## 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
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