326
10 Recombination
holes. The capture rate of electrons is
r c = v th σ n n N t (1 − f t ) .
(10.42)
The emission rate from filled traps is
g c = e n N t f t ,
(10.43)
where e n denotes the emission probability. In a similar way, the emission and capture rates for holes
can be written:
r v = v th σ p p N t f t
(10.44)
g v = e p N t (1 − f t ) .
(10.45)
In thermodynamical equilibrium, capture and generation rates are equal, i.e. r c = g c and r v = g v .
Thus, the emission probability is
e n = v th σ n n 0
1 − f
0
t
f
0
t
.
(10.46)
Using
1− f
0
t
f
0
t
= exp
E t −E F
kT
, (7.10) and (7.11) the emission probabilities can be written as
e n = v th σ n n t
(10.47)
e p = v th σ p p t ,
(10.48)
with
n t = N C exp
E t − E C
kT
(10.49)
p t = N V exp
−
E t − E V
kT
.
(10.50)
We note that n t p t = n 0 p 0 (cf. (7.15)).
The temperature dependence of the thermal velocity is ∝ T
1/2 , the temperature dependence of the
band-edge density of states is ∝ T
3/2 (7.8) and (7.9). Thus, the temperature dependence of the emission
(a)
(b)
(c)
(d)
E C
E V
E t
Fig. 10.28 Band-to-impurity processes at an impurity with one level (left: initial, right: final state in each part): a electron
capture (from conduction band), b electron emission (into conduction band), c hole capture (from valence band), d hole
emission (into valence band). The arrows indicate the transition of the electron