4.1 I-V characteristics of MOSFET

Current in MOSFET

Physical design

2

Physical parameters

The length of MOSFET. Itis typically a feature size of

the technology.

The width of n-chMOSFET

The width of the power source wiring. It depends on

the power consumption.

The width of p-chMOSFET

The performance of the logic circuit depends on the physical parameters of MOSFET and interconnects.

4.1.1 Summary of I-V characteristics

4

Definition of voltage and current in MOSFET

n-ch MOSFET p-ch MOSFET

Gate Gate

Drain Drain

Source Source

Body Body

Current Idsn Current Idsp

Vgsn Vgsp

VdgpVdgn

Vsbn Vsbp

VdspVdsn

Note: A p-ch MOSFET operates with negative voltages and current.

Measurement circuits of I-V characteristics

5

Idsn-Vdsn characteristicIdsn-Vgsn characteristic

Constant

ConstantVariable Variable

VariableVariable

When Vsbn = 0, the variables are Vgsn, Vdsn, and Idsn.

Nore: The values of Vgsn, Vdsn, Idsn are negative for p-ch MOSFET.

6

Regions of I-V characteristicsVdsn

Idsn

VgsnVtn0

Idsn

Vdsn

Vgsn

Vdsn = Vgsn –Vtn0 = Vov

Saturation region

Linear region(Triode region)

Sub-threshold

Sub-threshold region

Threshold voltage(閾値電圧)is controlled by the manufacture.

Boundary of the regions

7

Approximate expression of I-Vcharacteristics

VdsnIdsn

VgsnVtn0

Idsn

Vdsn

Vgsn

Vdsn = Vgsn –Vtn0 = Vov

Saturation region

Linear region

Sub-threshold region

Quadratic Linear QuadraticConstant

Idsn ≒ 0

Exponential(I ≒ 0)

Saturation region

Linear region

8

Threshold voltage

MOS interface

The gate voltage is divided into Vox in SiO2 and s in Si. The channel is generated when the gate voltage exceeds the threshold voltage.

p-type Si

Depletion layer

A depletion layer is generated near MOS interface.

(Animation)

SiO2

Metal (poly-Si)

Si

○ Acceptor ion, h+ Hole, - Free electron

Charge

Free electron (Inversion layer)

Acceptor ion (Depletion layer)

Gate

4.1.2 Saturation characteristic

9

Pinch-off

10

p

n

GateDrainSource

Body

nVgsn

＋

n-ch MOSFET

Vdsn = Vgsn – Vtn0 = Pinch-off voltage

Vtn0 is applied between the gate and the drain edge of the channel.

When Vdsn = Vgsn - Vtn0, the channel disappears at the drain edge.

11

Saturation of the current

p

n nEl

ectro

n po

tent

ial

Vdsn > Vgsn – Vtn0

SG

D

B

Vgsn > Vtn0

Vdsn < Vgsn – Vtn0Vdsn = Vgsn – Vtn0Vdsn > Vgsn – Vtn0

The resistance of the pinch-off point is higher than the channel.

The flow rate of the water does not depend on the waterfall.

4.1.3 Mathematical expression of I-V characteristics

12

13

Shape and size of MOSFETpoly-Si (G)

S Dcontact contact

n-activep-well

W

LL: Gate length (ゲート長）W: Gate width （ゲート幅）Leff: Effective channel lengthWeff: Effective channel widthxj: Junction depthtox: Gate oxide thickness （ゲート酸化膜厚）toxf: Field oxide thicknesstm: Poly-Si thickness

contact

substratep-well

n+n+

xj

toxf

Leff

Shallow Trench Isolation

GD

SB

p+

D

STISTI

toxtm

poly

-Si

p-w

ell

subs

trate

Weff

G

STI

STI

p-active

B

Note: p+ and n+ mean the highly-doped semiconductors.

14

Parameters of MOSFETPara-meter

Description Typical values in 0.5um technology

Responsibility

L Gate length 0.5um DesignerW Gate width > 3um DesignerLeff Effective gate length Leff < L ManufacturerWeff Effective gate width Weff < W Manufacturerxj Junction depth 0.2um Manufacturertox Thickness of gate oxide 10nm (100Å) Manufacturertoxf Thickness of field oxide 1um Manufacturertm Thickness of gate 0.5um Manufacturer

Note: Strictly speaking, the electrical characteristics of MOSFET depends on Leff, Weff, and tOX. Leff and Weff can be approximated by L and W, respectively.

15

Ids-Vds characteristic of MOSFET

Linear region Saturation region

Sub-threshold region (Exponential)

0tngsndsn VVV 0tngsndsn VVV

0tngsn VV

0tngsndsn VVV

Vdsn

I dsn

Linear region(Quadratic)

Saturation region(Constant)

16

Ids-Vgs characteristic of MOSFET

Linear region(Linear)

Saturationregion(Quadratic)

Sub-thresholdregion（Exponential）

Vgsn

I dsn

Vtn0

17

Mathematical expression of linear region

}21){(

}21){(

20

20

dsndsntngsnn

dsndsntngsnOnn

ndsn

VVVV

VVVVCLWI

Linear region (Gradual Channel Approximation*)

Linear function of Vgsn Quadratic function of Vdsn

* See appendix for more information.

(1)

𝜇 :𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦 𝑚 /𝑉𝑠𝐶 :𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑎 𝑔𝑎𝑡𝑒 𝑜𝑥𝑖𝑑𝑒 𝐹/𝑚2

𝑉 :𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 𝑎𝑡 𝑉 0𝑉

18

Boundary of the regions

0tngsndsn VVV

0}){( 0 dsntngsnndsn

dsn VVVdVdI

0tngsndsn VVV

Peak of the curve in linear region

Vdsn

I dsn

0tngsn VV

Linear Saturation

(1)

Boundary of linear region and saturation region (Overdrive voltage)

0tngsndsn VVV

(2)

19

Mathematical expression of saturation region

20

2000

)(2

})(21)(){(

tngsnn

tngsntngsntngsnndsn

VV

VVVVVVI

Saturation region (Gradual Channel Approximation)

Quadratic function of Vgsn

Constant for Vdsn

Overdrive voltage

(3)

𝑉 𝑉 𝑉 𝑉

4.1.4 Improved model of MOSFET

20

21

Channel length modulation0V Vgsn Vdsn

0tndsngsn VVV

Gate

DrainSourcep

n n

ΔL

0tndsngsn VVV Saturation region

Channel length = Leff – ΔL (ΔL is proportional to Vdsn0.5 )

The channel length is decreased with increasing Vdsn and the Idsn is gradually increased with increasing Vdsn.

Channel length modulation parameter

Eq. (3)Vdsn

I dsn

Eq. (3)Eq. (4)

(4)

Leff

𝐼𝛽2 𝑉 𝑉 1 𝜆 𝑉 𝑉

22

Body effect 1

MOSFET typically operates under the condition that the body potential VB = GND potential, but the substrate voltage Vbsn isnot equal to zero, when the source potential VS ≠ GND potential.

)2(212 0 bsnfpArO

fpFBtn VNqCVV

Substrate voltageImpurity concentration in channel region

When Vbsn< 0, The threshold voltage Vth0 is increased. (See next slide.)

gsn

dsn

bsn

(5)

VB

VS

23

Body effect 2

Vgsn

I dsn

Vbsn < 0

24

Short channel MOSFET

1. Short channel effect– A threshold voltages Vtn0 and |Vtp0| are decreased with decreasing a

gate length L.

2. Velocity saturation of carrier– In a long channel MOSFET, a drift velocity of a carrier is

proportional to an electric field. On the other hand, a drift velocity of a carrier is constant in a high electric field of a short channel MOSFET.

– As the result, Ids-Vgs characteristic in a saturation region is not expressed by a quadratic function, but a linear function.

Short channel MOSFET (L < 0.3μm)

A device model incorporated in circuit simulators takes the short channel effects into account.

4.1.5 Summary of MOSFET model

25

26

Summary of n-ch MOSFET modelRegion Model equation

Linear region

Saturation region

Onn

nn

dsndsntngsnndsn

CLW

VVVVI

}21){( 20

0tngsndsn VVV

20

20

)(2

)1()(2

tngsnn

dsntngsnn

dsn

VV

VVVI

0tngsndsn VVV

Ln and Wn are determined by the circuit designer.CO is controlled by the semiconductor manufacturer.

OXSiOO t

C 120

Capacitance of a gate oxide(F/m2)

n：Electron mobility (m2/Vs）An electron mobility is a material constant.

27

Summary of p-ch MOSFET modelRegion Model equation

Linear region

Saturation region

Opp

pp

dspdsptpgsppdsp

CLW

VVVVI

}21){( 20

|||| 0tpgspdsp VVV

20

20

)(2

)1()(2

tpgspp

dsptpgspp

dsp

VV

VVVI

|||| 0tpgspdsp VVV

Note: Vgsp, Vdsp, Idsp < 0

OXSiOO t

C 120

Capacitance of a gate oxide(F/m2)

n：Electron mobility (m2/Vs）An electron mobility is a material constant.

Ln and Wn are determined by the circuit designer.CO is controlled by the semiconductor manufacturer.

p-ch and n-ch MOSFET

28

n-chIds

VgsVtn0

Ids

Vds

Ids: A current flowing from a drain to a source is positive.

Vdsn =Vgsn –Vtn0

Vtp0

p-chVdsp =Vgsp –Vtp0

n-ch

p-ch

The polarity of the voltage and the current of a p-ch MOSFET and a n-ch MOSFET are opposite each other.

Reference potential of MOSFET

29

p-ch MOSFET

n-ch MOSFET

Reference level of p-ch MOSFET

Reference level of n-ch MOSFET

Vgsp < 0

Vgsn > 0

Vdsp < 0

Vdsn > 0

30

Type of MOSFET

FBBBFBBOX

BASitn VVC

qNV

222

22 00

n-chIds

Vgs

Vtn0> 0

Vtp0< 0

p-ch

Vtn0< 0

Vtp0> 0

The threshold voltage is controlled by VFB (Flat-band voltage) and NA(Acceptor concentration).

n-chVtn0 > 0 Enhancement modeVtn0 < 0 Depletion mode

p-chVtp0 > 0 Depletion modeVtp0 < 0 Enhancement mode

The enhancement mode MOSFET isused both of logic and analog circuits.