Electron-hole Pair in Semiconductors

extrinsic - doped semiconductor - p-type - acceptorIn the semiconductor, free charge carriers are electrons and electron holes (electron-hole pairs). Electrons and holes are created by excitation of electron from valence band to the conduction band. An electron hole (often simply called a hole) is the lack of an electron at a position where one could exist in an atom or atomic lattice. It is one of the two types of charge carriers that are responsible for creating electric current in semiconducting materials. Since in a normal atom or crystal lattice the negative charge of the electrons is balanced by the positive charge of the atomic nuclei, the absence of an electron leaves a net positive charge at the hole’s location. Positively charged holes can move from atom to atom in semiconducting materials as electrons leave their positions. When an electron meets with a hole, they recombine and these free carriers effectively vanish. The recombination means an electron which has been excited from the valence band to the conduction band falls back to the empty state in the valence band, known as the holes.

The conductivity of a semiconductor can be modeled in terms of the band theory of solids. The band model of a semiconductor suggests that at ordinary temperatures there is a finite possibility that electrons can reach the conduction band and contribute to electrical conduction. In the semiconductor, free charge carriers (electron-hole pairs) are created by excitation of electron from valence band to the conduction band. This excitation left a hole in the valence band which behaves as positive charge and an electron-hole pair is created. Holes can sometimes be confusing as they are not physical particles in the way that electrons are, rather they are the absence of an electron in an atom. Holes can move from atom to atom in semiconducting materials as electrons leave their positions.

Electron Excitation in Semiconductors

Energy for the excitation can be obtained by different ways.

Thermal Excitation

Electron-hole pairs are constantly generated from thermal energy as well, in the absence of any external energy source. Thermal excitation does not require any other form of starting impulse. This phenomenon occurs also at room temperature. It is caused by impurities, irregularity in structure lattice or by dopant. It strongly depends on the Egap (a distance between valence and conduction band), so that for lower Egap a number of thermally excited charge carriers increases. Since thermal excitation results in the detector noise, active cooling is required for some types of semiconductors (e.g. germanium). Detectors based on silicon have sufficiently low noise even by room temperature. This is caused by the large band gap of silicon (Egap= 1.12 eV), which allows us to operate the detector at room temperature, but cooling is prefered to reduce noise.

Optical Excitation

Note that, energy of a single photon of visible light spectrum is comparable with these band gaps. Photons of wave lengths 700 nm – 400 nm have energies of  1.77 eV 3.10 eV. As a result, also visible light is able to excite electrons to the conduction band. Actually, this is the principle of photovoltaic panels that generate electric current.

Excitation by Ionizing Radiation

Electrons may reach the conduction band, when they are excited by ionizing radiation (i.e. they must obtain energy higher than Egap). In general, heavy charged particles transfer energy mostly by:

  • Excitation. The charged particle can transfer energy to the atom, raising electrons to a higher energy levels.
  • Ionization. Ionization can occur, when the charged particle have enough energy to remove an electron. This results in a creation of ion pairs in surrounding matter.

A convenient variable that describes the ionization properties of surrounding medium is the stopping power. The classical expression that describes the specific energy loss is known as the Bethe formula. For alpha particles and heavier particles the stopping power of most materials is very high for heavy charged particles and these particles have very short ranges.

In addition to these interactions, beta particles also lose energy by radiative process known as the bremsstrahlung. From classical theory, when a charged particle is accelerated or decelerated, it must radiate energy and the deceleration radiation is known as the bremsstrahlung (“braking radiation”).

Photons (gamma rays and X-rays) can ionize atoms directly (despite they are electrically neutral) through the Photoelectric effect and the Compton effect, but secondary (indirect) ionization is much more significant. Although a large number of possible interactions are known, there are three key interaction mechanisms  with matter.

In all cases, a particle of ionizing radiation deposits a portion of its energy along its path. Particle passing through the detector ionizes the atoms of semiconductor, producing the electron-hole pairs. For example, typical thickness of silicon detector is about 300 µm so the number of generated electron-hole pairs by minimum ionizing particle (MIP) passing perpendicular through the detector is about 3.2 x 104. This value is minor in comparison the total number of free carriers in intrinsic semiconductor of a surface of 1 cm2 and the same thickness. Note that, a sample of pure germanium at 20 °C contains about 1.26×1021 atoms, but also contains 7.5 x 1011 free electrons and 7.5 x 1011 holes constantly generated from thermal energy. As can be seen, the signal to noise ratio (S/N) would be minimal. The addition of 0.001% of arsenic (an impurity) donates an extra 1015 free electrons in the same volume and the electrical conductivity is increased by a factor of 10,000. In doped material the signal to noise ratio (S/N) would be even smaller. Cooling of the semiconductor is one way to lower this ratio.

Improvement can be reached by use of a reverse-bias voltage to the P-N junction to deplete the detector of free carriers, which is the principle of the most silicon radiation detectors. In this case, negative voltage is applied to the p-side and positive to the second one. Holes in the p-region are attracted from the junction towards the p contact and similarly for electrons and the n contact.

References:

Radiation Protection:

  1. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. ISBN-13: 978-0470131480.
  2. Stabin, Michael G., Radiation Protection and Dosimetry: An Introduction to Health Physics, Springer, 10/2010. ISBN-13: 978-1441923912.
  3. Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4/2013. ISBN-13: 978-3527411764.
  4. U.S.NRC, NUCLEAR REACTOR CONCEPTS
  5. U.S. Department of Energy, Instrumantation and Control. DOE Fundamentals Handbook, Volume 2 of 2. June 1992.

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

See above:

Properties of Semiconductors