1. Lecture 3 OUTLINE Semiconductor Basics (cont’d) PN Junction Diodes
Carrier drift and diffusion
PN Junction Diodes
Electrostatics
Capacitance
Reading: Chapter

2. Electrical ResistanceV + _ L t W I
homogeneously doped sample
where r is the resistivity
Resistance
(Unit: ohms)

3. Carrier Diffusion
Due to thermally induced random motion, mobile particles tend to move from a region of high concentration to a region of low concentration.
Analogy: ink droplet in water
Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient.
The proportionality constant is the diffusion constant.
Notation:
Dp  hole diffusion constant (cm2/s)
Dn  electron diffusion constant (cm2/s)

4. Diffusion Examples Linear concentration profile
 constant diffusion current
Non-linear concentration profile
 varying diffusion current

5. Diffusion Current
Diffusion current within a semiconductor consists of hole and electron components:
The total current flowing in a semiconductor is the sum of drift current and diffusion current:

6. The Einstein Relation
The characteristic constants for drift and diffusion are related:
Note that at room temperature (300K)
This is often referred to as the “thermal voltage”.

7. The PN Junction Diode
When a P-type semiconductor region and an N-type semiconductor region are in contact, a PN junction diode is formed. VD – + ID

8. Diode Operating Regions
In order to understand the operation of a diode, it is necessary to study its behavior in three operation regions: equilibrium, reverse bias, and forward bias.
VD = 0
VD < 0
VD > 0

9. Carrier Diffusion across the Junction
Because of the differences in hole and electron concentrations on each side of the junction, carriers diffuse across the junction:
Notation:
nn  electron concentration on N-type side (cm-3)
pn  hole concentration on N-type side (cm-3)
pp  hole concentration on P-type side (cm-3)
np  electron concentration on P-type side (cm-3)

10. Depletion Region
As conduction electrons and holes diffuse across the junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed.
The charge density in the depletion region is not zero.
The carriers which diffuse across the junction recombine with majority carriers, i.e. they are annihilated.
quasi-neutral region
quasi-neutral region
width=Wdep

11. The Depletion Approximation
Because charge density ≠ 0 in the depletion region, a large E-field exists in this region:
In the depletion region on the N side:
r(x)
In the depletion region on the P side:
qND a -b x
-qNA

12. Carrier Drift across the Junction

13. PN Junction in Equilibrium
In equilibrium, the drift and diffusion components of current are balanced; therefore the net current flowing across the junction is zero.

14. Built-in Potential, V0
Because there is a large electric field in the depletion region, there is a significant potential drop across this region:
(Unit: Volts)

15. Built-In Potential Example
Estimate the built-in potential for PN junction below.
Note that N P
ND = 1018 cm-3
NA = 1015 cm-3

16. 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.
r(x)
qND a -b x
-qNA ID
V(x) V0 -b a x

17. 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'
Equilbrium concentration of electrons on the P side:

18. 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 (Dpn, Dnp) of minority carriers in the quasi-neutral regions, under forward bias.
Within the quasi-neutral regions, the excess minority-carrier concentrations decay exponentially with distance from the depletion region, to zero:
Notation:
Ln  electron diffusion length (cm) x'

19. Diode Current under Forward Bias
The current flowing across the junction is comprised of hole diffusion and electron diffusion components:
Assuming that the diffusion current components are constant within the depletion region (i.e. no recombination occurs in the depletion region):