Universal Relationship between Low-Field Mobility and High-Field Carrier Velocity in High-κ and SiO2 Gate Dielectric MOSFETs

Masumi Saitoh and Ken Uchida Advanced LSI Technology Laboratory, Corporate R&D Center, Toshiba Corporation, 8 Shinsugita-cho, Isogo-ku, Yokohama

235-8522, Japan, Tel: +81-45-770-3273, Fax: +81-45-770-3286, E-mail: masumi.saitoh@toshiba.co.jp Abstract

The relationships between velocity, v, and mobility, µ, are investigated to clarify the effectiveness of µ enhancement to increase v in short channel FETs with SiO2 as well as high-κ gate dielectric. The v-µ relationships were extracted on the basis of accurate understanding of Vsub dependence of µ; Vsub dependences of µ in high-κ, high Nsub, and short-channel FETs were carefully studied and the deviations from the standard Vsub dependence were found in each case. It was found that v-µ relationship is universal, namely independent of gate dielectrics, in Si nFETs with Leff of down to 80 nm. Due to lower µ and resultant weaker v saturation in high-κ FETs, µ booster technologies more significantly contribute to v and Ion enhancements in short-channel high-κ FETs than in SiO2 FETs.

Introduction The carrier velocity (v) enhancement is a key to boost

nano-scaled FET performance. Recently, high mobility channels such as strained Si have been intensively studied as technology boosters, because higher low-field mobility (µ) is believed to result in higher v. However, in short-channel FETs, the impact of µ enhancement on high-field velocity v and resultant Ion is still unclear. Meanwhile, high-κ insulators have been introduced for Tinv scaling with low gate leakage. As shown in Fig.1, low-field µ of high-κ nFETs degrades compared to SiO2 nFETs due to scattering mechanisms inherent to high-κ such as remote Coulomb scattering or remote phonon scattering (1,2). However, high-field transport such as velocity saturation phenomena and the impact of lower µ on v in short-channel high-κ devices have rarely been studied.

In this work, the relationship between µ and v in high-κ and SiO2 FETs is experimentally investigated for the first time based on accurate understanding on Vsub dependence of µ. Effectiveness of mobility boosters in short-channel high-κ FETs is also examined.

Substrate-Bias Dependence of Low-Field Mobility µ of a single MOSFET is controlled by Vsub. Although

Vsub dependence of µ has been understood within the framework of the universal µ curve (3) so far, µ universality in practical devices, that is, high-Nsub (1018 cm-3) and short-channel devices has never been examined. In this work, µ universality in these devices is examined for the first time. A. High-Nsub FETs

Fig.2 shows the measured µ as a function of the effective field Eeff in nFETs with various Nsub. Inversion charge density Ninv and depletion charge density Ndepl were obtained

by integrating C-V curves measured using split C-V method. µ-Eeff relationships of high-Nsub devices deviate from those of low-Nsub devices in high Eeff, suggesting that in order to realize universality in a wide range of Nsub, the definition of Eeff (∝ η*Ninv + Ndepl) has to be changed. In the previous report (4), η was optimized for each Nsub. Therefore, η optimization is firstly examined. Fig.3 shows µ-Eeff in nFETs with low-Nsub and high-Nsub, where η of high-Nsub FETs is optimized to realize universality. Universality is obtained in middle Eeff, but it fails in high Eeff.

Instead of η optimization, Ndepl is modified to Ndepl’ to reproduce the universal curve; Eeff is redefined as η*Ninv+Ndepl’ in this work. Fig.4 shows Ndepl’ optimized to realize universality at each Ndepl. Vsub is varied at each Nsub. It is found that Ndepl’ at high Ndepl is lower than Ndepl used in conventional Eeff definition and can be expressed as a quadratic formula. By using the newly defined Eeff, “true” universality is obtained in a wide range of Nsub as well as Vsub as shown in Fig.5. When Vsub is increased at a fixed Nsub, the effect of Ndepl on Eeff can be represented by ζ (= dNdepl’/ dNdepl: slope of Ndepl’-Ndepl curve in Fig.4). Fig.6 shows ζ as a function of Nsub. ζ decreases with Nsub, corresponding to the decrease in the slope of Ndepl’-Ndepl in Fig.4.

Fig.7 shows the measured µ as a function of Ndepl at Ninv of 8e12 cm-2. Conventional universal curve (ζ =1) underestimates µ of high-Nsub devices at high Ndepl, because it assumes larger ζ (higher Eeff) than the newly defined Eeff. To clarify the reason for the failure of conventional Eeff definition, zinv (averaged inversion layer thickness) is investigated, since µ is strongly related to the quantum confinement. Fig.8 shows zinv calculated using Schrödinger- Poisson solver as a function of Ndepl. zinv firstly decreases with Ndepl, but starts to saturate at high Ndepl, since it approaches de Broglie wavelength. The relationship between ∆µ (µ underestimation by conventional Eeff calculated using Matthiessen’s rule) in Fig.7 and ∆zinv (zinv underestimation by extrapolation of zinv at low Ndepl) in Fig.8 is plotted in Fig.9. Clear correlation indicates that zinv saturation at high Nsub (Ndepl) causes the failure of conventional Eeff definition. B. Short-channel FETs

Fig.10 shows the measured µ-Eeff in 100-nm nFET. µ of short-channel devices is extracted by using the long-channel C-V curve in the same way as in (5). By using ζ of 0.475, the “true” universality is also obtained in short-channel devices. This ζ is much smaller than the value (0.61) expected from Fig.6 (long-channel). Fig.11 shows ζ and Vth as a function of Leff. ζ decreases with Leff. Since ζ reduction is strongly correlated with Vth roll-off, it is probably caused

by short-channel effect (penetration of lateral field from source/drain). ζ reduction in high-Nsub and short-channel FETs must be considered for accurate mobility modeling. C. High-κ FETs

Mobility behavior in HfSiON devices is also studied in terms of Vsub dependence. Figs.12 and 13 show the measured µ-Eeff and µ-Ndepl in HfSiON nFETs, respectively. |dµ/dNdepl| is smaller in HfSiON than in SiO2. As shown in Fig.1, Eeff dependence of HfSiON mobility at high Eeff (limited by surface roughness scattering) is weaker than SiO2. This results in smaller |dµ/dNdepl| in HfSiON. Fig.14 shows |dµ/dNdepl| as a function of Leff. In short-channel devices, |dµ/dNdepl| further decreases. Fig.15 summarizes |dµ/dVth| (∝ |dµ/dNdepl|) in long/short-channel SiO2/HfSiON nFETs. Short-channel HfSiON device shows extremely small |dµ/dVth|, indicating that Vth can be adjusted without affecting µ. This is suitable for body-biasing circuits to suppress Vth variations and leakage (6).

High-Field Carrier Velocity vs. Low-Field Mobility v-µ relationship in short-channel FETs is measured by

changing µ with Vsub. The measurement sequence is shown in Fig.16. v (carrier velocity near the potential top) in short-channel FETs is extracted by using long-channel C-V (5). Although the gate overdrive (Vg - Vth) or Ninv was fixed when Vsub is changed in the previous report (7), we propose fixing of pinch-off voltage Vdsat. As shown in the inset of Fig.16, the potential drop from the potential top to the pinch-off point and lateral electric field is made almost the same at each Vsub by fixing Vdsat. As a result, v-µ at fixed lateral field is extracted, and the effect of only µ (not lateral field) on v can be clarified. The measured v-µ in SiO2 nFETs and pFETs is shown in Figs.17(a) and (b), respectively. v can be expressed as the power of µ (v ∝ µα). α represents the impact of µ enhancement on v in short-channel FETs. α is plotted against Leff in Fig.18. For L longer than 1 µm (low lateral field), α is almost unity (v ∝ µ). For shorter L, α decreases due to velocity saturation. As a result of higher µ in nFETs, α decreases faster in nFETs than in pFETs. Higher Vdsat (higher field) results in faster decrease of α. For comparison, Fig.19 shows α-Leff obtained by fixing Ninv at each Vsub. Since lateral field increases with |Vsub| when Ninv is fixed, α is underestimated. This indicates the superiority of our v-extraction technique where Vdsat is fixed.

To confirm the extracted v-µ, 2-D device simulation is performed. Here, the relationship between v and lateral field E extracted from thick-tox SiO2 FETs shown in Fig.20 is assumed. Fig.21 shows v-µ of 0.1-µm nFET calculated by drift-diffusion model (DDM) and energy transport model (ETM). The agreement of ETM result with the experiment indicates the importance of velocity overshoot in sub-0.1 µm devices. Fig.22 shows v-µ at each Leff calculated using ETM. Calculation reproduces the experiment for a wide range of Leff, indicating the validity of our extraction. Fig.23 shows α-Leff calculated using DDM and ETM. Velocity overshoot

recovers α in sub-0.1 µm devices. v-µ in HfSiON nFETs is also studied. Fig.24 shows

extracted v-µ in HfSiO(N) and SiO2 nFETs. Calculation results assuming v saturation model of SiO2 are also shown. Experimental data of all devices (down to Leff of 80 nm) are located on the calculated curves, clearly demonstrating that v saturation model (v-E relationship & saturation velocity vsat) are the same in HfSiO(N) and SiO2 nFETs. Namely, v-µ relationship is universal and independent of gate dielectrics. v of short-channel FETs can be predicted from these universal v-µ curves once long-channel µ is known.

Next, the effectiveness of µ boosters in short-channel high-κ FETs is examined. Figs.25 and 26 show the measured Ion and v as a function of Leff, respectively. v and resultant Ion degradations in short-channel HfSiON FETs as compared to SiO2 FETs (10~20%) are much smaller than the degradations in long-channel FETs which correspond to µ degradation (30~40%). The smaller v degradation in shorter- channel HfSiON FETs can be explained by smaller µ and weaker v saturation in HfSiON as shown in Fig.24. Calculated α-Leff in SiO2 and HfSiON nFETs is shown in Fig.27. Due to weaker v saturation, α of HfSiON FETs is larger than 0.5 even in sub-0.1 µm regime. This means that µ enhancement by technology boosters significantly contributes to v and Ion enhancements in short-channel HfSiON FETs. Fig.28 shows calculated α-µ for various Leff. Although constant Nsub (constant µ) is assumed throughout the whole Leff range in Fig.27, Nsub increase for suppressing short-channel effects results in lower µ and higher α.

Summary High-field transport in short-channel high-κ and SiO2

FETs was investigated to clarify the impact of µ enhance- ment on v. v-µ relationship (v ∝ µα) was accurately extracted by applying Vsub. It was newly found that Vsub dependence of µ (µ universality) significantly changes in high-Nsub FETs, short-channel FETs, and high-κ FETs. We found for the first time that v-µ relationship is universal in Si nFETs (independent of gate dielectrics). Due to lower µ of high-κ FETs, µ boosters have a greater impact on v and Ion enhance- ments in short-channel high-κ FETs than in SiO2 FETs.

Acknowledgements The authors would like to thank Drs. T. Watanabe and M.

Takayanagi for offering their samples and Drs. A. Kinoshita, Y. Nakabayashi, and M. Koyama for fruitful discussions. They also thank Drs. N. Fukushima and A. Nishiyama for continuous supports.

References (1) M. V. Fischetti et al., J. Appl. Phys. 90, 4587 (2001). (2) R. Iijima et al., IEDM Tech. Dig., p. 433 (2005). (3) S. Takagi et al., IEEE Trans. ED 41, 2357 (1994). (4) H. Irie et al., IEDM Tech. Dig., p. 459 (2003). (5) A. Lochtefeld et al., IBM. J. Res. & Dev. 46, 347 (2002). (6) J. Tschanz et al., ISSCC Tech. Dig., p. 422. (2002). (7) R. Ohba et al., IEEE Trans. ED 48, 338 (2001).

100

200

300

400

500

0.4 0.5 0.6 0.70.8 1

SiO2

HfSiON

Eeff

(MV/cm)

- 30 %

Nsub

~ 1e18 cm-3

200

300

400500600700800900

1000

0.1 1

9e15 2.8e16 1.1e17

2.8e17 4.5e17 9.3e17

Eeff

= (q/εSi

)(η*Ninv

+ Ndepl

) (MV/cm)

Nsub

(cm-3)

Notuniversal

η = 0.5L : 10 µm

100

200

300

400

500

0.5 0.6 0.7 0.8 0.9 1

Nsub

: 9.3e17cm-3

η : 0.415 (optimized)

Nsub

: 9.0e15cm-3

Eeff

= (q/εSi)(η*Ninv + Ndepl) (MV/cm)

η : 0.5

Notuniversal

0

1x1012

2x1012

3x1012

4x1012

5x1012

0 1x1012 3x1012 5x1012

Ndepl

(cm-2)

9.3e17

4.5e17

1.1e179e15

Conv. Eeff Def.

Increase

- 1.9e-14*Ndepl

2N

depl' = 0.86*N

depl

IncreaseV

sub

Nsub (cm-3)

(Ndepl

' = Ndepl

)

New Eeff Def.

Fig.1. µ-Eeff in SiO2 nFETs and HfSiON nFETs. µ of HfSiON FETs degrades as compared to SiO2 FETs by about 30 %.

Fig.2. µ-Eeff in nFETs with various Nsub (conventional Eeff def.). µ-Eeff of high-Nsub FETs deviate from those of low-Nsub FETs in high-Eeff region.

Fig.3. µ-Eeff in nFETs with low-Nsub and high-Nsub. η of high-Nsub FETs is optimized. Universality is obtained only in middle Eeff.

Fig.4. Ndepl’ (symbols) optimized to realize universality at each Ndepl. Ndepl’ at high Ndepl is lower than Ndepl and can be expressed as a quadratic formula.

200

300

400500600700800900

1000

0.1 1

9e15 2.8e16 1.1e17

2.8e17 4.5e17 9.3e17

Eeff

= (q/εSi

)(0.5*Ninv

+ Ndepl

' ) (MV/cm)

Nsub (cm-3)

Universal

- 1.9e-14*Ndepl2

Ndepl' =

0.86*Ndepl

Increase Vsub 0.5

0.6

0.7

0.8

0.9

1

1x1016 1x1017 1x1018 1x1019

Nsub

(cm-3)

ζ = dNdepl

'/dNdepl

200

300

400

0 1x1012 2x1012 3x1012 4x1012 5x1012

Ndepl (cm-2)

9.3e17

4.5e17

1.1e17

Ninv : 8e12 cm-2

9e15

∆µ

Conv. Eeff Def.

IncreaseNsub (cm-3)

IncreaseV

sub

0.4

0.41

0.42

0.43

0.44

0.45

0.46

0 1x1012 2x1012 3x1012 4x1012

Ndepl

(cm-2)

∆zinv

Extrapolated from zinv at low Ndepl

Fig.5. µ-Eeff in nFETs with various Nsub and Vsub (new Eeff def.). “True” universality is obtained for a wide range of Nsub and Vsub.

Fig.6. Extracted ζ (=dNdepl’/dNdepl) as a function of Nsub. ζ decreases with Nsub. This corresponds to the decrease in the slope of Ndepl’-Ndepl in Fig.4.

Fig.7. Measured µ (symbols) as a function of Ndepl at Ninv of 8e12 cm-2. Conventional Eeff def. underestimates µ at high Ndepl.

Fig.8. Calculated zinv as a function of Ndepl. zinv decreases with Ndepl, but starts to saturate at high Ndepl, since it approaches de Broglie wavelength.

2000

4000

60008000

1x104

3x104

0.01 0.1∆zinv (nm)

100

1000

0.1 1

Leff

: 100 nm

Universal Curve

Eeff

= (q/εSi)(0.5*Ninv + Ndepl') (MV/cm)

Increase Vsub

from 0 to -1 V

ζ = 0.475

(Nsub

~ 1e18 cm-3)

0.4

0.45

0.5

0.55

0.6

0.65

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.1 1 10L

eff (µm)

HfSiON

5060708090

100

200

300

0.3 0.4 0.5 0.6 0.8 1

L : 1 µm

Eeff

= (q/εSi

)(0.5*Ninv

+ Ndepl

') (MV/cm)

Increase Vsub

from 0 to -1 V

(Nsub ~ 1e18 cm-3)

Fig.9. Relationship between ∆µ in Fig.7 (extracted using Matthiessen’s rule) and ∆zinv in Fig.8. Clear relationship is obtained.

Fig.10. µ-Eeff in 100-nm nFETs. To realize universality, we must assume ζ of 0.475, much smaller than 0.61 for long-L FETs with the same Nsub.

Fig.11. ζ and Vth as a function of Leff. ζ decreases with Leff. ζ reduction corresponds to Vth roll-off, indicating it is caused by short-channel effect.

Fig.12. µ-Eeff in 1-µm HfSiON nFETs. Hf conc. is 30 % and Tinv is 2.65 nm. Mobility universality is not obtained within this Eeff range.

SiO2Nsub ~ 1e18

200

300

400

0 1x1012 3x1012 5x1012

Ndepl

(cm-2)

HfSiONN

sub ~ 1e18

Ninv

:

Measurement (SiO2)

Increase Vsub

IncreaseVsub

8e12 cm-2

Long channel

0

2x10-14

4x10-14

6x10-14

8x10-14

1x10-13

0.1 1

SiO2

HfSiON

Leff (µm)

Ninv

: 8e12 cm-2

nMOS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

SiO2

Leff

: 10 µm

100 nm 1 µm

150 nmHfSiON

Ninv : 8e12 cm-2

Fig.13. Measured µ (symbols) as a function of Ndepl changed by Vsub in SiO2 and HfSiON nFETs (long channel). The slope of µ-Ndepl is more gradual in HfSiON.

Fig.14. |dµ/dNdepl| as a function of Leff in SiO2 and HfSiON. |dµ/dNdepl| is divided by µ0 (µ at Vsub = 0) for normalization. |dµ/dNdepl| in HfSiON rapidly decreases with Leff.

Fig.15. Summary of µ change rate when Vth (Ndepl) is increased by Vsub in long/short- channel SiO2/HfSiON nFETs. The rate decreases in shorter-L and HfSiON.

Source

DrainPinch-offpoint

VdsatVds

Leff

@fixed Leff

Measure Id-Vg @low Vds (5mV), each VsubCalculate µ-Eeff and ζ

Measure Id-Vd @each Vg, each VsubCalculate Vdsat @each Vg from linear extrapolation of dId/dVd – VdFind Vg (=Vg’(Vsub)) @each Vsubfor which Vdsat = Vdsat’

Measure Id @high Vds(1V), Vg’(Vsub), each VsubCalculate v @Vdsat’, each Vsub

Extract µ @Vg’(Vsub), each Vsub from the universal µ-Eeff curve

Obtain v-µ @Vdsat’, each Vsub

E

LateralField

Source

DrainPinch-offpoint

VdsatVds

Leff

@fixed Leff

Measure Id-Vg @low Vds (5mV), each VsubCalculate µ-Eeff and ζ

Measure Id-Vd @each Vg, each VsubCalculate Vdsat @each Vg from linear extrapolation of dId/dVd – VdFind Vg (=Vg’(Vsub)) @each Vsubfor which Vdsat = Vdsat’

Measure Id @high Vds(1V), Vg’(Vsub), each VsubCalculate v @Vdsat’, each Vsub

Extract µ @Vg’(Vsub), each Vsub from the universal µ-Eeff curve

Obtain v-µ @Vdsat’, each Vsub

E

LateralField

6x105

8x1051x106

2x106

3x106

4x1065x106

200 220 240 260 280 300Mobility (cm2/Vs)

ReduceLeff (µm)

0.10.14

0.19

0.3

0.45

1

Vdsat : 0.5 VVd : 1 V

(a) nMOS

Increase Vsub

3x105

4x1055x1056x105

8x1051x106

2x106

30 40 50 60 70Mobility (cm2/Vs)

0.1

0.14

0.19

0.3Vdsat : -0.5 VVd : -1 V

0.08

(b) pMOS

ReduceLeff (µm)

Fig.16. Measurement sequence of v-µ relationship in short-channel FETs. As shown in the inset, pinch-off voltage Vdsat corresponds to the voltage drop from the potential top near the source to the pinch-off point. By fixing Vdsat to Vdsat’ at each Vsub, lateral electric field is made almost the same and v-µ at fixed lateral field is extracted.

Fig.17. Measured v-µ at each Leff in SiO2 (a) nFETs and (b) pFETs. |Vsub| is varied from 0 to |1 V| at each Leff to modulate µ. The effect of parasitic resistance Rsd is also considered in v calculation. v can be expressed as the power of µ (v ∝ µα) at each Leff. The power index α decreases with reducing Leff (increasing lateral field).

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10

0.40.50.6

Leff (µm)

|Vd| : 1 V

|Vdsat

| (V)

pMOS

nMOS

IncreaseV

dsat

Low EHigh E

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10

nMOSpMOS

Leff (µm)

|Vdsat

|

Ninv

: 5e12 cm-2

Underestimate

: 0.5 V

0

2x106

4x106

6x106

8x106

1x107

0 2x104 4x104 6x104 8x104

Lateral Field (V/cm)

vsat = 8.5e6 cm/s

Electron (β = 1.4)

Hole (β = 1.3)

0

1x106

2x106

3x106

4x106

5x106

0 50 100 150 200 250 300

Calc. (ETM) Calc. (DDM) Exp. (SiO

2)

Vdsat : 0.5 V, Vd : 1 V

Mobility (cm2/Vs)

Leff : 0.1 µm

nMOS

Fig.18. Extracted α as a function of Leff. α decreases faster in nFETs due to higher µ. Higher Vdsat (higher lateral field) leads to faster α decrease.

Fig.19. α-Leff when Vdsat is fixed or Ninv (or Vg - Vth) is fixed at each Vsub. Since lateral field changes with Vsub when Ninv is fixed, α is underestimated.

Fig.20. v as a function of lateral field (E) measured using thick-tox SiO2 FETs. Measured results were fitted to velocity saturation model (inset).

Fig.21. v-µ at Leff of 0.1 µm calculated by ETM and DDM. To reproduce the experiment, velocity overshoot (ETM) must be considered.

0

1x106

2x106

3x106

4x106

5x106

0 50 100 150 200 250 300Mobility (cm2/Vs)

0.1

0.14

0.19

0.3

0.451

|Vdsat

| : 0.5 V, |Vd| : 1 V

pMOS

nMOSLine : Calc. (ETM)

ReduceL

eff (µm)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1

Calc. (ETM)Calc. (DDM)Exp.

Leff

(µm)

Vdsat : 0.5 V, Vd : 1 VnMOS

α recovery by v overshoot

0

1x106

2x106

3x106

4x106

5x106

0 50 100 150 200 250 300Mobility (cm2/Vs)

Leff (µm) 0.1

0.14

0.19

0.3

0.45

1

Vdsat

: 0.5 VV

d : 1 V

pMOS

SiO2,nMOS

Line : Calc.

0.08HfSiON

HfSiO

v : -19%

µ : -39%

SiO2,

Fig.22. ETM calculation (lines) and measurement (SiO2, symbols) of v-µ at each Leff. Calculation reproduces the experiment for a wide range of Leff.

Fig.23. α-Leff calculated by ETM and DDM. In sub-0.1 µm devices, α by ETM is larger than DDM, indicating velocity overshoot recovers α.

Fig.24. Measured results (symbols) of v-µ at each Leff in SiO2 and HfSiO(N). Calculation (lines) assumes v saturation model of SiO2. All the data (down to Leff of 80 nm) are located on the calculated curves. Smaller v degradation at short Leff in HfSiON can be explained by weaker v saturation.

2

3

456789

10

0.1 1

HfSiON SiO

2- 33%

Leff

(µm)

- 12 % Vd : 1 V

Vg - V

th : 0.8 V

nMOS

4x105

6x105

8x1051x106

3x106

5x106

0.1 1

SiO2

HfSiON

Vd : 1 V

Vdsat

: 0.5 V

- 35%

- 19 %

Leff

(µm)

nMOS

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1

SiO2

HfSiON

Leff (µm)

Calc.

Vdsat

: 0.5 V, Vd : 1 V

nMOS

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400Mobility (cm2/Vs)

Vdsat

: 0.5 VV

d : 1 V

Leff (µm)

0.0650.080.10.14

0.19

0.30.45

HfSiON SiO2

Calc.

1

Const.N

sub

IncreasingNsub

Fig.25. Measured Idsat-Leff in SiO2 and HfSiON nFETs. Idsat is mutiplied by Tinv for Qinv normalization. Idsat degradation at short Leff is much smaller than degradation at long Leff.

Fig.26. Measured v-Leff in SiO2 and HfSiON nFETs. v degradation at short Leff is much smaller than v degradation at long Leff, which corresponds to µ degradation.

Fig.27. α-Leff calculated assuming µ of SiO2 and HfSiON. Due to smaller µ and weaker v saturation, α of HfSiON is larger than 0.5 even in sub-0.1 µm regime.

Fig.28. Calculated α as a function of µ at each Leff. Although constant Nsub (µ) is assumed throughout the whole Leff range in Fig.27, µ reduction by increasing Nsub leads to higher α.

( )[ ] ββµµ

/1/1 satvE

Ev+

=