Optical characterization techniques are the most commonly used for measurement in the semiconductor industry. Optical measurements are attractive because they are almost always non-contacting with minimal sample preparation and nondestructive property. The instrumentation, for many optical techniques is commercially available and the measurements can have very high sensitivity. In this chapter, the photoluminescence mechanism and related knowledge [17-21] will be introduced.
For photoluminescence experiments, laser beam is absorbed by the semiconductor if the photon energy is larger than the semiconductor band gap. In the meantime, electrons and holes can be generated. The electrons and holes may be scattered and then redistribute near their respective conduction band minimum and valence band maximum, through the process of carrier-phonon interaction. Some electrons could be attracted by holes through Coulomb interaction to form excitons.
Excitons could be further trapped by acceptors or donors. Free Excitons or trapped excitons could recombine radiatively and emit photons. Electrons/holes could also radiatively recombine with acceptors/donors. In some semiconductors, non-radiative transitions, which involves electrons and holes recombine with defects, could dominate. The emission efficiency is affected by the competition between radiative recombination and non-radiative recombination. In this chapter, radiative and non-radiative recombinations are discussed in detail as follows:
(A) Radiative Transition
Radiative recombination process includes (1) band to band transition, (2) excitonic recombination, and (3) defect (donor and/or acceptor) related transitions.
(I) Band to Band Recombination
Band to band transition involving free electrons in the conduction band minimum and holes in the valence band maximum usually occurs in direct-gap materials with the momentum conservation. The electron-hole pairs (e-h) will recombine radiatively.
The recombination rate is almost proportion to the product of electron and hole concentrations, as shown in Fig. 2-1. But in the indirect band gap semiconductors, the transition must be assisted by an additional particle – “phonon” (in order to satisfy the momentum conservation rule). Thus, the radiative probability will be reduced, and the emission efficiency is much lower than the direct band gap semiconductors.
(II) Excitonic Recombination
Electron and hole can attract each other by the Coulomb interaction to form a hydrogen-like free exciton (FE) state. Its energy is slightly less than the band-gap energy required to create a separated electron-hole pair. An exciton can move through the crystal, but because it is a bound electron-hole pair, both electron and hole move together and neither photoconductivity nor current results. Free exciton recombination dominates when the material is sufficiently pure.
In another case, when a free hole can combine with a neutral donor to form a positively charged excitonic ion or bound exciton (BE). The electron bound to the donor travels in a wide orbit about the donor. Similarly electrons combining with neutral acceptors also form bound excitons. Bound exciton recombination dominates over free exciton recombination for less pure material. In these excitonic recombination processes, the photon energy is also less than the band-gap energy which similar to free exciton (FE). And in the direct band gap materials, this
phenomenon can explain by the Eq. 2-1:
hν = Eg -Ex Eq. 2-1 where Ex is the excitonic binding energy. Therefore, in indirect band-gap semiconductors, momentum conservation requires the emission of a phonon, giving hν = Eg - Ex - Ep Eq. 2-2 where Ep is the phonon energy.
(III) Donor Acceptor Pair Recombination (DAP)
When both of the donor and acceptor concentrations of intentionally doped semiconductor or impure intrinsic semiconductor are not very low, the neutral donor electron and the acceptor hole could recombine, it can be expressed by:
D0 + A0 → hν + D+ + A- Eq. 2-3 It can emit photon with an energy as described by the following formula:
EDAP = hν = Eg - (ED + EA) +
DA
e R
2
ε⋅ Eq. 2-4 Where, Eg is the energy gap of semiconductor, ED and EA is the respective binding energy for the electron to the donor and the hole to the acceptor. RDA is the distance between the donor and the acceptor. If the RDA increases, the transition probability will reduce, so does the PL intensity.
(B) Non-Radiative Transition
Electrons and holes can recombine nonradiatively. In fact, in many semiconductors the nonradiative transition is the dominant process. There are several recombination processes which do not result in external photon emission and thus reduce the emission efficiency. They are depicted as follows:
(I) The e-h pair is scattered by the phonon or carriers and loses its energy.
(II) The e-h pair recombines at defect, dislocation, grain boundary or surface, and
loses its excess energy, the so-called “cascade process”.
(III) In the Auger effect, the energy released by a recombining electron is immediately absorbed by another electron which then dissipates this energy by emitting phonons.
Thus this three-body collision, involving two electrons and a hole, results in no net photon emission. Auger process increases its importance with the increasing carrier concentration.
All the non-radiation transitions will compete with radiation transitions, the stronger the non-radiation transition, the lower the PL intensity.
(C) Carrier Lifetime
Carrier lifetime is an useful information to understand the mechanism of recombination processes. Photoluminescence decay is one of optical measurements to obtain the carrier lifetime. Carriers can be generated by a short pulse of incident photons with energy hν > Eg. When the laser ceases, the excited carrier will exponentially decay, as the following equation 2-5:
N( t ) = N0 exp( -t /τ) Eq. 2-5 Where, N(t) is the density of excess carrier, N0 is the density of injected carriers, t is the delay time, and τ is the time constant. The light intensity I(t) is given by the following equation:
For the light intensity I(t) we have
I(t) ~ τ τ Because of the special properties of the exponential function, the light intensity decays with the same time constant τ as the carrier population decay.
We will consider a n-type semiconductor throughout this introduction. The recombination rate R depends nonlinearly on the departure of the carrier densities
from their equilibrium values. If we confine to linear, quadratic, and third-order terms, then R can be written as:
R=A(n-n0) +B(pn-p0n0) +Cp(p2n-p02n0) +Cn(pn2-p0n02) Eq. 2-7 Where, A is the Shockley-Read-Hall recombination coefficient, B is the radiative recombination coefficient, Cp is the Auger recombination coefficient for holes, Cn is the Auger recombination coefficient for electrons, n=n0+Δn, p=p0+Δp, n0 and p0 are the respective electron and hole equilibrium densities, and Δn and Δp the excess electron and hole densities. In the absent of trapping, Δn=Δp, allowing R to be simplified to R~A Δn+B(n0+ Δn) Δn+Cp (p02+2p0 Δn+ Δn2) Δn+Cn(n02+2n0 Δn+ Δn2) Δn Eq. 2-8 Here, some terms containing p0 have been dropped because n0 >> p0 in a n-type material. The recombination lifetime is defined as
τr=
Three main recombination mechanisms determine the recombination lifetime:
Shockley-Read-Hall or multiphonon recombination characterized by the lifetime τSRH , radiative recombination characterized by τrad and Auger recombination characterized by τAuger (details will be discussed later). The three recombination mechanisms are illustrated in Fig. 2-2. The recombination lifetime τr is determined by the three mechanisms according to the relationship
During SRH recombination, electron-hole pairs recombine through the
assistance of deep-level impurities, characterized by the impurity density NT, energy level ET in the band gap, and capture cross sections σn and σp for electrons and holes, respectively. The energy liberated during the recombination event is dissipated by lattice vibrations or phonons, illustrated in Fig. 2-2(a). The SRH lifetime is given by
and νth represent the carrier velocity. Equation τSRH can be simplified for low-level and high level injection. For low-level hole injection, the excess minority carrier density is low compared to the equilibrium majority carrier density, Δn << n0. Similarly high-level injection holds whenΔn >> n0.
For the low level injection,
While, for the high level injection,
During radiative recombination electron-hole pairs recombine directly from band to band with the energy carried away by photons shown in Fig. 2-2(b). The radiative lifetime is
Where, B is the radiative recombination coefficient. The radiative lifetime is inversely proportional to the carrier density because in band-to-band processes both electrons and holes must be present simultaneously for a recombination event to take place.
For the low level injection,
For the high level injection,
n
rad ≈ B1Δ
τ Eq. 2-18
(III) Auger recombination
During the Auger recombination, illustrated in Fig. 2-2(c), the recombination energy is absorbed by a third carrier. Because three carriers are involved in the recombination event, the Auger lifetime is inversely proportional to the square of the carrier density. For a n-type semiconductor, the Auger lifetime is given by
Where, Cp is the Auger recombination coefficient for holes and Cn for electrons.
For the low level injection,
2 For the high level injection,
2
(a) Direct transition
(b) Indirect transition
Fig. 2-1 Schematic representations for the (a) direct and (b) indirect transition.
Fig. 2-2 Recombination mechanisms: (a) SRH, (b) radiative, (c) Auger.