], (4.8)
0 .
, , , , . , (4.4) , :
B = B2f(2) [1 - f(1)] - B1f(1) [1 - f(2)], (4.9)
1 2 - . (4.8) (4.9) (4.6) (4.2) (4.5) :
exp (hn/kT) 1 = 22/0{B1/B2exp[(E2-E1)/kT] 1}. (4.10)
hn 2 1, hn=(2 - 1). (4.10) , 1 = 2 = 0/2 (4.9) :
B = 0/2 [f(2) - f(1)]. (4.11)
2→ 1, (4.11), : [f(2) - f(1)]>0. (4.12)
2 1 , , , (4.3). , f(2) f(1) :
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f(2)=[1+exp(E2 EFc)/kT]-1, f(1)=[1+exp(E1 EFu )/kT]-1, (4.13)
(4.12) :
(EFc -EFu )> (2 - 1) = hn. (4.14)
, , , g, . . : g = (c - u)< hn<(EFc - EFu). (4.15)
, 2→1 : (EFc - EFu)>g. (4.16)
, 2 1 , .