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

Mostafizur Rahmanrahmanmo@umkc.edu

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

Recap

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Outline

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

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P-N Junction Devices..

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P and N doped Materials

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Time < 0

P-type piece N-type piece

Time < 0: Pieces separated

At time = 0, slam the two pieces together

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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

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Depletion Approximation

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Electrostatics

• Poisson’s Equation

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Drawing Band diagram

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Electric Field is Discontinuous for Heterojunction

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Homojunction

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Built-in Potential (Vbi)

How wide is the depletion region?

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Depletion Approximation-step junction

x

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Solution for E

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Solution for E

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Solution for V

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Depletion Width

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I-V Characteristics

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Applying a Bias

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Depletion Width

• Would current flow? Diffusion/Drift?

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Effect of Bias

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I-V Curve for Ideal Diode

qkT

V

eII VVA

0

/0 )1( 0

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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)

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Applications

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Solar Cells

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Solar Cells

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Solar Cells

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Summary

• P-N diodes are simplest semiconductor devices

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