Chapter 3a

Excess carriers, essential for device operation, are created by optical excitation, electron bombardment, or injected across a forward-biased p-n junction.
These excess carriers can dominate the conduction process in semiconductor materials.

Optical Absorption

This includes photons in the optical range as well as those in the infrared region.
Photons of various wavelengths (frequencies) are directed at the sample, and their relative transmission is measured.
Note: photons having energies greater than the band gap energy are absorbed (the sample behaves opaque for this kind of illumination), whereas those having energies less than the band gap energy are transmitted (the sample behaves transparent), this experiment gives an accurate measure of the band gap energy.
When photons having energies h Eg are absorbed, they create EHPs and the probability of this absorption is very high, since there are lots of electrons in the valence band and lots of empty states in the conduction band.
Electrons excited to EC may initially have energies much higher than EC, however, they lose this excess energy due to scattering with the lattice until their equilibrium energy becomes equal to EC.
Note: these EHPs are called excess carriers, since they are out of balance, and, thus, would eventually recombine.
However, while these excess carriers remain in the respective bands, they can contribute to the current conduction.
The transmitted intensity It of a beam of photons of wavelength through a sample of thickness t can be given by

where is called the absorption oefficient, and varies with materials and photon wavelength

Fig.3.1 The variation of the absorption coefficient as a function of the wavelength of the incident light.

Fig.3.2 Band gaps of some common semiconductors relative to the optical spectrum.

Absorption cutoff occurs at
GaAs, Si, Ge, and InSb band gaps are such that c occurs beyond the visible region (in the infrared), whereas GaP and CdS have band gaps with c falling within the visible range.

Luminescence

When recombination occurs between a conduction band electron and a valence band hole, the energy released can be given off in the form of light (luminescence).
Direct band-to-band recombination in direct band gap semiconductors have a much higher probability of light emission as compared to those in indirect materials.
Broadly divided into three categories:
Photoluminescence: if the recombining carriers were caused by optical excitation.
Cathodoluminescence: if the recombining carriers were caused by high energy electron bombardment.
Electroluminescence: if the recombining carriers were caused by injection of excess carriers (by forward biasing a p-n junction, for example).

Photoluminescence

For steady state excitation, the recombination rate and the generation rate for EHPs are equal, and one photon is emitted for each photon absorbed.
Direct band-to-band recombination is a fast process with typical lifetime of excess carriers 10 8 sec => known as fluorescence (example: fluorescent lamp).
In some indirect materials, the trap states within the band gap captures carriers, and slows down the recombination process, thus, emission continues for seconds or minutes after the excitation is removed => known as phosphorescence and the materials are known as phosphors.
The trap states can hold the carriers for indefinite times, and the carriers can either get reexcited to the conduction band or fall to the valence band (and, thus, recombine) => this creates the delay between excitation and recombination.

EXAMPLE 3.1: A 0.5 m thick sample of

thick sample of In is illuminated with monochromatic light of

The absorption coefficient

The power incident on the sample is 15 mW.
(a) Find the total energy absorbed by the sample per second (J/sec).
(b) Find the rate of excess thermal energy given up by the electrons to the lattice before recombination (J/sec).
(c) Find the number of photons per second given off from recombination events, assuming perfect quantum efficiency.

SOLUTION:

(a)The transmitted intensity

Therefore, the absorbed power
(15 9.1) mW = 5.9 mW = 5.9 10 3 J/sec.
(b)Since the energy of the incident photon is greater than the band gap energy, hence, the excess energy of the excited electron will be dissipated as heat to the lattice. The fraction of energy converted to heat is given by

(1.5 1.34)/1.5 = 0.107. Thus, the amount of energy converted to heat per second
(c) For perfect quantum efficiency, one photon is emitted for each photon absorbed. Thus, the number of photons emitter per second

or, alternately, recombination radiation accounts for 5.9 0.63 = 5.27 mW at 1.34 eV/photon. Thus,

Cathodoluminescence

Best example: cathode ray tube (CRT) basis of television sets, oscilloscopes, and other display systems.
Electrons emitted from the heated cathode are accelerated towards the anode by high field, deflected by electric or magnetic fields by the horizontal and vertical plates, and made to hit the screen (coated with a phosphor) at desired locations.
When electrons hit these phosphors, the energy of the electrons gets transferred to the electrons of the phosphors, and they get excited to higher states, and eventually fall to the ground state, thus causing recombination and light emission.
Three phosphor dots are used for each pixel, capable of transmitting three primary colors: red, green, and blue (RGB) thus by varying the intensity and position of the electron beam, a wide range of colors and picture can be attained.

Electroluminescence

Best examples: LEDs and LASERs, where carriers are injected across a forward biased p-n junction and are made to recombine (either naturally or by carrier confinement) => called injection electroluminescence.

Carrier Lifetime and Photoconductivity

Photoconductivity: increase in the conductivity of a sample due to excess carriers created by optical excitation.
With excitation turned off, the photoconductivity decreases to zero since all excess carriers eventually recombine.

Direct Recombination of Electrons and Holes

Direct recombination occurs spontaneously, i.e., the probability that an electron and a hole will recombine is constant in time, which leads to an exponential solution for the decay of the excess carriers.
The net rate of change in the conduction band electron concentration at any time t
where the first term is the generation rate and the second term is the recombination rate.
Let excess EHPs n and p (with n = p, since they are created in pairs) are created at t = 0 by a short flash of light.
Define n(t) and p(t) (again n = p) as the instantaneous excess carrier concentrations and n and p for their values at t = 0.
Note: n(t) = n0 + n(t), and p(t) = p0 + p(t).
Thus,

Similarly, excess holes in an n-type material recombine with a rate
Note: for direct recombination, the excess majority carriers (which is equal to the excess minority carriers) decay at exactly the same rate as the minority carriers, however, there is a large percentage change in the minority carriers as compared to the majority carriers.
A more general expression for carrier lifetime for near not sufficiently extrinsic samples is