10.5:
Carrier Transport
Carrier transport in semiconductors generates current, through drift and diffusion mechanisms.
Drift current arises when an external electric field causes charged particles to accelerate between collisions.
Considering the electrons, the additional velocity added to the electrons' thermal motion is called the drift velocity. It can be obtained by equating the momentum lost during collisions and the momentum gained from the applied field.
The proportionality factor-mobility- characterizes electron and hole transport due to drift.
The drift current densities for both carriers can be expressed as the product of charge density, mobility, and electric field intensity. The sum of these two gives the total drift current density. Here, the term in parentheses gives conductivity.
Diffusion current results from the random thermal motion of carriers from high to low carrier density regions.
The diffusion current density equals the product of carrier flux and proportionality constant, which includes elementary charge and diffusion coefficient. Its ratio with mobility gives the Einstein relation.
If both an electric field and concentration gradient are present, both the drift and diffusion current contribute to the total current.
10.5:
Carrier Transport
The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
Where μe is the electron mobility and E is the electric field intensity.
The current density (J) due to drift for electrons (Jn) and holes (Jp) can be expressed as:
Where q is the elementary charge, n and p, are the concentrations of electrons and holes, respectively, and μn and μp are the mobilities of electrons and holes. The total drift current density (Jtotal) is the sum of the electron and hole current densities:
The conductance (σ) is then the sum of the products of charge density, mobility for each type of carrier:
Diffusion Current:
Diffusion occurs due to the thermal motion of carriers, moving from regions of higher concentration to regions of lower concentration. The current density (Jdiffusion) is:
Dn and Dp are the diffusion coefficients for electrons and holes, respectively, and dn/dx and dp/dx are the concentration gradients for electrons and holes.
The Einstein relations link mobility and diffusion coefficient for both electrons and holes:
Where k is the Boltzmann constant, and T is the absolute temperature.
When both an electric field and a concentration gradient are present, the total current density is the sum of the drift and diffusion components. In real-world applications, these phenomena are analyzed using the semiconductor equations, a set of differential equations that describe the behavior of charge carriers in a semiconductor.