Carrier Transport

Drift current arises when an external electric field causes charged particles to accelerate between collisions with lattice atoms. Electrons and holes gain drift velocity proportional to the applied field intensity and their mobility. The drift current density equals the product of charge density, mobility, and electric field intensity for each carrier type.

Mobility is the proportionality factor that characterizes how easily electrons and holes respond to an applied electric field. Drift velocity is directly proportional to mobility and electric field intensity. Higher mobility means carriers accelerate more readily, resulting in greater drift velocity and increased current density in the semiconductor.

Diffusion current results from the random thermal motion of carriers moving from regions of high concentration to regions of low concentration. This concentration gradient drives carriers without requiring an external electric field. The diffusion current density depends on the diffusion coefficient and the concentration gradient of electrons and holes.

The Einstein relation links the diffusion coefficient and mobility for both electrons and holes through fundamental constants. It shows that the ratio of diffusion coefficient to mobility equals the thermal voltage, which depends on Boltzmann's constant and absolute temperature. This relationship connects drift and diffusion transport mechanisms in semiconductors.

Total conductivity is the sum of contributions from both electrons and holes, calculated as the product of charge density and mobility for each carrier type. The conductivity term appears in the total drift current density expression. This combined conductivity determines how readily a semiconductor conducts current under an applied electric field.

When both an external electric field and a concentration gradient exist simultaneously, the total current density is the sum of drift and diffusion components. Drift current dominates in regions with strong electric fields, while diffusion current dominates where concentration gradients are steep. Understanding both mechanisms is essential for analyzing carrier generation and recombination processes.

Drift velocity represents the net motion of charge carriers superimposed on their random thermal motion due to an applied electric field. It directly determines the magnitude of drift current density through its relationship with mobility and field intensity. Calculating drift velocity is fundamental to predicting current behavior in semiconductor devices and understanding device performance.