Lecture6 PN junction and diode

LECTURE 6: PN JUNCTION AND DIODE




The density gradient as producing a "diffusion force" that
acts on the majority carriers, called as diffusion forces.



•

The net positive and negative charges in the n and p regions induce an electric field in the region near the junction, in the direction from the

positive to the negative charge, or from the n to the p region

•

The electric field in the space charge region produces another force on the electrons and holes which is in the opposite direction to the

diffusion force for each type of particle. In thermal equilibrium, the diffusion force and the E-field force exactly balance each other


Charge density






More on the Built-In Potential (V0)

Q: Why can’t we harness V0 and use the PN junction as a battery?
+

?

A: A built-in potential also exists at a junction between a metal and
V0 a semiconductor (e.g. at a
contact).
–
If we connect the P and N regions together, there is no net voltage drop across the device:

•

No net current flows across the junction when the externally
applied voltage is 0 V!

V(x)
V0
Vbn+V0+Vbp=0
-b
Vbn

V0

Vbp

0

a

x


Space charge width

ND × a
b=
NA
 2ε sVbi
a=
 e
 2ε sVbi
b=
 e
Thermal voltage or built in voltage:

kT
VT =
q

Wdep

1/ 2

 NA  
 
1




 N D   N A + N D  

1/ 2

 ND  
 
1



 N A   N A + N D  

 2ε sVbi
= a+b = 
 e

1/ 2

 N A + N D  


N
×
N
 A
D 



Wdep

 2ε s ( Vbi + VR )
= a+b = 
e


1/ 2

 N A + N D  


N
×
N
 A
D 








Effect of Applied Voltage

•

The quasi-neutral N-type and P-type regions have low resistivity, whereas the depletion region has high
resistivity.

– Thus, when an external voltage VD is applied across the diode, almost all of this voltage is
dropped across the depletion region. (Think of a voltage divider circuit.)

•

If VD < 0 (reverse bias), the potential barrier to carrier diffusion is increased by the applied voltage.

•

If VD > 0 (forward bias), the potential barrier to carrier diffusion is reduced by the applied voltage.

–

VD

+

ID


•

PN Junction under Forward Bias
A forward bias decreases the potential drop across the junction. As a result, the
magnitude of the electric field decreases and the width of the depletion region
narrows.
ρ (x)
qND
a

-b

x
-qNA

ID

V(x)
V0

-b

0

a

x


Minority Carrier Injection under Forward Bias

•

The potential barrier to carrier diffusion is decreased by a forward bias; thus, carriers diffuse
across the junction.

– The carriers which diffuse across the junction become minority carriers in the quasi-neutral
regions; they recombine with majority carriers, “dying out” with distance.

np(x)

np0

x'
edge of depletion region

x'
0
Equilbrium concentration of electrons on the P side:

np0

ni2
=
NA


Minority Carrier Concentrations
at the Edges of the Depletion Region

•
•

The minority-carrier concentrations at the edges of the depletion region are changed by the factor
There is an excess concentration (∆pn, ∆np) of minority carriers in the quasi-neutral regions,
qVD / kT
VD / VT
under forward bias.
Within the quasi-neutral regions, the excess minority-carrier concentrations decay exponentially
with distance from the depletion region, to zero:

–

=e

e

n p ( x′) = n p 0 + ∆n p ( x′)
∆n p ( x′) =

2
i

(

VD / VT

n e

NA

)e

−1

Notation:

− x′ / Ln

J n ,diff

x'

Ln ≡ electron diffusion length (cm)

(

)

dn p qDn ni2 qVD / VT
= qDn
=
e
− 1 e − x′ / Ln
dx′
N A Ln


Diode Current under Forward Bias

•

The current flowing across the junction is comprised of hole diffusion and electron diffusion
components:

•

Assuming tot
that the diffusion
components
are constant

within the depletion
region (i.e. no
p , drift current
n
,
drift
p
,
diff
n
,
diff
=0
x =0
x =0
recombination occurs in the xdepletion
region): x = 0

J

J n ,diff

x =0

=J

+J

(

+J

)

qDn ni2 VD / VT
=
e
−1
N A Ln

(

J tot = J S e

VD / VT

+J

J p ,diff

x =0

=

qD p ni2
N D Lp

(e

VD / VT

 Dn
Dp 

− 1 where J S = qn 
+
N L N L 
D p 
 A n

)

2
i

)

−1


I-V Characteristic of a PN Junction

•

Current increases exponentially with applied forward bias voltage, and
“saturates” at a relatively small negative current level for reverse bias voltages.

“Ideal diode” equation:

(

)

I D = I S eVD / VT − 1

 Dn
Dp 

I S = AJ S = Aqn 
+
N L N L 
D p 
 A n
2
i