14

p

dp

q

Tk dx)x(E

⋅

⋅

−=

By integrating

ia the path of the space-charge region the diffusion voltageU

D

.

canbe calculated:

∫

∫

⋅

⋅

=

⋅

⋅

=

−=

0p

0n

p

n

p

p

0n

0p

x

x

D

p

p

ln

q

Tk

p

dp

q

Tk dx)x(E U

U

D

: Diffusion voltage [V]

x

n

: Depth of penetrationof the electrical field into the n-region [cm]

x

p

: Depth of penetrationof the electrical field into the p-region [cm]

p

p0

: Hole density at the edge of the space-charge region in the

p-region [cm

-3

]

p

n0

: Electron density at the edge of the space-charge region in the

p-region [cm

-3

]

The hole density p

p0

at the edge of the p-region represents the density of the acceptors

N

A

in the region.With the aido

p

n0

can be calculated as:

D

2

i

0n

2

i

0n

N

n

n

n p

= =

N

D

: Donor density

n

n0

in this equation is identical to the donor density in the n-region. For the diffusion

voltageU

D

, therefore

anbe reformulated to:

2

i

D A

D

n

NN ln

q

Tk U

⋅

⋅

⋅

=

N

A

: Acceptor density

Example:

The diffusion voltage in silicon, with an acceptor density of

3

17

A

cm 10 N

−

=

, a donor

density of

3

16

D

cm 10 N

−

=

and with an intrinsic charge carrier density of

3

10

i

cm 10 45.1 n

−

⋅

=

at room temperature (300K), results in a valueof:

V75.0

)

cm 10 45.1(

cm 10

cm 10 ln

C 10

60218 .1

K300

K

J 10

38065 .1

U

23

10

3

16

3

17

19

23

D

=

⋅

⋅

⋅

⋅

⋅

⋅

=

−

−

−

−

−

The equilibrium state can be influenced by the application of an external voltage. If the

positive terminal of a power supply is connected with the n-conducting zone and the

negative terminal with the p-conducting zone, the electrical field that ensues has the

same direction as the space-charge field around the pn-junction and increases its effect.

This gives the result that no significant current can flow through the barrier region.

However, there is a low reverse current within the barrier region, due exclusively to

thermal energy applied from outside, as electron-hole pairs are constantly being formed

SEO Version