ISDRS 2009, December 9-11, 2009, College Park, MD, USA

ISDRS 2009 – http://www.ece.umd.edu/ISDRS2009

Ballistic Mobility Degradation in Scaled-Down Channel of a MOSFET

Munawar Riyadia,b, Christopher Pollardc, Vijay K. Aroraa,c

aFaculty of Electrical Engineering, Universiti Teknologi Malaysia, UTM Skudai, Johor 81310, Malaysia

bDepartment of Electrical Engineering, Diponegoro University, Semarang 50271, Indonesia cDivision of Engineering and Physics, Wilkes University, Wilkes-Barre, PA18707, U. S. A., E-Mail:

vijay.arora@wilkes.edu The ballistic mobility data by Luskawoski et. al [1] is interpreted by using recently published formalism [2]. The mobility is shown to be ballistic when the ballistic mean free path in a nanoscale transistor exceeds the channel length. This ballistic mobility affects the critical voltage Vc that can be as low as the thermal voltage 2 Vt (0.0518 V at room temperature) for a quasi-2-domensional (Q2D) nanostructure at the onset of nonlinearity in current-voltage relationship. The applied voltage V=0.08 V is higher than the thermal voltage triggering decline of mobility at low channel lengths due to high fields present. The general formalism is in excellent agreement with the experimental data. Ballistic transport is a collision-free carrier drift with a hope that a uni-directional electrons are accelerated to very high speeds. However, all experimental results do not show an enhanced transport behavior in ballistic channels. This is due to the stochastic motion of the carriers split along and opposite to the direction of an applied electric filed. The transport in these miniaturized devices is a complex undertaking [2]. Robertson and Dumin [3] have investigated the ballistic transport and properties of submicrometer channels of length 0.2 m, 0.7 m 1.7 m from 300 to 4.2 K. It is found that even if the long-channel mobility in a 500- m square device was 25000 cm2/V.s at 4.2 K, the effective mobility in a 0.2- m device sharply drops to only 800 cm2/V.s This experimental study led to the conclusive evidence that the ballistic transport is inhibited by high fields even for devices operating with driving voltage as low as 0.1 V. Arora [4] postulated high-field nonequilibrium distribution function for a bulk 3-D semiconductor that has been elaborated for all dimensionalities in [1]. For size-limited ballistic mobility L , the model employed in Ref. 1 is that proposed by Shur [5]. Wang and Lundsrom [6] also proposed a ballistic model similar to that of Shur except ballistic injection velocity used was half that of Shur. The rationale for using half velocity arises from only half electrons travelling from contacts to the channel. An average over only half the electrons is required if half the Maxwellian distribution is used as applicable to nondegenerate carrier statistics, giving the injection velocity consistent with that of Shur [5]. Nondegenerate carrier statistics is certainly not applicable for Schottky contacts where electrons are injected into the channel through the tunneling process. The Fermi energy F cE E for an Aluminum contacts is 13 eV. Therefore, nondegenerate carrier-injection intrinsic velocity is not the appropriate choice for ballistic contacts. Electrons are injected with the Fermi velocity

62( ) / 2.1 10 /F F c ov E E m m s with high tunneling probability. The channel intrinsic velocity is distinct from the contact’s injection velocity. When corrected for the intrinsic velocity

2iv for arbitrary degeneracy in the channel and injection velocity injv from the contacts, the

application of Matthiessen-like rule modifies the expression for L given by Shur [5] that is given by

/ 1 / (1 ( / ))L B L (1) with ( / )B inj mv v (2)

where is the long-channel mean free path mv is the mobility velocity. The mobility expression obtained following the procedure by Arora [1] and that delineated in[7-8] is

L B/ 1 exp L / (3)

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ISDRS 2009, December 9-11, 2009, College Park, MD, USA

ISDRS 2009 – http://www.ece.umd.edu/ISDRS2009

Figure 1 shows the comparison of Eqs. (1) and (3) to the experimental data obtained in [9] that has been discussed in [10]. The mean free path to fit the ballistic mobility data was found to be much larger than extracted from long-channel mobility, consistent with Eq. (2). Figure 2 shows the comparison to the experimental data of [1] for a variety of carrier concentrations. The increase in ballistic mean free path was shown due to the existence of intentional and unintentional doped pockets [1]. The extended mean free path of [1] contradicts the enhanced scattering due to pockets that must decrease the mean free path. Eq. (2) indicates that the enhanced scattering length is consistent with the injection velocity from the Schottky contacts.

References [1] J. Lusakowski, W. Knap, Y. Meziani, J.-P. Cesso, A. El Fatimy, R. Tauk, N. Dyskova, G.

Ghibaudo, F. Boeuf and T. Skotnicki, “Ballistic and pocket limitations of mobility in nanometer Si metal-oxide semiconductor field-effect transistors,” Appl. Phy. Lett. 87, 053507 (2005).

[2] Vijay K. Arora, “Theory of Scattering-Limited and Ballistic Mobility and Saturation Velocity in Low-Dimensional Nanostructures,”Current Nanoscience (CNANO) 5, 227(2009).

[3] Perry J. Robertson and David J. Dumin, Ballistic Transport and P erties of Submicrometer Silicon M0SFET”s from 300 to 4.2 K,” IEEE Transactions on Electron Devices ED-33, 494(1986).

[4] Vijay K. Arora, “High-field distribution and mobility in semiconductors,” Japanese Journal of Applied Physics 24, 537(1985).

[5] M. S. Shur, “Low ballistic mobility in submicron HEMT’s,” IEEE Electron Devices Letters 23, 511(2002).

[6] J. Wang and M. Lundstrom, IEEE Trans. Electron Devices, “Ballistic transport in high electron mobility transistors,” IEEE Transactions on Electron Devices 50 1604 (2003).

[7] Vijay K. Arora, Michael L. P. Tan, Ismail Saad, and Razali Ismail, “Ballistic quantum transport in a nanoscale metal-oxide-semiconductor field effect transistor,” Applied Physics Letters 91, 103510 (2007).

[8] Michael L. P. Tan, Vijay K. Arora, Ismail Saad, Mohammad Taghi Ahmadi, and Razali Ismail, “The drain velocity overshoot in an 80-nm metal-oxide-semiconductor field-effect-transistor,” Journal of Applied Physics 105, 074503 (2009).

[9] F. Andrieu, F. Transistors CMOS Decananometriques a Canaux Contraints sur Silicium Massif ou sur SOI. Ph. D. thesis, INPG, France, 2005;

[10] K. Hue, J. Saint-Martin, A. Bournel, S. Galdin-Retailleau, P. Dollfus, G. Ghibaudo, M. Mouis, “Monte Carlo study of apparent mobility reduction in nano-MOSFETs, Proceedings of Solid State Device Research Conference, 2007 (37th European ESSDERC 2007), 11-13 Sept. 2007, Page(s):382 - 385 . Digital Object Identifier 10.1109/ESSDERC.2007.4430958 (Available in IEEE Xplore).

0 2 4 6 8 10 12 14 16 18 200

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L /

AroraShurExperimentHigh-FieldBallistic

Fig. 1. Normalized mobility versus normalized channel length with experimental data from Ref. [9].

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AroraShur5.0x1010 cm-2

5.0x1011 cm-2

1.0x1012 cm-2

2.0x1012 cm-2

5.0x1012 cm-2

Fig. 2. Normalized mobility versus normalized channel length with experimental data from Ref. [1].