Electron mobility
However, in a solid, the electron repeatedly scatters off crystal defects, phonons, impurities, etc., so that it loses some energy and changes direction.
The two charge carriers, electrons and holes, will typically have different drift velocities for the same electric field.
is the mean free time Since we only care about how the drift velocity changes with the electric field, we lump the loose terms together to get
[4] Organic semiconductors (polymer, oligomer) developed thus far have carrier mobilities below 50 cm2/(V⋅s), and typically below 1, with well performing materials measured below 10.
Another is the Gunn effect, where a sufficiently high electric field can cause intervalley electron transfer, which reduces drift velocity.
In the regime of velocity saturation (or other high-field effects), mobility is a strong function of electric field.
This phenomenon is usually modeled by assuming that lattice vibrations cause small shifts in energy bands.
The additional potential causing the scattering process is generated by the deviations of bands due to these small transitions from frozen lattice positions.
If these scatterers are near the interface, the complexity of the problem increases due to the existence of crystal defects and disorders.
Charge trapping centers that scatter free carriers form in many cases due to defects associated with dangling bonds.
Interfacial roughness also causes short-range scattering limiting the mobility of quasi-two-dimensional electrons at the interface.
[15] At any temperature above absolute zero, the vibrating atoms create pressure (acoustic) waves in the crystal, which are termed phonons.
These electric fields arise from the distortion of the basic unit cell as strain is applied in certain directions in the lattice.
As with elastic phonon scattering also in the inelastic case, the potential arises from energy band deformations caused by atomic vibrations.
This rule is not valid if the factors affecting the mobility depend on each other, because individual scattering probabilities cannot be summed unless they are independent of each other.
Theoretical calculations reveal that the mobility in non-polar semiconductors, such as silicon and germanium, is dominated by acoustic phonon interaction.
Experimentally, values of the temperature dependence of the mobility in Si, Ge and GaAs are listed in table.
In here, the following definition for the scattering cross section is used: number of particles scattered into solid angle dΩ per unit time divided by number of particles per area per time (incident intensity), which comes from classical mechanics.
For scattering from acoustic phonons, for temperatures well above Debye temperature, the estimated cross section Σph is determined from the square of the average vibrational amplitude of a phonon to be proportional to T. The scattering from charged defects (ionized donors or acceptors) leads to the cross section
The temperature dependencies of these two scattering mechanism in semiconductors can be determined by combining formulas for τ, Σ and
[14] Thus, the carriers spend less time near an ionized impurity as they pass and the scattering effect of the ions is thus reduced.
While in crystalline materials electrons can be described by wavefunctions extended over the entire solid,[23] this is not the case in systems with appreciable structural disorder, such as polycrystalline or amorphous semiconductors.
Localized states are described as being confined to finite region of real space, normalizable, and not contributing to transport.
Because the probability of an electron being released from a trap depends on its thermal energy, mobility can be described by an Arrhenius relationship in such a system:
In such a system, electrons can only travel by tunnelling for one site to another, in a process called variable range hopping.
Consider a semiconductor sample with a rectangular cross section as shown in the figures, a current is flowing in the x-direction and a magnetic field is applied in the z-direction.
Next, the square root of this saturated current is plotted against the gate voltage, and the slope msat is measured.
[30] In this technique,[29] the transistor is operated in the linear region (or "ohmic mode"), where VDS is small and
In practice, this technique may overestimate the true mobility, because if VDS is not small enough and VG is not large enough, the MOSFET may not stay in the linear region.
[36] A pulsed optical laser is used to create electrons and holes in a semiconductor, which are then detected as an increase in photoconductance.
