1. Chapter 4 Excess Carriers in Semiconductors
“Most semiconductor devices operate by the creation of charge carriers in
excess of the thermal equilibrium values”
In this Chapter we will study:
The creation of excess charge carriers by optical absorption
Luminescence and photoconductivity
The EHP recombination (direct and indirect)
The diffusion of excess carriers

2. Excess carriers can be created by optical excitation.
4.1 Optical Absorption
Excess carriers can be created by optical excitation.
Provides a technique for measuring the band gap of a semiconductor.
Photons with hv  Eg can be absorbed
Photons with hv ≤ Eg will pass through the material
Optical Absorption is a statistical process:
the valence band contains many electrons, and
the conduction band has many empty states
 high probability of photon absorption.

3. The intensity of transmitted light through the sample thickness l is:
(cm-1) is called absorption coefficient - it is a function of wavelength 

4. excess carriers
Figure 4-1 (a) excitation; (b) thermalization; (c ) recombination

5. Determination of Eg by Absorption Measurements
Figure 4—3
Dependence of optical absorption coefficient a for a semiconductor on the wavelength of incident light.

6. Try to memorize the approximate Eg
Figure 4—4
Band gaps of some common semiconductors relative to the optical spectrum.

7. Example 4.1 – the Fluorescence of GaAs
4.2 Luminescence
Luminescence is light emission not caused by the rise in temperature.
- luminescence is categorized by the excitation mechanism:
- photoluminescence; electroluminescence; cathodoluminescence; chemiluminescence; bioluminescence…
4.2.1 Photoluminescence
Photoluminescence (PL) is light emission caused by the absorption of photons.
- fluorescence — fast PL (~10-8s) by direct recombination
- phosphorescence — slow PL process by indirect recombination
Example 4.1 – the Fluorescence of GaAs
A 0.46 m thick sample of GaAs is illuminated with monochromatic light of h = 2 eV. The absorption coefficient is 5  104 cm-1. The power incident on the sample is 10 mW.
a) Find the total energy absorbed by the sample per second.
b) Find the rate of excess thermal energy given up by the electrons to the latttice before recombination.
c) Find the number of photons per second given off from recombination events, assuming perfect quantum efficiency.

8. Photoluminescence of GaAs → fluorescence → direct (band to band) recombination
Figure 4—6
Excitation and band-to-band recombination leading to photoluminescence.

9. Phosphorescence (indirect recombination)
EHP is created by an incoming photon with
h > Eg
The excited electron losses energy by scattering
until it is at the bottom of the conduction band
(c) The electron is trapped at impurity level Et
The trapped electron is reexcited thermally to
the conduction band
Direct recombination occurs and a photon with
h ≈ Eg is emitted
Example of Phosphors : ZnS
Application: color TV screen
Figure 4-5 Phosphorescence with
a trapping level for electrons
4.2.2 Electroluminescence
Electroluminescence (EL) light emission generated by electrical energy.
(note: incandescence is not EL)
Injection electroluminescence in LEDs (Chapter 8)
- first observed EL → Destriau effect (ZnS)

10. Figure 4—5
Excitation and recombination mechanisms in photoluminescence with a trapping level for electrons.

11. important for many device applications.
4.3 Carrier Lifetime and Photoconductivity
- Excess holes and electrons increase the conductivity of a semiconductor.
(3.43)
If the excess carriers are the result of Optical Luminescence then the increase in conductivity is called Photoconductivity.
important for many device applications.
we know how the excess carriers are generated,
we wish to study how they are annihilated.
 Recombination

12. 4.3.1 Direct Recombination of Electrons and Holes
in Direct Recombination, an excess population of electrons and holes decays by electrons falling from the conduction band to the valence band.
the energy lost by the electron is emitted as a photon.
Direct recombination occurs spontaneously
 the probability of an electron recombining with a hole remains constant in time.
recall that at equilibrium, the thermal generation rate of EHPs, g, is equal to the recombination rate, r, thus:
if we assume that at t = 0 there is a short flash of light and EHPs are generated with initial excess carrier concentrations: ∆n=∆p
then these excess carriers will recombine at a rate that is proportional to the concentration of electrons in the conduction band, and the concentration of holes in the valence band.
that is:

13. - the net rate of change in the conduction band electron concentration is the thermal generation rate, r ni2, minus the recombination rate, that is:
- at t > 0 the instantaneous concentrations of excess carriers n(t) and p(t) are also equal as the electrons and holes recombine in pairs: n(t) = p(t)
we can write the total concentrations above in terms of the equilibrium values n0 and p0 and the excess carrier concentrations n(t) and p(t) as:
if the excess carrier concentration is small, then we can neglect the n2(t) term
if the material is extrinsic, then we can neglect the equilibrium minority carrier term

14. - the solution to this is:
- for example, if the material is p-type, (p0>>n0), then for light excitation, we have:
- the solution to this is:
(4-7)
the decay constant n =(r p0)-1 is called the Recombination Lifetime
note that the recombination lifetime is in terms of the minority carrier, thus n is often called the Minority Carrier Lifetime.
the decay of excess holes in an n-type material is: p =(r n0)-1
the excess majority carriers and the excess minority carriers decay at exactly the same rate.
there is a large percentage change in minority carrier concentration and a small percentage change in the majority carrier concentration.

15. a general expression valid for both n- type and p-type material under a low excitation level is:
(4-8)
Example 4.2
A numerical example may be helpful in visualizing the approximations made in the analysis of direct recombination. Let us assume a sample of GaAs is doped with 1015 acceptors/cm3. The intrinsic carrier concentration of GaAs is approximately 106 cm-3; thus the minority electron concentration is n0 = ni2/p0 = 10-3 cm-3. Certainly the approximation p0 » n0 is valid in this case. Now if 1014 EHP/cm3 are created at t = 0, we can calculate the decay of these carriers in time. The approximation of n « p0 is reasonable, as Figure 4.7 indicates. This figure shows the decay in time of the excess populations for a carrier recombination lifetime of n = p = 10-8 s.

16. Figure 4—7
Decay of excess electrons and holes by recombination, for Dn = Dp = 0.1p0, with n0 negligible, and t = 10 ns (Example 4–2). The exponential decay of dn(t) is linear on this semilogarithmic graph.