Light Emitting Diode (LED) Principles
The Key mechanism of the Light emission in LEDs is
Band - to -Band recombination (radiation)
Not ANY recombination produces the RADIATION.
In case of indirect transitions, the recombination produces phonons rather than photons.
This is the case for Si.
Si cannot be used for efficient LEDs
Non-equilibrium conditions:
If the concentration of e-h pairs increases, n = ∆n+n0; p = ∆p+p0; the recombination rate also increases:
0
RSP = Br n0 p0
ex
RSP = Br ⎡ ∆p ⋅ n0 + ∆n ⋅ p0 + ∆n ⋅∆p ⎤
⎣
⎦
Thermal generation rate G does not change as it does not depend on n and p
Rex is the excess recombination rate producing the light
Forward biased p-n junction and light emission
Excess electrons
Excess holes
n p = n p 0 eqV / kT p p = p0
pn = pn0 eqV / kT nn = n0
pn nn = p0 n0 ⋅ eqV / kT
pn nn = p0 n0 ⋅ eqV / kT
2 pn nn = n i ⋅ eqV / kT
2 pn nn = n i ⋅ eqV / kT
Under the forward bias,
The change in the electron concentration in the p-region:
Excess electrons
∆n p = n p − n p 0 = n p 0 (eqV / kT − 1); ∆p ≈ 0
ex
RSP = Br ⎡ ∆p ⋅ n0 + ∆n ⋅ p0 + ∆n ⋅∆p ⎤ = Br ∆n ⋅ p0 ;
⎣
⎦ ex ∆n = n p 0 ( eqV / kT − 1); → RSP = Br n p 0 p p 0 ( eqV / kT − 1) ex 0
RSP = RSP ( eqV / kT − 1)
Under the forward bias,
The change in the hole concentration in the n-region:
Excess holes
∆pn = pn − pn0 = pn0 ( eqV / kT − 1); ∆n ≈ 0
ex
RSP = Br ⎡ ∆p ⋅ n0 + ∆n ⋅ p0 + ∆n ⋅∆p ⎤ = Br ∆p ⋅ n0 ;
⎣
⎦ ex ∆p = pn0 ( eqV / kT − 1); → RSP = Br pn0 nn0 ( eqV / kT − 1) ex 0
RSP = RSP ( eqV / kT − 1)
Under the forward bias,
Excess electrons
Excess holes
On both n- and p-sides of the forward-biased p-n junction the excess recombination rate increases exponentially with the bias: ex 0
RSP = RSP ( eqV / kT − 1)
The forward current of p-n junction:
I = I S ( eqV / kT − 1)
Hence, recombination rate increases linearly with the forward current:
RSPex ~ I
Color of the light emitted by LEDs
The emitted photon energy, h ν ≈ Єg;
(for band-to-band recombination).
Typical LED structure:
LED efficiency
LED efficiency = Optical Power/Consumed power
The overall efficiency, consists, in general of 3 components: ηin - injection efficiency, ηr - recombination efficiency, ηe - extraction efficiency.
(1) The Injection efficiency determines how efficiently injected carriers contribute into recombination
When the injection occurs,
Light emission results from ∆n and ∆p recombination.
ηin - injection efficiency (cont.)
Injection efficiency as a function of junction doping
Consider n-side of the junction, close to the junction plane (x = 0):
∆p = pn0 [exp (qV/kT) – 1] >> pn0;
∆n ≅ 0; nn0 ≈ ND;
Rnex = B × nn0 × ∆p ≈ ND × ∆pn = ND × pn0 [exp (qV/kT) – 1] ; pn0 = ni2/n0 ≈ ni2/ND;
Hence,
R = B × ND × ni2/ND×exp(qV/kT) =
R = B × ni2 ×exp(qV/kT)
1. R does not depend on the doping.
2. The R values are same for the p-side of the p-n junction.
3. Under “normal” injection conditions, the injection efficiency does not depend on the p- and n- doping levels.
High-brightness LEDs:
Strong injection in asymmetric p-n junction.
Consider n+ - p junction, ND >> NA
When the forward voltage applied is very high,
np ~ exp(qV/kT) >> pp
Injected electrons
Injected electrons
Holes redistribute to compensate the excess electron charge
pp0 ≈ NA np0 ≈ ni2/ NA x This condition is referred to as “strong injection”
For strong injection into p-side: np(0) = np0 × exp(qV/kT) >> pp(0);
Due to the charge neutrality: pp(0) = np(0) >> NA
Rp(0) = B × np(0) × pp(0) ≈ B × np(0)2
= B × (ni2/NA)2 ×exp(2qV/kT)
On the n-side, the injection still remains “normal”, because
pn < nn ~ ND
Rn(0) = ni2 ×exp(qV/kT)
Total recombination rate (on the n- and p-sides, at x = 0):
R (0) = B × (ni2/NA)2 ×exp(2qV/kT) + ni2 ×exp(qV/kT)
The recombination rate increases with decreasing NA;
For strongly asymmetrical p-n junctions, the current formed by highly-doped region (the electron current in n+ - p junction) contributes primarily into the recombination rate of LED
Therefore, the injection efficiency (for n+ - p junction), ηi = (Ie/I0) = Ie/ (Ie +Ih)
The current components of the p-n junctions are:
I e = qA
De n p0
Le
ISn
⎛ De n p 0 ⎞ ηi = ⎜ qA
⎟
⎜
Le ⎟
⎝
⎠
(e
qV/kT
-1
)
(
Dh pn0 qV/kT
I h = qA e -1
Lh
From these,
⎛ De n p0
D p qA + qA h n0
⎜
⎜
Le
Lh
⎝
ISp
De n p0 / Le
⎞
⎟=
⎟ D n /L +D p /L e p0 e h n0 h
⎠
To increase ηi, pn0 has to be minimal, i.e. ND needs to be maximized
)
2) ηr - recombination efficiency
In the presence of defects, some electron-hole pairs recombine without emitting photons: non- radiative recombination.
The rate of non-radiative recombination, Rnr =
The rate of radiative recombination, ∆n
Rr =
τ nr
∆n
τr
τnr is “non-radiative”
τr is “radiative”
recombination lifetime
recombination lifetime
Total recombination rate,
RSp = Rr + Rnr
The recombination efficiency
τ nr
Rr
= ηr =
Rr + Rnr τ nr +τ r
From
We can express
Using the lifetime definition,
At very high excitation level,
∆n >> n0, p0, and
Rspex = Br (∆n)2
Radiative lifetime decreases with pumping
helps increasing recombination efficiency
Efficiency
Optical power Typical recombination efficiency – current dependence for p-n junction with high trap (defect) concentration
Current
Radiation efficiency increases Heating decreases the efficiency 