10

dx

dn d )0(n )d(n

⋅ − = −

dx

dp d )0(p )d(p

⋅ − = −

By using

r

it follows:

n,th

n

v

dx

dn d )0(n5.0 )d(R

⋅

⋅ − ⋅

= −

p,th

p

v

dx

dp d )0(p5.0 )d(R

⋅

⋅ − ⋅

= −

The same applies for the rates of the charge carriers that flow left from the point d to the

point 0:

n,th

n

v

dx

dn d )0(n5.0 )d(R

⋅

⋅ + ⋅

=

p,th

p

v

dx

dp d )0(p5.0 )d(R

⋅

⋅ + ⋅

=

By summarising the charge carrier rates that effectively flow through point 0, it follows

that:

dx

dn D

dx

dn d v )d(R)d(R R

n

n,th

n

n n

⋅

= ⋅ ⋅

= − −

=

dx

dp D

dx

dp d v )d(R)d(R R

p

p,th

p

p

p

⋅

= ⋅ ⋅

= − −

=

D: Diffusion constant

s

cm

2

If the rate of the charge carrier is multiplied by the relevant elementary charge q, the

result is thediffusiondensity:

dx

dn Dq

dx

dn Dq J

n

n

diff ,n

⋅

⋅ = ⋅

⋅ =

dx

dp Dq

dx

dp Dq J

p

p

diff ,p

⋅

⋅ = ⋅

⋅ =

Finally, for the total charge carrier density fromdrift anddiffusion, it follows that:

The Taylor's theorem and the Taylor series are named after the English mathematician Brook Taylor (1685 -

1731). The approximationusedhere takes a=0 and breaks off after the secondmember of theTaylor series.

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