Chapter 3

Carrier Transport

Electrical current flow in semiconductors is mainly dominated by driftand diffusion of electrons and holes. This chapter reviews the physicalmechanisms that affect the carrier transport in optoelectronic devices, includ-ing pn-junctions, thermionic emission at heterojunctions, and tunneling.Simple formulas for the carrier mobility and for various carrier generationand recombination mechanisms are given. Advanced transport models areoutlined at the end.

3.1 Drift and DiffusionSemiconductor device simulation software most commonly uses the driftdiffusion model to compute the flow of electrons and holes. Drift current isgenerated by an electric field F and it is proportional to the conductivity of elec-trons n = qnn and holes p = qpp. Diffusion current is driven by theconcentration gradient of electrons n and holes p. It is proportional to the dif-fusion coefficient Dn and Dp, respectively. For uniform semiconductors, the totalcurrent density of electrons and holes is written as

jn = qnn F + qDnn (3.1)jp = qpp F qDpp. (3.2)

We consider the elementary charge q to always be a positive number, so that thecurrent flows in the direction of the electric field while the electrons move in oppo-site direction. Both carriers diffuse downhill toward lower carrier concentrationwhile n and p point in the uphill direction.

Changes in the local carrier concentration in time must be accompanied by aspatial change in current flow ( j ) and/or by the generation (rate G) or recombi-nation (rate R) of electronhole pairs. This relation is expressed by the continuityequations

qn

t= jn q(R G) (3.3)

qp

t= jp q(R G). (3.4)

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