1. P-N Junctions
ECE 663

2. So far we learned the basics of semiconductor physics, culminating
in the Minority Carrier Diffusion Equation
We now encounter our simplest electronic device, a diode
Understanding the principle requires the ability to draw band-diagrams
Making this quantitative requires ability to solve MCDE
(only exponentials!)
Here we only do the equilibrium analysis
ECE 663

3. P-N junction diode V I
ECE 663

4. P-N junction diode I V I = I0(eqV/hkT-1) Ip0 = q(ni2/ND) (Lp/tp) pn v
ECE 663

5. P-N Junctions - Equilibrium
What happens when these bandstructures collide?
Fermi energy must be constant at equilibrium, so bands
must bend near interface
Far from the interface, bandstructures must revert
ECE 663

6. Time < 0: Pieces separated

7. ECE 663

8. Gradients drive diffusion
left
ECE 663

9. Gradients drive diffusion
ECE 663

10. - - - + + - - + + - + - + - - + + - - + + +
But charges can’t venture too
far from the interface because
their Coulomb forces pull them back!
ECE 663

11. Separation of a sea of charge, leaving behind a charge depleted region
ECE 663

12. Resulting in a barrier across a depletion region
ECE 663

13. E
Depletion
Region E
ECE 663

14. How much is the Built-in Voltage?
N side
P side
ECE 663

15. How much is the Built-in Voltage?
Na acceptor level on the p side
Nd donor level on the n side
ECE 663

16. Special case: One-sided Junctions
One side very heavily doped so that Fermi level is at band edge.
e.g. p+-n junction (heavy B implant into lightly doped substrate)
ECE 663

17. How wide is the depletion region?
ECE 663

18. Depletion Approximation-step junction x
ECE 663

19. Depletion approximation-step junction
Exponentials replaced with step-functions
ECE 663

20. Doping Charge Density Electric Field Electrostatic Potential
NAxp = NDxn
= WD/(NA-1 + ND-1)
Kse0Em = -qNAxp = -qNDxn
= -qWD/(NA-1 + ND-1)
Vbi = ½|Em|WD
ECE 663

21. Depletion Width
ECE 663

22. Em = 2qVbi/kse0(NA-1+ND-1)
Maximum Field
Em = 2qVbi/kse0(NA-1+ND-1)
ECE 663

23. How far does Wd extend into each junction?
Depletion width on the n-side depends on the doping on the p-side
Depletion width on the p-side depends on the doping on the n-side
e.g. if NA>>ND then xn>>xp One-sided junction
ECE 663

24. ECE 663

25. ECE 663

26. P-N Junction with applied voltage
ECE 663

27. Reverse Bias +Voltage to the n side and –Voltage to the p side:
Depletion region will be larger
ECE 663

28. Reverse Bias Band Diagram
ECE 663

29. Reverse Bias depletion
Applied voltage disturbs equilibrium EF no longer constant
Reverse bias adds to the effect of built-in voltage
ECE 663

30. Forward Bias + - Negative voltage to n side positive to p side
+ -
Negative voltage to n side positive to p side
More electrons supplied to n, more holes to p
Depletion region gets smaller
ECE 663

31. Forward Bias Depletion
ECE 663

32. General Expression Convention = Vappl= + for forward bias
Vappl= - for reverse bias
ECE 663

33. n = nie(Fn-Ei)/kT p = nie(Ei-Fp)/kT
Positive voltage pulls bands down- bands are plots of electron energy
n = nie(Fn-Ei)/kT
p = nie(Ei-Fp)/kT Fn Fp
Fermi level is not constant  Current Flow
ECE 663

34. In summary A p-n junction at equilibrium sees a depletion width
and a built-in potential barrier. Their values depend on
the individual doping concentrations
Forward biasing the junction shrinks the depletion width
and the barrier, allowing thermionic emission and higher
current. The current is driven by the splitting of the
quasi-Fermi levels
Reverse biasing the junction extends the depletion width
and the barrier, cutting off current and creating a strong
I-V asymmetry
In the next lecture, we’ll make this analysis quantitative
by solving the MCDE with suitable boundary conditions