PHYSICAL REVIEW B 66, 201202~R! ~2002!
Electric-field dependent spin diffusion and spin injection into semiconductors
Z. G. Yu and M. E. Flatté
Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242
~Received 22 January 2002; revised manuscript received 7 May 2002; published 14 November 2002!
We derive a drift-diffusion equation for spin polarization in semiconductors by consistently taking into
account electric-field effects and nondegenerate electron statistics. We identify a high electric-field diffusive
regime which has no analog in metals. In this regime there are two distinct spin-diffusion lengths. Furthermore,
spin injection from a ferromagnetic metal into a semiconductor is enhanced by several orders of magnitude.
This enhancement also occurs for high electric-field spin injection through a spin-selective interfacial barrier.
PACS number~s!: 72.25.Dc, 72.20.Ht, 72.25.Hg, 72.25.Mk
Semiconductor devices based on the control and manipu-
lation of electron spin ~semiconductor spintronics! have re-
cently attracted considerable attention.1 Spin transport and
injection properties of semiconductors and heterostructures
strongly constrain the design of new spintronic devices. In
theoretical studies of spin
transport and injection in
semiconductors2–4 the spin polarization is usually assumed
to obey the same diffusion equation as in metals,5
is the electrochemical potential of up-spin
~down-spin! electrons. In this diffusion equation the electric
field does not play any role, and spin polarization decays
away on a length scale of L from an injection point. This is
reasonable for degenerate systems because the electric field
E is essentially screened. For semiconductor spintronic de-
vices, however, the semiconductor often is lightly doped and
nondegenerate, and experiments have shown the electric
field can change spin diffusion dramatically.6,7 Equation ~1!
corresponds to neglecting drift in the