Y neling hot-electron transistor (RHET) and demonstrated

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1 EEE TRANSACTONS ON ELECTRON DEVCES, VOL 36, NO O. OCTOBER 1989 Modeling Electron Transport in ngaas-based Resonant-Tunneling Hot-Electron Transistors 2335 HROAK OHNSH, NAOK YOKOYAMA, MEMBER, EEE, AND AKHRO SHBATOM, MEMBER, EEE Abstract-This paper describes the modeling of the resonant-tunneling hot-electron transistor (RHET). n the analysis of the resonanttunneling harrier, we solved the Schrodinger and the Poisson equations self-consistently. We simulated the electron transport in the base and the collector barrier region using the Monte Carlo method, taking account of the space charge in the collector barrier. Our model includes the effect of coupled plasmon-lo phonon scattering and electron-electron scattering in the base region. We calculated the transit time in the base and the collector harrier region. The 5-nm base transit time was.59 ps. On the other hand, the 2-nm collector barrier transit time was larger than 1 ps due to intervalley scattering in the collector barrier region. We showed that the collector barrier transit time was reduced to.89 ps in the 5-nm collector barrier RHET at a collectorbase voltage of.5 V.. NTRODUCTON OKOYAMA et al. [ 11-[3] fabricated a resonant-tun- Y neling hot-electron transistor (RHET) and demonstrated some circuit applications. The most important features of the RHET are its resonant-tunneling emitter barrier and its hot-electron transport in the base and the collector barrier region. The resonant-tunneling (RT) barrier generates negative transconductance and is a hot-electron injector. Electron transport through the RT barrier is a quantum mechanical phenomenon. We have already proposed a self-consistent model using the Schrodinger and the Poisson equations [4] to calculate the currentvoltage (Z-V) characteristics of the RT barrier. We simulated hot-electron transport in the base region using the Monte Carlo method and showed that electron transport was greatly affected by electron-electron (e-e) scattering [5]. However, to understand the operation of a RHET, we must simulate the electron transport from the emitter to the collector. n this paper, we describe the modeling of the ngaas /n ( AlGa) As RHET including the electron transport in the collector barrier region. 11. DEVCE STRUCTURE Fig. 1 shows the RHET structure we used in our study. The resonant-tunneling emitter barrier is a 3.8-nm Manuscript received January 3, 1989; revised June 6, This work was performed under the management of the R&D Association for Future Electron Devices as part of the R&D of Basic Technology for Future ndustries sponsored by the New Energy and ndustrial Technology Development Organization. The authors are with Fujitsu, Ltd., 1-1 Morinosato-Wakamiya, Atsugi Japan. EEE Log Number nalas ngaas nalas 4 4 n ~ 3. nm nm n(aga)as 2 nm Emitter Base Collector WsAsE = 5 nm NBAsE = 1 x 1l8 cm3 Fig. 1 Band diagram of the ngaas/n( A1Ga)As RHET. The resonanttunneling barrier layers and the collector barrier layer are undoped. no,s3g~.47as quantum well sandwiched between 4.4-nm n.52a1.48as barriers, the same as the one fabricated by mamura et al. [2]. The base width is 5 nm, and the doping density is 1 X 1" crnp3. The collector barrier is 2-nm n.s2 ( A1.5Ga.5 ).4XAS EMTTER CURRENT-VOLTAGE CHARACTERSTCS First, we calculated the emitter Z-V characteristics. We solved the following equations self-consistently to account for band bending and space-charge buildup in the quantum well [4] -" 2 dz [LE] m* dz + V(z)P(k,, z) = E,P(k,, z) (2) n(z) = C AE, Epimer)) n (z) = k k at emitter P (k,, z) 12f( E, Eremitter)) at RT barrier n(z) = Cf(E, E?=)) at base. k (3) n the Poisson equation (see (l)), 4 ( z) is the electrostatic potential for electrons and E (z) is the dielectric constant. Equation (2) is the effective mass Schrodinger equation and determines the wave function P(k,, z) in the resonant-tunneling barrier and the tunneling probability. The carrier distribution n ( z) is calculated from (3), where f(e, E') is the Fermi distribution function and Ef is the Fermi energy /89/1-2335$1.OO O 1989 EEE

2 2336 EEE TRANSACTONS ON ELECTRON DEVCES, VOL. 36. NO. O, OCTOBER o 1.5 Base-emitter voltage (V) Fig. 2. Calculated emitter current-voltage characteristics at 77 K. lm Emitter current is given by J=B m*ek de,( 1 + 2an,EZ) T(E,) 2 ~ 2 zt- 1 + exp (Ez - 'v.) 1 * n (E, - Ef ib;va + ev 1 + exp where m* is the effective mass, and anon is the nonparabolicity of ngaas. T(E,) is the tunneling probability through the RT barrier. V, is the voltage drop in the accumulation region at the emitter. Fig. 2 shows the calculated emitter Z-V characteristics at 77 K. We assumed the effective masses and nonparabolicities to be.42 and ev-' for ngaas and.75 and.586 ev-' for nalas, respectively, and the conduction band discontinuity between them to be.53 ev. The peak current density is 4.7 X lo4 A/cm2 at a base-emitter voltage (V,,) of.65 V and the peak-tovalley ratio is 33. V. MONTE CARLO SMULATON We investigated the motion of electrons in the base and the collector barrier region using the Monte Carlo simulation method. As well as conventional scattering mechanisms, ionized impurity scattering, acoustic phonon scattering, inter-valley scattering, and alloy scattering, we have included the coupled plasmon-lo phonon scattering and e-e scattering in the ngaas base. At a base doping density of 1l8 cmp3, the plasma frequency is comparable to the LO phonon frequency. This gives rise to electron scattering by the strongly coupled plasmon-lo phonon mode [6]. n addition to the coupled mode scattering, hot electrons are scattered by the e-e scattering in the Landau damped regime [5], [7]-[9]. The scattering rates of these two mechanisms are calculated from (5) et( q, U) is the dynamic susceptibility calculated from the random phase approximation [S. We considered the Lind- hard function to be the contribution from degenerate electrons. As a hot electron experiences e-e scattering, one electron is excited from the Fermi sea. We simulated the transport of these excited electrons and the original hot electrons in a similar way. n the collector barrier region, we considered LO phonon scattering, acoustic phonon scattering, inter-valley scattering, and alloy scattering. Hot electrons are injected through the RT emitter barrier. We calculated the injected hot-electron distribution using the wave function q (K,, z). f:(e,) = c f(e, E;mitter) 1 \k(k,, z) f :od ffoml(e,) = kx, k> k ate (k) = E f(e, Ejmitter) q(k, z) l2 12. (6) (E) is the total energy distribution and f: (E,) is the distribution in the direction of injection (z-direction). Fig. 3 shows the injected hot-electron distribution at V,, =.4 V. Because hot electrons are injected through the quasibound state in the ngaas quantum well, the energy spread is very small. The full width at half maximum of this distribution is.59 mev, and this corresponds to the spread of the quasi-bound state. However, total energy distribution of hot electrons f~,,, (E) is wider and its spread is 8 mev, almost equal to the difference between the Fermi energy and the bottom of the quasi-bound level. The electron distribution after traveling through the 5- nm base region at V,, =.4 V is shown in Fig. 4. The peak at.46 ev represents electrons near-ballistically transported through the base. The energy of the ballistic electrons is larger than the injection energy due to the acceleration field in the base depletion region. The increased energy spread of this peak is due to band nonparabolicity. Because each electron has a different total energy, they have different effective masses, m*( 1 + 2anon E ). This leads the different k, after accelerating in the base region. There is a broad peak around.6 ev, representing electrons excited from the Fermi sea due to e-e scattering. Hot electrons that lost kinetic energy due to e-e scattering are widely distributed. This is because they have more of a chance to experience further elastic and/or inelastic scatterings in the base region. After traveling through the base region, some electrons surmount or tunnel through the collector barrier. We assumed that electrons enter the collector barrier if r < T( E,), where r is random number equally distributed between and l, and T(E,) is the tunneling probability of the collector barrier. The motion of electrons in the collector barrier was also simulated using the Monte Carlo method. Fig. 5 is the collector transfer ratio calculated as a function of collector-base voltage ( VcB) at V,, =.4 V. Q is the total transfer ratio and al is the component of L-valley electrons. At V,, =, Q sharply increases. At VcB <, electrons must travel through the base and the collector barrier near-ballistically to reach the collector region. At VcB =, the electron potential at the middle of the collector barrier is higher than both sides. f electrons are

3 OHNSH et al.: MODELNG ELECTRON TRANSPORT N RHET S 2337 C bd $5 c.8 e^, Z 5w - VeE:.4 V - 2 c C - =,.= s= n u)l Brn - 1 3z s= Z W.4 - W (a) VBE:.4.- V Zz Near ballistic+ L valley - w Energy (ev) Fig. 4. Calculated hot-electron distribution after traveling through 5-nm base at V,, =.4 V. 1.,,,,, ~ vcs: 2 v ? (b) Fig. 6. Carrier distribution in the RHET. (a) r-valley electron distribution. (b) L-valley electron distribution. V,, =.4 V and Vcs = 2 V Collector-base voltage (V) Fig. 5. Calculated transfer ratio as a function of V,, at V,, =.4 V. scattered many times and lose kinetic energy in the direction of injection, they cannot surmount the potential and they turn back to the base. Therefore, the transfer ratio is small. However, at VcB > electrons reach the collector region if they can cross the junction between the base and the collector barrier. So cy becomes large. At VcB >, the transfer ratio gradually increases. This is due to the lowering of the effective collector barrier height. The increase of the voltage drop in the accumulation region at the base-collector barrier junction makes the collector barrier height lower. As shown in Fig. 4, electrons are distributed toward the lower energy side. As the effective collector barrier height decreases, these electrons begin to tunnel through the collector barrier. At VBE =.4 V, only r-valley electrons pass through the base and the collector barrier. However, as VcB goes above.25 V, cyl increases. This means that electrons undergo inter-valley scattering at VcB >.25 V in the collector barrier region. Fig. 6 shows the electron distribution in a RHET at VBE =.4 V and VcB = 2 V. Elec- trons are still hot within 5 nm of the collector barrier. After that,?-valley electrons are few because of the intervalley scattering. The large scattering rates of the L-valley electrons and their large effective mass make the mean free path of the L-valley electron very short, and most electrons are distributed along the bottom of the L-valley. Fig. 7 is the calculated mean velocity in the base and the collector barrier at VBE =.4 V and VcB = 2 V. The mean velocity is 5 X lo7 cm/s in the base side of the collector barrier region where r-valley electrons are dominant. However, mean velocity rapidly decreases. n a large region of the collector barrier, the mean velocity is only 1 X lo7 cm/s due to the large effective mass of the L-valley. Therefore, the collector barrier transit time is large, 1.35 ps. Electron transport in the collector barrier region greatly affects the transit time. We show the calculated mean transit time as a function of VcB in Fig. 8. The base-emitter voltage is.4 V. The broken line represents that mean base transit time, and the solid line represents that for the collector barrier. The injection energy into the base is less than the r-l separation energy in the base. Therefore, the base transit time is very small: less than.1 ps. As VcB increases, the base transit time increases slightly because the electrons in the lower energy side begin to surmount the collector barrier. The collector barrier transit time is much larger than the base transit time. At VcB = -.2 V, electrons pass through the collector barrier ballistically, so the transit

4 2338 EEE TRANSACTONS ON ELECTRON DEVCES, VOL. 36, NO. O, OCTOBER 1989 lo.ol,? +Collector Collector barrier x 5. v - O 2 3 Fig. 7. Velocity distribution in the base and the collector barrier region VBE =.4 V and V,, = 2 V. -o.4 WSC: 5 nm Position (nm) (a) 2.E c 1.- c n 2 - Collector barrier.._ O Collector-base voltage (V) Fig. 8. Calculated mean base transit time and mean collector bamer transit time as a function of VcB at VBE =.4 V. time is fastest. However, even this value is one order of magnitude larger than the base transit time. The collector barrier transit time strongly depends on VcB. From VcB = to.5 V, the collector barrier transit time decreases because electrons travel in the r-valley and are accelerated in the collector barrier. However, as electron energy begins to become larger than the r-l separation, electrons begin to undergo inter-valley scattering, which increases the transit time. As shown in Fig. 7, the mean velocity is only 1 x lo7 cm/s in a large region of the collector barrier. f this region is reduced, it is expected that the collector barrier transit time greatly decreases. As the collector barrier width decreases, the collector barrier transit time is expected to decrease. However, the decrease of the collector barrier width reduces the breakdown voltage of the collector barrier. So it is necessary to decrease the collectorbase applied voltage. We simulated the electron transport in a 5-nm collector barrier RHET at VBE =.4 V and VcB =.5 V and show the electron distribution in Fig. 9. Electrons in the collector barrier region are transported near-ballistically, and L-valley electrons are very few. Therefore, in this RHET the collector barrier transit time is.89 ps and is much smaller than the 2-nm collector barrier RHET. V. SUMMARY We modeled the electron transport in the RHET. Electron transport in the resonant-tunneling barrier was treated as quantum mechanical transport. We self-consistently solved the Schrodinger and the Poisson equations. n the -o.4 WBC: 5 nm i Position (nm) (b) Fig. 9. Carrier distribution in the 5-nm collector barrier RHET. (a) r- valley electron distribution. (b) L-valley electron distribution. VBE =.4 V and VcB =.5 V. base and the collector barrier region, we simulated electron transport using the Monte Carlo method. We calculated the transit time of the 5-nm base and 2-nm collector barrier RHET. The base transit time was as small as.59 ps. However, the collector barrier transit time was one order of magnitude larger than the base transit time because of the inter-valley scattering in the collector barrier region. The decrease of collector barrier width and collector-base applied voltage is needed to reduce the collector barrier transit time. We showed the collector barrier transit time was reduced to.89 ps in the 5-nm collector barrier RHET. REFERENCES [l] N. Yokoyama, K. mamura, S. Muto, S. Hiyarnizu, and H. Nishi, Japan. J. Appl. Phys., vol. 24, p. L853, [2] K. mamura, S. Muto, H. Ohnishi, T. Fujii, and N. Yokoyama, Electron. Lett., vol. 23, p. 87, [3] K. mamura, T. Mori, H. Ohnishi, S. Muto, and N. Yokoyama, Electron. Lett., vol. 25, p. 34, [4] H. Ohnishi, T. nata, S. Muto, N. Yokoyama, and A. Shibatomi, Appl. Phys. Lett., vol. 49, p. 1248, [5] H. Ohnishi, N. Yokoyarna, and A. Shibatorni, in EDM Tech. Dig., 1988, p. 83. [6] M. A. Hollis, S. C. Polmasteer, L. F. Eastrnan, N. V. Danker, and P. M. Smith, EEE Electron Device Lett., vol. EDL-4, p. 1842, [7] A. P. Long, P. H. Beton, and M. J. Kelly, J. Appl. Phys., vol. 62, p. 1842, [8] M. E. Kim, A. Das, and S. D. Senturia, Phys. Rev. B, vol. 19, p. 689, [9] K. KimandK. Hess, J. Appl. Phys., vol. 64, p. 357, 1988.

5 OHNSH et al.: MODELNG ELECTRON TRANSPORT N RHET S 2339 Hiroaki Ohnishi was born on October 7, 1957 in Ehime, Japan. He received B.S. and M.S. degrees in basic engineering from Osaka University in 198 and 1982, respectively. He joined Fujitsu, Ltd., in He has been engaged in the design of GaAs MESFET memories and in the development of super-lattice devices. Mr. Ohnishi is a member of the Japanese Applied Physics Society. * Naoki Yokoyama (M 78) was born March 28, 1949 in Osaka,. Japan. He received the B.S. degree in physics from Osaka City University in 1971, and the M.S. degree in physics in 1973 and the Ph.D. degree in electrical engineering in 1984 from Osaka University. n 1973, he joined the Semiconductor Devices Laboratory of Fujitsu Laboratories, Ltd., Japan. His work there has focused on the research and development of compound semiconductor devices. Highlights include the development of self- aligned GaAs MESFET s using refractory-metal-silicide Schottky gates, the first success in fabricating hot-electron transistors, and the invention of resonant-tunneling transistors. He is currently a Manager in the exploratory-devices section and is responsible for the research and development of heterojunction devices including heterojunction bipolar transistors and wave-function engineering devices. Dr. Yokoyama received the Young Scientist Award at the 1987 nternational Symposium on Gallium Arsenide and Related Compounds for his development of the GaAs MESFET and hot-electron devices. He is a member of the EEE Electron Devices Society, the American nstitute of Physics, the Japan Society of Applied Physics, and the nstitute of Electronics and Communication Engineers of Japan. * Akihiro Shibatomi (M 83) received the B.S. degree in physics from Kanazawa University in 1965 and the Ph.D. degree in electrical engineering from Osaka University in He joined Kobe Kogyo in 1965, which was absorbed by Fujitsu, Ltd. in He has been involved in the research and development of GaAs crystal growth, GaAs high-frequency and highspeed devices, and C s. Dr. Shibatomi is a member of the Japanese Applied Physics Society.