SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

(Greg DeLong) #1
3.9. CURRENT CONTINUITY 137

asET∼Eifor efficient recombination. Then the recombination rate becomes:


U=

σpσnvthNt
σnnn

[

nnpn−n^2 i

]

(3.8.43)

=σpvthNt

[

pn−n^2 i/nn

]

(3.8.44)

=σpvthNt[pn−pn 0 ] (3.8.45)

U=

Δpn
τp

(3.8.46)

where the minority carrier lifetime,τpis defined as


1
τp

=σpvthNt (3.8.47)

Here the rate limiting step is the capture of the minority carrier. This is also achieved by recog-
nizing the hole capture rate,rcis the dominant step. In ann−type semiconductor, sinceEFis
close to the conduction band andf(ET)→ 1 which makesraandrdboth negligible. Typical
values ofσare 10 −^15 − 10 −^16 cm−^2.
Generation occurs whenn^2 ipn. From equation 3.8.39


U=−

σpσnvthNtn^2 i
σn[n+niexp (Et−i/kBT)] +σp[p+niexp (Ei−t/kBT)]

=−

σpσnvthNtni
σnexp (Et−i/kBT)+σpniexp (Ei−t/kBT)
For the caseσn=σp=σ
U=−

σvthNtni
2 cosh (Et−i/kBT)

(3.8.48)

Thus, generation rate peaks when the trap energy is at mid-gap:


U=−

ni
2 τ

(3.8.49)

whenEi→Etthe lifetime


τ=

1

σvthNT

3.9 CURRENT CONTINUITY(The law of conservation


of electrons and holes separately)


In the previous sections we have considered several elements of non-equilibrium phenomena
in semiconductors. These include drift and diffusion, carrier generation and recombination.

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