Ihara, S.

Kagaya, O.

Katayama, K.

Mizuta, Hiroshi

Ohbu, I.

Ohkura, Y.

English

Southampton (e-Prints Soton)

Semicond. Sci. Technol. 9 (1994) 811-814.  Printed in the UK I The electron mobility transition in n-GaAs  '  heatli!y dcped channe!s  I I Y Ohkura, H  Mizuta, I Ohbu, 0 Kagaya, K  Katayama and S lhara Central Research Laboratory, Hitachi  itd, Kokubunji, Tokyo  185, Japan Abstract. Low-field electron transport properties in heavily doped  n-GaAs channels at 300 K are investigated by Monte Carlo simulation. The matrix  element for electron-impurity scattering is  obtained from the Fourier-transformed Coulomb potential  accounting for the screening effects of  the two-dimensional electron gas. The  effects of  the screening and  the impurity profile are analysed. Electron mobility is calculated for several values of  sheet electron density and  n-GaAs thickness. For  low  sheet electron density, the calculated mobility increases with the sheet electron density and is almost independent of  n-GaAs thickness. For high sheet electron density, the mobility approaches a constant value and becomes independent of  sheet electron density. These findings are explained for the first time as a transition from a two- to three-dimensional nature and are well confirmed  by our experiments 1.  Introduction n-GaAs heavily doped channel FETS  [l] show superior current drive capability and higher breakdown voltage, especially in  short-channel  devices,  because  the  gate injection current is lower than in conventional HEMTS. Since the doping density increases with the reduction in device  size,  it  is  crucial  to  understand  the  electron- impurity interaction and to predict the transport proper- been investigated fully for heavily doped channels. In the present work. low-field transport properties in heavily  doped  n-GaAs  channels  are  investigated  by Monte Carlo simulation where a parabolic band model rrrennpa  ;r\n;.r~~~;mn,,n'+.i  in+pr.,r+inn  r? xi  fnr  +hp two-dimensional  electron  gas  (ZDEG)  were  used.  A transition  from  a  two-  to three-dimensional nature is studied by simulation as well as experiment. &:--  U  -...-.. ~-  *,.  -..-  La-&  1 ,--...  I-rln..  +L<-  dXe-+  ha-  --+ UT&  IIUWCiYF;I) LU  UUI  UGJL &,,Uw,=u~G  LlUD C'ICCL  1"lo  UUL Y'lV  LlULIllllY I".III"Y  ""yu',.,  'll..2.lUll."AI  LA, a,  ."I  .I_ 2.  The electron density profiles Before  performing  the  Monte  Carlo  simulation,  the electronic states of  the six lowest subbands at 300 K are calculated  first  by  solving  Poisson  and  Schrodinger equations self-consistently for a heavily-doped n-GaAs channel heterostructure (see table 1)  [2].  The wavefunction parallel to the heterointerface is assumed to be  a plane wave. We  account for sue quantization effects only in the r  valley as we treat only low-field mobility. Since the AI,Ga,-,As  layer under the Schottky gate is depleted in this work, we neglect the penetration of the wavefunction of  electrons  in  Al,Ga,_,As  region,  and  assume  the heterointerface to be abrupt. The results of  the electron 0268-12442/94/050811+04  $19.50 0 1994 IOP Publishing Ltd Table 1.  Assumed  parameters for i-AI,Ga,-fis/n-GaAs/ p-GaAs structure (grown on  a semi-insulating GaAs substrate). Impurity concentration  Thickness Layer  Material  (~m-~)  (nml I  AI,,,Ga,,,As  Undoped  10 II  n-GaAs  N, 3 x 10''  15/25/35 111  p-GaAs  N,  3 x  10'6  300 density profiles for  n-GaAs  thickness d = 15,  25  and 35 nm  (see table  1) are shown in figure 1 for various ;,aloes  of  skeet ekctron density x,. On the p-5aP.s  side, carriers are depleted and the electron density profiles are not sensitive to n, or the position of  the heterointerface (z = -d).  On the gate side, the profile is  affected by d. However, as long as the Al,Ga,-Js  region is depleted at  relatively  low  n,,  the  electron  profile  is  almost independent of  n-GaAs thickness. As n, is increased by applying  a  higher  gate  bias,  a  nearly  charge-neutral region develops and extends toward the interface. As  a result, the subband separation is reduced, and the nature of the electronic states in the channel is expected to be close to those in bulk material (three-dimensional). The minimum subband separation was found to be  54 mV for  n, = 1 x 10"  cm-'  and  23 mV  for  n, = 7  x 10" Note  that  this  transition  from  two-  to  three- dimensional states does not occur, for example, in  an inversion layer of  an si-MOSFET or  HEMT, where electrons are always localized, keeping a two-dimensional nature irrespective of  n,. We will comment on the effect of  this transition on electron mobility in section 4. 81  1 Y Ohkura eta/ ND -40  -30  -20  -10  0  io  20 Distance z (nm) Figure 1.  Calculated electron distribution for n-GaAs thickness d (a) 15 nm,  (6)  25 nm, and  (c) 35 nm for various values of  sheet electron density. The impurity concentration in the n-GaAs (3 x 10'8cm-3)  is  also shown as No. 3.  Electron-impurity  interaction UClFirllru  I"I11L=u  ullpurlry  bbtlLLCiU~  I"1  LllG  LWV- dimensional electron gas  (ZDEG),  which  is  used  in the Monte Carlo simulations,  was calculated by the approach originally proposed for MOSFETS  [3].  The matrix element M,,,,(Q)  is  calculated  from  the  Fourier-transformed Coulomb potential #(e, z) accounting for the screening effects of the ZDEG [2, 31; here m  and n are subband indices and  Q = Ik, -  k,l  and k, and k, are initial and &a1 wavevectors, respectively, parallel to the layer interface. The calculated square of the intrasubband matrix element !Mm&)!'  versus  Q is  shown  in  figure  2  with  (4) two-dimensional  electron density n,,  (b)  n-GaAs thickness d and (e) subband index as parameters. The potential b(Q,  z) induced by  an impurity on located at zo decays approximately .as exp(-Qlz,  -  zl) [2].  In other words, only the impurities within a distance l/Q  contribute to thescattering. Thescreening by electrons affects IM,(Q)l2 as follows. For small Q,  b(Q,  z) is  slowly varying, and IMmm(Q)12  corresponds  to  the  weak  scattering  by impurities in a wide range. Thus the screening effect is very large. For large Q.  qb(Q,z)  is  confined to a small region and therefore, lMm,,,(Q)!'  corresponds to strong scattering by the impurities in a very small distance and the screening effect is small. C--..*-*A  :-..:..-A  :  :...  ---a.--:--  C^_  .L-  ..... 812 IO  -I5 ry  Subbmd  index 10 10 10 d  = 15nm ns =2x10 cm 12  -2 10  10  10 Q  (cm-') Figure 2.  Calculated square of intrasubband matrix elements ]Mm,(Q)12  for (a)  different  values of sheet electron density n,  with  n-GaAs thickness d = 15 nm and m  = 1, (b)  three different  n-GaAs thlcknesses at ns =  2 x  IO'*  cm-* and m =  1. and (c) thqfirst four subbands with d=  15 nm and n, =  2 x IO" cm-'.  Circles indicate Q =SI  (the screening constant of  the first subband) in (a)  and Q = l/d (n-GaAs thickness) in  (b). As  shown  in  figure  2(u), with  an  increase  in  ns, lM1,(Q)I2 decreases for small Q  due to  the  screening effect. The screening constant of  the first subband (S,) [2,3]  for  the three n,  values is  1.39,  1.79  and  1.95 x lo6 cm-'  respectively. For Q <  S,, the screening effect is dominant. The dependence of  I Mll(Q)I2  on the n-GaAs thickness for n, =  2 x  10"  is  shown in figure 2(b). Circles in the figure indicate the points Q = l/d. For Q smaller thza !.,U,  #(Q,  z)  decays s!ow!y.  Thq  it is clear that the n-GaAs thickness has a significant  effect on IMm,(Q)I2. Finally in figure 2(c),  intrasubband matrix elements IM,,(Q)l2 versus Q are shown for the first four subbands. In the present structure, IMm(Q)12  becomes smaller for the  higher  subbands,  as  the  wavefunction  of  higher subbands extends over the low-doped p-GaAs region. For large Q,  the profile of  the  wavefunctions greatly affects !M,,(Q)12. The subband dependence is decreased with  a  decrease in  Q, as  impurities in  a  wider  area contribute to the scattering. This variation of  lMmm(Q)12 is found to be entirely different from that seen for HEMTS [2];  in HEMTS  the donor ions are spatially separated from the ZDEG  and the scattering is mainly due to the acceptor Electron mobility transition in n-GaAs .. *-  10 E VI  8- >  * 2  6-  ., 24 2500 T  = 300K T  = 300K  - 1. mi. -pulk d  = 15nm  I 0.0  0.1  0.2  0.3 Elecrron energy (eV) Figure 3.  ionized impurity scattering rates for the lowest subband for (a)  different values of n, at d = 15 nm and m = 1, (6)  different values of d at n,  =  2 x  IO"  cm+.  The energies are measured from the bottom of the lowest subband. ions in  the channel. For  a  higher subband index, the wavefunction extends to the region of  weak  screening, and thus lM,,(Q)l2  is larger for higher subbands. Impurity  scattering  rates  for  the  first  subband including intersubband transition  calculated  from  the matrix elements are shown in figure 3 for different values of  (a) two-dimensional electron density n,,  (b) n-GaAs thickness d. The dependence on a, and d is observed for all energy values. These are due to the screening effect of  the electrons and the impurity profiles respectively. as discussed previously. In the high-n, regime, the electrons are degenerate and the subband separation is small, so the matrix value for the intrasubband transition decreases while that for theintersuhband transition increases.  The total scattering rates are found to be only weakly dependent on n,. 4.  Results for low-field transport' We  first describe the Monte Carlo model used  for the mobility calculation. A parabolic band approximation is used and the six lowest subbands in the r valley of GaAs are considered.. Material parameters are taken from [4]. In addition to ionized impurities, scattering rates are also calculated for polar  optical, acoustic and optical phonons, following [2,5] and including both intra- and intersubband transitions. Calculated scattering rates for phonons are not very sensitive to a, and d, and below lo"  s-'  much less than those for impurity scattering for the present structure. A constant electric field 1  kV cm-' is applied in the calculation. For this field, the average electron temperature was found to be below 400 K, so *  d=Znm d  =35nm +  Measured d = 15nm I 0  2  4  6  8 Sheer Electron Denniry (10'k2) + $":" + . '+  A  I d  =15nm A  d  =25nm m  d =35nm +  Measuredd = 15nm " 0.0  0.2  0.4  0.6  0.8  1.0  1.2 linr (lo.''cm2) Figure 4.  (a)  Calculated electron mobility versus sheet electron density for three values of  n-GaAs thickness. The measured Hall  mobility for d = 15 nm is  also stiown. For comparison, the measured  bulk mobility for No = 3  x 10'8cm-3 is  shown by the arrow on the right-hand  mobility axis. (6)  Data  in (a)  shown as a lip versus l/n, plot. the electron density profile will not significantly deviate from the equilibrium profile. Similarly, real-space electron transfer to the AlGaAs layer and transfer to higher (L, X) valleys are negligible. Therefore, we  treat  the electron density profile  and  the  screening  as  constant  during the simulation. The degeneracy effects are included using an approximated distribution function [6]  in which the Fermi energy is assumed to be the equilibrium value  in section 2. An ensemble of  1000 particles is simulated for 20 ps  with  a  constant  time  step (0.5 fs)  discretization scheme. The  calculated  low-field  electron  mobility  (p) is shown in figure 4(a). Statistical fluctuations of the results are about 100 (cm'  V-'s-' ). We found that the mobility increases significantly with n,.  For low n,, the mobility is almost independent of d. This is due to the screening effect. The variation with  respect  to  d  is  small when l/d < S,.  The  mobility  is  found  to  have  a  simple dependence on n,,  namely, l/,u 'U  a/% +  p, where c(  and p are constants (see figure 4(b)). In inversion layers, for low  n,,  it has been  shown that this dependence arises from the two-dimensional nature of  electrons [3]. On the contrary, for high n, and large d, the linearity is broken and the mobility approaches a constant value independent of  n, due to the strong screening effect, as long  as  the  channel is  nearly  charge-neutral. As  we 813 Y Ohkura el a/ observed in section 2, for a large value of  n,, a bulk-like charge-neutral region appears in the  n-GaAs channel. Therefore, the constant mobility mentioned above can be  expected to be close to the three-dimensional value. Note that the three-dimensional mobility in this work is the  bulk  value (d is very large) and  n, is less than the doped impurity density so AlGaAs is  depleted. For the very high n, regime, the electron mobility will  decrease due  to  real-space  electron  transfer  to  AIGaAs.  The decrease in mobility has been studied extensively in the p."L L,,.  nuwGYG',  UG1G WG IG>L,ILL  UUL  LLCLCllllUll  LU  LILC case where there is no significant real-space transfer. To compare with  the  results  of  the  simulation, a heavily doped channel structure is fabricated by epitaxial growth  with  d = 15 nm,  ND = 3 x 10"~m-~  for  the fabrication process will be  published elsewhere. The n, dependence of  Hall electron mobility has been measured at 300 K  (see  figure 4),  for various  thicknesses of  the undoped top GaAs layer grown on an i-AlGaAs layer. Bulk mobility at 300 K is also measured and shown in the figure. The low-n,  properties are in good agreement with experiments. As n, is increased the subband separation is reduced and we  expect the electron behaviour to be closer to  bulk.  The calculated mobility in the  high-n; regime is in fairly good agreement with  the measured bulk mobility, as expected. Thus we have clearly shown, both theoretically and experimentally,  that as n, increases there  is  a  transition  in  the  mobility  from  the  two- dimensional to the bulk value. The calculated mobility is about 10-20%  larger than the  measured  one.  The probable reason  for  this  dis- crepancy  is  that  we  ignored  non-parabolicity  and many-body effects. The latter problem has been treated in the past for the bulk case [8,9].  However, it has not been satisfactorily resolved in the ZDEG case. We also calculated the channel electron mobility with bulk model [SI  using a two-dimensional (in real space) ensemble Monte Carlo simulator, in which the screening effect was  treated using the Brooks-Herring  approach [lo].  The results show the n,  dependence due to  the screening  effect.  However,  as  the  screening  in  this approach  is defined  from  'local'  electron density, the r77  U  "-  l.---  ... ^ ---*-'-.  ...A--.:-..  +^  .&" ..--..I  n-fhA~  (the  1.1-  firet  ... 1.  FIQP  _1"" in  table  1). n-e  det&  of the remoteimpurity interaction is underestimated  in addition to  the  many-body  effect  [8,9].  We  found  that  the calculated mobility using this model  is  1.5  to 2 times larger  than  that  shown  in  figure  4,  and  that  the dependence on n, is weaker. 5.  Conclusion Low-field electron transport properties in heavily-doped r-.,dr  rh,.nn~~r  "+  annu ..I~.O  :...ml+:no+.~  h.,  hd....+n Carlo simulation. The electron-impurity  interaction was obtained from the Fourier-transformed Coulomb poten- tial  accounting for  the  screening effects  of  the  two- dimensional electron gas. The effects  of  the  screening and the impurity profi!e  were discussed. In addition, the subband  dependence  of  impurity  scattering  matrix elements was found to be different from that for HE~S. For low sheet electron density, mobility increases with the sheet electron density and is almost independent of the n-GaAs thickness. For high sheet electron density, the  mobility approaches the  bulk  (three-dimensional) value independently of  electron density. These findings were  explained for the first  time as a transition from two- to three-dimensional nature and are well confirmed by our experiments. IL-uY-0  IllaYIIIIa YL  _I""  LL  nllr  ""CZ.L'&'LLCU  L,J  ll'YLllC Acknowledgments We would like to thank Drs M B Patil and Y Okuyama and T Toyabe for many useful discussions. References iiidd ii et ui i986 iEDivi Tech. Dig. 759 Yokoyama K and Hess K 1986 Phys. Rev. B 33 5595 Stern F and Howard W E 1967 Phys. Rev. 163 816 Adachi S 1985 J. Appl. Phys. 58 RI Jacoboni C  and Reggiani L 1983 Rev.  Mod. Phys. 55 645 Fischetti M V and Laux  S E 1988 Phys. Rev. B 38 9721 Littlejohn M  A et 01 1980 J. Appl. Phys. 51 5445 Ferry D K er  ai 1991 Compur. Phys. Commun. 61 119 Moore E J 1967 Phys. Rev. 160 618 Brooks H and Herring C 1951 Phys. Rev. 83 879 814 

iiidd ii et ui i986 iEDivi

The electron mobility transition in n-GaAs heavily doped channel

The electron mobility transition in n-GaAs heavily doped channel

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