Jpn. J. Appl. Phys. Vol. 39 (2000) pp. 2312–2317
Part 1, No. 4B, April 2000
c
°2000
The Japan Society of Applied Physics

Optimum Conditions of Body Effect Factor and Substrate Bias
in Variable Threshold Voltage MOSFETs
Hiroshi KOURA1,∗ , Makoto TAKAMIYA1 and Toshiro H IRAMOTO1,2
1 Institute of Industrial Science, University of Tokyo, Roppongi, Minato-ku, Tokyo 106-8558, Japan
2 VLSI Design and Education Center, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan(Received October 8, 1999; accepted for publication January 28, 2000)

The effects of body effect factor (γ ) and substrate bias (Vbs ) in a variable threshold voltage metal oxide semiconductor
field effect transistor (VTMOS) have been systematically examined by device simulation. The characteristics of a VTMOS are
significantly affected by the value of γ and the Vbs difference (1Vbs ) between the active mode and the standby mode. Optimalγ and 1Vbs to obtain higher on-current in the active mode and lower off-current in the standby mode are derived. When offcurrent in the active mode is limited, a larger 1Vbs and smaller γ are preferable to obtain a higher drive current. When γ is
fixed, |1Vbs | should be as large as the breakdown and leakage current permits. When 1Vbs is fixed for some reason, such as
breakdown, the optimum γ depends on the relationship between 1Vbs and Vdd : γ should be larger when a large |1Vbs | canbe applied, while it should be smaller when the |1Vbs | is small. The scalability of VTMOS is also discussed and it is foundthat channel engineering is strongly required in a scaled VTMOS. These results will greatly help in designing ultra-low power
VTMOS VLSIs, and the VTMOS could be expected to survive in the 50 nm generation depending on the scaling scenario andapplications.
KEYWORDS: body effect, variable threshold voltage metal oxide semiconductor field effect transistor (VTMOS), substrate bias,
low power, active mode, standby mode, channel engineering

1. Introduction

V

The variable threshold voltage metal oxide semiconductor field effect transistor (VTMOS) has recently attracted
much attention for ultra-low power very large scale integration (VLSI) applications at low supply voltage (Vdd ).1–3) Utilizing the body effect, the substrate bias (Vbs ) is controlled toshift the threshold voltage (Vth ), and a high Vth in the stand-bymode and low Vth in the active mode are obtained. Vth fluctuations between chips are also suppressed by Vbs control.1)
The Vth shift (1Vth ) is given byVth(s)

slope:γVth(a)= γ |Vbs (s) − Vbs (a)|,log Ids

Ion(a)

A

active mode
Vbs=0V

B

A

Ioff(a)∆Vth=γ |Vbs|

B

Standby
mode

γA<γB

Ioff(s)
Vdd

Vgs

(b)

2. Simulation and Results∗ E-mail address: koura@nano.iis.u-tokyo.ac.jp|Vbs |

Vbs(s)(a)(1)

where γ is the body effect factor, 1Vbs the difference of substrate bias between the active mode and the standby mode,
Vbs (s) the substrate bias in the standby mode, and Vbs (a) the
substrate bias in the active mode. Therefore, γ and 1Vbs are
the most important device parameters in relation to VTMOS
and their optimization is essential to take full advantage of
VTMOS. However, no study has previously been made on
the optimum conditions of γ and 1Vbs .
In this study, the dependence of VTMOS performance on γ
and 1Vbs is systematically investigated by device simulationand the optimum conditions are discussed. It is found that
1Vbs should be as large as possible, while the optimum valueof γ depends on the relationship between 1Vbs and Vdd . The
scalability of VTMOS is also discussed. It is found that engineering of the doping profiles in the channel region (channel
engineering)4) is strongly required in scaled VTMOS.

2.1 Definition of the body effect factor
In this study, the body effect factor γ is defined as|Vth (s) − Vth (a)|Cd
|1Vth |==,
γ ≡|1Vbs |
|Vbs (s) − Vbs (a)|
C ox

∆Vbs

Vbs(a)=0V

1Vth = γ |1Vbs |

∆Vth
th

(2)

Fig. 1. (a) A schematic of the relationship among 1Vth , 1Vbs and γ in avalue of VTMOS. γ is given by the slope of 1Vth /1Vbs . (b) Schematic of
the characteristics of a VTMOS with different at γ (device A has smaller γ
than device B). The off-current in the standby mode (Ioff (s)) is set constantat 10−13 A/µm. The off-current in the active mode (Ioff (a)) is also set tobe the same in this figure. Device A has higher on-current (Ion (a)) due tothe smaller S factor and higher mobility but requires large |1Vbs | to attain
low Ioff (s) due to the small γ .

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Jpn. J. Appl. Phys. Vol. 39 (2000) Pt. 1, No. 4B

H. KOURA et al.

where Vth (s) and Vth (a) are the threshold voltage in thestandby and active modes, respectively, C d is the depletion
capacitance and C ox is the gate oxide capacitance, so that
1Vth is given by eq. (1).5) Generally, 1Vth is dependent on
the square root of 1Vbs and the body effect factor is given
by6)
√
2qεNA
0
γ =
,
(3)
C ox
where q is the electric charge, ε is the permittivity in silicon
and NA is the channel doping concentration. However, γ 0
in eq. (3) is valid only in MOSFETs with uniform channel
concentration. Moreover, the relation between 1Vth and γ 0
is not clear. Therefore, we adopted the definition of eq. (2).
Figure 1(a) shows a schematic of the relationship among γ ,1Vbs , and 1Vth . γ is given by a slope of 1Vth /1Vbs . Please
note that the value of γ changes with 1Vbs when 1Vth is notproportional to 1Vbs as shown in the figure. However, eq. (1)is always valid when the definition of eq. (2) is used.
On the other hand, subthreshold swing (S factor) is given
at room temperature by¶µ
Cd[mV/dec].
(4)
S = 60 1 +C oxThen, the relation between γ and S is given from eqs. (2) and(4) as
S = 60(1 + γ )[mV/dec].

(5)

gate
n

This equation indicates that a device with larger γ has a larger
S factor.
2.2 Qualitative predictions
Figure 1(b) shows a schematic of the characteristics ofVTMOS’s with different value of γ . Device A has a smaller
γ than device B. When the off-current in the standby mode
(Ioff (s)) is the same for the two devices, device A requires alarger |1Vbs | to attain a certain 1Vth due to smaller γ than device B. However, device A with a smaller γ will have a higher
on-current (Ion (a)) as shown in Fig. 1(b). This is because
device A has a steeper S swing (hence low Vth ) and higher
mobility due to the weaker vertical electric field. Therefore,
the optimal value of γ is not clear from this the qualitative
discussion alone. More detailed discussion based on device
simulation7) is presented in the following subsections.
2.3 Simulated device structures
Figure 2 shows a schematic of the device structures usedin the simulation. Figure 2(a) shows the uniformly doped
MOSFET (uniform MOS) where the channel doping profile
is uniform. Uniform MOS generally has a small γ due tothe large depletion layer width. Figure 2(c) shows the deltadoped MOSFET (delta MOS) where the channel doping profile is step-like as shown in figure.8) Delta MOS has a γ twiceas large as uniform MOS, because the depletion layer width ofdelta MOS is half of that of the uniform MOS at a fixed Vth .8)
On the other hand, the state-of-the-art MOSFETs with high

gate
n

n

gate
n

n

p

gate

n
p- t

p

Na

p++
Na

Na

tn

t
p

ld

p+

p

depth

Uniformly-doped MOS(uniform MOS)(a)ld

Retrograde MOS
(b)

p++

p-

depth

n-- n
n- tn

n
ND

p++
Na

2313

ld

n--

depth

p++

n-

ld depth

Delta-doped MOS* Counter-doped MOS(delta MOS)
(counter MOS)(c)(d)

Fig. 2. Schematic of the device structures used in the device simulation. Gate length is 0.18 µm, gate oxide thickness is 3 nm,
source/drain junction depth is 50 nm, and supply voltage is 1.5 V (a) Uniformly doped MOSFET (uniform MOS), in which thechannel concentration is varied to change γ and Vth . (b) Retrograde channel MOSFET with a low doping concentration at the surface
and a high concentration in depth (retrograde MOS). Although this structure is not simulated in this study, the characteristics areintermediate between those of uniform MOS and delta MOS. (c) Delta-doped MOSFET8) (delta MOS), in which the thickness (t) of
the low concentration layer is varied to vary γ and Vth . (d) Counter-doped MOSFET (counter MOS), in which the thickness (tn) andconcentration (ND) of the middle layer is varied to change γ and Vth over a wide range.

2314

Jpn. J. Appl. Phys. Vol. 39 (2000) Pt. 1, No. 4B

H. KOURA et al.

short channel effect immunity have a gradual channel profile
with a low concentration at the surface and high concentrationin depth due to the channel engineering as shown in Fig. 2(b),which is generally referred to as a MOSFET with a retrograde
channel profile (retrograde MOS).9) Although the characteristics of a retrograde MOS depend on the actual channel profile, they are intermediate between those of a uniform MOS
and delta MOS.5, 9) Therefore, we first simulated the characteristics of these two extreme device structures: uniform MOS
and delta MOS. In uniform MOS, the channel concentration
is varied to change the value of γ and Vth . In delta MOS, thethickness of the low concentration layer (t) is varied to change
the value of γ and Vth .
Figure 3(a) shows the relation between the off-current in
the active mode (Ioff (a)) and Ion (a), and Figure 3(b) shows
the relation between Vth and γ of the two devices. The numbers indicated in Fig. 3(a) are the values of γ . The device
parameters used are based on the 180-nm technology nodein the International Technology Roadmap for Semiconductors (ITRS).10) Uniform MOS has a higher Ion (a) but the required |1Vbs | would be extremely high due to the very small
γ . The retrograde MOS covers the area between the twolines. It is suggested from Fig. 3(b) that the covered rangeof γ and Vth is limited when only uniform MOS and delta

Ioff (a) (A/µm)@Vgs =0V

1x10-6γ =0.09
Vdd=1.5V

1x10-70.13

delta MOS

1x10-81x10-9 RetrogradeMOS

1x10-10

0.02

0.17

0.03

0.07

0.35

10

uniform MOS
0.52

Ioff(s)=10-13A/µm

0.12
-13

10

0.2

2.4 Simulation conditions and method
The off-current in the standby mode (Ioff (s)) is set at
10−13 A/µm, and the on-current in the active mode (Ion (a)) is
compared in this study. The same results are obtained whenIon (a) is fixed and Ioff (s) is compared. Vbs in the active mode
(Vbs (a)) is set to 0 V in the simulation, since Vbs (a) is usuallyalmost 0 V in the VTMOS.1) Therefore, 1Vbs corresponds to
Vbs in the standby mode (Vbs (s)) in this study. The I –V characteristics are simulated for a device parameter set at Vbs = 0(active mode), and the on-current (Ion (a)), off-current (Ioff (a)),
and Vth in the active mode are derived. Then, Vbs is applied(the standby mode), and 1Vbs is obtained so that Ioff (s) is
10−13 A/µm in the standby mode. Then, 1Vth is derived fromVth ’s in the active and standby modes, and γ is obtained fromeq. (2). The simulation is carried out for various device parameters. Ion (a), Ioff (a), γ , 1Vbs are derived for each parameter set by the above-mentioned method. Then, Ion (a) and
Ioff (a) of each device are plotted in a Ioff (a)-Ion (a) plane, andcontour lines of γ and 1Vbs are obtained.

0.26

-11

10-12

MOS are simulated. In order to investigate the effect of γ
systematically over a wider range of Ion (a) and Ioff (a), therefore, counter-doped MOSFETs (counter MOS) are also simulated. Figure 2(d) shows the structure of the counter MOS
where the polarity of channel doping is the opposite near thesurface. The counter MOS has a lower Vth (higher Ioff (a))
than uniform MOS and delta MOS due to the counter-doping,
and a larger γ at a fixed Vth . γ is varied over a wide range
by changing the thickness of the counter-doped layer and Vthis varied by changing the concentration of the counter doped
layer.

0.4

0.6

0.8

Ion(a)(mA/µm)@Vgs=1.5V

1.0

(a)

2.5 Simulated results
Figure 4 shows the device simulation results. Ioff (s) is fixedat 10−13 A/µm. This figure shows the contour lines of Vbs(solid lines) and γ (dashed lines) as a function of Ioff (a) andIon (a). Since this figure is rather complicated, we discuss theresults in the following three boundary conditions.
2.5.1 Constant Ioff (a)In the first boundary condition, Ioff (a) is set at a constantvalue in addition to the constant Ioff (s). When Vth is extremely

uniform MOS
0.5
0.4

Retrograde
MOS

0.3
0.2

delta MOS

0.1
0.0

0.1

0.2

γ

0.3

0.4

0.5

0.6

(b)
Fig. 3. (a) Relation between Ioff (a) and Ion (a) in a uniform MOS and delta
MOS. Ioff (s) of each device is fixed at 10−13 A/µm. The value of γ eachdevice are shown. (b) Relation between Vth and γ in a uniform MOS anddelta MOS. The channel-engineered MOSFETs, such as retrograde MOS,
cover the area between the two lines. |Vbs | and γ cannot be varied widely
by using only uniform, retrograde or delta MOS.

Ioff (a)(A/ µ m)@Vgs =0V

Vth (V)@Vbs =0V

0.6
10

-4

10

-5

solid line=contour line of V bs
dashed line=contour line of γ

10-6

-1V -1.2V -1.5V -2V

-0.8V

-3V

-5V

10-7
10

-0.7V

-8

γ=0.6

10-9
10

-10

10

-11

Vbs=-0.3V

0.3

0.24
0.17

10-12
10

0.45 0.36

-13

0.2

0V

Ioff(s)=10 (A/µm)

0.4
0.6 γ =0
Ion(a)(mA/µm)@Vgs=1.5V

-13

0.8

Fig. 4. Contour lines of Vbs (solid lines) and γ (dashed lines) in a
VTMOS as a function of Ioff (a) and Ion (a). Ioff (s) is set at 10−13(A/µm). Ioff (a) = 10−8 A/µm under the first boundary condition (constant Ioff (a)), γ = 0.3 under the second boundary condition (constant γ ),and 1Vbs = −2 V and −0.3 V under the third boundary condition (constant 1Vbs ) are shown by bold lines.

Jpn. J. Appl. Phys. Vol. 39 (2000) Pt. 1, No. 4B

I on (a) (mA/ µm)@Vgs=1.5V

0.80

Ioff(s)=10-13(A/µm)
Ioff(a)=10-8(A/µm)

0.75
0.70
0.65
0.60
0.55

0.2

0.3

0.4

γ

I on(a) (mA/µm)@Vgs =1.5V

(a)
0.80
0.75
0.70
0.65

Ioff(s)=10-13(A/µm)

0.60
0.55

Ioff(a)=10-8(A/µm)
1.0

1.5

2.0

2.5

|Vbs|(V)(b)
Fig. 5. Simulation results for the first boundary condition: constant Ioff (a).
Ioff (s) is also constant (10−13 A/µm). (a) Relation between Ion (a) and γ .
(b) Relation between Ion (a) and |1Vbs |. To obtain larger Ion (a), γ should
be small and |1Vbs | should be large under the condition of constant Ioff (a).

2315

2.5
-4

I on(a)=7.5X10 (A/µm)-13

Ioff(s)=10(A/µm)

2.0
-4

7X10

|∆Vbs|(V)low, Ioff (a) becomes very large and the circuits consume a lotof power and sometimes do not work properly.11, 12) Therefore, Ioff (a) should be limited to a certain maximum value.
This condition roughly corresponds to a constant Vth . Figure 5
shows the simulation results of VTMOS under the conditionof fixed Ioff (s) and Ioff (a). Figure 5(a) shows the relationof Ion (a) and γ to obtain a constant Ioff (s) of 10−13 A/µm
and constant Ioff (a) of 10−8 A/µm, and Figure 5(b) shows the
1Vbs dependence of Ion (a) under this condition. This condition is shown by a horizontal line in Fig. 4. Under this condition, |1Vbs | should be large and a device with relatively small
γ is preferable, as shown in Fig. 5.
2.5.2 Constant γ
The second boundary condition is a constant γ . When thedevice is fixed, γ is also fixed. The relation between Ioff (a)and Ion (a) is expressed in the corresponding contour line of
γ , as shown in Fig. 4 with γ = 0.3 as an example. It is evident from the contour lines that |1Vbs | should be as large as
possible to achieve a higher Ion (a), although Ioff (a) also increases. In actual devices, |1Vbs | is usually limited by junction leakage current or junciton breakdown. Under this condition, |1Vbs | should be set to a value as large as is permitted
by the leakage or breakdown.
2.5.3 Constant |1Vbs |The third boundary condition is a constant |1Vbs |. As men-

H. KOURA et al.

Vdd =1.5V

1.5-4

6.5X10

1.0

-4

6X10

-4

0.5

5.5X10-45X10

4.5X10

0.0
0.0

-4

0.2

-4

4X10

γ

0.4

0.6

Fig. 6. Contour lines of Ion (a) in a VTMOS as a function of |1Vbs | andγ . The Vdd is 1.5 V. When |1Vbs | is larger than 1.2 V, a higher Ion (a) is
obtained for larger γ . On the other hand, when |1Vbs | is less than 1.2 V,
higher Ion (a) is obtained for smaller γ .

tioned above, |1Vbs | is limited by leakage current or breakdown of the pn junctions and the maximum |1Vbs | strongly
depends on the device structures and process. Please notethat all the contour lines of 1Vbs converge to one point in
Fig. 4. This point corresponds to the device with γ = 0.
The line of |1Vbs | = 0 V is also shown in Fig. 4. When
|1Vbs | = 0 V, Ioff (a) equals to Ioff (s) and only Ion (a) changes
because 1Vth = 0 V. It should be also noted that at a certain value of 1Vbs , Ion (a) becomes constant regardless of thevalue of γ , as shown in Fig. 4. This 1Vbs is defined as Vo .
In this case, Vo is about −1.2 V. When |1Vbs | is larger than|Vo |, for example 1Vbs = −2 V, a larger Ion (a) is obtained forlarger γ . On the other hand, when |1Vbs | is smaller than |Vo |,for example 1Vbs = −0.3 V, a larger Ion (a) is obtained for asmaller γ . Figure 6 shows the same results in a different way,where the contour lines of Ion (a) are shown as a function of
1Vbs and γ . The slope of the contour lines changes from positive to negative at |1Vbs | = |Vo |. When |1Vbs | is larger than|Vo |, the slope is negative. Thus, a higher Ion (a) is achieved
for larger γ . However, when |Vbs | is smaller than |Vo |, theresult is the opposite.
2.5.4 Optimum condition of γThis interesting result is well explained qualitatively as
follows. Figure 7 shows a schematic of the relation between Ion (a) and γ . Ioff (s) is fixed. In a normal MOSFET(Vbs = 0 V), Ion (a) decreases with increasing γ due to degradation of the S factor and smaller mobility.5) The slope of
the Ion (a)-γ curve is negative. When Vbs is applied, Ion (a) increases and the increase of Ion (a) is larger for larger γ . Therefore, when Vbs is sufficiently large, Ion (a) becomes larger forlarger γ and the slope of the Ion (a)-γ curve becomes positive. The value of |Vo | is slightly smaller than that of Vdd asshown in Fig. 6. The reason is discussed qualitatively in thefollowing.
Here, let us consider a device with 1Vbs = −Vdd and a device with 1Vbs = Vdd . Note that the device with 1Vbs = Vdd
is the dynamic-threshold MOS (DTMOS) where the gate isconnected to the body.13) Although the Vdd of the DTMOS
should be lower than the forward voltage of the pn junction,it has been reported that the Ion (a) of a DTMOS increases
with increasing γ .5, 14) On the other hand, the device with
1Vbs = −Vdd would show almost the same characteristeics as2316

Jpn. J. Appl. Phys. Vol. 39 (2000) Pt. 1, No. 4B

H. KOURA et al.

Ioff(s)=10-13A/ m

Ion(a)

0.4

0.3 Vth=0.3V 0.26V

0.5V
0.1V

delta MOSγ large|Vbs|=Vdd(DTMOS)γγ small

0.7V
0.14V

1.0V
0.2V

Vdd=1.5V 1.3V

|Vbs|>VoIo

0.2

Retrograde
RetrogradeMOS
MOS

0.1

|Vbs|=Vo

uniform MOS

0.0|Vbs|<Vo

1999

2002

2005

year

|Vbs|=0V (normal MOS)γ

this DTMOS when the Vbs dependence of γ is linear. Therefore, the device with 1Vbs = −Vdd roughly corresponds tothe dashed line in Fig. 7. The horizontal line in Fig. 7 corresponds to Vbs = Vo . Therefore, |Vo | is slightly smaller than
Vdd . As shown in this figure, Ion (a) becomes larger with increasing γ when |1Vbs | is larger than |Vo |, while Ion (a) becomes smaller with increasing γ when |1Vbs | is smaller than|Vo |.

2011(a)|Vbs | (obtain Ioff (s) of 10-13 (A/µm))

Fig. 7. Schematic of the relationship between Ion (a) and γ that qualitatively explains the optimum condition of γ under the condition of constant|1Vbs |. Four solid lines show the VTMOS. The dashed line shows the
DTMOS. Since a larger Ion (a) is obtained for larger γ in DTMOS, |Vo | isslightly smaller than Vdd. When |1Vbs | > |Vo |, a larger Ion (a) is obtainedlarger γ , while when |1Vbs | < |Vo |, a larger Ion (a) is obtained for smaller
γ.

2008

10
8

unifom MOS
Retrograde MOS

6
4
2
0

delta MOS
1999

2002

2005

2008

2011

year

(b)
Fig. 8. Scalability of VTMOS in the scaling scenario with scaled Vth . (a)Variation of γ in each generation. (b) Required |1Vbs | to obtain an Ioff (s)of 10−13 A/µm. γ becomes larger by the channel engineering and therequired |1Vbs | can be suppressed by channel engineering.

3. Scalability of VTMOS
1.0

delta MOS
0.8

V th (V)One of the major concerns about regarding a VTMOS is its
scalability.15) We discuss the scalability of VTMOS’s in thissection. The device parameters in each technology generation are mainly based on ITRS.10) Two scaling scenarios of
VTMOS’s are considered in this study: Vth in the active mode
(Vth (a)) is scaled like other device parameters in the first scenario, while Vth (a) is kept constant in the second one.

0.6

uniform MOS
0.4
0.2

3.1 A Scaling scenario with scaled Vth
In the first scaling scenario, Vth (a) is scaled. The other device parameters are also scaled based on ITRS.10) Figure 8(a)shows the variation of γ with the technology generation. The
supply voltage Vdd and Vth (a) in each generation are shownin the figure. The channel-engineered MOS, such as retrograde channel MOS, is just between the two lines (the linesof uniform MOS and delta MOS). Figure 8(a) indicates that γ
becomes larger by the channel engineering. However, in this
scenario, γ decreases as the device is scaled.
Figure 8(b) shows the variation of 1Vbs that is required
to obtain Ioff (s) = 10−13 A/µm. 1Vbs rapidly increases in
uniform MOS, as also in delta MOS. This is a serious problem
because the breakdown voltage would decrease as the device
is scaled. It must be noted that the required Vbs is greatly
suppressed by the channel engineering.
The advantage of channel-engineered MOS is not only inthe large γ but also the Vbs dependence of γ . Figure 9 shows
Vth as a function of Vbs in a uniform MOS and delta MOS. In
the uniform MOS, 1Vth is proportional to the square root of
Vbs , and the effect of back bias is not effective. In the delta
MOS, on the other hand, 1Vth is almost proportional to Vbs .

Vth=0.3V (@|Vbs|=0V)
0.0

0

2

4

|Vbs|(V)68

10

Fig. 9. Relation between Vth and |Vbs |. In a uniform MOS, 1Vth is proportional to the square root of Vbs . In delta MOS, 1Vth is almost proportional
to Vbs . Channel profile should be as steep as in the delta MOS, and a super
steep channel profile is strongly desired in scaled VTMOS.

This is because in delta MOS, the depletion layer width is
kept almost constant even if Vbs is applied. Therefore, thechannel profile of VTMOS should be as steep as that of thedelta MOS, and a super steep channel profile is strongly desired.
3.2 A Scaling scenario with constant Vth
In the second scenario, Ioff (a), and hence Vth (a), are kept
constant, while other parameters such as Vdd , gate lengthand gate oxide thickness are scaled according to ITRS.10)
In VTMOS, Vth (a) can be extremely low because subthreshold leakage is suppressed in the standby mode. Therefore,
this scenario is more practical than the first scenario. Figure 10 shows the variation of γ and the required 1Vbs for aJpn. J. Appl. Phys. Vol. 39 (2000) Pt. 1, No. 4B

H. KOURA et al.

2317

ing on the scaling scenario and applications.
4. Conclusions
The effects of γ and 1Vbs in a VTMOS have been systematically examined by simulation under a condition of fixed
off-current in the standby mode, and the optimal γ and 1Vbs
are derived to obtain a higher on-current in the active modeby means of device simulation. When off-current in the active mode is limited, a larger |1Vbs | and smaller γ are preferable to obtain a higher drive current. When γ is fixed, |1Vbs |should be as large as is permitted by the breakdown and leakage current. When 1Vbs is fixed for some reason, such as
the breakdown, the optimum γ depends on the relationshipbetween |1Vbs | and Vdd . The same optimal conditions are
obtained for a lower off-current and fixed on-current. The
scalability of a VTMOS is also discussed and it is found thatchannel engineering is required in scaled VTMOS. These results are expected to be of great help in designing ultra-low
power VTMOS VLSIs, and the VTMOS will survive in the
50 nm generation depending on the scaling scenario and applications.
Acknowledgement
The authors would like to thank Prof. T. Sakurai for the
fruitful discussions. This work was partly supported by JSPS
Research for the Future Program.

Fig. 10. Scalability of VTMOS in the scenario with constant Vth . (a) Variation of γ in each generation. (b) Required |1Vbs | to obtain Ioff (s) of
10−13 A/µm. The advantage of the constant Vth scenario is that γ is kept
almost constant and the required |1Vbs | remains almost the same. However, the disadvantage is that Ion (a) becomes too small due to the constant
Vth . The best scaling scenario for a VTMOS would depend on the application.

delta MOS. The uniform MOS is not shown here because
the required 1Vbs is too large. In this scenario, the depletion
layer width should decrease rapidly in order to keep Vth constant. Therefore, γ is kept almost constant, and the required
1Vbs is also almost constant. This is a great advantage for
VTMOS. However, a disadvantage of this scenario is that
Ion (a) is greatly degraded due to constant Vth (a) as the device
is scaled.
These discussions suggest that the scalability of VTMOS
depends on the scaling scenario and it also depends on theapplications. In the 50 nm generation with very low supply
voltage, all the requirements for scaled devices, such as highspeed, low standby off-current, low active off-current, will
not fulfilled by normal MOSFETs without threshold control.
VTMOS will certainly satisfy more requirements than normal
MOSFETs and will survive in the 50 nm generation depend-

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