MOSFET

MOSFET Operation

97.398*, Physical Electronics, Lecture 21David J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 2

Lecture Outline

 Last lecture examined the MOSFET structure and required

processing steps

 Now move on to basic MOSFET operation, some of which

may be familiar

 First consider drift, the movement of carriers due to an

electric field – this is the basic conduction mechanism in

the MOSFET

 Then review basic regions of operation and charge

mechanisms in MOSFET operationDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 3

Drift

 The movement of charged particles under the influence of

an electric field is termed drift

 The current density due to conduction by drift can be

written in terms of the electron and hole velocities vn and

vp (cm/sec) as

 This relationship is general in that it merely accounts for

particles passing a certain point with a given velocity

J qnv qpv = +n pDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 4

Mobility and Velocity Saturation

 At low values of electric field

E, the carrier velocity is

proportional to E - the

proportionality constant is the

mobility µ

 At low fields, the current

density can therefore be written

 At high E, scattering limits the

velocity to a maximum value

and the relationship above no

longer holds - this is termed

velocity saturation

! !

J qn qp n

v

p

n v p

= µ E+ E µDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 5

Factors Influencing Mobility

 The value of mobility (velocity per unit electric field) is

influenced by several factors

– The mechanisms of conduction through the valence and

conduction bands are different, and so the mobilities associated

with electrons and holes are different. The value for electrons is

more than twice that for holes at low values of doping

– As the density of dopants increases, more scattering occurs during

conduction - mobility therefore decreases as doping increases

– At low temperatures, electrons and holes gain more energy than

the lattice with increasing T, therefore mobility increases. At high

temperatures, lattice scattering dominates, and thus mobility falls

– Conduction through bulk material (diodes, BJTs) experiences less

scattering than conduction along a surface (MOSFET), hence bulk

mobility is higher than surface mobility (see Table 21.1)David J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 6

Resistivity and Conductivity

 The expression for J in terms of µ and E can be written as

 The first term is the conductivity σ, in (Ωcm)-1, and its

inverse is the resistivity ρ, already used in the calculation

of series resistance in the diode structure

J qn qp = +n p ( ) µ µ E

σ

ρ

=≡ + µ µ

1

qn qp n pDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 7

MOS Structure in Depletion

 A +ve VGB applied to the gate of a

MOS structure whose substrate is

grounded produces E penetrating

into the substrate

 For a p-type substrate, E repels

majority holes from the surface,

creating a depletion region

 Some minority electrons are

attracted to the surface, but at low

values of VGB their numbers are not

sufficient to cause much effect

 Charge balance is primarily +ve

holes on gate, -ve ionized acceptors

 This is termed depletion operationDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 8

MOS Structure in Inversion

 At large VGB, a dense inversion

layer of electrons forms under

the surface

 Further increases in VGB only

change the density of the

inversion layer

 The potential at which the

inversion layer dominates the

substrate behaviour is the

threshold voltage VT

 This inversion layer will form

the conductive channel between

the source and drain of the

MOSFETDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 9

Electric Fields in the MOSFET

 Two distinct electric field distributions exist in the MOSFET structure

– The transverse field is caused by the potential difference between the

conductive gate and the substrate. This field is supports the substrate

depletion region and inversion layer

– The lateral field arises due to a non-zero source to drain potential, and is

(in the simple model) the main mechanism for current flow in the

MOSFETDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 10

Qualitative MOSFET Operation

 Assume an n-channel MOSFET, i.e. n+ source and drain

regions in a uniformly doped p-type substrate

 Source and substrate are grounded

 Results discussed here apply to p-channel (n-type

substrate) devices with reversal of polaritiesDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 11

n-Channel MOSFET With VGS < VT

 With VGS < VT, there is no inversion layer present under the surface

 At VDS = 0, the source and drain depletion regions are symmetrical

 A positive VDS reverse biases the drain substrate junction, hence the

depletion region around the drain widens, and since the drain is

adjacent to the gate edge, the depletion region widens in the channel

 No current flows even for VDS > 0, since there is no conductive channel

between the source and drain for VGS < VTDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 12

n-Channel MOSFET With VGS > VT , small VDS

 With VGS > VT, a conductive channel forms under the surface - a nonzero

transverse field is present

 ID is zero for VDS = 0 since no lateral field is present

 For VDS > 0, transverse E is present and current flows

 The increased reverse bias on the drain substrate junction in contact

with the inversion layer causes inversion layer density to decrease David J. Walkey  97.398*, Physical Electronics: MOSFET Operation (21) Page 13

n-Channel MOSFET With VGS > VT , large VDS

 The point at which the inversion layer density becomes very small

(essentially zero) at the drain end is termed pinch-off

    The value of VDS at pinchoff is denoted VDS,sat

   Past pinchoff , further increases in lateral electric field are absorbed by

the creation of a narrow high field region with low carrier density

(Jn=qnµnE, so if n is small E is large)David J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 14

MOSFET Regions of Operation  

    There are three regions of operation in the MOSFET

– When VGS < VT, no conductive channel is present and ID = 0, the

cutoff region

– If VGS < VT and VDS < VDS,sat, the device is in the triode region of

operation. Increasing VDS increases the lateral field in the channel,

and hence the current. Increasing VGS increases the transverse field

and hence the inversion layer density, which also increases the

current

– If VGS < VT and VDS > VDS,sat, the device is in the saturation region

of operation. Since the drain end channel density has become

small, the current is much less dependent on VDS , but is still

dependent on VGS, since increased VGS still increases the inversion

layer densityDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 15

MOSFET ID-VDS Characteristic

    For VGS < VT , ID = 0

    As VDS increases at a fixed VGS ,

ID increases in the triode region

due to the increased lateral

field, but at a decreasing rate

since the inversion layer density

is decreasing

     Once pinchoff is reached,

further VDS increases only

increase ID due to the formation

of the high field region

     The device starts in triode, and

moves into saturation at higher

VDSDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 16

MOSFET ID-VGS Characteristic

     As ID is increased at fixed VDS,

no current flows until the

inversion layer is established

     For VGS slightly above

threshold, the device is in

saturation since there is little

inversion layer density (the

drain end is pinched off) 

    As VGS increases, a point is

reached where the drain end is

no longer pinched off, and the

device is in the triode region

         A larger VDS value postpones

the point of transition to triodeDavid J. Walkey 97.398*, Physical Electronics: MOSFET Operation (21) Page 17

Lecture Summary

       Examined drift, the movement of carriers under the

influence of an electric field

       Mobility characterizes the ease with which carriers can

move by drift (velocity per unit electric field), and is

influenced by dopant density, temperature, surface vs bulk

conduction and the type of carrier

       Mobility is the proportionality constant between velocity

and electric field for low field magnitudes - for high fields,

carrier velocity is limited to a maximum value, referred to

as velocity saturation