Vth Definition

8/17/2019 Vth Definition

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SIiVIULATION OF SEiVIICONDUCTOR DEVICES AND PROCESSES Vol.

6

Edited

by H. Ryssel P.

Pichler September

1995

A M ethod for Extra cting th e Threshold Voltage

of M O SF E T s Based on Current Components

K. AOYAMA

NTT LSI Laboratories,

3-1, Morinosato Wakamiya, Atsugi-shi, Kanagawa Pref., 243-01 JAPAN

Abstract

A new method for extracting the threshold voltage of MOSFETs is presented.

The threshold voltage is the gate voltage at which the second difference of the

logarithm of the drain current takes a minimum value. The method is applied to

a 0.6-pm NMOSFET. The threshold voltage characteristics are compared with

ones measured with previous methods and it is shown that the proposed method

overcomes previous problems. The threshold voltage is extracted based on a

physical background verified with 2D device simulation and shows a transition

voltage at which drift and diffusion components in the drain current are equal.

1. Introduction

A serious problem is that threshold voltage definitions in measurements differ from

the one in compact MOSFET models. The threshold voltage in compact models is

defined as the gate voltage at which the surface potential 4 f the channel reaches

the double Fermi potential in the bulk 2d f. This definition is very popular but has the

disadvantages tha t the position where 4 2dj in the channel is not clear and it is

difficult to measure

4

in MOSFETs. On the other hand, threshold voltages in mea-

surements are extracted by the constant current CC) , the linear extrapolation LE)

and the transconductance change TC ) methods [ I], [2]. With

C C

the difficulties are

measuring the effective channel length and width and defining

a.

constant value of the

drain current. LE should be applied only in the low drain voltage region. In the high

drain voltage region, however, the square root of current extrapolation SRE) should

be applied. With extrapolation methods such as LE and SRE, th e continuity in all

operation voltages is lost. The threshold voltage characteristics with T C are strange

for drain voltage changes, as shown in Fig. 1. A threshold voltage definition th at

overcomes the above disadvantages is needed. This paper presents a new method for

extracting the threshold voltage: the second difference of the logarithm of the drain

current minimum SDLM).

2.

Method

The diffusion component and the drift component can be respectively approximated

by an exponential function and a polynomial expression, as shown in Fig. 2. The

first difference of the logarithm of the drain current almost stays constant when


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K. Aoyam a: Method for Extra cting the Threshold Voltage of MO SFET s

119

th e diffusion comp onent is domin ant and grad ually app ro acl~ es ero when th e drift

comp onent is dom inant, as shown in Fig. 3 (a) . Fig.

3

( b ) s.hows the second difference

takes a minim um value at th e unique transition voltage in an N M OS FE T. In this work,

this voltage is defined as the thresh old voltage. Th is threshold voltage is shown in

Fig. 1 for various drain voltages com pared to ones extrac ted w ith previous meth ods .

Th e characteristics are reasonable even for drain voltage changes.

3 Verification

With a view to certify that the dominant component in the drain current changes

from diffusion to drift at the threshold voltage extracted with the above method, the

rate of each comp onent was calculated by 2D device simulation. In the sim ulation , an

NM OSFET wi th L 1.Opm was used w ith Vd, 3.OV an d sb OV. As a result, the

min imu m value is calculated with this meth od a s shown in Fig.

4

like in measu rem ents

and the po tent ia l dis tr ibutions a t the interfaceof Si and SiOz obta ined are those shown

in Fig. 5. T he drift comp onent and diffusion conlponent [id s(d ij/)] re

where is th e electron mobility,

n

is th e electron density, is th e cond uction band

potent ia l ,

4

[, is the relative potential an d

[

is the electron q uasi-Fermi potential.

At each position at the interface, the rates of drift and diffusion compete with the

rates of (d$ /dx) and

[-d(

,)/dx]. Fig.

6

shows the distribu tion of the r ate of

current com ponents throu gh t he channel. T he average rate of th e drift compo nent in

th e channel region is

where x, and xd ar e the source edge an d th e drain edge and

L

is t h e channel length.

Fig.

7

shows the rate of the drift component in the channel increases as the gate

voltage increases. At

V

0.215V, drift equals diffusion. The refore , the threshold

voltage defined with this m ethod shows th e unique gate voltage th at is the trans ition

voltage in the dom inant com ponent in th e dra in current .

4.

Summary

A method for extracting the threshold voltage with the second difference of the loga-

rithm of the drain current was proposed and verified from the physical point of view

using 2D device sim ulation. Th e ex trac ted threshold voltage has the following fea-

tures: It is extrac ted from only th e drain current without both th e effective channel

leng th and w idth and has a physical meaning. It shows th e ga te voltage a t which

drift and diffusion in the drain current are equal each other. These features may be

useful for unifying the threshold voltage in compact models and in measurement.

References

[ I ] M.

J.

Deen and

Z. X.

Yan, A new meth od for measuring t h e threshold v oltage of

small-geometry M OS FET s from subthreshold conduct ion , Sol id-Sta te Electron-

ics, vol. 33, no. 5, pp. 503-511, 1990.

[2]

H. S.

Wong,

M. H.

White ,

T. J.

Krutsick and

R.

V. Bo oth , Mo deling of transco n-

ductance degradation and extraction of threshold voltage in thin oxide MOS-

FETs , Solid-State Electronics, vol. 30, no. 9, pp. 953-968, 1987.


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12

K.

Aoyama: A Method for Extracting the Threshold Voltage of

MOSFETs

NMOSF T

Lp=Odpm Wpe l l OW V s W V

transition polynomial

- voltage expression

diffusion

exponential

. . . . . .

. . . . .

function

I I

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

gate voltage: Vgs

drain voltage: Vds V)

Fig. 2. The idea of extracting the

Fig.

1.

Comparison of the threshold voltages

threshold voltage in this work.

extracted with previous methods and SDLM

for various drain voltages using the measured

drain current in the NMOSFET.

12

g-10

-

-

V

N

f 8 8-20

>

V

z

A

V

4

M

30

-

-

0

-40

0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2

gate voltage: Vgs V)


a) b)

Fig. 3. Results for this method when applied to a submicron NMOSFET for the

various substrate voltages. a) The first difference-of he drain current.

b)

The

second difference of the drain current.

16

--

0

il

M

-

0

V

-20

f 8

6 -40

V

-

. 4

3

60

8 ;

4

-80

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0



a) b)

Fig. 4. The derivatives of the drain current calculated from 2D device simulation.

a) The first difference of the drain current. b) The second difference of the drain current.


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K.

Aoyarna: A Method for E xtracting the Threshold Voltage of MOSFET s 12

1

. . . . . .

. . . . .

. . . . .

. . . . .

. . .

j j

4.0

ativd pot edti al.... '..... hk

onduct~on and potential

4.5

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

distance: x pm )

Fig. 5. The conduction band potential and the relative

potential distribution at the interface at Vds=3.0V and

Vgs=02V using 2D device simulation results. The device

structure used in the simulation is also shown.

1.3 1.4 1.5 1.6 1.7 1.8 1.9

distance: x pm)

Fig.

6 The rate of the two drain current

components in the channel calculated

using the conduction band potential and

the relative potential at the interface of Si

and S i0 2 .

Vth

extracted with S LM method

0.15 0.20 0.25 0.30 0.35


Fig.

7

The RATE of the drift current

component at the interface for various

gate voltages. At Vgs=0.215V, the drift

component is equal to the diffusion

component.

Vth Definition

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