328
10 Recombination
Fig. 10.29 Minority
carrier lifetime at room
temperature as a function
of majority carrier
concentration in n-type and
p-type silicon. The dashed
lines have the slopes N −1
and N −2 . Data
from [1024]
In Fig. 10.29 various data on minority carrier lifetime in silicon are compiled. Over some doping
range, a dependence of the lifetime ∝ N
−1 as in (10.54) prevails. For doping beyond the 10
19 cm
−3
range, Auger recombination (Sect. 10.8) with τ ∝ N
−2 is dominant. A more detailed discussion can
be found in [1023, 1024]. Generally the lifetimes are temperature dependent [1025] as expected from
(10.52).
10.9.2 Multilevel Traps
Traps with multiple levels in the band gap have generally similar but more complicated dynamics as
compared to single-level traps. Lifetimes are an average over negatively and positively charged states
of the trap.
10.10 ABC Model
Summarizing the results on band-impurity recombination (Sect. 10.9), bimolecular recombination
(Sect. 10.2) and Auger recombination (Sect. 10.8), the total recombination rate R can be written simplified as
R = A n + B n
2
+ C n
3
,
(10.58)
where A is the coefficient for the band-impurity recombination, B the bimolecular recombination
coefficient and C the Auger recombination coefficient; n denotes the carrier density. This model is
known as the ‘ABC’ model. It can be refined separating effects of electrons and holes and including
higher terms. Often such model is used to investigate recombination in devices as a function of injection,
e.g. [1026, 1027].
The internal radiative quantum efficiency η int is given by ratio of the radiative recombination rate
and the total recombination rate,
10 Recombination
Fig. 10.29 Minority
carrier lifetime at room
temperature as a function
of majority carrier
concentration in n-type and
p-type silicon. The dashed
lines have the slopes N −1
and N −2 . Data
from [1024]
In Fig. 10.29 various data on minority carrier lifetime in silicon are compiled. Over some doping
range, a dependence of the lifetime ∝ N
−1 as in (10.54) prevails. For doping beyond the 10
19 cm
−3
range, Auger recombination (Sect. 10.8) with τ ∝ N
−2 is dominant. A more detailed discussion can
be found in [1023, 1024]. Generally the lifetimes are temperature dependent [1025] as expected from
(10.52).
10.9.2 Multilevel Traps
Traps with multiple levels in the band gap have generally similar but more complicated dynamics as
compared to single-level traps. Lifetimes are an average over negatively and positively charged states
of the trap.
10.10 ABC Model
Summarizing the results on band-impurity recombination (Sect. 10.9), bimolecular recombination
(Sect. 10.2) and Auger recombination (Sect. 10.8), the total recombination rate R can be written simplified as
R = A n + B n
2
+ C n
3
,
(10.58)
where A is the coefficient for the band-impurity recombination, B the bimolecular recombination
coefficient and C the Auger recombination coefficient; n denotes the carrier density. This model is
known as the ‘ABC’ model. It can be refined separating effects of electrons and holes and including
higher terms. Often such model is used to investigate recombination in devices as a function of injection,
e.g. [1026, 1027].
The internal radiative quantum efficiency η int is given by ratio of the radiative recombination rate
and the total recombination rate,