Device Characterization

ECE/ChE 4752: Microelectronics ECE/ChE 4752: Microelectronics Processing LaboratoryProcessing Laboratory

Gary S. May

April 1, 2004

Outline

NMOS Device PhysicsNMOS Device Physics PMOS Device PhysicsPMOS Device Physics CMOS InverterCMOS Inverter

MOSFET MOSFET = “Metal-Oxide-Semiconductor

Field-Effect Transistor”

Terminals: G = gate D = drain S = source B = body (substrate)

D

G B

S

IDn

VGS

VDS+

-

VBS

+

-

+

-

n-channel device

MOSFET Key Quantities Currents:

IG = 0 (due to insulating oxide layer) ID

IS

=> since IG = 0, ID = IS (Kirchhoff’s Current Law) Voltages:

VG

VD

VS = 0 (usually) VB = 0 (usually)

Most important quantities: ID, VGS, VDS

MOSFET Cross-Section

S VG

oxide

VD > 0

n+ n+ID

ID

L

p-type Si

cross-sectional view (not to scale)

G

D S

top view (not to scale)

Biasing1) Source and substrate grounded (zero voltage)

2) (+) voltage on the gate Attracts e-s to Si/SiO2 interface

When threshold voltage (VGS = VTn) is reached, an inversion layer is formed

3) (+) voltage on the drain e-s in the channel drift from source to drain current flows from drain to source

I-V Characteristics IIDnDn vs. V vs. VGSGS::

VVTnTn = “threshold voltage” = “threshold voltage” Voltage where Si/SiOVoltage where Si/SiO22 interface becomes strongly interface becomes strongly

inverted with electronsinverted with electrons Voltage were NMOS transistor “turns on”Voltage were NMOS transistor “turns on”

VGSVTn

IDn

I-V Characteristics (cont.) IIDnDn vs. V vs. VDSDS::

VGS increasing

VGS = 0V

VDS

IDn (2)

(1)

Linear Region Labeled “(1)” on previous plotLabeled “(1)” on previous plot IIDnDn = f(V = f(VGSGS, V, VDSDS) and V) and VDSDS < V < VGSGS – V – VTnTn, V, VGSGS ≥ V≥ VTnTn

Equation:Equation:

where: n = electron mobility in the channel, Cox = ox/tox, tox = oxide thickness, ox = oxide

permittivity (3.90 for SiO2)

2)(

2DS

DSTnGSoxn

Dn

VVVV

L

CWI

Saturation Region

Labeled “(2)” on the previous plotLabeled “(2)” on the previous plot IIDnsatDnsat = f(V = f(VGSGS) and V) and VDSDS ≥≥ V VGSGS – V – VTnTn, V, VGSGS ≥ V≥ VTnTn

Equation:Equation:

2

2 TnGSoxn

Dnsat VVL

CWI

Transconductance

In the saturation region:In the saturation region:

where: “Q” represents the quiescent operating point (i.e., fixed DC values of VGS, VDS)

DnoxnTnGSoxn

QGS

Dmn IC

L

WVVC

L

W

v

ig

2)(

Outline

NMOS Device PhysicsNMOS Device Physics PMOS Device PhysicsPMOS Device Physics CMOS InverterCMOS Inverter

Circuit Symbol

S

G B

D

-IDp

VSD

+

-

VSG

+

-

VSB

+

-

p-channel device

Cross-Section

Appropriate I-V equations found by:

1) reversing the direction of ID

2) reversing the polarity of all bias voltages (VBS => VSB, VGS => VSG, VDS => VSD)

S VSG

oxide

VSD > 0

p+ p+IDp

ID

L

n-type Si

Biasing1) Source and substrate grounded (zero voltage)

2) (-) voltage on the gate Attracts h+s to Si/SiO2 interface

When threshold voltage (VSG = -VTp) is reached, an inversion layer is formed

3) (-) voltage on the drain h+s in the channel drift from source to drain current flows from source to drain

Currents

Linear: VLinear: VSDSD ≤≤ V VSGSG + V + VTpTp, V, VSGSG ≥ -V≥ -VTpTp

2)(

2SD

SDTpSGoxp

Dp

VVVV

L

CWI

Saturation: VVSDSD ≥ V ≥ VSGSG + V + VTpTp, V, VSGSG ≥ -V ≥ -VTpTp

22 TpSG

oxpDpsat VV

L

CWI

Transconductance

In the saturation region:In the saturation region:

)(2)( DpoxpTpSGoxp

QSG

Dmp IC

L

WVVC

L

W

v

ig

Outline

NMOS Device PhysicsNMOS Device Physics PMOS Device PhysicsPMOS Device Physics CMOS InverterCMOS Inverter

Inverter Logic

Logic symbol:

Function:

Truth table: AA YY

00 11

11 00

A Y

AY

Ideal Voltage Transfer Characteristic

V+ = supply voltageVM = V+/2 = switching point of inverter (where input

voltage = output voltage)

Actual Transfer Characteristic

Voltage Definitions VIL = input voltage where slope of transfer characteristic is

-1 VIH = larger input voltage where slope of transfer

characteristic is -1 VOH = output voltage at input voltage of VIL

VOL = output voltage at input voltage of VIH

VM = voltage where output voltage equals input voltage VMAX = output voltage when input voltage is zero (usually

VMAX = V+) VMIN = output voltage when input voltage is V+ (usually

VMIN ~ 0)

Voltage Definitions (cont.)

VOH = minimum output voltage for valid logic 1

VOL = maximum output voltage for valid logic 0

VIH = minimum input voltage for valid logic 0

VIL = maximum input voltage for valid logic 1

Noise Margins Noise = unwanted variations in voltage which, if too

great, can cause logic errors Noise margin high (NMH): tolerable voltage range for

which we interpret the inverter output as a logic 1

NMH = VOH – VIH

Noise margin low (NML): tolerable voltage range for which we interpret the inverter output as a logic 0

NML = VIL - VOL

Switch Representation

Switching Dynamics

Input high: turn on bottom switch and discharge capacitive loadPMOS offNMOS on (linear)

Input low: turn on the top switch and charge capacitive loadPMOS on (linear)NMOS off

VTC: Another Look

(1) Input voltage = 0 V, output voltage = VDD

(2) NMOS saturated, PMOS linear

(3) Both transistors saturated

(4) NMOS linear, PMOS saturated

(5) Input voltage = VDD, output voltage = 0 V

Approximate VTC

VOH = VMAX; VOL = VMIN

VM is input voltage where VOUT =VIN = VM

Currents

NMOS current at VIN = VM is:

PMOS current at VIN = VM is:

2

2

1TnMoxn

nDn VVC

L

WI

22

1TpMDDoxp

pDp VVVC

L

WI

Deriving VM

Define: Define:

and and

Setting ISetting IDnDn = -I = -IDpDp gives: gives:

oxnn

n CL

Wk

oxpp

p CL

Wk

n

p

TpDDn

pTn

M

k

k

VVk

kV

V

1

)(

Computing Noise Margins

To compute noise margins, the next step is to calculate VIL and VIH

Do so by determining the slope of the transfer characteristic at VIN = VM (i.e., voltage gain)

Then: Project a line to intersect at VOUT = VMIN = 0 V

to find VIH

Project a line to intersect at VOUT = VMAX = VDD to find VIL

Voltage Gain Voltage gain can be shown to be:

where: ron and rop are output resistances of the NMOS and PMOS transistors, respectively

In general: and

We can find ro by inverting the slope of the ID vs. VDS characteristic

)||)(( oponmpmnin

outv rrgg

v

vA

oo g

r1

QDS

Do v

ig

Noise Margins We can find VIL and VIH using the slope (Av) of

the VTC:

Noise margins:

v

MDDMIL A

VVVV

)(

vMMIH AVVV /

vMDDMOLILL AVVVVVNM /)(

vMMDDIHOHH AVVVVVNM /