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On the Experimental Determination of Channel Backscattering Characteristics-Limitation and Application for the Process Monitoring Purpose

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Abstract—This paper reports a generalized

temperature-dependent channel backscattering extraction method that can self-consistently determine the temperature sensitivity of the low-field mobility and the critical length in nanoscale MOSFETs. Through comparing the gate voltage and temperature dependence, we have shown that assuming constant temperature sensitivity of the low-field mobility and the critical length will result in unphysical backscattering characteristics. We have also investigated the lim-itation in this self-consistent method and proposed guidelines for experimental extraction. Our results show that channel backscat-tering is increased for NMOSFETs with higher body doping and HfO2 dielectric and can be reduced for PMOSFETs when the process-induced uniaxial compressive strain technology is em-ployed. This paper indicates that the self-consistent temperature-dependent method is competent to be routinely used in technology development for the process monitoring purpose.

Index Terms—Ballistic transport, channel backscattering,

CMOSFET, process monitoring.

I. INTRODUCTION

S

INCE the introduction of channel backscattering theory [1], [2], there has been great interest in determining how close to the ballistic limit the CMOS device can be operated. Indeed, the 2007 edition of the International Technology Roadmap of Semiconductors has reported that, to attain ad-equate drive current for the highly scaled MOSFETs, quasi-ballistic operation with enhanced thermal velocity and injection at the source end appears to be needed [3]. In addition, the continued aggressive scaling of CMOS is driving the industry toward a number of major technological innovations such as high-k dielectrics and uniaxial-strain technologies. Therefore, there is a strong motivation on developing techniques to exper-imentally estimate backscattering coefficient (rsat) for

provid-ing guidelines in CMOS processes and determinprovid-ing impacts of modern technologies on the ballistic efficiency.

To this purpose, Lochtefeld and Antoniadis [4] have pro-posed a technique to determine the thermal limit (the ballistic limit) by comparing the measured effective velocity to the

Manuscript received December 5, 2008; revised May 27, 2009. First published August 25, 2009; current version published September 23, 2009. This work was supported in part by the National Science Council of Taiwan under Contract NSC 98-2221-E-009-178 and in part by the Ministry of Education in Taiwan under ATU Program. The review of this paper was arranged by Editor C. McAndrew.

The authors are with the Department of Electronics Engineering, Na-tional Chiao Tung University, Hsinchu 300, Taiwan (e-mail: jarjar.ee92g@ nctu.edu.tw; pinsu@faculty.nctu.edu.tw).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TED.2009.2028376

simulated injection velocity. Moreover, Barral et al. [5], [6] presented an experimental rsat extraction methodology with

consideration of multisubband population based on the simu-lated corrective factor. Although both studies have originally presented determination of the ballistic efficiency, relying on simulation in extraction procedures is inconvenient to be rou-tinely used in technology development. So far, to the best of our knowledge, the method in [7] and [8] evaluating rsatbased

on the temperature-dependent characteristics of drain current is the only fully experimental method and has been used for process-monitoring purposes [9]–[15]. However, this method assumes that the low-field mobility (μ0) is phonon limited and

proportional to T−1.5, which is questionable for state-of-the-art nanoscale MOSFETs [18]–[20]. For example, Ren et al. [19] have shown that the electron mobility in high-k (HfO2) devices

is relatively insensitive to temperature (∼T−1). Moreover, the temperature dependence of the critical length l may change with devices [20] and has not been considered. Therefore, a correct backscattering extraction method considering accurate temperature dependence of μ0and l is needed.

In this paper, we report a generalized temperature-dependent channel backscattering extraction that can self-consistently de-termine the temperature sensitivity of μ0 and l in nanoscale

MOSFETs. The validity of our method for the process moni-toring purpose is assessed based on various types of devices: high versus low body doping, HfO2 versus SiO2 dielectric,

and unstrained versus uniaxially strained. The organization of this paper is as follows. In Section II, we present the generalized temperature-dependent method and possible error sources. Then, we present several experimental guidelines in utilizing the generalized self-consistent method in Section III. In Section IV, the extracted coefficients on different kinds of devices are discussed. Finally, the conclusion will be drawn in Section V.

II. SELF-CONSISTENT

TEMPERATURE-DEPENDENCEMETHOD

According to the channel backscattering theory [1], [2], the transistor drain current per channel width W in saturation region can be expressed as [21]

Id,sat W = Qinv  1− rsat 1 + rsat   2kBT πm∗  1 2(ηF) 0(ηF)  . (1)

The first factor on the right-hand side (RHS) of (1) is the inversion layer charge at the top of the source-to-channel barrier

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2286 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 56, NO. 10, OCTOBER 2009

Fig. 1. Schematic diagram illustrating the backscattering theory [1]. Carrier in the critical length l has a backscattering ratio rsat. The average injection

velocity υinjis determined by the equilibrium thermal velocity υthermand rsatas υinj= υtherm(1− rsat)/(1 + rsat).

(Fig. 1), which is normally determined by the MOS electrosta-tics [2], i.e., Cox(Vgs− VT ,sat), where Cox is the gate

capaci-tance and VT ,satis the saturation threshold voltage. The second

factor is defined as the ballistic efficiency Bsat and describes

the reduction of injection carriers due to channel backscattering

rsat. The rsatdepends on the mean-free path λ and the critical

length l as rsat= 1/(1 + λ/l). The third factor is the

degener-ate thermal velocity υtherm, which is a function of the Fermi

level EFnormalized to kBT , i.e., ηF = (EF− Ei)/kBT [21].

The temperature-dependent analytic model derived from (1) can be employed to extract the λ/l as well as rsat[10]

∂Id,sat Id,sat∂T = ∂VT ,sat (Vgs− VT ,sat)∂T  1 1 + rsat + 1 1− rsat  ∂rsat ∂T + 1 υtherm ∂υtherm ∂T . (2) Note that we can obtain ∂rsat/∂T =−[(1 + α + (βμ−

βl)− γ)rsat(1− rsat)]/T and ∂υtherm/∂T = (υthermγ)/T

from the temperature dependence of λ/l and υtherm[21], [22]

υtherm=  2kBT πm∗  1/2(ηF) 0(ηF)  ∝Tγ (3a) λ 2kBT μ0 υthermqL  0(ηF) −1(ηF)  qVDS kBT βl ∝ T1+α+(βμ−βl)−γ (3b) where α, βμ, βl, and γ are defined as the temperature

sensi-tivities of the degenerate factor [21], the low-field mobility μ0,

the kBT layer’s width [32], and the thermal velocity υtherm,

respectively. L is the metallurgical channel length [32]. In [7]– [15], the nondegenerate limit α = 0 [21], βμ=−1.5, and βl=

1 were assumed. To generalize (3b), we propose using

λ

∝ T

β−γ (3c)

where (β− γ) accounts for the temperature sensitivity of λ/l. Then, we can obtain ∂rsat/∂T =−[(β − γ)rsat(1− rsat)]/T .

Finally, (2) can be expressed as follows [7], [8], [10], [16]:

λ = −2(β − γ) γ− ∂Id,sat Id,sat∂T + ∂VT ,sat (Vgs−VT ,sat)∂T T − 2. (4)

Fig. 2. Measured Id,sat and VT ,sat versus T characteristics for the

NMOSFET with Lg= 120 nm. Linear dependence of Id,sat and VT ,sat

on T is shown for T = 233∼ 373 K. VT ,sat is determined by maximum

transconductance method with DIBL considered, i.e., VT ,sat= VT ,lin−

DIBL. DIBL is the gate-voltage difference between gate voltages at Id=

100 nA/μm for Vds= 0.05 and 1.5 V.

Note that (4) is derived without the following assump-tions: υtherm= (2kBT /πm∗)0.5, λ = (2kBT μ0/qυtherm), l∝

(kBT )βl, μ0∝ Tβμ, and the nondegenerate limit. When α =

0, βμ=−1.5, βl= 1, and γ = 0.5, β =−1.5 and (4) reduces

to the original model used in [7]–[15]. Although (4) can be used to experimentally extract λ/l as well as rsatfrom the measured

Id,sat− T and VT ,sat− T characteristics, the validity of the

extracted λ/l relies on the accuracy of Id,sat, VT ,sat, β, and γ. In

the following sections, we will examine each of the parameters separately.

Fig. 2 shows measured Id,sat and VT ,sat versus

tempera-ture characteristics for the NMOSFET with Lg= 120 nm.

Linear temperature dependence of Id,sat and VT ,sat can be

observed for T = 233∼ 373 K. From the slope, ∂Id,sat/∂T and ∂VT ,sat/∂T can then be determined. VT ,satwas calculated from the linear threshold voltage VT ,lin, which was determined

by the maximum transconductance method at Vds= 0.05 V,

with drain-induced barrier lowering (DIBL) consideration, i.e.,

VT ,sat= VT ,lin− DIBL. DIBL was characterized from the

subthreshold characteristics as in [7] and [10]. Using VT ,sat

instead of VT ,lin in estimating Qinv is important to accurately

account for the DIBL effect on the reduction of threshold voltage. Fig. 3 shows the calculated−(∂VT/∂T )/(Vgs− VT)

with and without DIBL consideration. Significant discrepancy can be seen as Lg reduces. We have noted that the estimated −(∂VT/∂T )/(Vgs− VT) with DIBL consideration shows the

same Lg dependence as the simulated (∂Qinv/∂T )/Qinv in

[20]. Moreover, to exclude the doping effect [20] and the nonequilibrium effect [28] on the validity of Qinv= Cox(Vgs

VT) for ultrashort channel devices, one can directly obtain (∂Qinv/∂T )/Qinv from the C–V measurement instead of

using −(∂VT/∂T )/(Vgs− VT) in (4). Note that the validity

of Qinv∼ Cox(Vgs− VT) has been confirmed by the C–V

measurement in this paper.

From (3b) and (3c), we know that the physical meaning of

β is related to the mean-free path λ, the low-field mobility μ0,

and the critical length l. However, the backscattering extraction in [7]–[15] involves constant β (i.e., β =−1.5) that is not nec-essarily correct in state-of-the-art MOSFETs with technology

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Fig. 3. Different estimations of−(∂VT/∂T )/(Vgs− VT). VT ,linis

extrap-olated from the maximum transconductance. DIBL was characterized from the subthreshold characteristics.

innovations (such as halo implantation, high-k dielectric, and strain technologies). There is evidence in plenty to show that carrier scattering mechanisms may change from phonon scat-tering (βμ=−1.5 [25]) to Coulomb scattering (βμ> 0) for

devices with different size and technologies [17]–[19]. More-over, one cannot consider λ independent of the carrier energy [30]. In addition, it has been suggested that the entire channel or a more significant part of the channel may participate in the backscattering [29], [30]. While the concept of the kBT

layer [2] can correctly explain MOSFET operation (at least in saturation), the temperature exponent of the critical length

l may not necessarily be equal to one [18], [20], [32]. In

other words, it is difficult to predict an accurate value of β for nanoscale state-of-the-art MOSFETs in the backscattering extraction. Therefore, we propose to use (3c) and (4) to deter-mine β and λ/l self-consistently. The procedure starts with the first guess of β =−1.5 and γ = 0.5. From (4), one can obtain

λ/l at different T and, thus, the temperature power exponent of λ/l. Then, a new guess of β is made for a new λ/l versus T

characteristics. This procedure is repeated until the constraint of (3c) is satisfied. Fig. 4 shows λ/l− T characteristics for the first guess of β =−1.5 and the final self-consistently determined β =−1.185. It can be seen that the calculated

λ/l with β =−1.5 is proportional to T−1.3193. From (3c), we obtain a value of β =−0.8193. It is worth noting that the self-consistently determined β =−1.185 lies in between β = −1.5 and β =−0.8193. Moreover, the temperature dependent of

λ/l can satisfy the constraint of (3c) for self-consistent β, but

not for β =−1.5. Although the difference between the self-consistently determined β and−1.5 is only 0.315, significant discrepancy in λ/l can be seen.

To further verify the extracted self-consistent β, we have di-rectly extracted βμbased on the effective mobility μ, measured

by the split C–V method at Vds= 5 mV with the Rsdcorrection

as in [31]. Fig. 5 shows the comparison of self-consistent β and

βμ for the device with Lg= 120 nm. Although the effective

mobility μ may not be identical to the low-field mobility μ0(as

defined by λ [2], [21]), similar Vgsdependence can be seen. The

increased βμ, as well as β with decreasing Vgs, manifests the

Fig. 4. λ/l versus T characteristics show the need of self-consistent β for

the backscattering coefficient extraction. In [7]–[15], β =−1.5 from β ∼ 1 + (βμ− βl), βμ=−1.5, and βl= 1. Note that different values of Id,satand

VT ,satare considered in (4) at the corresponding temperature.

Fig. 5. Extracted β and βμ versus Vgscharacteristics for the NMOSFET

with Lg= 120 nm. βμ(  ) is observed based on the effective mobility

μ, which is extracted at different temperature by the split C–V method with Rsdcorrection.

importance of Coulomb scattering in the weak inversion region [31]. Fig. 6 shows the extracted rsatand μ for the NMOSFET

with Lg= 120 nm. It can be seen that the assumption of β = −1.5 results in insensitive rsat− Vgsdependence. On the other

hand, the rsat value extracted by the self-consistent β shows

significant Vgsdependence. The increased rsatwith decreasing

Vgsresults from the decreased μ (through λ) and manifests the

importance of Coulomb scattering in the weak inversion region [31]. Moreover, the decreased potential gradient of the source-channel junction barrier (i.e., increased l) with decreasing Vgs

may also account for such Vgsdependence of the rsat[8].

III. LIMITATION ANDGUIDELINES

This self-consistent temperature-dependent method still has limitations because of the uncertainty in γ. From (3a), we know that γ decreases from 0.5 (nondegenerate limit: ηF → 0) to 0

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2288 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 56, NO. 10, OCTOBER 2009

Fig. 6. Extracted rsatand the effective mobility μ versus Vgscharacteristics

for the NMOSFET with Lg= 120 nm.

we propose using γ = 0.5 as a first approximation and then estimating the impact of the γ = 0.5 assumption on the ex-tracted rsat. From rsat= 1/(1 + λ/l) and (4), ∂rsat/∂γ can

be expressed as ∂rsat ∂γ = rsat(1− rsat) γ− ∂Id,sat Id,sat∂T + ∂VT ,sat (Vgs−VT ,sat)∂T T . (5)

We know from (4) and (5) that the RHS value of (5) is positive, which implies that an overestimated γ (Δγ) may result in an overrated rsat (Δrsat). Based on (5), we propose

several experimental guidelines to increase accuracy of rsat

extraction.

1) To reduce the impact of Δγ, one can reduce the RHS value of (5) by increasing the measurement temperature. 2) Δγ can also be reduced when temperature increases

because the degenerate effect is reduced and ηF → 0

(i.e., γ → 0.5).

3) Comparison under the same effective electrical field (Eeff) is needed to minimize Δrsat due to different ηF. Eeff = (Vgs + (n− 1)VT − nVFB − 2nΦB)/3nTOX,

where n is an empirical factor with the values ∼2 and

∼3 commonly used for electrons and holes, respectively

[34]. VFBis the flatband voltage, and ΦB is the potential

difference between the Fermi level and the intrinsic Fermi level.

4) On the other hand, Δγ may be similar under the same

Eeff and can be neglected for the purpose of qualitative

comparison.

5) Since Δγ, as well as Δrsat, varies with Vgs, a comparison

from weak inversion to strong inversion is suggested. 6) Once γ can be determined by other methods such as

Monte Carlo simulations [20], one can use (5) to estimate Δrsatand correct the extracted rsat.

7) In case the Qinvis different from Cox(Vgs− VT), one can

directly obtain (∂Qinv/∂T )/Qinv from the C–V

mea-surement [33] instead of using−(∂VT/∂T )/(Vgs− VT)

in (4).

To further assess the impact of Δγ on rsat, the results of

multisubband Monte Carlo (MSMC) simulation in [20] are investigated. Fig. 7 shows the calculated ballistic efficiency

Fig. 7. Calculated ballistic efficiency (1− rsat)/(1 + rsat) versus Lgbased

on the MSMC results in [20]. In [20], γ≈ 0.2 was extracted for different Lg.

Fig. 8. (a) Extracted β and (b) rsatversus Eeffcharacteristics for 100-nm Lg

NMOSFETs with high and low body doping Na.

Bsatversus Lgbased on the results in [20]. It can be seen that

after considering the VT ,sat and Lg dependence of β in (4),

the observed Bsat for γ = 0.5 (set B) and 0.2 (set C) present

almost the same Lg dependence as predicted by the MSMC

simulation. Note that γ≈ 0.2 for different Lgwas extracted in [20]. Moreover, Fig. 7 reveals the importance of Lgdependence

of β. Since β can be physically determined, the self-consistent temperature-dependent method is competent to be routinely used in technology development for the process monitoring purpose. Three examples of technology comparison (including high versus low body doping, HfO2 versus SiO2 dielectric,

and the impact of uniaxial strain) for the process monitoring purpose are presented in the next section.

IV. RESULT ANDDISCUSSION

A. High Versus Low Body Doping

Fig. 8 shows the extracted β and rsat versus Eeff

charac-teristics for the 100-nm Lg NMOSFETs with high and low

body doping Na. It is clear that the self-consistently determined β really presents the increased βμ due to increased Coulomb

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Fig. 9. (a) Extracted β and (b) rsatversus Eeffcharacteristics for 100-nm Lg

NMOSFETs with HfO2and SiO2gate dielectrics.

increasing Na on rsat can be observed through comparing

the extracted rsat in the whole Vgs region. In contrast to the

result for β =−1.5, the rsat extracted by the self-consistent

β is increased for the high Na device. The increased rsat is

consistent with the prediction in [26] and may result from the reduced carrier mobility [24] due to increased Coulomb scattering.

B. HfO2Versus SiO2Dielectric

Coprocessed NMOSFETs with HfO2 and SiO2 dielectrics

were implanted by the same Nacondition and showed similar

DIBL characteristics. Fig. 9 shows the extracted β and rsat

versus Eeff characteristics for the 100-nm LgNMOSFETs with

HfO2 and SiO2 dielectrics. It is worth noting that the

self-consistently determined β is increased for the HfO2dielectric.

The result is consistent with the simulation predictions in [19] and can be explained by the active low-energy interfacial phonons [19] and excess Coulomb scattering [27]. Moreover, reduced carrier mobility has been reported for high-k devices [19] and was expected to reduce λ as well as increase rsat.

However, as shown in Fig. 9(b), the extracted rsat cannot

respond to the reduced mobility unless the self-consistent β is applied.

C. Impact of Uniaxial Strain

Process-induced uniaxially strained silicon technologies fea-turing compressive SiGe source/drain and compressive contact etch stop layer were employed for the strained device. Related strain characteristics of these devices have been reported in our previous studies [16], [23], [24]. Fig. 10 shows the extracted

β and rsat versus Eeff characteristics for the unstrained and

strained PMOSFETs with Lg = 100 nm, respectively. It can

be seen that the self-consistently determined β is far from

−1.5, particularly for the unstrained device. Similar behavior

also shows in the measured Id,sat−Vgscharacteristics [16], in

which the Id,sat of the strained device shows more

phonon-limited behavior (i.e., Id,satdecreases as temperature increases)

and thus β decreases. Moreover, rsat is actually reduced in

the compressive-strained PFET, which is contrary to previ-ous studies [9], [10] using β =−1.5. Note that the γ = 0.5 assumption may result in underestimation for the impact of

Fig. 10. (a) Extracted β and (b) rsatversus Eeffcharacteristics for 100-nm LgPMOSFETs with and without uniaxially compressive strain [23], [24]. The

Rsdeffect has been corrected (Rsd∼ 125 Ω · μm for the strained device and

214 Ω· μm for the unstrained device).

compressive strain on the reduction of rsat because the

de-generate effect is more significant for the strained PMOSFET, resulting in more overestimated γ as well as rsat. In addition,

we have carefully extracted the source/drain resistance Rsd(per

one side) for strained (∼125 Ω · μm) and unstrained devices (∼214 Ω · μm), respectively [35]. The effect of Rsd can then

be considered by replacing Vgsin (4) with (Vgs−Id,satRsd) [7].

It is clear in Fig. 10(b) that rsatwith the Rsd correction is still

reduced in the compressive-strained PFET. V. CONCLUSION

We have reported a generalized temperature-dependent chan-nel backscattering extraction method that can self-consistently determine β in nanoscale MOSFETs. Through comparing the

Vgsand temperature dependence, we have shown that assuming

βμ and βl constants will result in unphysical backscattering

characteristics. We have also investigated the limitation in this self-consistent method and proposed guidelines for experimen-tal extraction. Our results indicate that rsat is increased for

NMOSFETs with higher Na and HfO2 dielectric and can be

reduced for PMOSFETs when the process-induced uniaxial compressive strain technology is employed. Since β and rsat

can be physically determined by our developed program, the self-consistent temperature-dependent method is competent to be routinely used in technology development for the process monitoring purpose.

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Wei Lee (S’03) was born in Taipei, Taiwan, in

1979. He received the B.S. degree from the Depart-ment of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan, in 2001 and the M.S. degree from the Department of Elec-trical Engineering, National Chiao Tung University (NCTU), Hsinchu, Taiwan, in 2003. He is currently working toward the Ph.D. degree in the Institute of Electronics, NCTU.

From 2003 to 2009, he conducted his doctoral research in physics and characterization of advanced CMOS devices in the NCTU. He has also been an intern student with the Taiwan Semiconductor Manufacturing Company, Hsinchu. His research inter-ests include mesophysics, carrier transport, single-electron transistors, channel backscattering characteristics, and silicon-based nanoelectronics.

Pin Su (S’98–M’02) received the B.S. and M.S.

degrees in electronics engineering from the National Chiao Tung University (NCTU), Hsinchu, Taiwan, and the Ph.D. degree from the Department of Electri-cal Engineering and Computer Sciences, University of California, Berkeley.

From 1997 to 2003, he conducted his doctoral and postdoctoral research in silicon-on-insulator (SOI) devices at Berkeley. He was also one of the major contributors to the unified BSIMSOI model, the first industrial standard SOI MOSFET model for circuit design. Since August 2003, he has been with the Department of Electronics Engineering, NCTU, where he is currently an Associate Professor. He has authored or coauthored over 85 research papers in international journals and conference proceedings. His research interests include silicon-based nanoelec-tronics, modeling and design for advanced CMOS devices, and device/circuit interactions in ultrascaled CMOS.

數據

Fig. 1. Schematic diagram illustrating the backscattering theory [1]. Carrier in the critical length l has a backscattering ratio r sat
Fig. 4. λ/l versus T characteristics show the need of self-consistent β for
Fig. 6. Extracted r sat and the effective mobility μ versus V gs characteristics
Fig. 10. (a) Extracted β and (b) r sat versus E eff characteristics for 100-nm L g PMOSFETs with and without uniaxially compressive strain [23], [24]

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