Continuity Equation

1. Continuity equation
kamlesh singh rawat

2. INTRODUCTION
The continuity equation which describes the
distribution of electrons and holes when there is
excess carrier generation recombination and
carrier movement. We will consider some of the
simplifications which are used for deriving the
characteristics, how the equations can be
simplified. And finally we will summarize the
characteristic material parameters which
describe a semiconductor device. So let us begin
with the continuity equation.

3. As per law of conservation of charge rate
of change of number of electrons inside
the semiconductor is equal to the no of
electrons entering per second minus
number of electrons leaving per second
plus number of electrons generated per
second by generation process minus
number of electrons lost per second by
recombination process.

4. Derivation of Continuity Equation
• Consider carrier-flux into/out-of an infinitesimal volume:
Jn(x) Jn(x+dx)
dx
Area A, volume Adx
  AdxRAdxGAdxxJAxJ
qt
n
Adx nnnn 







)()(
1
Continuity Equation TEC-101

5. n
n
n
nn
R
x
xJ
qt
n
dx
x
xJ
xJdxxJ










)(1
)(
)()(
Lp
p
Ln
n
GR
x
xJ
qt
p
GR
x
xJ
qt
n
)(1
)(1












Continuity
Equations:
TEC-101Continuity Equation

6. Summary: Continuity Equations
• The continuity equations are established based on
conservation of carriers, and therefore hold generally:
• The minority carrier diffusion equations are derived from
the continuity equations, specifically for minority carriers
under certain conditions (small E-field, low-level injection,
uniform doping profile):
Lp
n
Ln
n
GR
x
xJ
qt
p
GR
x
xJ
qt
n )(1)(1












Lp
n
P
n
Ln
p
N
p
GR
x
p
D
t
p
GR
x
n
D
t
n
2
2
2
2












TEC-101Continuity Equation