Energy Band Treatment of Mosfets

ECE-305: Spring 2015

MOSFETs: An Energy Band Treatment

Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA [email protected]

Lundstrom’s lecture notes: Lecture 3

Lundstrom4/8/15 ECE 305 F15

understanding MOSFETs

V > V GS T V 0 D

n-Si n-Si

p-Si

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

Lundstrom ECE 305 F15 normal to the channel

ΔVOX

EC φS

EV Si EFM

3 x metal

understanding MOSFETs

V > V GS T V 0 D

n-Si n-Si

x p-Si

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

Lundstrom ECE 305 F15 equilibrium E-band diagram: 3 separate pieces

V 0 GS 0

n-Si n-Si

x p-Si

y E E C C E E F E F F E E V V source channel drain

Lundstrom ECE 305 F15

equilibrium E-band diagram: 3 separate pieces

E E C C E E F E F F E E V V source channel drain 1) Equilibrium: Fermi level is constant

2) Changes in electrostatic potential, change the electron’s energy. E y = E − qφ y C ( ) C0 ( ) E y = E − qφ y V ( ) V 0 ( ) Lundstrom ECE 305 F15 putting the 3 pieces together (equilibrium)

E E C F

E V y source channel drain

E y = E − qφ y C ( ) C0 ( ) E x = E − qφ y V ( ) V 0 ( ) Lundstrom ECE 305 F15

final result: one semiconductor with 3 regions

Now, what effect does a gate voltage have? E

E E C F

E V y source channel drain

E y = E − qφ y C ( ) C0 ( ) E y = E − qφ y V ( ) V 0 ( ) Lundstrom ECE 305 F15 equilibrium energy band diagram

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

V GS 0 0

n-Si n-Si

x p-Si

Lundstrom ECE 305 F15

the transistor as a barrier controlled device

V E G

ß low gate voltage

EF EF

ß VD = VS = 0

EC EC

source channel drain

y Lundstrom March 5, 2015 the transistor as a barrier controlled device

V E G

ß low gate voltage

E = −qV Fn

source channel drain

Fn ß high drain voltage y

Lundstrom March 5, 2015

the transistor as a barrier controlled device

V E G

ß high gate voltage

E = −qV

F n EC

F source n ß high drain voltage y

Lundstrom March 5, 2015 effect of gate voltage first

ß low gate voltage E EC

EC = EC 0 − qφs

ß high gate voltage EF

Lundstrom ECE 305 F15

Now add a small drain voltage

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

1) The Fermi level in the drain is lowered.

F n 2) The conduction band is lowered too, but the y electron density stays the same. constant electric field substantial electron density

Lundstrom ECE 305 F15 how transistors work

2007 N-MOSFET

VGS

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

Lundstrom ECE 305 F15

understanding DIBL

↑ threshold voltage

I VT (VDS ) D I (mA µm) ON

VDS = VDD

VDS = 0.05 V

VGS

VDD VTSAT VTLIN

Lundstrom ECE 305 F15 understanding DIBL transfer characteristics:

↑ ION VDS = VDD log10 I D

(mA µm) VDS = 0.05 V

ΔV DIBL ≡ GS (mV V) ΔVDS

VGS VTSAT VTLIN VDD

Lundstrom ECE 305 F15

understanding DIBL

V E G DIBL

Fn (low VDS ) EC

source channel drain

Fn (high VDS ) y

Lundstrom ECE 305 F15 understanding DIBL

V GS V > 0 0 DS

n-Si n-Si E y

p-Si

Lundstrom ECE 305 F15

2D energy band diagrams

V > V GS T V 0 D

n-Si n-Si

y p-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.

Lundstrom ECE 305 F15 2D energy band diagram on n-MOSFET

(a) a) device

(b) b) equilibrium (flat band)

(c)

c) equilibrium (ψS > 0)

(d)

d) non-equilibrium with VG and VD > 0 applied FN S.M. Sze, Physics of SemiconductorLundstrom ECE Devices, 305 F15 1981 and Pao and Sah.

essential physics of a transistor

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

Lundstrom ECE 305 F15 limits to barrier control: quantum tunneling

4) 3)

2) 1)

from M. Luisier, ETH Zurich / Purdue