9

Based on

and

it follows for the total charge carrier density, which

represents a current per surface area:

) p n()x(Eq )x(E pq )x(E nq

J

J J

p

n

p

n

drift

,p

drift

,n

drift

µ⋅ +µ⋅ ⋅

⋅ = ⋅µ⋅ ⋅ + ⋅µ⋅ ⋅ = + =

The expression

) p n(q

p

n

µ⋅ +µ⋅ ⋅

is also described as the specific conductivity of the

semiconductor. Accordingly, the specific resistance

ρ

is defined as:

) p n(q

1

p

n

µ⋅ +µ⋅ ⋅

=ρ

ρ

:Specific resistance

[

]

cm

⋅Ω

In contrast to the carrier drift, the diffusionmovement originates in the thermal motion of

charge carriers. Thesemove at the average speed v

th

in the time t over the distanced.

Movement in the semiconductor by diffusion

Provided that there is a consistent temperature in a semiconductor, it canmore or less

be assumed that the direction of movement is free and consistent. Taking point 0 in a

semiconductor

, the probability that a charge carrier at point -dwill move to the

right in direction 0 is equal to the probability that it will move to the left, i.e. 50% in each

case. The rate of electrons that flow from the point -d to thepoint 0 can bedescribedas:

n,th

n

v)d(n5.0 )d(R

⋅ − ⋅

= −

R: Carrier flow rate

⋅

s cm

1

2

Accordingly, for the rate of holes:

p,th

p

v)d(p5.0 )d(R

⋅ − ⋅

= −

For theexpression n(-d), it canbe approximated, according toTaylor's theore

that:

9

Taylor's theorem postulates that any given function f(x) can be approximated sufficiently accurately using a

Taylor series:

)a( f

!n

)ax(

...

)a(''f

!2

)ax( )a('f

!1

)ax( )a(f )x(f

)n(

0n

n

2

⋅

−

= + ⋅

−

+ ⋅

−

+ =

∑

∞

=

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