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 ...
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