1132 IEEE ELECTRON DEVICE LETTERS, VOL. 28, NO. 12, DECEMBER 2007
A Constant-Mobility Method to Enable MOSFET
Series-Resistance Extraction
Da-Wen Lin, Ming-Lung Cheng, Shyh-Wei Wang, Chung-Cheng Wu, and Ming-Jer Chen
Abstract—A new method of extracting the MOSFET series resistance Rsdis proposed. This method requires only simple dc
measurements on a single test device. Experimental demonstration is presented, without requiring quantities such as gate-oxide thick-ness, physical gate length, or effective channel length. The merit of the method stems from the specifically arranged bias conditions in which the channel carrier mobility remains constant for high vertical electric fields. It is this unique property which makes the proposed method suitable for short-channel devices.
Index Terms—Mobility, MOSFET, series resistance.
I. INTRODUCTION
O
N THE BASIS of the MOSFET equivalent circuit (the inset in Fig. 1), the series resistance Rsdleads to excess potential drop, reducing the intrinsic voltages and degrading the drive capacity. As the gate length Lgate shrinks, the Rsd becomes a larger portion of the total resistance. Hence, the drive current degradation is more serious in short-channel devices. Many methods of extracting Rsd, which rely on the hypothesis that the channel dopant concentration and/or the carrier mobility is independent of Lgate, have been published in previous literature [1]–[3]. However, in today’s MOSFET tech-nology, halo ion implantation and mechanical-stress-dependent dopant diffusion [4] can cause significant nonuniform channel dopant profiles; therefore, use of the traditional methods is problematic.Here, we present a new method along with experimental demonstration and verification, without accounting for the gate or channel length. This is achieved by means of specifically arranged bias conditions under which the channel carrier mo-bility is kept constant, regardless of the varying channel dopant concentration caused by threshold-voltage adjustment or the local dopant fluctuation. Unlike the previous methods [1]–[3], [5], which require a considerable number of device samples with different Lgatevalues and/or C–V measurements, the Rsd
Manuscript received July 24, 2007. This work was supported by the National Science Council of Taiwan under Contract NSC 95-2221-E-009-295-MY3. The review of this letter was arranged by Editor K. De Meyer.
D.-W. Lin is with the Taiwan Semiconductor Manufacturing Company, Hsinchu 300, Taiwan, R.O.C., and also with the Department of Electronics Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C. (e-mail: dwlin@tsmc.com).
M.-L. Cheng, S.-W. Wang, and C.-C. Wu are with the Taiwan Semiconductor Manufacturing Company, Hsinchu 300, Taiwan, R.O.C.
M.-J. Chen is with the Department of Electronics Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C.
Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LED.2007.909850
Fig. 1. Measured mobility behavior under different Vbsbias conditions. The
inversion carrier mobility converges to the same trend when Eeffis sufficiently
high. The inset is a schematic illustration of the equivalent circuit of the device used in the Rsdextraction.
extraction can be realized on a single test device with only dc measurements using this new method.
II. CONSTANT-MOBILITYBIASCONDITIONS
Fig. 1 shows a typical relationship between the measured channel carrier mobility versus the effective silicon vertical electrical field (Eeff) at the SiO2/Si interface. Under various back-bias (Vbs) conditions, the carrier mobility appears to converge toward the universal curve in the high Eeff region [6], where surface-roughness scattering becomes the dominant mechanism. If the device is operated in the high Eeff region, a constant mobility is achieved for a given Eeff, regardless of the varying impurity- and phonon-scattering counterparts. The corresponding Eeff can be expressed as
Eeff = 1 εSi |Qd| +1 η|Qi| (1) where εSiis the silicon permittivity, Qdis the depletion charge,
and Qi is the inversion-layer charge. η is an empirical factor
with the values∼2 and ∼3 commonly used for electrons and holes at room temperature, respectively [6]–[11]. Based on the derivation procedure described elsewhere [12], (1) can be further written as Eeff = Vgs+ (η− 1)Vth− ηVFB− 2ηΨB 3ηTOX (2) 0741-3106/$25.00 © 2007 IEEE
LIN et al.: CONSTANT-MOBILITY METHOD TO ENABLE MOSFET SERIES-RESISTANCE EXTRACTION 1133
where VFB is the flatband voltage, and ΨB is the potential
difference between the Fermi level and the intrinsic Fermi level. Both VFBand ΨBare essentially unchanged for a single device
operated under different bias conditions. It follows from (2) that the gate-to-source voltage Vgs and the threshold voltage
Vthcan be adjusted simultaneously to achieve a constant Eeff under different Vbs’s. Given an initial Vgs(0) and Vth(0), the same
Eeffvalue can be preserved for other biases Vgs(1)and Vth(1), sat-isfying Vgs(1)= Vgs(0)+ (η− 1)(Vth(0)− Vth(1)). Consequently, a constant mobility can be obtained.
III. SERIES-RESISTANCEEXTRACTION
By incorporating the constant-mobility criterion into the cur-rent equation of MOSFETs operating in the linear region, the results for the two specific bias conditions (separately labeled with the superscripts 1 and 2) are
Id(1) =CoxWeffµ (1) Leff Vgs(1)− Vth(1)−1 2Vds ×Vds− RsdId(1) (3) Id(2) =CoxWeffµ (2) Leff Vgs(2)− Vth(2)−1 2Vds ×Vds− RsdId(2) . (4)
Here, Vds= 0.05 V is used to ensure a linear operation mode. As previously mentioned, the mobility is the same between the two specific voltages Vgs and Vth, i.e., µ(1)= µ(2) under a high Eeff condition. By dividing (3) by (4), the Rsd can be derived as Rsd= B Id(2) − A Id(1) Vds η Vth(1)− Vth(2) (5) where A = Vgs(1)− Vth(1)− 0.5Vds, and B = Vgs(1)+ (η− 1)
Vth(1)− ηVth(2)− 0.5Vds. The inversion gate-oxide capacitance
Cox, the channel length Leff, and the channel width Weff are cancelled out because they are identical for a single device. This unique property makes the proposed method particularly favor-able for the short-channel devices in which an unambiguous definition of Cox, Leff, and Weff is difficult to achieve.
IV. RESULTS ANDDISCUSSION
In this letter, the state-of-the-art low-power devices featuring 17.5-Å (effective oxide thickness) gate oxide and heavily doped source/drain extensions (S/D-exts) are utilized. The devices underwent advanced strain engineering involving a neutral shallow-trench-isolation gap-fill process, a stress memorization technique [13], and a tensile contact etch-stop layer. A mil-lisecond anneal process was also employed to improve device performance.
Experimental demonstration with a mask gate length Lmask of 100 nm is presented here. In order to obtain a constant carrier mobility under different bias conditions, a sufficiently high Eeff (high Vgs) is necessary to force the carrier mobility to converge
Fig. 2. Extracted Rsdas a function of Eeff. Erroneous Rsdvalues appear in
the low Eeff region because the Eeff is insufficiently high and the
“constant-mobility” criterion is not satisfied. Rsdapproaches a constant and exhibits no
dependence on Vbsin the sufficiently high Eeff region. The inset shows the Rsdvalues extracted from the proposed method in this letter and the method in
[14]. A good agreement is achieved.
toward the universal curve. When Eeffis insufficiently high, the carrier mobility does not converge even under the same Eeff. The extracted Rsd, as shown in the low Eeff region in Fig. 2, shows anomalous values as well as a strong dependence on the Vbs bias. This undesired result is due to the failure of the constant-mobility conditions. As we further increase Eeff, the electron mobility begins to converge toward the universal curve. Consequently, the extracted Rsd values approach a constant, and no dependence on the Vbsbias can be observed, as shown in the high Eeff region in Fig. 2. In this letter, the gate current is at least six orders of magnitude lower than the drain–current under all bias conditions because the tunneling current is limited by the gate area of the short-channel device. Hence, the gate current has a negligible effect on the Rsdextraction.
The proposed method has also been applied to both NMOSFETs and PMOSFETs. The inset in Fig. 2 lists some of the extracted Rsdvalues. Also shown for comparison are those extracted from a considerable number of devices using BSIM simulation [14]. A reasonable agreement is achieved between the two methods.
In Fig. 3, an obvious degradation in driving capability is observed when external resistors are additionally connected to the device under test. The Rsdand these external resistors are extracted using the proposed method. The Rsdvalues faithfully reflect the presence of the external resistors, as shown in the in-set of Fig. 3. Therefore, this proposed method is well qualified. A SPICE model is calibrated using the extracted Rsdin the case of “Rext= 0.” The simulated data match the measurement. The quality of the SPICE model is therefore verified. Without modifying any parameters, the simulated data further match the measurement in both cases of “2Rext= 102 Ω” and “2Rext= 200 Ω.” Obviously, Rsd and Rext are additive to each other. Hence, any difference in Rsdcaused by process change can be extracted by this proposed method.
Since the surface potential is modulated by Vbs, the cen-troid of the carrier distribution (Zc) changes accordingly [15]–
[17]. Fig. 4 shows the inversion-layer carrier distribution, which is calculated using 2-D numerical simulators, namely,
1134 IEEE ELECTRON DEVICE LETTERS, VOL. 28, NO. 12, DECEMBER 2007
Fig. 3. Measured and simulated Id–Vgs characteristics of a typical
NMOSFET with Wmask/Lgate= 1 µm/0.1 µm under Vds= 0.05 V.
External resistors Rextare connected to the device, as shown in the inset.
The extracted Rsdvalues, listed in the inset, faithfully reflect the presence or
absence of the Rext.
Fig. 4. Inversion-layer electron density distribution f , which is calculated using the 2-D numerical simulators, namely, TSUPREM4 and MEDICI, normal to the channel surface under various Vbs conditions. The inset shows the
centroid of the carrier distribution (Zc). When Vbschanges from 0 to−1.5 V, Zcdecreases by only∼0.1 nm which is equivalent to ∼0.03-nm decrease in
Tox_inv. This change should have a negligible effect on the Rsd extraction
proposed in this letter.
TSUPREM4 and MEDICI, normal to the channel surface. As
Vbs changes from 0 to −1.5 V, Zc decreases by ∼0.1 nm which is equivalent to∼0.03-nm change in the inversion-oxide thickness (Tox_inv). This difference is no more than 1.5% for the aggressively scaled oxide down to 2-nm Tox_inv. This effect on the extracted Rsdshould be negligible.
Finally, for the advanced MOSFET technology, shallow and heavily doped S/D-ext regions are widely used. The dopant concentration inside the S/D-ext is often higher than 1020cm−3 with a sharp dopant transition (< 3 nm/dec, which is not shown in this letter) toward the substrate and the surface channel regions. The modulation of carrier concentration caused by high
Vgsand/or high Vbs is insignificant inside the S/D-ext, leading to an insignificant change in Rsd.
V. CONCLUSION
The extraction of series resistance for the short-channel MOSFET, with the heavily doped S/D-ext regions, using
sim-ple dc measurements without knowing Cox, Leff, Weff, and the carrier mobility has been demonstrated. Compared with many previous methods that need several devices in the Rsd extraction, this new method requires only a single device and can eliminate the uncertainty arising from process instabilities among devices. Hence, it provides immunity against process variation, which is a major issue as the physical device dimen-sions shrink. These merits make the new method particularly favorable for the short-channel devices.
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