M3 Transport: Drift and Diffusion

Topic

An applied electric field within this semiconductor material produces a drift current among the material's free charge carriers: the field accelerates these free charge carriers—either in the direction of the field or opposite to it, depending on whether they are electrons or holes—to a drift velocity proportional to the applied field, and it is this drift velocity of the free charge carriers that constitutes the drift current. Consequently, a stronger applied electric field results in a greater drift current.

Conversely, a concentration gradient of these same charge carriers within the semiconductor material—even in the absence of an applied electric field—produces a diffusion current: the charge carriers move via diffusion from the region of higher concentration to the region of lower concentration, and this net displacement of charge carriers, driven solely by the concentration gradient, constitutes the diffusion current. Consequently, a steeper concentration gradient results in a greater diffusion current.

Thus, this model—incorporating the drift and diffusion currents introduced earlier—links the charge carrier mobility (which governs the drift current) with the diffusion coefficient (which governs the diffusion current) via the Einstein relation; both parameters are related through the temperature of the semiconductor material. The Einstein relation reflects the fact that the same random thermal motion of free charge carriers underlies both mobility and the diffusion coefficient, meaning one cannot be determined independently of the other. The fact that this drift current and this diffusion current combine within the semiconductor material to form a total current—and that this same total current is balanced, alongside the generation and recombination of charge carriers (described in greater detail by another model in this set), within the material's continuity equation—means that this continuity equation ultimately governs how the concentration of these charge carriers evolves over time and space within the semiconductor material.

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