SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

3.9. CURRENT CONTINUITY 139

Jn(x+

Jn(x)

x x+

Δx)

Δ

Δ

x

R= recombination rate

x

Area A

Loss Gain

(a)

(b)

Particle current is conserved

IN OUT

Recombination

Loss

Generation

Gain

in volume

Δx

Figure 3.26: (a) A conceptual description of the continuity equation. (b) Geometry used to
develop the current continuity equation.

the time dependent continuity equation for electrons and holes, valid separately. These equations
will be used when we discuss the transient time responses of thep-ndiodes and bipolar transis-
tors. These equations are also used to study the steady-state charge profile in these devices. In
steady state we have (the time derivative is zero)

d^2 δn

dx^2

=

δn

Dnτn

=

δn

L^2 n

(3.9.10)

d^2 δp

dx^2

=

δp

Dpτp

=

δp

L^2 p

(3.9.11)