IEEE DEVICE LETTERS, VOL. EDL-6, NO. 12, DECEMBER 1985 665 Observation of Electron Velocity Overshoot in Sub- 100-nm-channelMOSFET’s in

Abstmct-n-channel MOSFET’s with channel lengths from 75 nm to raphies [6]. To increase the surface acceptor concentrationto 5 5 pm were fabricated in Si using combined X-ray and optical lithogra- x IOl7 cm -3, boron was implanted at 30 keV and a dose of 2 phies, and were characterized at 300, 77, and 4.2 K. Average channel x 10 l3 cm -2, followed by oxidation at 900°C in dry oxygen electron velocities we were extracted according to the equation ws=g,,,JCox, where g,, is the intrinsic transconductance and Coxis the capacitance of ambientfor 40min. Instead of using aself-aligned gate the gate oxide. We found that at 4.2 K the average electron velocity of a structure, PMMA resist lines of widths from 100 nm to 5 pm, 75-nm-channel MOSFET is1.7 X lo7 cm/s, which is 1.8 times higher patterned by X-raylithography, were used to mask the than the inversion layer saturation velocity reported in the literature, and channels during source-drain implantation of As, with energy 1.3 times higher than the saturation velocity in bulk Si at 4.2 K. As of 30 keV and a dose of 7 x IOl5 cm-2. Toprevent A1 spiking channel length increases, the average electron velocity drops sharply through the shallow junctions at contact areas, deeper junc- below the saturation velocity in bulk Si. These experimental results strongly suggest velocity overshoot in a 75-nm-channel MOSFET. tionswere formed under the source and drain contads by implanting P at 160 keV and a dose of 3 x 1015 cm-2, using I. INTRODUCTION photoresist as the implantation mask. After the implants, the photoresist, the PMMA, and the original SiOz were removed, VERSHOOT of electron velocity inSi following rapid and the wafers were oxidized at900°C in dry oxygen ambient changes of electric field was first predicted by Ruch in 0 for 25 min. Afterwards, A1 gates were patterned and 300 nm 1972 using the Monte Carlo calculation of electron scattering of CVD oxidewas deposited over the samples. Finally, [I]. Later,the same effect was also shown by using the contact cuts and A1 contacts were made to the A1 gates and the relaxationapproximation [2] and theelectron temperature source-drain regions. The calculated junction depthwas about method [3]. Velocity overshoot is due to the nonequivalenceof 0.1 pm [7]. The resulting total source-drain series resistance electronmomentum and energy relaxation times, and is was 4.4 mm. The thickness of gate oxide measured from expected to occur in a time scale which is shorter than the Q* capacitors fabricated on the same chip was 11 nm. energy relaxation time. Since the electron energy relaxation Channel lengths were determined by both what we call the time in Si is rather short, velocity overshoot in MOSFET’s is “closed-channel’’ method and by an electrical measurement expectedtobecome significant only when thedistance method.The “closed-channel’’ method relies on accurate between source and drainis shorter than 100 nm [ 11. To search SEM measurement of the width of PMMA lines used as the for velocity overshoot, we fabricated n-channel MOSFET’s implantationmask. Because of ourX-ray mask fabrication with channel lengths from 75 nm to 5 pm. The devices were technique [6], [SI, the linewidth varied systemetically around characterised at 300, 77, and 4.2 K. At 4.2 K, we found that a each nominal width value across the X-raymask area by about device with a channel length of 75 nm in saturation had an f 10 percent.Due lateralto dopant spreading averageelectron velocity of 1.7 X lo7 cmis, which is 1.8 duringimplantation and diffusionduring oxidation, devices times higher than the value reported by Fang and Fowler [4] that came from the narrower PMMA lines (100-160 nm) had forinversion layers in Si, and 1.3 timeshigher than the their channels closed and behaved like resistors. As the width saturationvelocity in bulkSi [5] atthe same temperature. of PMMAlines widened further, devices started showing Moreover,we found that theaverage electron velocity behavior. We found that resistor-transistor transis- dropped sharply as channel length increased, strongly suggest- tionsoccurred at PMMAlinewidths equal to 160 nm rt 10 ing velocity overshoot in the 75-nm-channel device. nm. This gives a lateral spread of 80 nm for each junction, 11. EXPERIMENTAL which is consistentwith the TEM results by Sheng and Marcus N-channel MOSFET’s were fabricated in p-type 20 cm [91. Q. Theelectrical measurement method was based on that (100) Si, using X-ray and optical direct-step-on-wafer lithog- proposed by Suciu and Johnston [lo], and it gave us both electrical channel length and series resistance for each device. Manuscript received August 7, 1985. This work was supported by the Joint Services Electronics Program. In the calculation, we made a reasonable assumption that the S. Y. Chou is with the Department of Physics, Massachusetts Institute of low-transverse-fieldmobility was thesame for all channel Technology, Cambridge, MA 02139. lengths, Channel lengths determined from the “closed-chan- D. A. Antoniadis and H. I. Smith are with the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology: nel” and the electrical-measurement methods agree with each Cambridge, MA 02 139. other well.

0741-3106/85/1200-0665$01.00 O 1985 IEEE 666 LETTERS,DEVICE ELECTRON IEEE NO.VOL. EDL-6, 12, DECEMBER 1985

111. RESULTS 101 11 1 I1 The devices had well-behaved characteristics down to an effective channel length of 75 nm. The I- V characteristics of such a device at 300 and 4.2 K are shown in Fig. 1. Fig. 2. showsmeasured saturation transconductances of 0 devices with different channel lengths at 300, 77 and 4.2 K. 0 04 0.8 1.2 1.6 2.0 All transconductances were measured at drain-source voltage VDs = 1.2 V, andwere rather insensitive to VDs. It is interesting to note that the transconductances of devices with 101 I1 channel length greater than 100 nm had temperature depen- dence consistentwith that of the saturationvelocities in bulk Si [5].This is not surprisingbecause the transconductance of 2 4pq devices with such short channel lengthsis generally dominated 2 4.2K 0 by velocity saturation. However, the temperature dependence 0 03 0.6 0.9 1.2 1.5 of transconductance of the 75-nm deviceis clearly anomalous. V,, (Volts) To be morequantitative, we have calculated theaverage (b) electron velocity u, from the equation Fig. 1. I- V characteristics of a 75-nm-channel MOSFET (a) at 300 K and (b) at 4.2 K. where g,i is theintrinsic transconductance of the device, which can be calculated from the measured transconductance [ 141, The average electronvelocities of devices with different channellengths at threetemperatures are given in Fig. 3. w 0 E 200 These velocities should be compared with theelectron saturation velocity in a Si inversion layer. Unfortunately, at present there are no consistent data available on the saturation 30p K \ velocity in inversion layers over the temperature range of our I00 60 80 100 120 140 experiment [4], [ll]. Therefore, we have used instead the CHANNEL LENGTH (nm) electron saturation velocity in the bulk Si as an upper limit of Fig. 2. Measured transconductances of the devices with different electrical saturation velocity in theinversion layer. This is justified channel lengths at 300, 77, and 4.2 K. becausesurface scattering makes saturation velocity in an inversion layer always smallerthan that in the bulk [ 121. Fig. 3 shows that at 300 K theaverage electron velocities for all devices are lower than the upper limit. At 77 K the average 1.5 electron velocities are still lower than the upper limit. However, at 4.2 K the average electronvelocity of the 75-nm- channel device is 1.7 x 10' cmis, which is 1.3 times higher than the saturation velocity in bulk Si [5], and 1.8 times higher than the inversion layer saturation velocity reported by Fang W 9 0.5 and Fowler at 4.2 K [4]. As channellength increases the SC 80 100 120 I40 average electron velocity drops quickly below the upper limit. ChANNEL LENGTH (nm) These results strongly suggest velocity overshoot in the 75- Fig. 3. Calculated average electron velocities of the devices with different nm-channel device. electrical channel lengths at 300, 77, and 4.2 K.

IV. DISCUSSION " "4' TABLE I In this section, we explain qualitively why in ourcase MOMEMTUM RELAXATION AND TRANSIT TIMES FOR A 75-nm MOSFET velocity overshoot is significant only at low temperatures. As mentioned in the introduction, velocity overshoot occurs on a Time time scale shorter than the energy relaxation time. If the time ~ rT:,"' Sat. Ve,ocIty TransitTime Mobility Mom. Re;. vss; [cm/secl ' t, [secl (1 pLg[crn'/,:.sl t, [secj j needed for to cross the 75-nm channel is shorterthan theenergy relaxation time, velocity overshoot can become 3CO 1.00 X 107 7.5 X 10-l~ 330 1 0.4 x 10-13 significant.Table I, thirdcolumn shows the calculated electron transit times t, across the 75-nm channel at different 77 125 x :07 ~ 6.0 X IO-'3 1100 1.3 X 10-l~ temperatures based on average velocities being equal to the 2200 2.7 X 1'3-'~ bulk saturation velocities. The last column in TableI gives the CHOU et al.: ELECTRON VELOCITY OVERSHOOT 667

momentum relaxation time t, calculated from t, = p0m*/q REFERENCES [ 131, where po is the measured low-longitudinal-field electron J. G. Ruch, IEEE Trans. Electron Devices, vol. ED-19, p. 652, 1972. mobility in our devices, m* is the effective electron mass in R. S. Huang and P. H. Ladbrooke, J. AppL Phys., vol. 48, p. 4791, 1977. the inversion layer, and q is the electron charge. Although the R. K. Cook and J. Frey, IEEE, Trans. Electron Devices, vol. ED-29> energy relaxation time cannot beobtained from the present p.970, 1982.

data, it is well knownthat it is always longer than the F. F. Fang and A. B. Fowler, J. Appl. Phys. ~ vol. 41, p. 1825, 1970. S. M. Sze, Physics of Devices, 2nd ed. New York: momentum relaxation time[3]. We can see from Table I thatat Wiley? 1981, p. 46. roomtemperature the momentum relaxation time is much S. Y. Chou, Henry I. Smith, and D.A. Antoniadis to be published in J. shorter than the transit time. Even though the energy relaxa- Vac. Sci. Technol. B, Nov./Dec.1985. D. A. Antoniadis, S. E. Hansen, and R. W. Dutton, “SUPREM 11-A tion timeis longer that themomentum relaxation time, it program for IC process modeling and simulation,” Stanford Univer- probably still remains shorter than the transit time. Therefore, sity, Stanford, CA, Tech. Rep. SEL 78-020, June 1978. velocity overshoot is not significant. However, at 4.2 K the S. Y. Chou, H. I. Smith, and D. A. Antoniadis, in Proc. 29th Int. Symp. Electron. Ion Phofon Beams (Portland, OR): alsoJ. Vac. Sci. momentum relaxation time is only two times smaller than the Technol. B, Jan./Feb. 1986. transittime, so it is quitelikely that the energy relaxation T. T. Sheng and R. B. Marcus, J. Elecrochem. Soc. Solid-State Sci. times and transittimes arecomparable, and thus velocity Tech., vol. 128, p. 881, 1981. p. I. Suciu and R. L. Johnston, IEEE Trans. Electron Devices, Val. overshoot becomes significant. ED-27, p. 1846,1980. J. A. Cooper Jr. and D. F. Nelson, IEEE Electron Device Lett., vol. EDL-2, p: 171, 1981. ACKNOWLEDGMENT T. Ando. A. B. Fowler, and F. Stern, Rev. Mod. Phys., vol. 54, p. 457,1982. The authors would like to acknowledge J. Meldgailis for K. Seeger, Semiconductor Physics. New York: Spring-Verlag, helpful discussions, and J. Carter, P. Maciel, and other 1973. Q. 52. S. Y. Chou and D. A. Antoniadis, “Relationship between measured members of the technical staff at M.1.T for their assistance at and intrisic transconductances of FET‘s,” submitted to IEEE Trans. various stages of device fabrication. Electron Devices.