PN Diode Fall'15

1

Lecture 7: Electrostatics and IV Characteristics of P-N DiodeECE5590: Nanoscale Devices and circuits

Mostafizur [email protected]

• R-G, Drift, Diffusion• Continuity Equation• P-N Junction

Recap

3

Outline

• P-N Junctions• Drawing Band Diagram• Solution in Equilibrium• Non-Equilibrium Conditions (I-V)• Summary

ECE5590 Fall 2015 MR

ECE5590 Fall 2015 MR 4

ECE5590 Fall 2015 MR 5

ECE5590 Fall 2015 MR 6

P-N Junction Devices..

ECE5590 Fall 2015 MR 7

P and N doped Materials

ECE5590 Fall 2015 MR 8

Time < 0

P-type piece N-type piece

Time < 0: Pieces separated

At time = 0, slam the two pieces together

ECE 663

At time = 0, slam the two pieces together

Hole gradient

Jp, diffusion = -qDp dp/dx = current right, holes right

Electron gradient

Jn,diffusion = -qDn dn/dx = current right, electrons right

Gradients drive diffusion

left

E

E

Depletion Region

ECE5590 Fall 2015 MR 13

Depletion Approximation

ECE5590 Fall 2015 MR 14

Electrostatics

• Poisson’s Equation

ECE5590 Fall 2015 MR 15

ECE5590 Fall 2015 MR 16

Drawing Band diagram

ECE5590 Fall 2015 MR 17

Electric Field is Discontinuous for Heterojunction

ECE5590 Fall 2015 MR 18

Homojunction

ECE5590 Fall 2015 MR 19

Built-in Potential (Vbi)

How wide is the depletion region?

ECE 663

Depletion Approximation-step junction

x

ECE5590 Fall 2015 MR 22

Solution for E

ECE5590 Fall 2015 MR 23

Solution for E

ECE5590 Fall 2015 MR 24

Solution for V

ECE5590 Fall 2015 MR 25

Depletion Width

ECE5590 Fall 2015 MR 26

I-V Characteristics

ECE5590 Fall 2015 MR 27

ECE5590 Fall 2015 MR 28

Applying a Bias

ECE5590 Fall 2015 MR 29

Depletion Width

• Would current flow? Diffusion/Drift?

ECE5590 Fall 2015 MR 30

ECE5590 Fall 2015 MR 31

Effect of Bias

ECE5590 Fall 2015 MR 32

ECE 663

I-V Curve for Ideal Diode

qkT

V

eII VVA

0

/0 )1( 0

ECE 663

Ideal P-N Junction Diode

Assumptions:

• Steady-State conditions• Non-degenerate doping• One-dimensional• Low Level Injection• Only drift, diffusion,thermal R-G (no photons)

ECE5590 Fall 2015 MR 35

ECE5590 Fall 2015 MR 36

Applications

ECE5590 Fall 2015 MR 37

ECE5590 Fall 2015 MR 38

Solar Cells

ECE5590 Fall 2015 MR 39

Solar Cells

ECE5590 Fall 2015 MR 40

Solar Cells

ECE5590 Fall 2015 MR 41

Summary

• P-N diodes are simplest semiconductor devices

• Operation lies in fundamental of physics• Useful for various applications