Essentials of MOSFETs

Unit 2: Essential Physics of the MOSFET

Lecture 2.2: Energy Band View of the MOSFET

Mark Lundstrom

lundstro@purdue.edu Electrical and Computer Engineering

Purdue University West Lafayette, Indiana USA

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Understanding MOSFETs

p-Si

n-Si n-Si

To understand any device, we should first draw an Energy Band Diagram.

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SiO2

Normal to the channel

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metal 3

SiO

2

Along the channel

p-Si

n-Si n-Si

To understand this device, we should first draw an Energy Band Diagram.

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Equilibrium E-band diagram

p-Si

n-Si n-Si

source channel drain Lundstrom: 2018

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Three separate semiconductors

source channel drain

1) Equilibrium: Fermi level is constant

2) Changes in electrostatic potential, change the electron’s energy.

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Putting the three pieces together

source channel drain

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Final result

source channel drain

Now, what effect does a gate voltage have?

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Equilibrium energy band diagram

p-Si

n-Si n-Si

A positive gate voltage will increase the electrostatic potential in the channel and therefore lower the electron energy in the channel.

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N-channel MOSFET: only electrons

source channel drain

Now, what effect does a gate voltage have?

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In the following slides, we will show only the conduction band.

The transistor as a barrier controlled device

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source drain channel

low gate voltage

VD = VS = 0

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Examine effect of gate voltage first

low gate voltage

high gate voltage

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Now add a small drain voltage

What if we apply a small positive voltage to the drain?

1) The Fermi level in the drain is lowered.

2) The conduction band is

lowered too, but the electron density stays the same.

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constant electric field substantial electron density

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Now increase the drain voltage

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high gate voltage

source high drain voltage

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ON-state

Now remove the gate voltage

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low gate voltage

source drain channel

high drain voltage

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OFF-state

How transistors work

2007 N-MOSFET

(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)

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DIBL

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transfer characteristics:

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Understanding DIBL with an e-band diagram

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source drain channel

DIBL

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2D energy band diagrams

p-Si

n-Si n-Si

We have been discussing energy band diagrams from the source to the drain along the top of the Si, but more generally, we should look at the 2D energy band diagram.

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2D energy band diagram on n-MOSFET

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(a)

(b)

(c)

(d)

S.M. Sze, Physics of Semiconductor Devices, 1981.

a) device b) equilibrium (flat band) c) equilibrium (S > 0) d) non-equilibrium with VG and VD > 0

applied FN 20

Essential physics of a transistor

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A MOSFET (and most transistors) are barrier-controlled devices.

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Limits to barrier control: quantum tunneling

from M. Luisier, ETH Zurich / Purdue

1) 2)

3) 4)

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Summary

1) Energy band diagrams provide a qualitative understanding of how MOSFETs operate.

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2) MOSFETs are barrier controlled devices – the drain current is controlled by the height of an energy barrier between the source and channel.

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3) In a well-designed transistor, the height of the energy barrier is strongly controlled by the gate voltage and weakly by the drain voltage (DIBL).

Next topic:

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In the next lecture, we will discuss traditional MOSFET theory, which describes the IV characteristics with simple analytical expressions.