lecture 4 - mos transistor

8/7/2019 Lecture 4 - MOS Transistor

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Integrated Electronics & Design

ELEC 100

M. Raja [2010]

Metal-Oxide Semiconductor Field-effecttransistor (MOSFET)



M. Raja [2010]

Typical conventional silicon transistors

Transistors

FET BJT

PNP NPNJFET MOSFET

Others

pMOS nMOS



Basic definitions

MOSFET is a unipolar transistor which acts as a voltage-controlled current deviceThe gate voltage V G determines the formation and conductivity of the channelThe drain voltage V D controls the current in the channel after formationThe source contact is normally grounded i.e. V S = 0 V

MOSFETs operates in ‘inversion mode’ i.e. the minority carriers (electrons) fromthe bulk of the p-substrate are generated on the surface

n+ n+

p

Gate

V G Drain

V D

Source

V S

MOS capacitor

For an n-MOSFET, it consists of

an n-channel formed betweenthe source and drain contacts



M. Raja [2010]

MOSFET as two diodes

When no voltage is applied to the gate, the MOSFET looks like two ‘back toback’ diodes and no current flows because one diode is reverse biased

p nI = 0

pnSOURCE DRAIN

p

V G = 0V D > 0V S = 0

n+n+



Basic operation of the n -MOSFET

p

V G

>> 0V D > 0V S = 0

When a large voltage is applied on the gate, an inversion layer is formed, with electrons

accumulated on the surface. A depletion is present at the back of the inversion layer

With application of drain voltage, current and/or electrons flow from the source to drain

What is the current flowing in the channel (below and above V T )?

Depletion layer with fixedionised acceptor ions

Inversionlayer with electrons - - - - - - - - -

n+ n+



Diffusion drain current

When V G < V T , electron concentrationat the interface is less than theconcentration of fixed acceptor ions indepletion region

The ions control surface potential and

remain constant resulting in zero fieldin x - direction

X

Z

The current in this case (i.e. low V G ) is simply due to the diffusion of electrons caused bythe difference in concentration between the contacts

The current density is thus given as:

D is the diffusion coefficient of the electrons, dn / dx is the change of electron concentrationwith distance and q is the electronic charge (1.6 x 10 -19 C)

V T > V G > 0

V D > 0V S = 0

L

W

acceptor ionsn+ n+



Drift drain currentWhen V

G > V

T , electron concentration

at the interface is increases

The transport mechanism for electronsbetween the contacts changes to drift

The channel obeys the ‘gradual

approximation’ i.e. E x reduces along thechannel as the voltage drops thechannel and also the field in the z-direction is greater than in x-direction

X

Z

The charge induced per unit area in the channel is given as:

C ox is the oxide capacitance per unit area and ( V G - V x) is potential across the oxide at point x

-ve sign due to opposite chargefrom the gate

The charge is also given as:

or

V G > V T

V D > 0V S = 0

L

W

- - - - - - - - -e I d

x dzn+ n+



Drift drain currentThe current density flowing through the channel in x -direction is :

Where n is the number of carriers in the channel, E x is field in x- direction, W is thechannel width, d z is thickness of the channel layer and µ is the mobility of the electrons

or

Rearranging the equation and integrating both sides,

Then,

orAlso,



Drift drain current

Rearranging the equation and integrating both sides,

Threshold voltage V T is

introduced due to workfunction difference, oxideand interface charges

Current in linear (triode) region is thus

The drain current increases linearly with drain voltage (for a given gate voltage) until a‘pinch -off’ point is reached when the current begins to saturate

Where V T is the threshold or turn-on voltage is the voltage required on the gate foronset of conduction and β is the device constant given as:



Pinch-off effectPinch off occurs when the potential inthe drain-source (in the channel) isgreater than the gate voltage resultingin a reverse in the field in the dielectrici.e. when V D = V G – V T

There are no inversion charge under

the gate, close to the drain contact

Any further increase in drain voltage(i.e. V D > V G – V T ) increase thepotential drop across the reverseddiode and hence causes the channel to‘shift’ further towards the source side

In this saturation region, the draincurrent is simply given as:

V G

> V T

V S = 0

L

V D = V G - V T

n+ n+

V G > V T

V S = 0

L *

V D >V G - V T

shift in the pinch-off point

n+ n+

E X

E Z



Typical Output characteristics of the transistor

The characteristics shows the variation of drain current with drain voltage, for differentgate voltages

The drain current increases with increase in gate voltage due to increase in electronconcentration in the channel

pinch-off point

V D = V G - V T

Increase in V G



Typical Transfer characteristics of the transistor

The characteristics shows the variation drain current with gate voltage for a given drainvoltage

-2 0 2 4 60

10

20

30

40

at constant V D

D r a

i n c u r r e n

t

[ a r b

i t r a

r y u n

i t ]

Gate to source voltage [V]

VT



Sub-threshold plot

-2 0 2 4 610 -3

10 -2

10 -1

10 0

101

10 2

at constant V D

D r a

i n c u r r e n

t

[ a r b

i t r a r y u

n i t ]

Gate to source voltage [V]

off current

on current when V D = VG -VT

Sub-threshold slope

VT

diffusion

drift

The subthreshold plot is the log I D against V G for a given V D . The plot shows the smallsubthreshold current flowing when V G < V T . The slope is important in the design ofdynamic circuits and useful in low power operations



Performance of MOSFET and parameter extraction

Drain Conductance (Output conductance)is obtained in the linear or ohmic regionand is given as:

at constant V G

For small values of V D in linear region,

negligiblysmall

Thus,

By plotting g D against V G or gm against V G , the field effect mobility and turn-on voltage can

be estimated

Transconductance is related to the speedof the device and obtained in thesaturation region and

at constant V D

In the saturation region,

Thus,

2

2

T G D

V V I



Transistor symbols

Enhancement mode MOSFETs: No channel is present at V G

= 0. The channel is formedwith applied gate voltage

n-channel p-channel

Depletion mode MOSFETs: A channel is present even at no gate bias (due to thepresence of a doped layer). The gate voltage controls the conductivity of the channel asin enhancement mode (e.g. ‘deplete’ a channel)

n-channel p-channel

lecture 4 - mos transistor

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