6
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER 1994 2357 On the Universality of Inversion Layer Mobility in Si MOSFET s: Part I-Effects of Substrate Impurity Concentration Shin-ichi Takagi, Member, IEEE, Akira Toriumi, Masao Iwase, and Hiroyuki Tango Abstr act- This paper reports the studies of the i nversion l ayer mobility in n- and p-channel Si MOSFET's with a wide range of substrate impurity concentrations to 10l8 cm- ). The validity and limitations of the universal relationship between the inversion layer mobility and the effective normal field E,E) are examined. It is found that the universality of both the electron and hole mobilities does hold up to lOIR cm-3. The dependences o f the universal curves are observed to differ betw een electrons and holes, particularly at lower temperatures. This result means a different influence of surface ro ughness scattering on the electron and hole transports. On substrates with higher impurity concentrations, the electron and hole mobilities significantly deviate from the universal curves at lower surface carrier concentrations because of Coulomb scattering by the substrate impurity. Also the deviation caused by the charged centers at the Si/SiO2 interface is observed in the mobility of MOSFET's degraded by Fowler-Nordheim electron injection. I. INTRODUCTION HE inversion layer mobility in Si MOSFET's has been T very important physical quantity as a parameter to describe the drain current and a probe to study the electric properties of a two-dimensional carrier system. Therefore, much study [ 11 since the 1960's has revealed dominant scatter- ing mechanisms determining the mobility. However, a compre- hensive understanding of the inversion layer mobility, which includes the quantitative description near room temperature, the effect of substrate impurity, the difference between the electron mobility and the hole mobility and the effect of surface orientation, is still insufficient. On the other hand, it has already been reported that the electron and hole mobilities in the inversion layer on a (100) surface follow the universal curves at room temperature independent of the substrate impurity concentration or the substrate bias when plotted as a function of effective normal fields, E,R [2]-[9]. E,ff is defined by the following equations. where y is the elementary charge, S~ s the permitivity of si, Ndpl is the surface concentration of the depletion charge, Manuscript received June 3, 1994. The review of this paper was arranged by Associate Editor K. Tada. S. Takagi is with the Solid State Electronics Laboratory, Stanford Univer- sity, Stanford, CA 94305 USA. A. Toriumi, M. Iwase, and H. Tango are with the ULSI Research Labo- ratories, Research & Development Center, Toshiba Corporation, 1 Kamukai Toshiba-cho, Saiwai-Ku, Kawasaki 210, Japan. IEEE Log Number 9405895. N, is the surface inversion carrier concentration. Here, 7 is a key parameter in defining E,R and it has been reported that, in order to provide the universal relationship, the value of q should taken to be 1/2 for the electron mobility [2] and 1/3 for the hole mobility [3]. This relationship has been often utilized as a precise mobility model in device simulators [lo]-[ 121. In spite of its usefulness, however, the origins of the universality, the value of and the effective field dependence of the universal curves have not been fully clarified yet. The aim of this paper (Part I) and the companion paper (Part 11) is to study the applicability and the physical meaning of the universal relationship. While the Part I demonstrates the validity and the limitation of the universality of the electron and hole mobilities on (100) surface experimentally, the Part I1 examines the physical meanings of E,ff and 7 , based on the new experimental findings regarding the surface orientation dependence. In this paper we concentrate on the effect of substrate impurity on the electron and hole mobilities. The motivations to study the effect of substrate impurity are twofold. One is to examine the validity of the universal relationship over a wide range of substrate impurity concentration. The substrate impurity concentration changes Ndpl in (1) and the resultant E,R, independent of N,. Therefore, the value of 7 that offers the universal relationship can be determined experimentally by comparing the mobilities on the different impurity con- centrations. However, the systematic study of the universality over a wide range of substrate impurity concentrations has not been done sufficiently. Such an extensive verification of the universality allows us to characterize the Eff dependence of the universal curve quantitatively. The second motivation is to examine the influence of substrate impurity scattering. Al- though Coulomb scattering by substrate impurity is considered to degrade the mobility on higher impurity concentration sub- strates, the quantitative characterization has been still lacking in spite of the practical importance in the scaled MOSFET's. From the above motivations, we investigate the electron and hole mobilities with the substrate impurity concentrations of 1015 to 10 cm-3 systematically in terms of the universal relationship. 11. SAMPLE PREPARATION AND MEASUREMENTS N-channel and p-channel MOSFET's used in this paper were fabricated on (100) Si wafers. The substrate impurity concentration was varied from to 10'' cmP3, using 0018-9383/94$04.00 994 IEEE ___~

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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER 1994 2357

On the Universality of Inversion Layer

Mobility in Si MOSFET s: Part I-Effects

of Substrate Impurity ConcentrationShin-ichi Takagi, Member, IEEE, Akira Toriumi, Masao Iwase, and Hiroyuki Tango

Abstract-This paper reports the studies of the inversion layermobility in n- and p-channel Si MOSFET's with a wide rangeof substrate impurity concentrations to 10l8 cm- ). Thevalidity and limitations of the universal relationship between theinversion layer mobility and the effective normal field E,E)areexamined.

It is found that the universality of both the electron and holemobilities does hold up to l O I R cm -3. The dependences of

the universal curves are observed to differ betw een electrons and

holes, particularly at lower temperatures. This result means adifferent influence of surface ro ughness scattering on the electronand hole transports.

On substrates with higher impurity concentrations, the electron

and h ole mobilities significantly deviate from the universal curvesat lower surface carrier concentrations because of Coulombscattering by the substrate impurity. Also the deviation causedby the charge d centers at the Si/SiO2 interface is observed in themobility of MOSFET's degraded by Fowler-Nordheim electroninjection.

I. INTRODUCTION

HE inversion layer mobility in Si MOSFET's has beenT very important physical quantity as a parameter to

describe the drain current and a probe to study the electric

properties of a two-dimensional carrier system. Therefore,

much study [11 since the 1960's has revealed dominant scatter-

ing mechanisms determining the mobility. However, a compre-

hensive understanding of the inversion layer mobility, which

includes the quantitative description near room temperature,the effect of substrate impurity, the difference between the

electron mobility and the hole mobility and the effect of

surface orientation, is still insufficient.

On the other hand, it has already been reported that the

electron and hole mobilities in the inversion layer on a

(100) surface follow the universal curves at room temperature

independent of the substrate impurity concentration or the

substrate bias when plotted as a function of effective normal

fields, E,R [2]-[9]. E,ff is defined by the following equations.

where y is the elementary charge, S ~ s the permitivity of

s i , N d p l is the surface concentration of the depletion charge,

Manuscript received June 3, 1994. The review of this paper was arrangedby Associate Editor K. Tada.

S. Takagi is with the Solid State Electronics Laboratory, Stanford Univer-sity, Stanford, CA 94305 USA.

A. Toriumi, M. Iwase, and H. Tango are with the ULSI Research Labo-ratories, Research & Development Center, Toshiba Corporation, 1 KamukaiToshiba-cho, Saiwai-Ku, Kawasaki 210, Japan.

IEEE Log Number 9405895.

N, is the surface inversion carrier concentration. Here, 7 is

a key parameter in defining E,R and it has been reported

that, in order to provide the universal relationship, the value

of q should taken to be 1/2 for the electron mobility [2]

and 1/3 for the hole mobility [3]. This relationship has been

often utilized as a precise mobility model in device simulators

[lo]-[ 121. In spite of its usefulness, however, the origins of the

universality, the value of 7 and the effective field dependence

of the universal curves have not been fully clarified yet.

The aim of this paper (Part I) and the companion paper (Part

11) is to study the applicability and the physical meaning of

the universal relationship. While the Part I demonstrates thevalidity and the limitation of the universality of the electron

and hole mobilities on (100) surface experimentally, the Part

I1 examines the physical meanings of E,ff and 7 ,based on the

new experimental findings regarding the surface orientation

dependence.

In this paper we concentrate on the effect of substrate

impurity on the electron and hole mobilities. The motivations

to study the effect of substrate impurity are twofold. One is

to examine the validity of the universal relationship over a

wide range of substrate impurity concentration. The substrate

impurity concentration changes N d p l in (1) and the resultant

E,R, independent of N,. Therefore, the value of 7 that offers

the universal relationship can be determined experimentally

by comparing the mobilities on the different impurity con-centrations. However, the systematic study of the universality

over a wide range of substrate impurity concentrations has not

been done sufficiently. Such an extensive verification of the

universality allows us to characterize the E ff dependence of

the universal curve quantitatively. The second motivation is

to examine the influence of substrate impurity scattering. Al-

though Coulomb scattering by substrate impurity is considered

to degrade the mobility on higher impurity concentration sub-

strates, the quantitative characterization has been still lacking

in spite of the practical importance in the scaled MOSFET's.

From the above motivations, we investigate the electron and

hole mobilities with the substrate impurity concentrations of

1015 to 10 cm- 3 systematically in terms of the universal

relationship.

11. SAMPLE PREPARATION AND MEASUREMENTS

N-channel and p-channel MOSFET's used in this paper

were fabricated on (100) Si wafers. The substrate impurity

concentration was varied from to 10'' cmP3, using

0018-9383/94$04.00 994 IEEE

___~

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2358 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER 1994

boron or phosphorus ion implantation, followed by a long and

high temperature annealing (1 1 9 0 ° C 60 min). This annealing

allowed the impurity profile to be considerably flat to a 3 p m

depth from the Si surface. All the devices were of the surface

channel type. The gate oxide was grown to a thickness of 25

nm in dry oxygen at 900°C . The gate materials were n+ and

p+-poly Si for n- and p-channel MO SFET 's, respectively. The

channel length, L , and the channel width, W , f the measureddevices were 200 pm and 100 pm , respectively.

The effective mobility in the inversion layer, pLeff as

determined from the drain conductance gd in the linear region.

.9d was measured at the drain voltage, Vd of 50 or 10mV. The

surface carrier concentration, N ,? V , ) , was determined directly

through gate-channel capacitance Cgc ,), measurement [141,

[151.

1;

YNS V,) = .I_,C,c Vg)~~Vg. 3 )

The measurement frequency was selected to be as low as0.4-1.0 kHz in order to avoid the influence of the resistive

component of the channel [15].

The value of Eefiwas determined from ( l ) , (4), and ( 5 ) .

4)

Here, 4~ is the bulk Fermi energy, Nsub is the substrate

impurity concentration, k~ is the Boltzman constant, and n is

the intrinsic carrier concentration. Nsut, was determined from

the minimum capacitance in the high frequency (100 kHz)

C-V curves of the MOS diodes. We have confirmed, using

the process simulator (TO PAZ) [16 ], that the variation in the

impurity concentration within the depletion layer is less than

-around 30% for the doping of boron more than

The main issue regarding the universal relationship is to de-

termine the value of 77 in (1). This can be done experimentally

from the experimental mobilities with the different substrate

impurity concentrations. When the universal relationship holds

and the value of 11 is chosen appropriately, the mobility

should be described as the single universal curve against E,n,

independent of the substrate impurity concentration. If 77 is

incorrect, the mobilities with the different substrate impurity

concentrations are to have different values for a same E,tf

value, because 71 changes the weights of N , and NdPl .

c m P3 .

111. EXPERIMENTALESULTS

A . Unitiersal Relationship o Electron and Hole M obilities

Figs. I and 2 show the Eeff ependences of the electron

and hole mobilities in the inversion layer, respectively, at

300 K and 77 K. The parameter is the substrate acceptor

concentration, N.4, or the substrate donor concentration, N p .d in the measurement of gel was taken to be IO mV.

Here, the values of rI for the electron and hole mobilities

10' I I INA c i 3

m0 ELECTRON

-=

I I

1.010' 1

0.1

EFFECTIVE FIELD [ MV/cm 1

Fig. 1. Electron mobility in inversion layer at 300 K and 77 K versuseffective field E,=, as a parameter of substrate acceptor concentration, S I .

Here, Ec,fr s defined by E,n. = q . + . . V* /ES;ith of 1/2.

are taken to be 1/2 and 1/3, respectively. As seen in Fig.1, the electron mobilities at 300 K are represented by the

universal curve as a function of E,R in the range of 0.05 to 1.5

MV/cm independent of the substrate impurity concentrations

by choosing the value of 77 to be 1/2. Similarly, the hole

mobilities are also represented by the universal curve as a

function of E,ff in the range of 0.05 to MV/cm by choosing

the value of to be 1/3, as observed in Fig. 2 . These results

confirm us that universal relationships of the electron and hole

mobilities on (100) surface do hold up to the substrate impurity

concentration of 0ls cm-3. It is confirmed simultaneously

that the values of 71 for the electron and hole mobilities are 1/2

and 1/3, respectively, for a wide range of Eeff nd the substrate

impurity concentration. These values are in agreement with

those reported previously [ 2 ] , SI. Moreover, the electron andhole mobilities at 77 K also have the universality in high Eee,

which was defined by the same value of 17 as at 300 K.

It is, however, observed that the electron and hole mobili-

ties with higher substrate concentrations exhibit a significant

deviation from the universal curves near the threshold v oltage.

This issue will be discussed in Section 111-C in detail.

B . Effectitve Field Dependences o Universal

Curves for Electrons and Holes

We have obtained the universal curves that hold for the

impurity concentrations of 10l5 to 10 cm-3 for both the

electron and hole mobilities in Section 111-A. However, the

origin of the Ecff ependences have not been fully understood

yet. Especially, the E,ff dependence of the hole mobilityhas been studied little so far. In this section we study the

E,ff dependence of the universal curve with emphasis on the

difference between the electron mobility and the hole mobility.

From Fig. 1 , the characteristics of the E,ff dependence of

the electron mobility are summarized as follows. 1 ) At 300

K, the mobility is proportional to E at E,tf lower than0.5 MV/cm over a one order of magnitude Eeff ange. 2 ) At

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TAKAGI et al.: ON THE UNIVERSALITY OF MOBILITY: PART I 2359

I I I I

m

20I 1

0.1 1.0

EFFECTIVE FIELD [ MV/cm IFig. 2. Hole mobility in inversion layer at 300 K and 77 K versus effectivefield, E,n as a parameter of substrate donor concentration, ,Yo. ere, E e ~is defined by E p ~q . NCv,,,,1 7 , ) / E s , with T of 1/3.

........ Total Mobi l i t y

EFFECTIVE FIELD Ee ff

Fig. 3. Schematic diagram of E,E or AV, dependence of mobility ininversion layer by three dominant scattering mechanisms.

300 K, the mobility decreases steeply at E,R higher than 0.5

MV/cm. 3) At 77 K, the mobility is roughly proportional toE;: at high E,R.

In contrast, the E e ~ependence of the hole mobility in Fig.

2 as described below. 1 At 300 K, the E,R dependence does

not exhibit a single power law over any E e ~ange and is a

little stronger than E ’. 2 ) At 300 K, the change in a slope

at high Eeff s not so marked a s for the electron mobility. 3 ) A t

77 K, the hole mobility is nearly proportional to E: which

is rather weaker than that for the electron mobility.

In order to understand these E,R dependences quantita-

tively, it is necessary to characterize the universal curve in

terms of scattering mechanism. Fig. 3 shows a schematic dia-

gram of the l ? ~or N , ) dependences on the basis of a general

understanding of the inversion layer mobility. According to

this diagram, the universal curve can be divided into phonon

scattering term and surface roughness scattering term. If thisis true, the difference in the E,R dependence between the

electron mobility and the hole mobility can be ascribed to

surface roughness scattering, because the difference becomes

larger at high E,tf and/or at low temperature. In order to

examine this interpretation, the temperature dependences of

the electron and hole mobilities were measured.

5000 1 I i

: 000

5U I 000

22 500

>

-Ik

0200

ELECTRON

-..a

.. .....

.*

397K

447K

- . XPERIMENT

MODEL

100 L 1 I

0.1 1.0

EFFECTIVE FIELD [ MV/cm 1

Fig. 4. E,fl dependences of electron mobility in the inversion layer on 100)

surface in the range of 77 K to 447 K. Substrate acceptor concentration was3.9 x 1OI5 ~ 1 1 1 ~ ~ .ere, E,fi is defined with 1 of 1/2. Open circles showthe experimental data. The solid curves were calculated using 6H8).

0 . 1 1.0

EFFECTIVE FIELD [ MV/cm 1

Fig. 5. dependences of hole mobility in inversion layer on 100) surfacein the range of 30K to 447 K . Substrate acceptor concentration w as 5.2 x 1OI5

cm-’. Here, E,fi is defined with 11 of 1/3.Open circles show the experimentaldata. The solid curves were calculated using (6)-(8).

Figs. 4 and 5 show the E,R dependences of the electron

mobility with N A of 3.9 x 1015 cm-’ and the hole mobility

with N o of 7.8 x 1015 cm-’. Here, Vd in the measurement

of gd was taken to be 50 mV, because we focused on

higher N , region. The almost no temperature dependence

of the hole mobility in the range of 30-77 K means that

the mobility in this temperature region is limited only by

surface roughness scattering. It has been, therefore, confirmed

that the mobility limited by surface roughness scattering has

remarkably different Eeff dependences between electrons and

holes. With increasing temperature, on the other hand, the

E e ~ependences of both the electron and hole mobilities

approach roughly This fact shows that the mobility

limited by photon scattering follows the same power law for

both electrons and holes.

Based on the above findings, a calculation using a sim-

ple model was performed. The mobility limited by phonon

scattering, &,h, was determined by

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2360 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER I994

Here, the constant coefficient A was taken to be 2.0 x IO5

and 6.1 x lo4 for the electron and hole mobilities on (loo),

respectively, where p E e ~nd T should be in cm2/V.s,

V/cm, and Kelvins. The power of -0.3, was taken from

the results in Figs. 4 and 5 . The power of T , -1.75, was

determined from the temperature dependence of the electron

mobility at E,R of 0.2 MV/cm, where the contributions

of surface roughness scattering and Coulomb scattering areso small that the temperature dependence of only phonon

scattering can be determined.

The mobility limited by surface roughness scattering, ,uL,,,

was modeled separately for the electron and hole mobilities.

For the electron mobility

(7)

Here, the parameter, 7 , was determined to be 2.6 so that the

total mobility at 77K fitted the experimental data. T he constant

coefficient, B, was taken to be 4.5 x 10 . The reason why

y is slightly different from the power at 77 K, which was

roughly -2, is that phonon scattering still has an influence on

the electron mobility at 77 K . As for the hole mobility, on the

other hand, the experimental mobility at 30 K was used as psr.

It should be noted that, as seen in Fig. 5, psr or holes cannot

be represented by the single power law of E,R.

Using Matthiessen's rule, the total mobility, ptot, s de-

scribed by

8)

The solid line in Figs. 4  and 5 represent the calculated

results. A good agreement between the experimental and

calculated mobilities is obtained at moderate or high E,R,

where Coulomb scattering is negligible. This fact confirms us

that the difference in the E e ~ependence between the electron

mobility and the hole mobility is attributed to the difference

in the E,tf dependence of pYr. lso, the deviation of the hole

mobility at 300 K from E e 2 s understood by considering

that surface roughness scattering affects the hole mobility overa wider E,R range even at 300 K.

p5r= B .E,;

l d Fpl; + P,l'

C. Deviation j i n m the Universal Curves

As already seen in Figs. 1 and 2, the electron and hole

mobilities deviate from the universal cures near the threshold

voltage even at 300K. Moreover, this deviation becomes larger

as the substrate impurity concentration increases. These facts

suggest that the mobility is considerably affected by Coulomb

scattering associated with substrate impurity. It has been

pointed out [17]-[191, on the other hand, that the application

of a finite drain voltage can lead to a decrease in carrier

concentration near the drain and a resulting lower p e ~t low

N,. In order to minimize this error, d was selected to be as

low as 10mV for an accurate characterization of the mobilityat low N , .

The behavior of the mobility component corresponding to

the deviation, i~,o,~olnt,,was studied quantitatively using (9), in

order to examine whether the deviation is caused by substrate

impurity scattering.

10 I

I O i 1I

I O i i I O i 2

Ns [ cm-2 1

Fig. 6. Electron mobility compo nent determined from dev iation from univer-

sal curve, p , , , , , lorr, l , , versus surfac e carrier concentration,S as a parameter

of substrate acceptor concentratio n, \ ~ x { ,.r,,,l<,,,Ll,was calculated from 9).

104

L

300 K

NS= 2x10

\

; oi 016 1017 10'8

NA,ND bm31

Fig. 7. Dependences of pr,,ul~l,,,l, or electrons and holes in inversionlayer at 300 K on substrate acceptor concentration, -V~nd substrate donor

concentration, S n espectively. Here .\ , is 2 x 10 cm- .

Here, jLcoulomb was determined as a function of N , , becausethe Coulomb scattering rate should be characterized as func-

tion of N,, which is directly related to the screening effect

and the electron energy [20].

Fig. 6 shows the N , dependence of pcoulomb for the electron

mobility at 300 K as a parameter of N q . It is seen that

p co l o rn ~ncreases in proportion to N: , independent of

Moreover, p,,,,lomt, is found to decrease with an increase

in N.4. Fig. 7 shows the substrate impurity concentration

dependences of p,,,lomb of the electron and hole mobilities

at N , of 2 x 10l1 cm-2. At 300 K, the deviation from the

universal curves is distinctly o bserved in the substrate impurity

concentration higher than 7.2 x 1016 cm- 3 for the electron

mobility and higher than 1.6x 10 l6 cm-3 for the hole mobility.

The inversely linear relationship between /L,o,lomh and thesubstrate impurity concentrations confirms that the substrate

impurity is the main Coulomb scattering center.

With substrate impurity concentrations lower than 5 x

10" cm P3 , however, other Coulomb scattering centers are

responsible. Fig. 8 shows p,-o,lomb of the electron mobility at77 K at N, = 2 , 5 a nd 10 x 10 cm-'. Here, pcoulomb was

determined by subtracting the contribution of p p h estimated

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TAKAGI et al.: ON THE UNIVERSALITY OF MOBILITY: PART I 2361

7.2 x 1016cm-3 has the weaker N A dependence. It is known - O

[l], [20] that there are three types of Coulomb scatteringcenters that can affect the inversion layer mobility; substrate

8impurities, interface state charges and charges trapped in SiO2.

5 .

for bcoulomb with N A lower than 7.2 x 1016 cmP3. In - 0 ' -

is also considered to come from the change in the type of the

\

Thus interface state charges or trapped charges are responsible

addition, it is found that the N dependence of pcoulomb in

this N A region becomes weaker. This weaker N , dependence

dominant scattering centers. The Coulomb interaction between

- 2 .9

2

10'

10 I I I I

- .A.\ N 300 K

E L E C T R O N

j;

*.k.

N I N J E C T I O N

~ ~ . ~ x ~ o " c m - '

I .

:

NS [cm-*]

l x l o 2

2 X 1 0 1 1

I 5x10"

E L E C T R O N

\ x 10"

N A = ~ . ~ x ~ ~ ~ c ~ T I -m.1

E F F E C T I V E F I E L D E e f f C M V / c m 3

a deviation from the universal curve can be examined by

studying the mobility of MOSFET's degraded by carrier

injection, because carrier injection into Si02 is known to

generate interface charges [211. Therefore, the inversion layer

mobility after Fowler-Nordheim (FN) tunneling injection into

Si0 2 was studied. Electrons were injected into S io s from the

inversion layer in n-channel MOSFET's. The injection current

was maintained at a constant value (1 in j = 2.65x loP4A/cm2.

Fig. 9 shows the E,R dependence of the electron mobility

before and after FN tunneling injection as a parameter of the

number of injected electrons per unit area, Ninj. After the

injection the deviation from the initial curve is clearly observed

and becomes larger at lower E,R (thus lower N , ) , similar to

the mobility on higher impurity concentration substrates. Also,the deviation becomes larger with an increase in Ninj. Fig. 10

shows the relationship between pCoulomb at N , of 2 x 10l1

cmP 2and the threshold voltage shift, A&, estimated from C -

V curves. The number of interface charged centers per unit

area, Nint, s also shown in the horizontal axis. Here, Nlnt

was calculated from AV,, under the assumption that all the

generated charges are located at the interface. bcoulomb is

found to be inversely proportional to Nint. It is confirmed

from this result that the mobility degradation is caused by the

generated interface charges.

IV. CONCLUSION

This paper has reported the studies of the inversion layer

mobility in n- and p-channel MOSFET's over a wide range

of substrate impurity concentrations from the viewpoint of a

universal relationship against the effective field, E,R. Uni-

versality has been found to be maintained up to a substrate

impurity concentration of 10'' c m p3 .

It has also been found that the E e ~ependence of theuniversal curves can be explained over a wide temperature

range by the combination of phonon scattering and surface

roughness scattering. While phonon scattering provides the

same E,R dependence between the electron mobility and the

hole mobility, a difference in the E,E dependences of the

mobility limited by surface roughness scattering has been ob-

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2362 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER 1994

served. It has been concluded that surface roughness scattering

affects the electron and hole transports differently.

On the other hand, a significant lowering from the universal

curve, which is attributable to substrate impurity scattering, has

been observed even at 300 K for the substrate impurity con-

centrations higher than 7 . 2 x and 1 .6 x c m P3

for the electron mobility and the hole mobility, respectively.

The inversion layer mobility limited by substrate impurityscattering has been found to be in proportion to the N:’

for both electrons and holes. It has also been experimentally

confirmed in stressed MOSFET’s that a marked deviation from

the universal curve can be ascribed to Coulomb scattering

associated with the generated interface charges.

Shin-ichi Takagi (M‘93) was bom in Tokyo, Japan,on August 25, 1959. He received the B.S., M S , nd

Ph.D. degrees in electronic5 engineenng from theUniversity of Tokyo, Tokyo, Japan, in 1982, 1984,and 1987, respectively

He joined the Toshiha Research and DevelopmentCenter, Kawasaki, Japan, in 1987, where he hasbeen engaged in research on the device physicsof Si MOSFET’s. including the carrier transport ininversion layer, the impact ionization phenom ena,

the hot came r degradation and the electnc propertiesof Si/SiOz interface. He is currently d Visiting Scholar at Stanford University,Stanford, CA, where he ir working on the Si/SiGe heterostructure devicesDr. akagi is a member of the IEEE Electron Device Society and the Japan

Society of Applied Phyws

ACKNOWLEDGMENT

The authors wish to thank K. Nishinohara and N. Shigyo for

their valuable comments concerning the measurement method.

They would like to acknowledge N. Konishi’s contribution of

performing the process simulation. They are also grateful to

M. Yoshimi, K. Natori, and T. Wada for their encouragement

throughout this work. They are indebted to F. Umibe for

reviewing the original manuscript and suggesting revisions inits English.

Akira Toriumi received the B S. degree in physicsand the M.S. and Ph D. degrees in applied physicsfrom the University of Tokyo, Tokyo, Japan, in1978, 1980, and 1983, respectively.

He Joined the Toshiba Research and DevelopmentCenter, Kawasaki, Japan, in 1983, where he hasbeen engaged in research on the MOSFET devicephysics. Dunng 1988-1990 he was a Visiting Sci-entist at the Massachusetts Institute of Technology,where he studied the physics of quantum effectdevices. He is currently working on the physics and

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technology o f 0.1 irm CM OS, thin Si02 reliability, a nd th e quantum effectsof very small silicon devices.

Dr. Toriumi is a member of the Physical Society of Japan, the Japan Societyof Applied Physics. and the American Physical Society.

Masao Iwase was born in Aom on, Japan, in 1963.He joined the Toshiba Research and D evelopment

Center, Kawasaki, Japan, in 1 982, where he hasbeen engaged in the development o f beam Iithog-

raphy and submicrometer CMOS technology. Heis currently in the Process Rewearch Department atToshiba ULSI Research Laboratones.

Mr. Iwase is a member of the Japan Society ofApplied Physics.

Hiroyuki Tango was born in Saitama Prefecture,Japan, on February IO, 1942 He received the B Sdegree in electncal communication engineering andthe M S and Ph.D. degrees in electronics engineer-ing, all from Tohoku University, Send ai. Japan. in

*i-

L” ’ 1965, 1967, and 1970In 1970, He joined the Toshiba Research and

Development Center. Kawasaki, Japan, where hestudied MOS device physics, MOS on bulk, andMOS on SOS integrated-circuit technology. From

1979 to 1983 he researched SOS LSI technoloevas the Head o f an SOS technology group at Toshiba. From 1 984 to I 9i khe supervised the research and development of MOS device physics, devicesimulation, MOS-LSI process. and MOS devices of SO1 technology. Since

1988 he has supervised the R&D of DRAM, EEPR OM, and CCD devices.Dr. Tango is a member of the Japan Society of Applied Physics and the

Institute of Electronics, Information, and Communication Engineers.