Chapter 2 Optical property of LEDs and instruments
2.1 Theorem on optical properties of semiconductor LEDs
The proposition considers the current injected into LEDs, and suggests it is desirable to have all of it contributes to electrons and holes which recombine in the active region. Since the definitions of the active region and the internal quantum efficiency, ηi, are so critical to further analysis. Active region, evolved into lowest band-gap region, is where recombining carriers contribute to photon emission. Band diagram of active region, includes separate confinement hetero-structure (SCH) band-gap region, illustrated in Fig. 2-1. Internal quantum efficiency, ηi, is the fraction of terminal current that generates carriers in the active region. It is important to realize that includes all of the carriers that are injected into active region, not just carriers that recombine induce radiating at the desired transition energy.
The carrier density, n, in the active region is governed by a dynamic process. In fact, we could compare the process of a certain steady-state carrier density in the active region to that a reservoir analogy, which is being simultaneously filled and drained, in a certain water level.
This is shown schematically in Fig. 2-2. For the double heterostructure active region, the injected current provides a generation term and various radiative and nonradiative recombination processes as well as carrier leakage provides recombination term. Thus, rate equation is determined as
rec
gen R
dt G
dn= −
where Ggen is the rate of injected electrons and Rrec is the rate of recombining electrons per unit volume in the active region. There are ηi I/e electrons per second being injected into the active region. V is the volume of the active region.
(2-1)
The recombination process is accompanied with spontaneous emission rate, Rsp, and a nonradiative recombination rate, Rnr, depicted in Fig. 2-2. Carrier leakage rate, Rl, must be occurred at the transverse and/or lateral potential barrier are not sufficiently high. Total recombination rate is expressed as below
l nr sp
rec R R R
R = + +
where the first three terms on the right refer to the natural carrier decay processes.
It is common to describe the natural decay processes by a carrier lifetime, τ. In the absence of photon generation term, the rate equation for carrier decay is, dn/dt = n/τ , where n/τ = Rsp+ Rnr+ Rl, by comparison to Eq. (2-2). This rate equation defines τ. Besides, this natural decay can be expressed in a power series of the carrier density, n, since each of the terms depends upon the existence of carriers. Besides, we can rewrite Eq. (2-2) as
(
3)
2 An Cn
Bn
Rrec = + +
where as the grouping suggests that and . The coefficient B is called the bimolecular recombination coefficient. The carrier rate equation in equivalent be expressed as
The spontaneous photon generation rate per unit volume is exactly equal to the spontaneous electron recombination rate, Rsp, since by definition every time an electron-hole pair recombines radiatively, a photon is generated. Under steady-state conditions (dn/dt =0), the generation rate equals the recombination rate, i.e.,
l
The spontaneously generated optical power, Psp, is obtained by multiplying the number of photons generated per unit time per unit volume, Rsp, by the energy per photon, hν, and the
(2-2)
volume of the active region, V. Then
e I VR h
h
Psp = ν sp =ηiηr ν where the radiative efficiency, ηr, is defined as
l
Usually, the ηr depends upon the carrier density and the product of ηiηr is the internal quantum efficiency, ηint. The internal quantum efficiency is defined as
e
= (the number of photons emitted from active region per second)/(the number of electrons injected into LED per second)
The active region of an ideal LED emits one photon for every electron injected. Each charge quantum-particle(electron) produces one light quantum-particle(photon). Thus the ideal active region of an LED has a quantum efficiency of unity.
In an ideal LED, all photons emitted by the active region are all emitted into free space.
Such an LED has unity extraction efficiency. However, in a real LED, not all the power emitted from the active region is emitted into free space. This is due to several possible loss mechanisms. For example, light emitted by the active region can be reabsorbed in the substrate of the LED, assuming that the substrate is absorbing at the emission wavelength.
Light may be incident on a metallic contact surface and be absorbed by the metal. In addition, the phenomenon of total internal reflection, also referred to as the trapped light phenomenon reduces the ability of the light to escape from the semiconductor. The light extraction
efficiency is defined as
=(the number of photons emitted into free space per second)/(the number of photons (2-6)
(2-7)
(2-8)
(2-9)
emitted from active region per second)
Where P is the optical power emitted into free space.
The extraction efficiency can be a severe limitation for high-performance LEDs. It is quite difficult to increase the extraction efficiency beyond 50% without resorting to highly sophisticated and costly device processes.
The external quantum efficiency is defined as
e
=(the number of photons emitted into free space per second)/(the number of electrons injected into LED per second)
=ηintηextraction
The external quantum efficiency gives the ratio of the number of useful light particles to the number of injected charge particles.
The power efficiency is defined as
IV P
power = η
Where IV is the electrical power provided to the LED. Informally, the power efficiency is also called the “wall-plug efficiency”.
We know the output power of LEDs is dominated by two efficiencies: internal quantum efficiency and extraction quantum efficiency. In order to increase the output power of LEDs, many groups have tried to improve the internal quantum efficiency and extraction efficiency [9-27]. There are two general methods for attaining high internal efficiency: increasing the radiative recombination probability and decreasing the non-radiative recombination probability. Additionally, many groups showed different ways to improve the extraction efficiency: for instance, shaping LED dies or scattering reflector.
(2-10)
(2-11)
(2-12)