The effects of degenerate Fermi statistics on electron injection currents for p+‐GaAs grown by molecular beam epitaxy are presented. To achieve Be dopant concentrations of greater than 8×1019 cm−3, the substrate temperature during growth was reduced to approximately 450 °C from the usual 600 °C. In this heavily doped material, we measure unexpectedly large electron injectioncurrents which are interpreted in terms of an effective narrowing of the band gap. At extremely heavy doping densities, the Fermi level pushes into the valence band and degenerate Fermi statistics must be taken into account. For doping concentrations greater than 1×1020 cm−3, effects due to degenerate Fermi statistics oppose the band‐gap shrinkage effects; consequently, a reduction in the electron injection currents is observed. The result is a substantial reduction in gain for AlGaAs/GaAs heterostructure bipolar transistors when the base is doped above 1020 cm−3

Harmon, E. S.

Lovejoy, Michael L.

Lundstrom, Mark S

Melloch, Michael R

English

Purdue E-Pubs

Purdue UniversityPurdue e-PubsDepartment of Electrical and ComputerEngineering Faculty PublicationsDepartment of Electrical and ComputerEngineering1991Experimental determination of the effects ofdegenerate Fermi statistics on heavily p‐dopedGaAsE. S. HarmonPurdue UniversityMichael R. MellochPurdue University, melloch@purdue.eduMark S. LundstromPurdue University, lundstro@purdue.eduMichael L. LovejoyPurdue UniversityFollow this and additional works at: https://docs.lib.purdue.edu/ecepubsPart of the Electrical and Computer Engineering CommonsThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Harmon, E. S.; Melloch, Michael R.; Lundstrom, Mark S.; and Lovejoy, Michael L., "Experimental determination of the effects ofdegenerate Fermi statistics on heavily p‐doped GaAs" (1991). Department of Electrical and Computer Engineering Faculty Publications.Paper 89.http://dx.doi.org/10.1063/1.105152Experimental determination of the effects of degenerate Fermi statistics onheavily p-doped GaAsE. S. Harmon, M. R. Melloch, M. S. Lundstrom, and M. L. LovejoyCitation:  58, (1991); doi: 10.1063/1.105152View online: http://dx.doi.org/10.1063/1.105152View Table of Contents: http://aip.scitation.org/toc/apl/58/15Published by the American Institute of PhysicsExperimental determination of the effects of degenerate Fermi statistics on heavily p-doped GaAs E. S. Harmon, M. R. Melloch, M. S. Lundstrom, and M. L. Lovejoy School of Electrical Engineering, Purdue University, West Lafayette, Indiana 47907 (Received 12 November 1990; accepted for publication 15 January 199 1) The effects of degenerate Fermi statistics on electron injection currents for p + -GaAs grown by molecular beam epitaxy are presented. To achieve Be dopant concentrations of greater than 8 X 1019 cm - 3, the substrate temperature during growth was reduced to approximately 450 “C from the usual 600 “C. In this heavily doped material, we measure unexpectedly large electron injection currents which are interpreted in terms of an effective narrowing of the band gap. At extremely heavy doping densities, the Fermi level pushes into the valence band and degenerate Fermi statistics must be taken into account. For doping concentrations greater than 1 x 102’ cm - 3, effects due to degenerate Fermi statistics oppose the band-gap shrinkage effects; consequently, a reduction in the electron injection currents is observed. The result is a substantial reduction in gain for AlGaAs/GaAs heterostructure bipolar transistors when the base is doped above 102’ cm- 3. The electron current injected into the base of an AlGaAs/GaAs heterojunction bipolar transistor (HBT) is strongly enhanced by heavy doping effects.lF2 This en- hancement has been attributed to doping-induced pertur- bations of the band structure which have the effect of in- creasing the n#o product.3 The increase in the ngo product may be interpreted as an effective shrinkage of the band gap in the base of the transistor.4’5 The results pre- sented by Klausmeier-Brown et ~1.‘~~ have included Be- doped GaAs in the range 6~ 1017- 8 x 10” cm - 3. With modern HBT design requiring progressively higher doping levels, the effects of these extremely high dopant levels on minority-carrier transport must be understood. The results presented here show significant band-gap shrinkage for all doping concentrations above 10’s cm - 3. However, for doping concentrations above 8 X lOI cm - 3, increases in injection currents due to perturbations of the band struc- ture are offset by reductions in injection currents due to degenerate Fermi statistics.5*6 To adequately model and design heavily doped GaAs bipolar devices, these heavy doping effects must be examined. The collector current density of an n-p-n homojunction bipolar transistor when the emitter-base junction is for- ward biased and the base-collector junction is reverse bi- ased may be described by Jc=e[ exp($$) - 11, (1) where & = nap, the equilibrium carrier concentration product, D, is the diffusion coefficient of the minority- carrier electrons, kB is the Boltzmann constant, and NA W, is the charge per unit area in the quasi-neutral base. The r&D,, product may be obtained directly from the Jc (col- lector current density) vs V,, (base-emitter bias) charac- teristics by utilizing Eq. ( 1) provided that the base doping is spatially uniform.7 The targeted transistor cross sections and doping pro- files are summarized in Fig. 1 and Table I. Homojunction bipolar transistors were chosen for this study instead of heterojunction bipolar transistors because misalignment of doping and compositional junctions, or improper grading of the junction may invalidate ( 1). These transistor films were grown in a Varian GEN-II molecular beam epitaxy (MBE) system on n +-GaAs substrates. To reduce out diffusion of Be in heterostructure bipolar transistors ( HBTs), the heavily doped base has been grown at a re- duced substrate temperature.8-‘0 Substrate temperatures during growth were approximately 600, 450, and 600 “C for collector, base, and emitter layers, respectively. The growth rate was 1 ,um/h as determined from the reflection high-energy electron diffraction (RHEED) pattern at the beginning of each film growth. The p-type dopant was Be and the n-type dopant was Si. Eight transistor films with base doping concentration ranging from 3X 10” to 1.4~ 102’ cm - 3 were studied. The slope of the measured carrier concentration versus the inverse Be oven tempera- ture was consistent with the vapor pressure curve of Be, implying the absence of significant precipitation of Be even at the highest doping levels.‘OP” All transistors were fabri- cated with standard optical lithography and wet etching procedures. Base doping profiles were characterized by both Hall effect measurements and by secondary-ion mass spectros- emitter0 base 0 collector A FIG. 1. Schematic representation of the GaAs bipolar transistors used to measure electron injection currents. 1647 Appt. Phys. Lett. 58 (15), 15 April 1991 0003-6951/91 I1 51647-03$02.00 @  1991 American Institute of Physics 1647 TABLE I. Summary of measurements on the heavily doped base of GaAs n-p-n bipolar transitors. Hall NA SIMS NA Hall p Base width n?&, (cm - “) (cm - ‘) (cm*s-‘) m (cm-4s-‘) 2.59 x lOI* 4.55x 10’8 136 1000 6.04x lOI 3.07x lo’s 3.31 x to’* 131 1000 6.83 x lOI4 4*30x IO” 6.13~ lOI 74 1000 1*33x 10’5 7.59 x 1oip 8.56x 10” 65 1000 1.20x 10’5 9.73 x 10’9 7.47 x lOI 63 500 6.99 x lOI4 1.28x 1020 1.37x 10’” 62 1000 8.99 x lOi 1.35x 1020 1.33x lo*@ 58 1000 9.00x 10’4 1.39x 10’” 1.06~ 10” 57 500 5.60x 10’4 copy (SIMS). MBE growth allows precise base thickness resolution if negligible outdiffusion of the Be dopant oc- curs. SIMS analysis performed by Charles Evans and As- sociates confirms that Be diffusion in these films grown at low substrate temperature is negligible (see Fig. 2). Hall effect measurements were performed on Hall structures ad- jacent to the BJTs. Values of mobility and hole concentra- tion were calculated assuming a Hall factor of unity. Note .that the NAPI’B product is measured directly by the Hall measurement technique so that there is no error in NA WB due to base thickness ( WB) estimation. The values for Hall and SIMS carrier concentration ( NA) are reported in Table I assuming an as-grown base thickness. The reported vai- ues of nfpn were calculated using the Hall measurements; if SIMS measurements were used instead, comparable val- ues for r&D, are obtained with more scatter in the data. The collector current density was measured as a func- tion of the applied base-emitter voltage with the base- collector junction held at a zero volt bias. The linear por- tion of the ln(lc) vs I’nE plot was then fit to Eq. (1). Device temperatures measured with a thermocouple in the probe station chuck agreed well with the temperature of the device as determined by the slope of the fit to Eq* ( I ). The quantity nf$,, was determined from the intercept of the linear fit to this data. These results were scaled to 300 K using the known temperature dependence of ni (Ref. 12) and are presented in Table I and Fig. 3. Inverting the transistor operation by forward biasing the base collector and reverse baising the base emitter was used to confirm the &D, product obtained from the normal operation con- figuration. No dependence on emitter perimeter to area distance Q.@nf FIG. 2 SIMS profile for the GaAs bipolar transistor with the base doped 1.35x IO’“cm-‘. Hall NA cm? FIG. 3. Plot of t&D,, at 300 K vs Hall concentration as deduced from bipolar transistor injection current measurements. The solid line repre- sents the best fit to th: data using Eqs. (2J-(3) and the dashed line represents the theoretic,%1 prediction of Jain el al. (see Ref. 6). ratio was observed. We estimate less than 5% error in the n$l, product due to collector current measurement accu- racy and an additional 5% error in the $9, due to the NA WB estimation. Several authors have pointed out that the Hal1 factor may be much different from unity,‘3”4 which may lead to an additional systematic error in the NA W, determination. Results from these low growth tem- perature structures are consistent with the results obtained for the normal temperature growth.“’ The significant fea- tures of Fig. 3 are the increase in the r@, product as base dopant concentration increases from 1 X lOi6 to 8X lOI cme3, and the rapid decrease in P&D, for higher dopant concentrations. Equation ( 1) is only valid as long as recombination in the base is not significant. We estimate that a diffusion length of less than 700 A would be required to reduce the measured collector current by 9% in the 500 A base width BJTs. However, a diffusion length of 700 A would reduce the measured collector current by 38% for the 1000 A base transistors. Thus, if the diffusion length in the transistor base is 700 A, measurements of transistors with 500 A base widths would yield an nT$, that is approximately 30% higher than that of transistors with 1000 A base widths. This is not the case with the measurements presented here, implying that the diffusion length in the transistor base is significantly longer than 700 A. An extrapolation of pub- lished lifetime datat5 gives a lifetime of 76 ps for p-GaAs doped 1.4~ 10” cm - 3. For D, = 20 cm2 s - ‘, a lifetime of 76 ps gives a diffusion length of 3900 A. Thus, for high- quality GaAs material, one would not necessarily expect much recombination in transistors with these thin bases. Also, the Hall measurements reported in Table I show very good majority-carrier mobilities, implying that this low growth temperature material is high-quality GaAs. These results can be interpreted using a simple rigid band shrinkage model for GaAs. This approach necessarily includes some error from the assumption for D,,. Here we use the fit given b,y Tiwari and Wright” for electron drift mobility (p,) and the Einstein relationship to obtain D,. The dependence 01.’ intrinsic carrier concentration upon de- generate Fermi statistics and band-gap shrinkage in p-type material may be r:presented by5*6*‘2 1648 Appl. Phys. Lett., Vol. 58, No. 15, 15 April 1991 Harmon et al. 9648 ni=@~dw)exP( - Eg/kBT)~112(~F) Xexp( - 77,~) (AE&T), (2) where ti71,2( vF) is the Fermi integral of order l/2, rlF is the normalized energy difference between the Fermi level and the valence-band edge, NP is the effective density of states of the conduction band, iV,(qF) is the effective den- sity of states of the valence band including a nonparabo- licity factor for the light hole band,6*t2 Eg is the intrinsic energy gap, and AE 3 is the amount of rigid band-gap shrinkage of the form AEg=ANA”3 (eV). (3) By fitting our measured r&D,, results to Eqs. (2)-(3) we obtain A = 2.85X lo- *, which is reasonably close to the theoretical projections of Jain et al.’ who obtain A = 2.6X 10 - 8 for p-GaAs (see Fig. 3). Recent measure- ments for electron drift mobility and diffusivity’7”8 give slightly lower values than predicted by Tiwari and Wright/ so our fit to & should be viewed as a lower limit. The results presented in Fig. 3 show a strong enhancement in electron injection implying that significant band-gap shrinkage occurs. Note that the turnover in the experimen- tal data points should be expected when degenerate Fermi statistics effects become strong enough to dominate over the band-gap shrinkage effects.375 We find an effective band-gap shrinkage which is significantly larger than that predicted by most theoretical calculations3*i9 but is reason- ably close to the calculations of Jain et aL6 These band-gap shrinkage and degenerate Fermi sta- tistics results have some interesting applications for device design. For solar cell structures it is common practice to use a doped isotype homojunction to confine minority car- riers. Chuang et al” demonstrated that for a p + doping of lOi cm - 3, the p + /p-GaAs isotype homojunction is not an effective barrier due to band-gap shrinkage. However, if the p + layer is doped greater than 102’ cm - 3, degenerate Fermi statistics counteract the effects of band-gap shrink- age and a p + /p isotype homojunction could effectively confine minority carriers as was recently demonstrated by de Lyon et aL2’ For HBT structures, the gain of the tran- sistor is enhanced by band-gap shrinkage and degraded by degenerate Fermi statistics effects.3”0 These effects can be treated by considering their infuence on the common emit- ter gain2 of a HBT which should be proportional to nf$,/N,. For example, consider two similar HBT struc- tures, the first with a base doped 2X 102’ cm - 3 and the other with a base doped 5X lOI cm - 3. Normally, one would expect the gain of the lighter doped HBT to be four times greater than the gain of the HBT with the heavier base doping. However, if band-gap shrinkage and Fermi degeneracy effects are included, the HBT with lighter base doping would have a gain that is almost 23 times greater than the gain of the heavier doped HBT. In summary, results that extend previous measure- ments of r&D, to Be doping densities of 1.4X 102’ cm- 3 have been presented. These experimental results show sig- nificant band-gap narrowing for all the doping densities studied. However, the effects of degenerate Fermi statistics strongly oppose the band-gap shrinkage effects for doping concentrations greater than 8~ lOI cm - 3, resulting in a decreasing r&D, for increasing doping. These results indi- cate that the gain of an AlGaAs/GaAs HBT is signifi- cantly degraded when the base is doped above - 102’ cme3. This work was supported by the National Science Foundation under grant number ECS-8901638. Author Lovejoy acknowledges support from the AT&T Ph.D. Scholarship Program. ’ M. E. Klausmeier-Brown, M. R. Melloch, and M. S. Lundstrom, Appl. Phys. Lett. 56, 160 (1990). *M. E. Klausmeier-Brown, M. S. Lundstrom, and M. R. Melloch, IEEE Trans. Electron Devices 36, 2146 ( 1989). 3H. S. Bennett and J. R. Lowney, J. Appl. Phys. 62, 521 (1987). 4J. A. de1 Alamo and R. M. Swanson, Solid State Electron. 30, 1127 (1987). ‘S. C. Jam, J. M. McGregor, and D. J. Roulston, J. Appl. Phys. 68, 3747 (1990). ‘B. Jalali, R. N. Nottenburg, A. F. J. Levi, R. A. Hamm, M. B. Panish, D. Sivco, and A. Y. Cho, Appl. Phys. Lett. 56, 1460 (1990). ‘K. M. Vliet and A. H. Marshak, IEDM Tech. Dig. 312 (1978). sP. Enquist, G. W. Wicks, L. F. Eastman, and C. Hitzman, J. Appl. Phys. 58, 4130 (1985). 9J. L. Lievin and F. Alexandre, Electron. Lett. 21, 413 (1985). “J L Lievin C. Dubon-Chevallier, F. Alexandre, G. Leroux, J. Dangla, . and D. A&i, IEEE Electron Device Lett. EDL-7, 129 (1986). “R. A. Hamm, M. B. Panish, R. N. Nottenburg, Y. K. Chen, and D. A, Humphrey, Appl. Phys. Lett. 54, 2586 (1989). 12J S. Blakemore, J. Appl. Phys. 53, R123 (1982). I351 D. Wiley, Semiconductors and Semimetals, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1975), Vol. 10, p. 91. “D. C. Look, Electrical Characterization of GaAs Materials and Devices (Wiley, New York, 1989), p. 59. “R K. Ahrenkiel, Current Topics in Photovoltaics, Vol. 3, pp. l-78, 1488. “S. Tiwari and S. L. Wright, Appl. Phys. Lett. 56, 563 (1990). “T. Furuta and M. Tomizawa, Appl. Phys. Lett. 56, 824 (1990). ‘*M. L. Lovejoy, B. M. Keyes, M. E. Klausmeier-Brown, M. R. Melloch, R. K. Ahrenkiel, and M. S. Lundstrom, 1990 International Conference on Solid State Devices and Materials, Sendai, Japan, August 22-24, 1990. 19W. Bardyszewski and D. Yevick, Phys. Rev. B 35, 619 (1987). 20H L Chuang, P. D. DeMoulin, M. E. Klausmeier-Brown, M. R. Mel- . loch, and M. S. Lundstrom, J. Appl. Phys. 64, 6361 (1988). 2’T. J. de Lyon, J. A. 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Experimental determination of the effects of degenerate Fermi statistics on heavily p‐doped GaAs

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Experimental determination of the effects of degenerate Fermi statistics on heavily p‐doped GaAs

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