144
7 III-Nitride LED Quantum Efficiency Improvement Technology
I Q E =
B
A S R H /n + B + C Auger n
(7.20)
This equation shows that the IQE ~ n curve is center-symmetric about n 0 =
A S R H
C Auger
. In fact, the IQE ~ n curve of typical InGaN blue-green LEDs exhibit noncentral symmetry. At n > n 0 (the carrier concentration corresponding to the IQE
peak), the IQE decays rapidly. We fit the typical InGaN blue and green LEDs using
the traditional ABC model. At the higher carrier concentration, the experimentally
measured IQE is lower than that obtained by fitting based on ABC model [37]. This
deviation is more pronounced as the carrier concentration increases. The above problems occur with the typical InGaN blue and green LEDs. Therefore, the traditional
ABC equation is not sufficient to fully describe the IQE characteristics, which is
theoretically insufficient, especially in the case of a large carrier concentration [37,
47]. It can be speculated that in the process of carrier radiation recombination, a
higher order term f (n) should also be introduced to explain the asymmetry of the
IQE-n curve [47].
7.5.2 Electronic Overflow
Schubert et al. from US Leinster Polytechnic Institute believe that the leakage of
electrons from the active region is the main cause of efficiency droop [48].
In the upper 7.18 equation, a higher order compound term f (n) is introduced, and
R (n) can be expressed as [49, 50]:
R(n) = A S R H n + Bn
2
+ C Auger n
3
+ f (n)
(7.21)
among them, f (n) = Dn
4
+ En
5
. . .
We can get:
I Q E =
Bn
2
A S R H n + Bn 2 + C Auger n 3 + f (n)
(7.22)
Using the most primitive pn junction theory [50], a higher-order term Dn
4 is
introduced in the carrier rate equation. Such a term may be used to describe the
characteristics of the carrier leak with certain physical meaning. Using this equation
to simulate, the agreement between the IQE ~ n curve and the experimental results
has been significantly improved. Theoretically, the non-central characteristics of IQE
~ n are caused by carrier leakage. This theoretical model is called the ABCD model,
Dn
4 is the carrier leakage term [50]. In the ABCD model, IQE can be expressed as:
I Q E =
Bn
2
A S R H n + Bn 2 + C Auger n 3 + Dn 4
7 III-Nitride LED Quantum Efficiency Improvement Technology
I Q E =
B
A S R H /n + B + C Auger n
(7.20)
This equation shows that the IQE ~ n curve is center-symmetric about n 0 =
A S R H
C Auger
. In fact, the IQE ~ n curve of typical InGaN blue-green LEDs exhibit noncentral symmetry. At n > n 0 (the carrier concentration corresponding to the IQE
peak), the IQE decays rapidly. We fit the typical InGaN blue and green LEDs using
the traditional ABC model. At the higher carrier concentration, the experimentally
measured IQE is lower than that obtained by fitting based on ABC model [37]. This
deviation is more pronounced as the carrier concentration increases. The above problems occur with the typical InGaN blue and green LEDs. Therefore, the traditional
ABC equation is not sufficient to fully describe the IQE characteristics, which is
theoretically insufficient, especially in the case of a large carrier concentration [37,
47]. It can be speculated that in the process of carrier radiation recombination, a
higher order term f (n) should also be introduced to explain the asymmetry of the
IQE-n curve [47].
7.5.2 Electronic Overflow
Schubert et al. from US Leinster Polytechnic Institute believe that the leakage of
electrons from the active region is the main cause of efficiency droop [48].
In the upper 7.18 equation, a higher order compound term f (n) is introduced, and
R (n) can be expressed as [49, 50]:
R(n) = A S R H n + Bn
2
+ C Auger n
3
+ f (n)
(7.21)
among them, f (n) = Dn
4
+ En
5
. . .
We can get:
I Q E =
Bn
2
A S R H n + Bn 2 + C Auger n 3 + f (n)
(7.22)
Using the most primitive pn junction theory [50], a higher-order term Dn
4 is
introduced in the carrier rate equation. Such a term may be used to describe the
characteristics of the carrier leak with certain physical meaning. Using this equation
to simulate, the agreement between the IQE ~ n curve and the experimental results
has been significantly improved. Theoretically, the non-central characteristics of IQE
~ n are caused by carrier leakage. This theoretical model is called the ABCD model,
Dn
4 is the carrier leakage term [50]. In the ABCD model, IQE can be expressed as:
I Q E =
Bn
2
A S R H n + Bn 2 + C Auger n 3 + Dn 4