Essentials of MOSFETs

Unit 3: MOS Electrostatics

Lecture 3.3: Gate Voltage and Surface Potential

Mark Lundstrom

lundstro@purdue.edu Electrical and Computer Engineering

Purdue University West Lafayette, Indiana USA

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Band bending depends on surface potential

What gate voltage produced this surface potential?

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Gate voltage and surface potential

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Normal D-field and sheet charge

+ + + + + +

- - - - - - P-Si

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Gate voltage and surface potential

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MOS electrostatics

• given ψS • determine QS • find VG

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Surface potential vs. gate voltage

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Threshold voltage

The gate voltage needed to make:

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A word about capacitance

+ + + + + + + + + + +

- - - - - - - - - - -

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Capacitor with two dielectrics

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Depletion capacitance

“metallic” plate

“metallic” plate

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Approximate ψS vs. VG relation (depletion)

Below threshold:

(depletion)

approximate solution

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Example

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Surface potential vs. gate voltage

What gate voltage produced this surface potential?

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Gate voltage

✓

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Surface potential at the onset of inversion

threshold voltage

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Internal quantities at the onset of inversion

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Gate voltage at the onset of inversion

✓

Note: This is a rather large threshold voltage because we have not included the effect of the metal-semiconductor work function difference (to be discussed in the next lecture).

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Summary

1) The gate voltage induces charge in the semiconductor by bending the bands.

2) There is a simple (exact) relation between the gate voltage and the surface potential, but it must be solved numerically.

3) There is an approximate relation between gate

voltage and surface potential that works well in depletion.

Next topic

We have discussed an ideal MOS capacitor. In the next lecture we will add two important factors that affect real MOS capacitors.

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