J. Phys. Chem. 1986,90, 5932-5937
5932
After some algebra, the condition (10) takes on the form -(2H
AE + 1)so + --(In hw
[(A
+ l ) E ~ / h E l+ 1) 0.5 In (AE hw)
If hw/kBT >> 1, then ii to
-So
+ E[ln hw
i=
(EM/AE)
>> -10.594
(11)
0, and this condition can be simplified
+ 11 - 0.5 In (AEhw) > -10.594 (12)
(b) For the case of high temperatures ( h o / k B T> 1 and the asymptotic expansion for this function can be applied. The condition (10) takes on the form
+
On the basis of the relations (1 l ) , (12), or (1 3), it is possible to determine the range of parameters favoring, say, the nonradiative capture. For instance, if the matrix is characterized by the parameters Soand h w , the nonradiative capture is preferred by the traps with the depth lEtl obeying the conditions lE,l[ln (EM) + 11 - lil (lEtl)(lEtl - 0.5hw) > hw(0.5 In (hw) - 10.594) + E M (14) at low temperatures ( h w / k B T >> 1) and E M - 3 k ~ T / 2- X € lEtl E M - 3 k ~ T / 2+ X
(15)
x = ~ ( E M ~ B10.247 T [ - 0.5 In (Ehlk~r)])”’ at high temperatures ( h w / k B T
