Resistivity and carrier concentration relationship

Electron mobility - Wikipedia

resistivity and carrier concentration relationship

In solid-state physics, the electron mobility characterizes how quickly an electron can move Semiconductor mobility depends on the impurity concentrations ( including There is a simple relation between mobility and electrical conductivity . .. σn or σp are either known or can be obtained from measuring the resistivity. Doping, Carrier Concentration, Mobility, and Conductivity . an extremely important relation, the mass action law (for electrons and holes), as follows. Resistivity and Carrier Transport Parameters in Silicon. Virginia In one dimension, the current density of electrons can be approximated with the following.

Scattering happens because after trapping a charge, the defect becomes charged and therefore starts interacting with free carriers. If scattered carriers are in the inversion layer at the interface, the reduced dimensionality of the carriers makes the case differ from the case of bulk impurity scattering as carriers move only in two dimensions. Interfacial roughness also causes short-range scattering limiting the mobility of quasi-two-dimensional electrons at the interface.

Like electrons, phonons can be considered to be particles. A phonon can interact collide with an electron or hole and scatter it. At higher temperature, there are more phonons, and thus increased electron scattering, which tends to reduce mobility. Piezoelectric scattering[ edit ] Piezoelectric effect can occur only in compound semiconductor due to their polar nature. It is small in most semiconductors but may lead to local electric fields that cause scattering of carriers by deflecting them, this effect is important mainly at low temperatures where other scattering mechanisms are weak.

These electric fields arise from the distortion of the basic unit cell as strain is applied in certain directions in the lattice.

resistivity and carrier concentration relationship

From high-resolution transmission electron micrographs, it has been determined that the interface is not abrupt on the atomic level, but actual position of the interfacial plane varies one or two atomic layers along the surface.

These variations are random and cause fluctuations of the energy levels at the interface, which then causes scattering. This can only happen in ternary or higher alloys as their crystal structure forms by randomly replacing some atoms in one of the sublattices sublattice of the crystal structure.

resistivity and carrier concentration relationship

Generally, this phenomenon is quite weak but in certain materials or circumstances, it can become dominant effect limiting conductivity. In bulk materials, interface scattering is usually ignored. As with elastic phonon scattering also in the inelastic case, the potential arises from energy band deformations caused by atomic vibrations.

Optical phonons causing inelastic scattering usually have the energy in the range meV, for comparison energies of acoustic phonon are typically less than 1 meV but some might have energy in order of 10 meV.

Electron mobility

There is significant change in carrier energy during the scattering process. Optical or high-energy acoustic phonons can also cause intervalley or interband scattering, which means that scattering is not limited within single valley. However, significantly above these limits electron—electron scattering starts to dominate.

Long range and nonlinearity of the Coulomb potential governing interactions between electrons make these interactions difficult to deal with. It is assumed that after each scattering event, the carrier's motion is randomized, so it has zero average velocity.

resistivity and carrier concentration relationship

After that, it accelerates uniformly in the electric field, until it scatters again. We thus have to look at the major scattering processes in semiconductors. There are three important mechanisms: The first and least important one is scattering at crystal defects like dislocations or unwanted impurity atoms. Since we consider only "perfect" semiconductors at this point, and since most economically important semiconductors are pretty perfect in this respect, we do not have to look into this mechanism here.

resistivity and carrier concentration relationship

However, we have to keep an open mind because semiconductors with a high density of lattice defects are coming into their own e. GaN or CuInSe2 and we should be aware that the mobilities in these semiconductors might be impaired by these defects.

Doping and Carrier Concentration

Secondwe have the scattering at wanted impurity atoms, in other word at the ionized doping atoms. This is a major scattering process which leads to decreasing mobilities with increasing doping concentration.

Examples for the relation between doping and mobilities can be found in the illustration.

resistivity and carrier concentration relationship

The scattering at dopant ions decreases with increasing temperature. Third we have scattering at phonons - the other important process.

2.9 Mobility - Resistivity - Sheet Resistance

Phonons are an expression of the thermally stimulated lattice vibrations and such strongly dependent on temperature. This part must scale with the density of phonons, i. It is thus not surprising that it dominates at high temperatures while scattering at dopant atoms may dominate at low temperatures. Scattering at phonons and dopant atoms together essentially dominate the mobilities.

The different and opposing temperature dependencies almost cancel each other to a certain extent for medium to high doping levels see the illustrationagain a very beneficial feature for technical applications where one doesn't want strongly temperature dependent device properties.