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The X1c conduction band minimum in high purity epitaxial n-type GaAs
Solid State Communications,
Vol. 8, Pp. 491—495, 1970.
Pergamon Press.
Printed in Great Britain
THE X1~CONDUCTION BAND MINIMUM IN HIGH PURITY EPITAXIAL n-TYPE GaAs G.D. Pitt and
J. Lees
Standard Telecommunication Laboratories Limited, London Road, Harlow, Essex (Received 9 January 1970 by C.W. McCombie)
High pressure Hall measurements to 60kbar on high purity epitaxial 2 V~sec’ at n-type indicate an X~mobility 50 kbarGaAs and room temperature. The X of 350 ±40 cm 10—F~sub-band gap is determined as 0.38 ±0.01 eV, and the X, ~ density of states effective mass is 0.85 ±0.10 me. Results show that there are probably three rather than six X~,minima, and that they are situated at the zone edge.
INTRODUCTION
up to now. This paper reports preliminary Hall measurements on some of the high quality, homogeneous n-type GaAs now available, from which the carrier ‘freeze out’ to X~c,impurity levels can be directly estimated. A simple two band model gives the density of states effective mass, and the X1 ,,—F~,,sub-band energy gap. An opposed Bridgman anvil apparatus8 was used, with a 2mm diameter Van der Pauw crystal
THE ELECTRICAL properties of the central F1~ conduction band in GaAs have been reasonably well determined. The dominant scattering mechanism at low electric fields is polar optical scattering’ and recent values for the effective mass at 2the of ~theAtband vary between andbottom O.065me larger values of k the 0.067me band departs from parabolicity. To date the electrical properties of the X 1 minima have largely been inferred from comparisons with Si and GaP, both of which have X1 conduction band electrons at atmospheric pressure. Such a procedure is open to criticism in view of the different scattering mechanism found in Si, and the difficult materials problems still associated with GaP.
immersed in epoxy resin, which acts as the pressure transmitting medium. Repeatability of pressure is ± lkbar, and the stress difference above 27kbar in the solid medium is less than lkbar. A magnetic field of 6.25 kG was used with a pole gap of 1.25 mm. The epitaxial GaAs layers were deposited on <100> orientated semi-insulating substrates. Tin contacts were alloyed to the degreased epitaxial layers at 300°Cin a hydrogen atmosphere.
The X1,, low field mobility in GaAs has been experimentally determined to betheoretical between 110 ~ 5cm2 V~sec’, while and 235 estimates6’7 have varied over a similarly wide range. The experimental uncertainties almost certainly result from (a) poor quality materials, and (b) carrier loss to deep impurity levels associated with the X 1~minima which complicates the simple resistivity pressure measurements made
RESULTS Figure 1 shows the variation of normalised resistivity, Hall constai~tand Hall mobility for the vapour epitaxial san~pleG.62A. The resistivity variation is characteristic of thatpressure observed 4’9 Under previously by other workers. 491
492
THE X1~CONDUCTION BAND MINIMUM IN n-TYPE GaAs
I
~
_________
Go.
Vol. 8, No. 7
1
:~nt~’~\~
o~.
_
_ FIG. 1. G.62A. Normalised resistivity (P/Pa ), Hall 1/iH constant /R H0)’ mobility ) for (RH n-type GaAsand to Hall 60 kbars at (J.LH 296°K. t~N 15crn3, 0 cm~, NA)=/~-H 1.65 x 10 p 0.51911 2V ‘sec~, 0= 7350 cm vapour epitaxial layer thickness 15 p.. Mobility at 50 kbar, 330 ±40 cm2V’1 sec’. —
J~I.
/1
Pressure k FIG. 2. LE11. Normalised resistivity (pip0), Hall constant (RH/RH ), and Hall mobility (/.1~H/itH~) 296°K. (N for n-type daAs to 60 kbars 3, at 0 NA) = 9.25 x 10’~ cm p 0.09211 cnf’, /2H 2V1 sec~’, 0 = 6900 cm liquid epitaxial layer thickness 46 p.. Mobility at 50 kbar, 350 ±40 cm2 V’ sec~ —
when the conductivities in both bands are the F~ 0band moves away from the stationary ~‘15 valence band at a rate near +10 x 10~eV bar’, while the ‘~ band is stationary or moves very slowly —1 x 10~eV the valence band, in(~‘ agreement withbar~’)towards the empirical rule which seems to exist for diamond and zinc-blende type band structures under pressure. Thus electrons transfer progressively to the X~minima under pressure. This is seen as a rapid rise in resistivity near 25 kbar. The saturation at 40kbar when the resistivity ratio is 27 ±1 corresponds to the state when all electrons are in the X~minima. The Hall constant curve passes through a maximum near 33 kbar and levels off at S0kbar above the original normalised value, This implies carrier loss to an impurity levels below the X 1~,minima. The maximum occurs
approximately equal, provided p. i.e. nreuj~ n~e~p.X. Near band cross-over the mobility drops rapidly to give a2 Vfinal X~ ~sec~. mobility at 50 kbar of 330 ±40 cm Figure 2 shows similar curves for a liquid epitaxial crystal LE11, For this sample, the final mobility was 350 ±40 cm2V _tsec~and RH returned to slightly below unity at 50 kbar, implying negligible carrier loss. ANALYSIS The resistivity increase up to 15 kbar is caused by the increase in effective mass as the I’~minimum moves away from the valence band. Since RH shows that there is no loss of
Vol. 8, No. 7
THE X~CONDUCTION BAND MINIMUM IN n-TYPE GaAs
carriers in this pressure range: this result indicates a mobility decrease for which, if polar scattering is dominant, p.s, m~*3/2 Our observed resistivity increase of 9 per cent to 10 kbar, agrees well with Connell’s 10 ‘hydrostatic’ value of 8 per cent considering the appreciable non-hydrostatic stresses and difficulties in calibration of our apparatus at these lower pressures. 00
At higher pressures when transfer takes place we must consider two-carrier Hall equations, and the charge balance equation must be satisfied, i.e. 2d (1) ND NA = nr + + where ND and NA are the total number of donors and acceptors respectively, ~ and ~ are the number of electrons in the F~and X~minima, while rid is the number of electrons on donor sites. We take ND NA at atmospheric pressure to be the carrier concentration measured by the Hall effect.
493
For equations (4) and (5) only n1. and ~ are unknown with pressure. p.~is taken to be the measured value at 50 kbar over the whole range, which is a reasonable assumption since the mobility in the Si X~minima is found to increase only very slowly at high pressures. p. x only becomes important in the calculations at pressures above 30 kbar and its increase over 20 kbar to 50 kbar will be no more than 6 per cent. This is consistent with the mobility variation actually found for a number of GaAs samples taken from 50—70 kbar. The F’~mobility variation and N~variation with pressure is taken to be a linear extrapolation of the 0—10 kbar result, assuming mechanism in thisnominimum. change in scattering
—
—
n
=
2 ‘2 \ mi~kr) h2
3/2
‘
F1/2
(EF kt E~) (2) ~ —
where mj * are the density of states effective masses including the number of minima v EF is the Fermi energy, and the density of states terms Nr and N~relate to the function preceeding the Fermi—Dirac integral of order ‘/2. For the low carrier concentration material, with which we are concerned here, the Fermi level is greater than 5 kT below Er, the energy of the I~ minimum, and we can approximate equation (2) to Nr
=
n~
)
/E~ E~\ kT —
exp
~
—
(3)
The conductivity is related to p.~and p.~through =
I.
n 2e
Ti
(~~_ ~
+ liX)
=
1 P
=
p.r p.X p.1.
~
—
—
The same paired values of density of states ratio and sub-hand gap fit the resistivity and Hall data for both LE11 and G62A, although for the latter the number of carriers lost to a donor level ~d’ has to be taken into account. rid is given by nd
ND
=
1
+
1
(6)
exp
~
~_______ kT ) —
where E~ is the energy of the impurity level, and g is the level degeneracy. A spin degeneracy of 2 is assumed. A level at 0.15 ±0.04 eV below E~fits the
(4)
results satisfactorily. Low temperature measurements are now being made to obtain an accurate determination of the level. The impurity level in LE11 could have any value below 0.06ev and stillactivation satisfy the resu1ts~so thegreat significance of the energies is not for the low
(5)
concentration material for which EF is much less than E~at high pressures.
and the Hall mobility is given by /p.x\ 2 + n1’ p.!1
The sub band pressure coefficient is found as d/8P (E~ Er) = 1.10 ±0.03 x 10~eV/bar by the method described previously.9 The experimental data can then be fitted using two related parameters only viz. (Nx) P = 0 and (E~ Er) P = 0,
494
THE X~c,CONDUCTION BAND MINIMUM IN n-TYPE GaAs
at room temperature, but not with the photoemission result of Spicer and Eden’4 of 0.33 eV.
92
8o~
/ •
/ •
=
/ 2
1
/
Vol. 8, No. 7
/ /
Gaylord and Rabs on’5 have recently calculated that there are six GaAs X 10 minima, using
/ /
Ehrenreich’s density of states effective mass of 1.2 me, situated away from the zone edge. The number of minima is ~iven by if we take n~ to 2~ and (m~)~~ (m1 mt be 0~23me after Pollak et ~il’s’6 k.p. calculation
/
m 7 to be 1.3 me, 1~’for afterm~’ Conwell and then = 0.82 we Vassell obtain v~.= 2.83. If the I
/
,,,~
r
minimum effective mass is taken as 0.067 me then from our results mx* = 0.85 me and = 2.98, with the effective mass as 0.41 in
~OjJ~
rJ ____________ ~‘ (E~.?~
_________
one minimum. Since we cannot have less than three our result would incicate thatedge, in GaAs minima the minima are situated at the zone
U
rather than a A70 point as in Si. FIG. 3. Paired parameters of
and (E E,) ~N1f po X I P-o / which fit the simple 2-band model. -
Typical mobility fits for the two samples are shown ininFigs. 1A For and a2A, and thegap paired parameters Fig. 3. sub-band of 0.38 eV we require a density of states ratio of 45. This would imply a density of states effective mass m~’= 0.82 me, if m = 0.065 m~.The sub-band gap of 0.38 eV was estimated from the maximum RH at 33 kbar, which occurs approximately, 1—2 kbar beforecoefficient band crossover. Taking the sub-band pressure as 11 x 10 ~ eV bar -l we have (E~— E 1. ~ = 0.38 ±0.01 eV. This agrees reasonably well 3 with the band gap of 0.38 eV found by Balslev’
CONCLUSIONS We conclude from these prelimary results (further measurements on GaAs over the impurity 3 will be concentration range presented later) that 1013 the X 10~cnf 1 Hall mobility 2 V-1 sec’, inthe GaAs at 50 kbar gap is 350 ±40 cm sub-band energy (Ex—E 1.) is 0.38 ±0.01 eV The mobility at atmospheric pressure will be 10 per cent lower if the 2 per cent per 10 kbar change in mobility at higher pressures extrapolates back to zero pressure. This would then give an atmospheric pressure Hall mobility 2 V’ sec’ for sample LE11. near 315 ±40 cm —
Acknowledgements This work was financed by a Ministry of Technology contract, the crystals were grown at STL by D.E.and Bolger and H.G.B. Hicks. —
REFERENCES 1. 2.
ENRENREICH H., Phys. Rev. 120, 1951 (1960). VREHEN Q.H.F., J. Phys. Chem. Solids, 29, 129 (1968).
3.
CHAMBERLAIN T.M. and STRADLING R.A., Solid State Cornmun., 7, 1275 (1969).
4.
HUTSON A.R., JAYARAMAN A. and CORIELL A.S., Phys. Rev. 155, 786 (1967).
5. 6.
KING G., LEES J. and WASSE M.P., Solid-St.. Elect ron .9, 601 (1966). FAWCETT W., BOARDMAN A.D. and SWAIN S.W., to be published (1970).
7. CONWELL E.M. and VASSALL M.O., Phys. Rev. 166, 797 (1968).
10
Vol. 8, No. 7
THE X10 CONDUCTION BAND MINIMUM IN n-TYPE GaAs
S.
PITT G.D., J. scient Jnstr.., (J. Physics E. Series II) 1, 915 (1968).
9.
LEES J. , WASSE M.P. and KING, G., Solid Stqte Commun., 5, 521, (1967).
495
10. CONNELL G.A.N., High Temp. High Press. 1, 77 (1969). 11. LEWIS B.F. and SONDHEIMER E.H., Proc. R. Soc. A227, 1169 (1955). 12. DOES DE BYE, J.A.W., VAN DE, and PETERS R.C., Philips Res. Rep. 24, 210 (1969). 13. BALSLEV I., Phys. Rev~,173, 762 (1968).
5 (1969).
14. W.E. andand EDEN R.C., T.A., Proc. Phys. In.. Conf. Moscow, p.6 15. SPICER GAYLORD T.K. ROBSON Len.Phys. 29A, Semiconductors, 716 (1969). 16. POLLAK F.H., HIGGINBOTHAM C.W. and CARDONA M., Pioc. Kyoto (1966), J. Phys. Soc. Japan (Suppi) 21, 20 (1966).
mt. Conf. Phys. Semiconductors,
Hailmessungen an hoch reinem, durch Epitaxie gewonnenem n-GaAs bei Drucken bis zu 60 kbar ergeben eine X, 2 V’ sec’ bei einem Druck0 von Tragerbeweglichkeit 50 kbar und von 350 ±40 cm Die X, Raumtemperatur. 0 —F~Sub-Bandlücke betrug 0,38 ±0,01 eV, und die X10—Minima haben eine totale effective Masse von 0,85 ±O,lOme. Resultate zeigen, dass en wahrscheinlich drei eher als sechs X10 Minima gibt, und dass sie an der Zonengrenze liegen.
Vol. 8, Pp. 491—495, 1970.
Pergamon Press.
Printed in Great Britain
THE X1~CONDUCTION BAND MINIMUM IN HIGH PURITY EPITAXIAL n-TYPE GaAs G.D. Pitt and
J. Lees
Standard Telecommunication Laboratories Limited, London Road, Harlow, Essex (Received 9 January 1970 by C.W. McCombie)
High pressure Hall measurements to 60kbar on high purity epitaxial 2 V~sec’ at n-type indicate an X~mobility 50 kbarGaAs and room temperature. The X of 350 ±40 cm 10—F~sub-band gap is determined as 0.38 ±0.01 eV, and the X, ~ density of states effective mass is 0.85 ±0.10 me. Results show that there are probably three rather than six X~,minima, and that they are situated at the zone edge.
INTRODUCTION
up to now. This paper reports preliminary Hall measurements on some of the high quality, homogeneous n-type GaAs now available, from which the carrier ‘freeze out’ to X~c,impurity levels can be directly estimated. A simple two band model gives the density of states effective mass, and the X1 ,,—F~,,sub-band energy gap. An opposed Bridgman anvil apparatus8 was used, with a 2mm diameter Van der Pauw crystal
THE ELECTRICAL properties of the central F1~ conduction band in GaAs have been reasonably well determined. The dominant scattering mechanism at low electric fields is polar optical scattering’ and recent values for the effective mass at 2the of ~theAtband vary between andbottom O.065me larger values of k the 0.067me band departs from parabolicity. To date the electrical properties of the X 1 minima have largely been inferred from comparisons with Si and GaP, both of which have X1 conduction band electrons at atmospheric pressure. Such a procedure is open to criticism in view of the different scattering mechanism found in Si, and the difficult materials problems still associated with GaP.
immersed in epoxy resin, which acts as the pressure transmitting medium. Repeatability of pressure is ± lkbar, and the stress difference above 27kbar in the solid medium is less than lkbar. A magnetic field of 6.25 kG was used with a pole gap of 1.25 mm. The epitaxial GaAs layers were deposited on <100> orientated semi-insulating substrates. Tin contacts were alloyed to the degreased epitaxial layers at 300°Cin a hydrogen atmosphere.
The X1,, low field mobility in GaAs has been experimentally determined to betheoretical between 110 ~ 5cm2 V~sec’, while and 235 estimates6’7 have varied over a similarly wide range. The experimental uncertainties almost certainly result from (a) poor quality materials, and (b) carrier loss to deep impurity levels associated with the X 1~minima which complicates the simple resistivity pressure measurements made
RESULTS Figure 1 shows the variation of normalised resistivity, Hall constai~tand Hall mobility for the vapour epitaxial san~pleG.62A. The resistivity variation is characteristic of thatpressure observed 4’9 Under previously by other workers. 491
492
THE X1~CONDUCTION BAND MINIMUM IN n-TYPE GaAs
I
~
_________
Go.
Vol. 8, No. 7
1
:~nt~’~\~
o~.
_
_ FIG. 1. G.62A. Normalised resistivity (P/Pa ), Hall 1/iH constant /R H0)’ mobility ) for (RH n-type GaAsand to Hall 60 kbars at (J.LH 296°K. t~N 15crn3, 0 cm~, NA)=/~-H 1.65 x 10 p 0.51911 2V ‘sec~, 0= 7350 cm vapour epitaxial layer thickness 15 p.. Mobility at 50 kbar, 330 ±40 cm2V’1 sec’. —
J~I.
/1
Pressure k FIG. 2. LE11. Normalised resistivity (pip0), Hall constant (RH/RH ), and Hall mobility (/.1~H/itH~) 296°K. (N for n-type daAs to 60 kbars 3, at 0 NA) = 9.25 x 10’~ cm p 0.09211 cnf’, /2H 2V1 sec~’, 0 = 6900 cm liquid epitaxial layer thickness 46 p.. Mobility at 50 kbar, 350 ±40 cm2 V’ sec~ —
when the conductivities in both bands are the F~ 0band moves away from the stationary ~‘15 valence band at a rate near +10 x 10~eV bar’, while the ‘~ band is stationary or moves very slowly —1 x 10~eV the valence band, in(~‘ agreement withbar~’)towards the empirical rule which seems to exist for diamond and zinc-blende type band structures under pressure. Thus electrons transfer progressively to the X~minima under pressure. This is seen as a rapid rise in resistivity near 25 kbar. The saturation at 40kbar when the resistivity ratio is 27 ±1 corresponds to the state when all electrons are in the X~minima. The Hall constant curve passes through a maximum near 33 kbar and levels off at S0kbar above the original normalised value, This implies carrier loss to an impurity levels below the X 1~,minima. The maximum occurs
approximately equal, provided p. i.e. nreuj~ n~e~p.X. Near band cross-over the mobility drops rapidly to give a2 Vfinal X~ ~sec~. mobility at 50 kbar of 330 ±40 cm Figure 2 shows similar curves for a liquid epitaxial crystal LE11, For this sample, the final mobility was 350 ±40 cm2V _tsec~and RH returned to slightly below unity at 50 kbar, implying negligible carrier loss. ANALYSIS The resistivity increase up to 15 kbar is caused by the increase in effective mass as the I’~minimum moves away from the valence band. Since RH shows that there is no loss of
Vol. 8, No. 7
THE X~CONDUCTION BAND MINIMUM IN n-TYPE GaAs
carriers in this pressure range: this result indicates a mobility decrease for which, if polar scattering is dominant, p.s, m~*3/2 Our observed resistivity increase of 9 per cent to 10 kbar, agrees well with Connell’s 10 ‘hydrostatic’ value of 8 per cent considering the appreciable non-hydrostatic stresses and difficulties in calibration of our apparatus at these lower pressures. 00
At higher pressures when transfer takes place we must consider two-carrier Hall equations, and the charge balance equation must be satisfied, i.e. 2d (1) ND NA = nr + + where ND and NA are the total number of donors and acceptors respectively, ~ and ~ are the number of electrons in the F~and X~minima, while rid is the number of electrons on donor sites. We take ND NA at atmospheric pressure to be the carrier concentration measured by the Hall effect.
493
For equations (4) and (5) only n1. and ~ are unknown with pressure. p.~is taken to be the measured value at 50 kbar over the whole range, which is a reasonable assumption since the mobility in the Si X~minima is found to increase only very slowly at high pressures. p. x only becomes important in the calculations at pressures above 30 kbar and its increase over 20 kbar to 50 kbar will be no more than 6 per cent. This is consistent with the mobility variation actually found for a number of GaAs samples taken from 50—70 kbar. The F’~mobility variation and N~variation with pressure is taken to be a linear extrapolation of the 0—10 kbar result, assuming mechanism in thisnominimum. change in scattering
—
—
n
=
2 ‘2 \ mi~kr) h2
3/2
‘
F1/2
(EF kt E~) (2) ~ —
where mj * are the density of states effective masses including the number of minima v EF is the Fermi energy, and the density of states terms Nr and N~relate to the function preceeding the Fermi—Dirac integral of order ‘/2. For the low carrier concentration material, with which we are concerned here, the Fermi level is greater than 5 kT below Er, the energy of the I~ minimum, and we can approximate equation (2) to Nr
=
n~
)
/E~ E~\ kT —
exp
~
—
(3)
The conductivity is related to p.~and p.~through =
I.
n 2e
Ti
(~~_ ~
+ liX)
=
1 P
=
p.r p.X p.1.
~
—
—
The same paired values of density of states ratio and sub-hand gap fit the resistivity and Hall data for both LE11 and G62A, although for the latter the number of carriers lost to a donor level ~d’ has to be taken into account. rid is given by nd
ND
=
1
+
1
(6)
exp
~
~_______ kT ) —
where E~ is the energy of the impurity level, and g is the level degeneracy. A spin degeneracy of 2 is assumed. A level at 0.15 ±0.04 eV below E~fits the
(4)
results satisfactorily. Low temperature measurements are now being made to obtain an accurate determination of the level. The impurity level in LE11 could have any value below 0.06ev and stillactivation satisfy the resu1ts~so thegreat significance of the energies is not for the low
(5)
concentration material for which EF is much less than E~at high pressures.
and the Hall mobility is given by /p.x\ 2 + n1’ p.!1
The sub band pressure coefficient is found as d/8P (E~ Er) = 1.10 ±0.03 x 10~eV/bar by the method described previously.9 The experimental data can then be fitted using two related parameters only viz. (Nx) P = 0 and (E~ Er) P = 0,
494
THE X~c,CONDUCTION BAND MINIMUM IN n-TYPE GaAs
at room temperature, but not with the photoemission result of Spicer and Eden’4 of 0.33 eV.
92
8o~
/ •
/ •
=
/ 2
1
/
Vol. 8, No. 7
/ /
Gaylord and Rabs on’5 have recently calculated that there are six GaAs X 10 minima, using
/ /
Ehrenreich’s density of states effective mass of 1.2 me, situated away from the zone edge. The number of minima is ~iven by if we take n~ to 2~ and (m~)~~ (m1 mt be 0~23me after Pollak et ~il’s’6 k.p. calculation
/
m 7 to be 1.3 me, 1~’for afterm~’ Conwell and then = 0.82 we Vassell obtain v~.= 2.83. If the I
/
,,,~
r
minimum effective mass is taken as 0.067 me then from our results mx* = 0.85 me and = 2.98, with the effective mass as 0.41 in
~OjJ~
rJ ____________ ~‘ (E~.?~
_________
one minimum. Since we cannot have less than three our result would incicate thatedge, in GaAs minima the minima are situated at the zone
U
rather than a A70 point as in Si. FIG. 3. Paired parameters of
and (E E,) ~N1f po X I P-o / which fit the simple 2-band model. -
Typical mobility fits for the two samples are shown ininFigs. 1A For and a2A, and thegap paired parameters Fig. 3. sub-band of 0.38 eV we require a density of states ratio of 45. This would imply a density of states effective mass m~’= 0.82 me, if m = 0.065 m~.The sub-band gap of 0.38 eV was estimated from the maximum RH at 33 kbar, which occurs approximately, 1—2 kbar beforecoefficient band crossover. Taking the sub-band pressure as 11 x 10 ~ eV bar -l we have (E~— E 1. ~ = 0.38 ±0.01 eV. This agrees reasonably well 3 with the band gap of 0.38 eV found by Balslev’
CONCLUSIONS We conclude from these prelimary results (further measurements on GaAs over the impurity 3 will be concentration range presented later) that 1013 the X 10~cnf 1 Hall mobility 2 V-1 sec’, inthe GaAs at 50 kbar gap is 350 ±40 cm sub-band energy (Ex—E 1.) is 0.38 ±0.01 eV The mobility at atmospheric pressure will be 10 per cent lower if the 2 per cent per 10 kbar change in mobility at higher pressures extrapolates back to zero pressure. This would then give an atmospheric pressure Hall mobility 2 V’ sec’ for sample LE11. near 315 ±40 cm —
Acknowledgements This work was financed by a Ministry of Technology contract, the crystals were grown at STL by D.E.and Bolger and H.G.B. Hicks. —
REFERENCES 1. 2.
ENRENREICH H., Phys. Rev. 120, 1951 (1960). VREHEN Q.H.F., J. Phys. Chem. Solids, 29, 129 (1968).
3.
CHAMBERLAIN T.M. and STRADLING R.A., Solid State Cornmun., 7, 1275 (1969).
4.
HUTSON A.R., JAYARAMAN A. and CORIELL A.S., Phys. Rev. 155, 786 (1967).
5. 6.
KING G., LEES J. and WASSE M.P., Solid-St.. Elect ron .9, 601 (1966). FAWCETT W., BOARDMAN A.D. and SWAIN S.W., to be published (1970).
7. CONWELL E.M. and VASSALL M.O., Phys. Rev. 166, 797 (1968).
10
Vol. 8, No. 7
THE X10 CONDUCTION BAND MINIMUM IN n-TYPE GaAs
S.
PITT G.D., J. scient Jnstr.., (J. Physics E. Series II) 1, 915 (1968).
9.
LEES J. , WASSE M.P. and KING, G., Solid Stqte Commun., 5, 521, (1967).
495
10. CONNELL G.A.N., High Temp. High Press. 1, 77 (1969). 11. LEWIS B.F. and SONDHEIMER E.H., Proc. R. Soc. A227, 1169 (1955). 12. DOES DE BYE, J.A.W., VAN DE, and PETERS R.C., Philips Res. Rep. 24, 210 (1969). 13. BALSLEV I., Phys. Rev~,173, 762 (1968).
5 (1969).
14. W.E. andand EDEN R.C., T.A., Proc. Phys. In.. Conf. Moscow, p.6 15. SPICER GAYLORD T.K. ROBSON Len.Phys. 29A, Semiconductors, 716 (1969). 16. POLLAK F.H., HIGGINBOTHAM C.W. and CARDONA M., Pioc. Kyoto (1966), J. Phys. Soc. Japan (Suppi) 21, 20 (1966).
mt. Conf. Phys. Semiconductors,
Hailmessungen an hoch reinem, durch Epitaxie gewonnenem n-GaAs bei Drucken bis zu 60 kbar ergeben eine X, 2 V’ sec’ bei einem Druck0 von Tragerbeweglichkeit 50 kbar und von 350 ±40 cm Die X, Raumtemperatur. 0 —F~Sub-Bandlücke betrug 0,38 ±0,01 eV, und die X10—Minima haben eine totale effective Masse von 0,85 ±O,lOme. Resultate zeigen, dass en wahrscheinlich drei eher als sechs X10 Minima gibt, und dass sie an der Zonengrenze liegen.