The Bipolar Transistor. Ambipolar Transport & Fundamental Concepts

The Bipolar Transistor Ambipolar Transport & Fundamental Concepts Nonequilibrium Excess Carriers Whenever there is current, the semiconductor is in ...
Author: Melinda Hoover
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The Bipolar Transistor Ambipolar Transport & Fundamental Concepts

Nonequilibrium Excess Carriers Whenever there is current, the semiconductor is in nonequilibrium state  Excess carriers are generated by various processes, but in pairs.  Transport of excess carriers determines the current 

Excess Carriers and Excess Carrier Life Time 

At thermal equilibrium

n0 p0 = ni2 

when in nonequilibrium state, excess carriers are (typically) excited in pairs

p = p0 + δp

n = n0 + δn 

recombination can be approximated as

(

dn = α r ni2 − np dt 

)

to the first order, or for low-level injection

dδn = −α r (n0 + p0 )δn dt

δp = δn

Excess Carrier Life Time dδn δn = −α r (n0 + p0 )δn = − dt τ ex



τex is called the excess carrier life time for n-type material n0>>p0 and



for p-type material p0>>n0 and



1 τ ex ≈ α r n0 1 τ ex ≈ α r p0

Generation-Recombination Processes 

Band-to-Band Generation and Recombination 



recombination-generation centers: defects, surface states, etc.

Auger Recombination

Continuity Equations

or

∂p 1 p + ∇J p = g p − ∂t e τp

∂n 1 p + ∇J n = g n − ∂t − e τn

J p = eµ p pE − eD p ∇p

J n = eµ n pE + eDn∇n

∂p p + ∇(µ p pE − D p ∇p ) = g p − ∂t τp

n = n0 + δn

∂n n − ∇(µ n nE + Dn∇n ) = g n − τn ∂t or

D p ∇ 2 p − µ p (E∇p + p∇E ) + g p −

p = p0 + δp p

τp

=

∂p ∂t

∂n Dn∇ n + µ n (E∇n + n∇E ) + g n − = τ n ∂t 2

n

δp = δn

Time-dependent diffusion equations for excess carriers 

Assume equilibrium carrier concentrations n0 and p0 are time and space invariant 

For example, Homogeneous region

D p ∇ 2δp − µ p (E∇δp + p∇E ) + g p −

Dn∇ 2δn + µ n (E∇δn + n∇E ) + g n −

n = n0 + δn

p = p0 + δp

p

τp n

τn

=

∂δp ∂t

=

∂δn ∂t

δp = δn

Ambipolar Transport of Excess Carriers 

Excess carriers tend to transport together   

Once they are separated, an additional internal field is created and tends to pull them back together Results in Ambipolar Transport especially in weak external field region The additional internal field itself may be small compare to external field, but its gradient can be large

E = Eapp + Eint Eint