Short Channel EffectsShort Channel Effects

in MOSFETsin MOSFETsFabio D’AgostinoFabio D’Agostino

Daniele QuerciaDaniele Quercia

Fall, 2000Fall, 2000

Presentation Presentation Outline

•Short-Channel Devices

•Short-Channel Effects (SCE)

•The modification of the threshold voltage due to SCE

•A numerical example

•Simulation: SCE impacts on the threshold voltage

•Simualtion: limiting effect of the saturation velocity

•Conclusion

DefinitionDefinition

•What is a “short-channel device”?

•A MOSFET is considered to be short when the channel length is the same order of magnitude as the depletion-layer widths (xdD, xdS)

Short Channel EffectsShort Channel Effects

•Five different physical phenonomena have to be considered in short-channel devices:

•Drain induced barrier lowering and Punchthrough

•Surface scattering

•Velocity saturation

•Impact ionization

•Hot electrons

Drain-induced barrier lowering Drain-induced barrier lowering (DIBL)(DIBL)

•The electrons (carriers) in the channel face a potential barrier that blocks their flows

•The potential barrier, in small-geometry MOSFETs, is controlled by a two-dimensional electric field vector (in other words by both VGS and VDS)

• If the drain voltage is increased the potential barrier in the channel decreases, leading to

Drain-Induced Barrier Lowering (DIBL)

Drain-induced barrier lowering (DIBL) and Drain-induced barrier lowering (DIBL) and PunchthroughPunchthrough•Under DIBL condiction electrons can flow between

the source and drain even if VGS < VT

•The channel current that flows in this case is called subthreshold current

Punchthrough

•The DIBL phenomenon can be accompanied by the so-called punchthrough, that occurs when the depletion region surrounding the drain extends to the source

•Punchthrough minimized with thinner oxide, larger substrate doping (and longer channel!)

Surface scatteringSurface scattering

•For small-geometry MOSFETs, the electrons mobility in the channel depends on a two-dimensional electric field (x, y)

Surface scatteringSurface scattering

•The surface scattering occurs when electrons are accelerated toward the surface by the vertical component of the electric field x

•The collision of the electrons causes a reduction in the mobility

•Electrons moves with great difficult parallel to the interface

•The average surface mobility is about half as much as that of the bulk mobility

Velocity saturationVelocity saturation

•For low y the electron drift velocity vde in the channel varies linearly with the electric field intensity

•As y increases above 104 V/cm the drift velocity tends to approach a saturation value of vde(sat)=107 cm/s around y =105 V/cm

•The velocity saturation reduces the transconductance of short-channel devices in the saturation condiction, as the following formula shows:

gm = W Cox vde(sat)

Impact ionizationImpact ionization

•The presence of high longitudinal fields can accelerate electrons that may be able of ionizing Si atoms by impacting against them

•Normally most of the e- are attracted by the drain, so it is plausible a higher concentration of holes near the source

• If the holes concentration on the source is able to creates a voltage drop on the source-substrate n-p junction of about 0.6V then

•e- may be injected from source to substrate•e- travel toward the drain, increasing their energy and create new e-h pairs•e- may escape the drain fields and afect other devices

Hot electronsHot electrons

•The channel Hot Electrons effect is caused by electrons flowing in the channel for large VDS

•e- arriving at the Si-SiO2 interface with enough kinetic energy to surmount the surface potential barrier are injected into the oxide

•This may degrade permanently the C-V characteristics of a MOSFETs

The modification of the The modification of the threshold voltagethreshold voltage

due to short-channel due to short-channel effectseffects

Modification of VModification of VTHTH due to SCE due to SCE

Equation giving the threshold voltage at zero-bias

ox

IFASi

oxFFBT C

qDNq

CVV

22

120

accurate for large MOS transistors

not accurate for short-channel MOS transistorsthe amount of bulk charge is overestimated

Modification of VModification of VTHTH due to SCE due to SCE

Large MOS transistor: the deplition is only due to the electric field created by the gate voltage.

Small-geometry transistor: in addition to the previous contribution, the deplition charge near n+ regions is induced by p-n junctions.

Modification of VModification of VTHTH due to SCE due to SCE

Modification of VModification of VTHTH due to SCE due to SCE

The bulk depletion charge is smaller than expected

the threshold voltage expression must be modified to account for this reduction:

00)(0 TTchannelshortT VVV

VT0: threshold

voltage shift

VT0: zero-bias threshold voltage

Modification of VModification of VTHTH due to SCE due to SCE

We find the following relationship:

222DjdmdDj Lxxxx

Modification of VModification of VTHTH due to SCE due to SCE

… and solving for LD we obtain :

where

1

212222

j

dDjdDjdDdmjjD x

xxxxxxxxL

0

2

DS

A

SidD V

qNx

Similarly, the length LS can also be found as follows:

where 0

2

A

SidS qN

x

1

21

j

dSjS x

xxL

Modification of VModification of VTHTH due to SCE due to SCE

The amount of the threshold voltage reduction

VT0 due to short-channel effects can be found as:

1

211

21

222

10

j

dS

j

dDjFASi

oxT x

x

x

x

L

xNq

CV

Modification of VModification of VTHTH due to SCE due to SCE

We consider an n-channel MOS process with the following parameters:

.substrate doping density NA=1016 cm-3,

.polysilicon gate doping density ND (gate) = 2 1020 cm-3,

.gate oxide tickness tox= 50 nm,

.oxide-interface fixed charge density Nox=4*1010cm-2 ,

.source and drain diffusion doping density ND= 1017 cm-3.

In addition, we assume that the channel region is implanted with p-type impurities (impurity concentration NI= 2 1011 cm-2

) Moreover, the junction depth of the source and drain diffusion regions is xj=1.0 m.

Numerical example

Modification of VModification of VTHTH due to SCE due to SCE

We obtain …

VT0= 0.855V - VT0 ;

where ___________

VT0= ( 0.343/ L[m] ) * (-0.724 + ( 1 + 2 xdD) _________________xDd = 0.13 (0.76 + VDS)

Modification of VModification of VTHTH due to SCE due to SCE

… and plotting the variation of the threshold voltage with the channel lenght

0 1 2 3 4 5 60.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

L: Channel length [um]

Vth

: T

hres

hold

vol

tage

[V

]

(Vth vs. L) @ Vds=1V [-----] Vds=3V [_._._] Vds=5V [_]

Simulation: impact of SCE on the threshold Simulation: impact of SCE on the threshold voltagevoltage

•We simulate four nMOSFETs in parallel, with different channel lengths and widths

•All the transistors have the same parameters; LEVEL 2 of Pspice is used

•For each transistor we generate the ID-VGS characteristic at VDS = 0.1V

•The plots show how devices with smaller geometry have higher drain currents at the same gate-to-source voltage (i.e., smaller threshold voltages)

Simulation: impact of SCE on the threshold Simulation: impact of SCE on the threshold voltagevoltage

Simulation: the limiting effects of the saturation Simulation: the limiting effects of the saturation velocityvelocity

•We simulate two nMOSFETs in parallel, with the same channel length and width

•One transistor has a limited saturation velocity of vde(sat) = 2·106 cm/s; LEVEL 2 of Pspice is used

•For each transistor we generate the ID-VDS characteristic at VGS = 5V

•The plots show the reduction of the transcoductance in the saturation mode

Simulation: the limiting effects of the saturation Simulation: the limiting effects of the saturation velocityvelocity

ConclusionConclusion

•SCE are governed by complex physical phenomena that can be mainly related to the

Influence of both vertical and horizontal electric field components on the flow

of the electrons in the channel

•Usually SCE interacts the one with the other

•SCE should be carefully considered in order to evaluate their impact on the general behaviour of the device, both for short-term and long-term