1. 4.4.6 Gradients in the Quasi-Fermi Levels
- At equilibrium, there is no gradient in the Fermi level EF
In the steady state, there is a gradient in the quasi-Fermi level due to drift and diffusion
The total electron current becomes:
(4-51)
(4-52a)
Modified Ohm’s Law
(4-52b)

2. first performed in 1951at Bell Telephone Laboratories
4.4.5 The Haynes-Shockley Experiment (Please read Section 4.4.5)
classic experiment demonstrating the drift and diffusion of minority carriers
first performed in 1951at Bell Telephone Laboratories
independent measurement of the minority carrier mobility and diffusion coefficient
Figure 4—18
Drift and diffusion of a hole pulse in an n-type bar: (a) sample geometry; (b) position and shape of the pulse for several times during its drift down the bar.

3. Figure 4—19
Calculation of Dp from the shape of the p distribution after time td. No drift or recombination is included

4. Figure 4—20
The Haynes–Shockley experiment: (a) circuit schematic; (b) typical trace on the oscilloscope screen.

5. Chapter 5 Junctions
p-n junctions
metal-semiconductor junctions
heterojunctions
Junctions
Fabrication
Equilibrium conditions
Biased junctions; steady state conditions
Reverse bias breakdown
Transient and AC conditions
Deviations from simple theory
p-n junctions
Strong qualitative understanding of the properties of p-n junctions
Know how to use the mathematics of p-n junctions to make
calculations
Goals

6. 5.1 Fabrication of p-n junctions
Major process steps (Please read Section 5.1)
Thermal Oxidation
Diffusion
Rapid Thermal Processing
Ion Implantation
Chemical Vapor Deposition (CVD)
Photolithography
Etching
Metallization
Crystal Growth and Wafer Preparation (Chap.1)
Process Simulation
Process Integration

7. Figure 5—10
Simplified description of steps in the fabrication of p-n junctions. For simplicity, only four diodes per wafer are shown, and the relative thicknesses of the oxide, PR, and the Al layers are exaggerated.

8. 5.2 Equilibrium Conditions
What will happen if we bring a p-type semiconductor and a n-type semiconductor together
to form a junction?
Based on knowledge gained from previous chapters, we expect:
Initially, current will flow due to diffusion
No net current can flow across the junction at equilibrium
An internal electric field E will build up as a result of
uncompensated donor ions (Nd+) and acceptor ions (Na−)
The electric field gives rise to a Contact Potential V0
across the junction E=-dV(x)/dx
The Fermi levels will be aligned at equilibrium

9. Figure 5—11
Properties of an equilibrium p-n junction: (a) isolated, neutral regions of p-type and n-type material and energy bands for the isolated regions; (b) junction, showing space charge in the transition region W, the resulting electric field % and contact potential V0, and the separation of the energy bands; (c) directions of the four components of particle flow within the transition region, and the resulting current directions.

10. 5.2.1 The Contact Potential
A step junction—uniform p-doping on one side of a sharp junction and uniform n-doping
on the other side. (vs. graded junction)
W  transition region, or space charge region,
or depletion region
V0=Vn-Vp contact potential
qV0  built-in potential energy barrier
x direction is taken from p to n

11. The derivation of V0
At equilibrium, the drift and diffusion currents must cancel for each type of carrier. For hole
current,
(5-4a)
Rearrange Eq. (5-4a) to obtain
(5-4b)
Using Einstein relation and E(x)=-dV(x)/dx , Eq. (5-4b) becomes
(5-5)
Integration over the junction limits
(5-6)

12. The derivation of V0 (cont’d)
Since Vn-Vp=V0,, Eq. (5-6) becomes
(5-7)
If we consider the step junction to be made up of material with Na acceptors/cm3 on the p-side and a concentration of Nd donors on the n-side, we can write Eq. (5-7) as:
(5-8)
Another useful form of Eq. (5-7) is
(5-10)
(We used equilibrium condition pnnn=ni2=ppnp in getting Eq. (5-10))

13. 5.2.2 Equilibrium Fermi Levels
Since we have assumed that pn and pp are given by their equilibrium values outside the
transition region, we have
(5-11a)
(5-11b)
(5-12)
(At equilibrium)
When bias V is applied to the junction,
the potential barrier is raised or lowered from the value of V0
the Fermi levels are shifted with respect to each other by the amount of eV