4.9. LIGHT EMITTING DIODE (LED) 203
From the previous example, we can see that forpequal to 1016 cm−^3 , we have (in the
previous example the value ofpwas ten times smaller)
τr=5. 7 × 10 −^7 s
In the case where thep-doping is high, the recombination time is given by the high-density
limit (see equation 4.9.10) as
1
τr
=
Rspon
n
=
1
τo
(
m∗r
m∗h
) 3 / 2
τr =
τo
0. 05
∼ 20 τo∼12 ns
For the low-doping case, the internal quantum efficiency for the diode is
ηQr=
1
1+tτnrr
=
1
1+(5.7)
=0. 15
For the more heavily dopedp-region diode, we have
ηQr=
1
1+ 2010 × 10 −^7 − 9
=0. 83
Thus there is an increase in the internal efficiency as thepdoping is increased.
Example 4.7Consider a GaAsp-ndiode with the following parameters at 300 K:
Electron diffusion coefficient, Dn =30cm^2 /V·s
Hole diffusion coefficient, Dp =15cm^2 /V·s
p-side doping, Na =5× 1016 cm−^3
n-side doping, Nd =5× 1017 cm−^3
Electron minority carrier lifetime, τn =10−^8 s
Hole minority carrier lifetime, τp =10−^7 s
Calculate the injection efficiency of the LED assuming no recombination due to traps.
The intrinsic carrier concentration in GaAs at 300 K is 1. 84 × 106 cm−^3 .Thisgives
np =
n^2 i
Na
=
(1. 84 × 106 )^2
5 × 1016
=6. 8 × 10 −^5 cm−^3
pn =
n^2 i
Nd
=
(1. 84 × 106 )^2
5 × 1017
=6. 8 × 10 −^6 cm−^3
The diffusion lengths are
Ln =
√
Dnτn=
[
(30)(10−^8 )
] 1 / 2
=5. 47 μm
Lp =
√
Dpτp=
[
(15)(10−^7 )
] 1 / 2
=12. 25 μm
