MOSFET Basics - people.Virginia.EDUpeople.virginia.edu/~ag7rq/663/Fall10/lec17… · PPT file ·...

transcript

ECE 663

MOSFET I-Vs

Substrate

Channel Drain

InsulatorGate

Operation of a transistorVSG > 0 n type operation

Positive gate bias attracts electrons into channelChannel now becomes more conductive

More electrons

Source

Some important equations in the inversion regime (Depth direction)

VT = ms + 2B + ox

Wdm = [2S(2B)/qNA]

Qinv = -Cox(VG - VT)

ox = Qs/Cox

Qs = qNAWdm

VT = ms + 2B + [4SBqNA]/Cox

Substrate

Channel Drain

InsulatorGate

Source

ECE 663

MOSFET Geometry

ECE 663

How to include y-dependent potential without doing the whole problem over?

ECE 663

Assume potential V(y) varies slowly along channel, so the x-dependent and y-dependent electrostats are independent (GRADUAL CHANNEL APPROXIMATION)

Ignore ∂Ex/∂y

Potential is separable inx and y

ECE 663

How to include y-dependent potentials?

S = 2B + V(y)

VG = S + [2SSqNA]/Cox

Need VG – V(y) > VT to invert channel at y (V increases threshold)

Since V(y) largest at drain end, that

end reverts from inversion todepletion first (Pinch off)

SATURATION [VDSAT = VG – VT]

j = qninvv = (Qinv/tinv)v

I = jA = jZtinv = ZQinvv

ECE 663

So current:

Qinv = -Cox[VG – VT - V(y)]

v = -effdV(y)/dy

ECE 663

So current:

I = eff ZCox[VG – VT - V(y)]dV(y)/dy

I = eff ZCox[(VG – VT )VD- VD2/2]/L

Continuity implies ∫Idy = IL

ECE 663

But this current behaves like a parabola !!

I = eff ZCox[(VG – VT )VD- VD2/2]/L

We have assumed inversion in our model (ie, always above pinch-off)

So we just extend the maximum current into saturation… Easy to check that above current is maximum for VDsat = VG - VT

Substituting, IDsat = (CoxeffZ/2L)(VG-VT)2

What’s Pinch off?

Now add in the drain voltage to drive a current. Initially you get an increasing current with increasing drain bias

When you reach VDsat = VG – VT, inversion is disabled at the drain end (pinch-off), but the source end is still inverted The charges still flow, just that you can’t draw more current with higher drain bias, and the current saturates

Square law theory of MOSFETs

I = eff ZCox[(VG – VT )VD- VD2/2]/L, VD < VG - VT

I = eff ZCox(VG – VT )2/2L, VD > VG - VT

J = qnvn ~ Cox(VG – VT )v ~ effVD /L

ECE 663

Ideal Characteristics of n-channel enhancement mode MOSFET

ECE 663

Drain current for REALLY small VD

DTGinD

DDTGinD

VVVCLZI

VVVVCLZI

Linear operation

Channel Conductance:

)( TGinVD

DD VVC

Transconductance:

ECE 663

In Saturation

• Channel Conductance:

• Transconductance:

2 TGinD VVCLZsatI

TGinVG

Dm VVC

ECE 663

Equivalent Circuit – Low Frequency AC

• Gate looks like open circuit• S-D output stage looks like current source with channel

conductance

ECE 663

• Input stage looks like capacitances gate-to-source(gate) and gate-to-drain(overlap)

• Output capacitances ignored -drain-to-source capacitance small

Equivalent Circuit – Higher Frequency AC

ECE 663

• Input circuit:

• Input capacitance is mainly gate capacitance

• Output circuit:

ggateggdgsin vfCjvCCji 2

gmout vgi

Equivalent Circuit – Higher Frequency AC

ECE 663

Maximum Frequency (not in saturation)

• Ci is capacitance per unit area and Cgate is total capacitance of the gate

• F=fmax when gain=1 (iout/iin=1)

ZLCC igate

ECE 663

Maximum Frequency (not in saturation)

2max 2 L

(Inverse transit time)

ECE 663

Switching Speed, Power Dissipation

ton = CoxZLVD/ION

Trade-off: If Cox too small, Cs and Cd take over and you losecontrol of the channel potential (e.g. saturation)

(DRAIN-INDUCED BARRIER LOWERING/DIBL)

If Cox increases, you want to make sure you don’t controlimmobile charges (parasitics) which do not contribute tocurrent.

ECE 663

Switching Speed, Power Dissipation

Pdyn = ½ CoxZLVD2f

Pst = IoffVD

ECE 663

NOT gate (inverter)

ECE 663

NOT gate (inverter)

Positive gate turns nMOS on

Vin = 1 Vout = 0

ECE 663

NOT gate (inverter)

Negative gate turns pMOS on

Vin = 0 Vout = 1

ECE 663

So what?

• If we can create a NOT gate we can create other gates (e.g. NAND, EXOR)

ECE 663

So what?

Ring Oscillator

ECE 663

So what?

• More importantly, since one is open and one is shut at steady state, no current except during turn-on/turn-off Low power dissipation

ECE 663

Getting the inverter output

ECE 663

TGinVG

Dm VVC

What’s the gain here?

ECE 663

Signal Restoration

ECE 663

BJT vs MOSFET

• RTL logic vs CMOS logic

• DC Input impedance of MOSFET (at gate end) is infinite Thus, current output can drive many inputs FANOUT

• CMOS static dissipation is low!! ~ IOFFVDD

• Normally BJTs have higher transconductance/current (faster!)

IC = (qni2Dn/WBND)exp(qVBE/kT) ID = CoxW(VG-VT) 2/L

gm = IC/VBE = IC/(kT/q) gm = ID/VG = ID/[(VG-VT)/2]

• Today’s MOSFET ID >> IC due to near ballistic operation

ECE 663

What if it isn’t ideal?• If work function differences and oxide charges are

present, threshold voltage is shifted just like for MOS capacitor:

• If the substrate is biased wrt the Source (VBS) the threshold voltage is also shifted

BAsBFBT

BSBAsBFBT C

ECE 663

Threshold Voltage Control

• Substrate Bias:

BSBAsBFBT C

BSTBSTT

ECE 663

Threshold Voltage Control-substrate bias

ECE 663

It also affects the I-VVG

The threshold voltage is increased due to the depletion regionthat grows at the drain end because the inversion layer shrinksthere and can’t screen it any more. (Wd > Wdm)

Qinv = -Cox[VG-VT(y)], I = -effZQinvdV(y)/dy

VT(y) = + √2sqNA/Cox = 2B + V(y)

ECE 663

It also affects the I-V

IL = ∫effZCox[VG – (2B+V) - √2sqNA(2B+V)/Cox]dV

I = (ZeffCox/L)[(VG–2B)VD –VD2/2

-2√2sqNA{(2B+VD)3/2-(2B)3/2}/3Cox]

ECE 663

We can approximately include this…

Include an additional charge term from the depletion layer capacitance controlling V(y)

Q = -Cox[VG-VT]+(Cox + Cd)V(y)

where Cd = s/Wdm

Q = -Cox[VG –VT - MV(y)], M = 1 + Cd/Cox

ID = (ZeffCox/L)[(VG-VT - MVD/2)VD]

ECE 663

Comparison between different models

Square Law Theory

Body Coefficient

Bulk Charge Theory

Still not good below threshold or above saturation

ECE 663

Mobility• Drain current model assumed constant mobility in

channel• Mobility of channel less than bulk – surface scattering• Mobility depends on gate voltage – carriers in inversion

channel are attracted to gate – increased surface scattering – reduced mobility

ECE 663

Mobility dependence on gate voltage

ECE 663

Sub-Threshold Behavior

• For gate voltage less than the threshold – weak inversion

• Diffusion is dominant current mechanism (not drift)

LLnonqAD

ynqADAJI nnDD

ECE 663

Sub-threshold

kTqkTqVkT

eeLenqADI //

We can approximate s with VG-VT below threshold since all voltage drops across depletion region

kTVVqkTqVkT

eeLenqADI //

•Sub-threshold current is exponential function of applied gate voltage•Sub-threshold current gets larger for smaller gates (L)

ECE 663

Subthreshold Characteristic

GD VIS

Subthreshold Swing

Tunneling transistor– Band filter like operation

J Appenzeller et al, PRL ‘04

Ghosh, Rakshit, Datta(Nanoletters, 2004)

(Sconf)min=2.3(kBT/e).(etox/m)

Hodgkin and Huxley, J. Physiol. 116, 449 (1952a)Subthreshold slope = (60/Z) mV/decade

Much of new research depends on reducing S !

• Increase ‘q’ by collective motion (e.g. relay) Ghosh, Rakshit, Datta, NL ‘03

• Effectively reduce N through interactions Salahuddin, Datta • Negative capacitance Salahuddin, Datta

• Non-thermionic switching (T-independent) Appenzeller et al, PRL

• Nonequilibrium switchingLi, Ghosh, Stan

• Impact IonizationPlummer

ECE 663

More complete model – sub-threshold to saturation

• Must include diffusion and drift currents• Still use gradual channel approximation• Yields sub-threshold and saturation behavior for long

channel MOSFETS• Exact Charge Model – numerical integration

ECE 663

Exact Charge Model (Pao-Sah)– Long Channel MOSFET

http://www.nsti.org/Nanotech2006/WCM2006/WCM2006-BJie.pdf

ECE 663

MOSFET Basics - people.Virginia.EDUpeople.virginia.edu/~ag7rq/663/Fall10/lec17… · PPT file ·...

Documents