Question

Define electron mobility in semiconductors and its temperature dependence.

Answer 1

Electron mobility is a crucial property of semiconductors that measures the speed at which electrons move in response to an electric field. It quantifies how easily electrons can move through a semiconductor material when subjected to an electric potential difference. Electron mobility is an essential factor in determining the performance of semiconductor devices such as transistors, diodes, and integrated circuits.

Mathematically, electron mobility (

μ) is defined as the ratio of the drift velocity (


v
d
    ​

) of electrons in response to an electric field (

E) to the magnitude of the electric field:


=


∣

∣
μ=
∣E∣
v
d
    ​

    ​


Here, the drift velocity is the average velocity of electrons as they move in response to the applied electric field.

Temperature dependence of electron mobility:
The mobility of electrons in semiconductors is influenced by temperature. Generally, the mobility of charge carriers (both electrons and holes) in a semiconductor decreases as the temperature increases. This behavior can be described by various scattering mechanisms that become more significant at higher temperatures. Some of the key scattering mechanisms that affect electron mobility include:

Lattice Scattering: At higher temperatures, lattice vibrations (phonons) become more pronounced. Electrons interact with these lattice vibrations, leading to scattering events that hinder their motion, thereby reducing mobility.

Impurity Scattering: Defects, impurities, and other crystal imperfections in the semiconductor lattice can scatter electrons, causing them to deviate from their original path and reducing mobility.

Phonon Scattering: Electrons can also interact with lattice vibrations, generating or absorbing phonons. These interactions can lead to scattering events and limit electron mobility.

Polar Optical Phonon Scattering: In some semiconductors, interactions with polar optical phonons can lead to significant scattering, particularly at higher temperatures.

The temperature dependence of electron mobility is typically described by the following empirical relationship:


(

)
=

0
−

⋅


μ(T)=μ
0
    ​

−α⋅T
n

Where:


(

)
μ(T) is the temperature-dependent mobility.

0
μ
0
    ​

 is the mobility at absolute zero temperature.

α is a temperature-dependent coefficient.

T is the absolute temperature.

n is an exponent that varies depending on the dominant scattering mechanisms.

In most cases,

n is between 1.5 and 2.5, and it reflects the specific scattering mechanisms dominating electron mobility at different temperature ranges. As temperature increases, the mobility decreases, and the semiconductor becomes less efficient for carrying electrical current. This temperature dependence of mobility is an important consideration in the design and performance analysis of semiconductor devices.