Charge Carrying Generation & Recombination

What happens after determining the number of electrons and holes are in the

semiconductor?

Parts of a semiconductor

In a graph, the band gap generally refers to the energy differences (in electron volts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors.

This is equivalent to the energy required to free an outer shell electron from its orbit about the nucleus to become a mobile charge carrier (able to move freely within the solid material).

Substances with large band gaps are generally insulators, smaller band gaps are semiconductors and conductors either have very small gaps or none because the valence and conduction bands overlap.

Charge carriers (electrons and holes)

Masses = 9.11 10

31

= 1.67 1027

= 1.67 1027

Effective Mass of electrons and holes: A particle's effective mass is the mass it appears to carry in transport in a crystal. Electrons and holes in a crystal respond to electric and magnetic fields almost as if they were particles with a mass dependent on their direction of travel (an effective mass tensor). = 1.602 10

19 = +1.602 1019

GaAs semiconductor bandgap

GaAs band structure produced by W. R. Frensley, Professor of EE @ UTD using an empirical Pseudo-potential method see also: Cohen and Bergstrasser, Phys. Rev. 141, 789 (1966).

Gallium arsenide (GaAs) is a semiconductor compound used in the manufacturing of devises such as microwave frequency integrated circuits, infrared light-emitting diodes, solar cells and optical windows.

Doping (n-type and p-type) materials

The conduction in a semiconductor can be changed through doping of foreign atoms such as B or As in Si. Doping with donors: ND (donor concentration) gives an n-type semiconductor and thus the

density of free electrons nn is larger than the density of free holes pn in an n-type material. Doping with acceptors: NA (acceptor concentration) gives a p-type material. The density of

free holes pp is larger than the density of free electrons np.

The subscript indicates the material type. n is the symbol for electron concentration, p for the hole concentration. Units are cm-3.

Doping with donor example Doping with an acceptor

N & P-type

Free carriers (free electrons and holes)

Free carriers consisting of electrons, holes, or both. Able to carry current in a semiconductor material.

Trapped carrier bound to a specific impurity atom,

defect (such as a vacancy) in the crystal, or bound to a specific surface state. Trapped carriers are typically not in the valence band and cannot carry current.

Free carriers are subject to move under the mechanisms of drift, as in an electric field with force of qE (where q is the electron charge and E is the electric field strenght), and of diffusion.

Important charge carrier processes in semiconductors

The free electron and hole concentration in bulk semiconductors (where the crystal lattice structure is assumed to be infinite) can be modified by the processes of generation and recombination, and also by the transport of electrons and holes through drift and diffusion. Generation: e.g., absorption of a photon generates a free electron and a free

hole (an electron-hole pair). Recombination: can be radiative, in which case a photon is emitted as the

electron returns to the valence band or non-radiative

Transport is the movement of charge carriers under forces based either on an electric field or on a concentration gradient: Drift refers to the motion of charge carriers under the force of an electric field.

Motion is typically not ballistc but instead includes the resistive action of scatter

Diffusion refers to motion of electron and holes due to the presence of a concentration gradient.

Recombination & Generation

Absorption of light generation rate

The number of electron-hole pairs created per unit time is defined as the generation rate

As light enters and travels through the semiconductor, the intensity of light drops exponentially as the photons are converted to electron-hole pairs by the process of photo generation.

= 0

Where is the absorption coefficient typically in cm-1 and x is the distance into the material. 0 is the light intensity just inside the surface of the semiconductor. Since each photon absorbed generates an e-h pair, this exponential decay also mimics the generation of carrier as a function of depth.

Absorption of light

Light incident on a semiconductor consist of photons with energy (E = hv = hc/).

Photons interact with the semiconductor depending on their energy: < : Photons with energy below the band gap energy are

transmitted through the material.

= : Photons with sufficient energy to be absorbed in the band-to-band transition, and generate an electron-hole pair. Absorption of these photons will be relatively week.

> : Photons with significantly greater energy than the

semiconductors bandgap are relatively strongly absorbed, and generate electron-hole pairs with initial excess kinetic energy. This excess kinetic energy is quickly lost to the lattice structure.

Carrier generation due to light absorption and ionization due to high-energy particle beams

Carrier generation due to light absorption

Carriers can be generated in semiconductors by illuminating the

semiconductor with light The energy of the incoming photons is used to bring an electron from a

lower energy level to a higher energy level. In the case where an electron is removed from the valence band and added to the conduction band, an electron-hole pair is generated. A necessary condition for this to happen is that the energy of the photon, Eph, is larger than the bandgap energy, Eg. As the energy of the photon is given of to the electron, the photon no longer exists.

Assuming that each absorbed photon creates one electron-hole pair, the electron and hole generation rates are given by:

Generation mechanism Impact ionization

Impact ionization is the generation mechanism which is caused by an electron (hole) with an energy much larger (smaller) than the conduction (valence) band edge.

More on generation and recombination

generation of carriers is happening continuously as long at the temperature is sufficiently high to break the valence electron-atom bonds. Of course other forms of energy can do the same. An example is light: shining light on a semiconductor, with the correct energy, larger than the energy gap, can also release electron-hole pairs.

Recombination is when an electron and hole will recombine and thus get fixed to the atom and become unavailable for conduction. This is a reduction of the number of free carriers. As with generation, recombination is also continuously happening.

Direct & indirect recombination Direct recombination of electron and holes means that excess electrons in

the conduction band recombine with holes in the valence band. Energy is lost by the electron and is given off as photons (light)

Indirect recombination are when impurity centres or lattice defects in the

semiconductors, called traps these will always be available as a 100% perfect semiconductor does not exist. In this case, the energy released by the electrons causes heating of the lattice

(Heating causes lattice vibrations. These vibrations can be seen as particles called phonons with which the carriers in the lattice can interact scatter. They can also be regarded as waves with certain energy and wavelength).

Non-radiative Band-to-Band recombination

Band-to-band recombination depends on the density of available electrons and holes. Since both carrier types need to be available in the recombination process, the rate is expected to be proportional to the product of n and p. However in thermal equilibrium the recombination rate must equal the generation rate since there is no net recombination or generation. As the product of n and p equals ni

2 in thermal equilibrium, the net recombination rate can be expressed as:

where b is the bimolecular recombination constant.

= ( 2)

Optical processes

The most important optoelectronic interaction in semiconductors is the band-to-band transition.

In the photon absorption process, the photon scatters an electron in the valence band, causing the electron to go into the valence band.

In the reverse process the electron in the conduction band recombines with a hole in the valence band to generate a photon

Conservation of energy

= + :

= :

Non-radiative Auger recombination

Counterpart to the impact ionization generation.

Auger recombination involves three particles: an electron and a hole which recombine in a a band-to-and transition and give off the resulting energy to another electron or hole. The expression for the net recombination rate is therefore similar to that of band-to-band recombination but includes the density of the electrons or hole which receive the released energy from the electron-hole annihilation:

a) would be likely in p-type materials,

b) would be effective for defects that can attract two carriers. The stair case represents the rapid thermalization back to the band edge.

Non-radiative recombination

In real semiconductors the forbidden band gap region always has intentional or unintentional impurities that produce electronic levels.

These regions can arise from chemical impurities or native defects such as a lattice vacancy.

Bandgap levels are states in which the electrons localised in a finite space near the defect not like free states.

As the electrons move in the allowed bands they can get trapped by these defect.

Such defects can allow the recombination of an electron (hole) without emission of a photon

This non-radiation process competes with radiative recombination