658 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 51, NO. 5, MAY 2004 Reduction of Base-Transit Time of InP–GaInAs HBTs Due to Electron Injection From an Energy Ramp and Base-Composition Grading Gal Zohar, Shimon Cohen, Victor Sidorov, Arkady Gavrilov, Benny Sheinman, and Dan Ritter, Member, IEEE Abstract—The dc current gain of InP–GaInAs heterojunction bipolar transistors with varying base thickness and composition was measured. Much larger composition grade values than previously reported were achieved using strain compensation. A simple two-parameter Monte Carlo simulation was developed to interpret the results. The simulation yields an accurate plot of the base transit time versus base thickness. Clear evidence for the reduction of base transit time due to hot electron injection was observed in devices with thin uniform bases. The current gain of 45-nm-thick graded base devices saturated as the grading was increased beyond standard values. Grading did not increase the gain of devices with a 20-nm-thick base. Index Terms—Base-composition grade, base-transit time, heterojunction bipolar transistor (HBT). I. INTRODUCTION II. BASE TRANSPORT THEORY A. Base-Transit Time: Thermal Injection From the Emitter Expressions for the base-transit time in thin-base bipolar junction transistors (BJTs) with no energy ramp at the emitter can be obtained by directly solving the Boltzmann transport equation  or by the scattering theory (flux method) . Both methods yield similar results. The flux method result (1) is simple to use. In (1), is the base-transit time, the base is the electron diffusivity. The velocity is width, and given by R EDUCTION OF base-transit time in heterojunction bipolar transistors (HBTs) due to injection of electrons from an abrupt energy ramp was proposed by Kroemer long before advanced HBTs were demonstrated , . However, today’s speed records of InP HBTs are obtained with either abrupt or graded base–emitter junctions, namely with and without injection from an energy ramp –. It thus appears that the injection of energetic electrons does not substantially improve the high-frequency performance of HBTs having base thicknesses larger than 30 nm. Base-composition grading , on the other hand, is widely used in advanced HBT structures, and is believed to improve device performance. In this paper, we study the benefits of electron injection from an energy ramp and base composition grading by measuring the dc current gain of devices with varying base width and composition. It is found that electron injection from an energy ramp significantly reduces base-transit time only in bases that are less than 30 nm thick. A much more significant reduction of the base-transit time is obtained by composition grading of 30–50-nm-thick bases. An important but unexplained observation is that contrary to the prediction of theory, the composition grading effect saturates. No further reduction of the base-transit time is obtained for grade values larger than 10%. Manuscript received October 28, 2003; revised February 4, 2004. The review of this paper was arranged by Editor J. N. Burghartz. The authors are with the Department of Electrical Engineering, Technion, Haifa, 32000 Israel. Digital Object Identifier 10.1109/TED.2004.826828 (2) is the electron effective mass, Boltzmann’s conwhere stant, and the temperature. In Ga In As at room temcm/s. perature An alternative method for solving the Boltzmann transport equation in the base layer of BJTs is a single-parameter Monte Carlo simulation . The simulation calculates the impulse response of the base by recording the transit time of each electron injected from the emitter. The momentum distribution of the injected electrons at the base–emitter junction is a velocity weighted Maxwellian . The single parameter of the simulation is the momentum relaxation rate, which is obtained from the electron diffusivity. A momentum relaxation event is modeled by a Gaussian momentum distribution and the rate of momentum relaxation events is determined by Poisson statistics. We have simulated base transport in BJTs using this approach, and compared the results to (1). For long and short bases, i.e., when either the first term or the second term in (1) dominates, the simulation reproduces the results of (1). For the transition region between long and short bases, the base-transit time obtained from the simulation is up to 12% longer than that given by (1). As mentioned in  and in , the analytic results are an approximation, which depends on the particular choice of the boundary conditions. It is therefore not surprising that the results of the Monte Carlo simulation are not identical to the analytic expression. The above discussion elucidates that the electron diffusivity is the key parameter that determines the base-transit time in BJTs. 0018-9383/04$20.00 © 2004 IEEE ZOHAR et al.: REDUCTION OF BASE-TRANSIT TIME OF InP–GaInAs HBTs DUE TO ELECTRON INJECTION 659 TABLE I REPORTED VALUES OF ELECTRON DIFFUSION COEFFICIENT IN P-TYPE GaInAs It was measured and calculated in heavily doped p-type GaInAs by several authors, as summarized in Table I. The most relevant and precise experimental result is obtained from the frequency response of HBTs with a thick base . In thick-based HBTs, the base-transit time is the dominant delay time of the device, and can therefore be accurately evaluated. Moreover, the effect of injection from the energy ramp can be safely ignored in thick-based HBTs. We have used the electron diffusivity value of 110 cm s throughout this paper. B. Base-Transit Time: Hot Electron Injection From the Emitter No analytic expression for the average base-transit time of abrupt base–emitter junction HBTs is available in the literature. Hence, we have used the simple Monte Carlo approach to interpret our experimental results. Ballistic injection of electrons was modeled in the simulation by assigning a forward velocity of cm/s to the electrons emerging from the emitter. The energy relaxation of the injected electrons was modeled by a single average parameter, the energy scattering rate . There are various ways to introduce an average energy relaxation rate into the simulation. We have tested several options, and verified that the results do not significantly depend on the particular choice made. Below, we describe the option that was used to generate the results presented in this paper. Denoting the momentum scattering rate by , we assumed that the probability that the first collision is an energy scattering event is and a momentum scattering event . An energy relaxation event was modeled in the simulation by a thermalized Gaussian velocity distribution and a uniform angle distribution in the forward direction only. A momentum relaxation event of an energetic electron was assumed identical to that of a thermalized electron, namely, it produced a thermalized Gaussian velocity distribution with a uniform angle distribution. Thus, the total energy relaxation rate in our simulation was . The momentum scattering rate was assumed equal for thermalized and hot electrons. The value of the electron momentum relaxation rate was set to s using and the Einstein relation. The value of the energy relaxation rate was set to s . This value was chosen to obtain s , so that the energy relaxation mean free path of the hot electrons is about 30 nm. The value of the energy relaxation mean free path determined by electroluminescence spectroscopy is 18 6 nm , while theory predicts a value of 60 nm . C. Transit Time of a Composition-Graded Base Using the drift diffusion approach , one obtains that for linear composition grading  (3) and is the difference between where the bandgap at the collector and emitter edges of the base. To be must be identical in both equations. consistent with (1) For short bases, the drift diffusion approach and, hence, (3), is not valid . We have therefore used our simple Monte Carlo simulation to model graded base transport. The value of the quasi-electric field induced by grading of the strained As base was obtained from the expression given in Ga In  for the bandgap of this material versus the deviation from lattice-matched layer composition (4) The second-order term in the above equation was neglected so that a constant electric field was obtained for a linearly graded base composition. Thermal electrons in the simulation were allowed to accelerate due to the presence of the electric field. Hot electrons injected from the energy ramp were assigned an effective mass 3.3 times larger than the thermal effective electron mass to take nonparabolocity into account . III. ROLE OF ELECTRON INJECTION FROM AN ENERGY RAMP—NO COMPOSITION GRADE Hot-electron effects were studied in this paper by comparing the base width dependence of the gain of abrupt HBTs to that predicted by theory for thermal injection. Similar work was published before , , however, more data on thin-base HBTs is presented here and the theoretical analysis is much more precise. A series of abrupt base–emitter junction InP–GaInAs HBT samples were prepared, with the base layer width varying between 10–45 nm. The remaining layer structure was identical in all samples. The samples were grown by a compact metalorganic molecular beam epitaxy system . Carbon and tin served as p-type and n-type dopants, respectively. The p-type cm , and hole doping level in the base was about mobility about 45 cm Vs. The base sheet conductance versus base width is plotted in Fig. 1. The linear dependence confirms the nominal values of the base width. The curve intersects the width axis at about 6 nm, probably due to Fermi-level pinning at the exposed surface and some etching during the selective wet etch process. 660 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 51, NO. 5, MAY 2004 Fig. 1. Extrinsic base sheet conductance versus base width. Fig. 3. Base-transit time versus base width. Calculated results are for the uniform composition case. Experimental results for graded base . Fig. 4. Variation of gallium content relative to lattice-match value versus position in the base and collector layers. Grading of the collector prevents formation of an energy barrier. Fig. 2. Measured and calculated current gain versus base width. The measured maximum dc current gain versus base width is plotted in Fig. 2. The solid line is obtained from the expresusing (1) with cm s, and with an sion determined to fit the 45-nm-thick electron lifetime base-gain value. Clearly, the gain of the very thin-base devices is much higher than predicted by (1). A calculation of the basetransit time by the Monte Carlo simulation, which includes hot electron injection, resolves this conflict. We conclude that injection from an energy ramp significantly affects base-transit time in bases less than 30 nm thick. The calculated base-transit time with and without hot electron injection is shown in Fig. 3. As mentioned above, the values obtained by the Monte Carlo simulation for the BJT case were larger by 10%–12% than the results obtained from (1). Hot electron injection reduced the base-transit time mainly in very narrow bases. Very thin bases are currently not used, but will eventually be used in future scaled-down devices. Experimental results obtained from high frequency measurements of abrupt base–emitter junction HBTs with a composition-graded base  are shown in the figure as well. We first note the excellent agreement between our simple theory and the measured data. Furthermore, it can be seen that composition grading of the base does not substantially reduce base-transit time for 25and 33-nm-thick bases. This result was confirmed by our experiments, described below. IV. COMPOSITION GRADING OF THE BASE LAYER A curve of the dc current gain versus composition grade in the base is useful for detecting changes in the base-transit time assuming that electron lifetime does not significantly vary with base composition. This assumption is not valid for doping grade, which was recently introduced to further accelerate the electrons in the base . Previous experiments showed that for 50-nmthick compositionally graded bases, the gain drops abruptly due is larger than 10% to defects introduced by the strain when . Here, we have used strain compensation to eliminate this up to 35% with no colproblem, and were able to increase lapse of the gain. The variation of the composition along the base and collector layers employed to achieve stain compensation is described in Fig. 4. At the base–emitter junction the As layer is set to gallium content of the Ga In (grade) above the lattice-match value, and at the base collector (grade) below the lattice-match value. The junction to collector layer is graded across a distance equal to one third of the base width to prevent the formation of an energy barrier. The total integrated strain of the entire structure is nominally zero. of a variety of devices are Curves of the gain versus shown in Fig. 5. Although the gain does not collapse, it satu. It is unlikely that the observed saturarates at tion is caused by an exact cancellation of the effect by defect formation. A comparison of the experimental data to the prediction of the drift diffusion model is shown in Fig. 6. Clearly, the ZOHAR et al.: REDUCTION OF BASE-TRANSIT TIME OF InP–GaInAs HBTs DUE TO ELECTRON INJECTION 661 The experimental results included in Fig. 3 indicate that composition grading of the base does not significantly reduce the base-transit time in abrupt thin-base HBTs. The results shown in Fig. 7 support this conclusion: for 20-nm-thick bases, hardly any change in gain can be observed with composition grading. V. CONCLUSION Fig. 5. Current gain versus composition grading of strain compensated HBTs having a 45-nm-thick base for two extrinsic base sheet resistance values: 485 10 = and 390 10 = . 6 Fig. 6. 6 Measured and calculated current gain versus base grading. Fig. 7. Current gain versus base composition gradient in abrupt base–emitter HBT with a 20-nm-thick base. drift diffusion expression does not agree with our data. It predicts a fourfold decrease of the base-transit time when is increased from 10% to 30%. The Monte Carlo simulation, on the other hand, does predict a less pronounced increase of the gain with composition gradient. Yet, the gain predicted by the simulation is twice as high as the experimental data at high composition gradients. More work is required to resolve this important discrepancy. The experimental results combined with the simulation presented in this paper enabled us to derive the base-transit time in various HBT structures. It appears that as base dimension are scaled down ballistic injection may play some role in the reduction of the base-transit time. Base composition grading, on the other hand, is more helpful in thicker bases. REFERENCES  H. Kroemer, “Heterostructure bipolar transistors: what should we build?,” J. 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Alexandre, and J. Godin, “Measurement of base and collector transit times in thin-base InGaAs/InP HBT,” IEEE Electron Devices Lett., vol. 24, pp. 430–432, July 2003.  M. Dahlström, X. M. Fang, D. Lubyshev, M. Urteaga, S. Krishnan, N. Parthasarathy, Y. M. Kim, Y. Wu, J. M. Fastenau, W. K. Liu, and M. J. W. Rodwell, “Wideband DHBTs using a graded carbon-doped InGaAs base,” IEEE Electron Device Lett., vol. 24, no. 7, pp. 433–435, July 2003.  J. L. Benchimol, J. Mba, B. Sermage, M. Riet, S. Blayac, P. Berdaguer, A. M. Duchenois, P. Andre, J. Thuret, C. Gonzale, and A. Konczykowska, “Investigation of carbon-doped base materials grown by CBE for Al-free InP HBTs,” J. Cryst. Growth, pp. 476–480, 2000. Gal Zohar was born in Haifa, Israel, in 1972. He received the B.A. degree in physics and the B.Sc. degree in material engineering in 1999, and the M.Sc. degree in electrical engineering in 2003, all from the Technion, Israel Institute of Technology, Haifa. During his graduate studies, he carried out research on base transport in InP-based HBTs. He is currently with the Quality and Reliability Group, Intel, Haifa, Israel. Shimon Cohen received the Practical Engineering degree in electrooptics from the Technion, Israel Institute of Technology, Haifa, in 1981. From 1981 to 1991, he worked on epitaxial crystal growth and growth of hydrogenated amorphous silicon at the Technion, Israel Institute of Technology. Since 1991, he works on the growth of InP-related materials using metal–organic molecular-beam epitaxy. His main interest is in physics and the technology of epitaxial crystal growth. Victor Sidorov received the M. Sc. degree (with honors) in chemistry from Voronezh University, USSR, in 1985. Since 1995 he is a Senior Research Assistant at Microelectronics Research Center, The Technion, Israel Institute of Technology, Haifa, working on III-V microwave and optoelectronic device and circuits manufacturing. Prior to this, he held an Engineer-Researcher position at Mizur Micromechanics Technologies working on microsensors manufacturing and micromachinning. He is now also with the Weizmann Institute of Science, Rehovot, Israel, working on nanotechnology projects. Arkady Gavrilov was born in St. Petersburg, Russia, in 1960. He received the Diploma in optics from the Mathematical Zveriev Physical Institute, St. Petersburg, in 1985. He is currently with the Technion Microelectronics Center, The Technion, Israel Institute of Technology, Haifa, Israel, where he develops the microfabrication technology of indium phosphide based HBTs. Benny Sheinman was born in Israel in 1969. He received the B.Sc. and M.Sc. in electrical engineering from The Technion, Israel Institute of Technology, Haifa, in 1991 and 1998 respectively. He is currently pursuing the Ph.D degree in electrical engineering at the Technion. His research focus is on design, growth, and modelling of InP-based HBTs and on microwave optoelectronic circuits. Dan Ritter (M’99) received the B.Sc, M.Sc, and Ph.D. degrees in electrical engineering from The Technion, Israel Institute of Technology, Haifa in 1981, 1984, and 1989, respectively. He then carried out post-doctoral research for three years at AT&T Bell Laboratories, Murray Hill, NJ. In 1992, he joined the Technion Electrical Engineering Department, where he is currently an Associate Professor. His group has been using the metalorganic molecular beam epitaxy method to grow the epitaxial layers. His main research interest is physics and the modeling of indium phosphide based devices. The focus of his current activity is heterojunction bipolar transistors.