324
10 Recombination
Fig. 10.26 Schematic
representation of Auger
recombination. An electron
recombines with a hole and
transfers the energy to a
another electron in the
conduction band, b another
electron in the valence band
(a)
e
hh
lh
k
E
E g
(b)
e
hh
lh
k
E
E g
Table 10.3 Auger recombination coefficients for some semiconductors. Data for InSb from [1013], SiC from [947],
others from [948]
material
C n (cm 6 /s)
C p (cm 6 /s)
4H-SiC
5 ×10 −31
2 ×10 −31
Si, Ge
2.8 ×10 −31
9.9 ×10 −32
GaAs, InP
5.0 ×10 −30
3.0 ×10 −30
InSb
1.2 × 10 −26
G th = C n n
2
0 p 0 + C p n 0 p
2
0 ,
(10.38)
where C n and C p denote the Auger recombination coefficients. The equation for the dynamics in the
presence of excess carriers (if solely Auger recombination is present) is given as
∂ δn
∂t
= G th − R = −C n (n
2 p − n
2
0 p 0 ) − C p (n p
2
− n 0 p
2
0 ) .
(10.39)
The Auger recombination rate typically used in SRH kinetics is
r Auger = (C n n + C p p) (np − n 0 p 0 ) .
(10.40)
Typical values for the Auger recombination coefficients are given in Table 10.3.
In Fig. 10.27a the electron lifetime in heavily p-doped (In,Ga)As (lattice matched to InP) is shown
[1014]. It follows τ
−1
n
= C p N
2
A as expected from (10.39) for p-type material. The Auger process in
silicon has been discussed in detail [1015]. In Fig. 10.27b experimental data for n-type and p-type Si
are summarized. Auger theory can predict the lifetimes in n-type material. The predicted rate in p-type
material is too small, thus a phonon-assisted process is evoked [1015].