Photoresponse of surface barriers on samples of Ga(As_(1−x_P_x) covering the range 0≤x≤1 has been measured. Thresholds corresponding to both direct and indirect band-to-band excitations within the semiconductor and also photoinjection from the metal have been identified. The threshold of the direct transition varies with composition from 1.37 eV in GaAs to 2.65 eV in GaP. The indirect transition was followed for x≳0.38 and again varied linearly from 2.2 eV in GaP to an extrapolated value in 1.62 eV in GaAs. The energy separation of the two conduction band minima in GaAs is in disagreement with previously reported values

Mead, C. A.

Spitzer, W. G.

Caltech Authors - Main

A872 DALE E. HILL
These results indicate that the 300'K fluorescence
for p-type GaAs does not involve the acceptor states.
The fluorescence for lightly doped n an-d p-type GaAs
occurs at nearly the same energy as the energy gap.
However, for heavily doped m-type GaAs, the recom-
bination leading to the fluorescence seems to originate
at an energy 1 to 2 kT below the Fermi level as com-
puted from the absorption measurements.
IV. SUMMARY AND CONCLUSIONS
From the absorption measurements it can be seen
that in general the shifts of the absorption edge with
increased doping level occur in either direction and
can be divided into two components. The shifts to
higher energy predominate in e-type GaAs at 77'K and
the shifts to lower energy predominate in p-type GaAs
at 300'K. The shifts to higher energy are caused by
the change of the Fermi level with doping. The shifts
to lower energy can probably be explained as an
eA'ective decrease in the band gap. An additional phe-
nomena which should be taken into account is the
change in energy gap which occurs when the lattice
parameter changes with doping level. The Burstein
type shifts are not satisfactorily explained in detail by
Eq. (1). This is not too surprising for such a simple
theory, but it is of interest to know where the principal
difhculties lie. Part, but not all of the problem lies in
not accounting for the nonparabolic nature of the con-
duction band. The eGect of impurities in decreasing
the band gap mentioned in the previous paragraph if
understood and properly accounted for may explain
most of the remaining differences. The shifts observed
for heavily sulfur-doped GaAs are anamolous and not
understood at the present time.
From the fluorescence measurements we see that the
acceptor state is involved in the recombination which
leads to fluorescence at 77'K, but not at 300'K. In
addition we have seen that Ge as a dopant in GaAs
produces a deep level, presumably an acceptor state
roughly 0.08 eV above the valence band edge. The
e-type fluorescence occurs essentially at the band gap
energy for low doping levels and although the Quo-
rescence energy increases at the highest doping levels,
the recombination resulting in this emission does not
primarily involve carriers in the neighborhood of the
Fermi level.
ACKNOWLEDGMENTS
The author would like to express his appreciation
to R. Dalrymple for carrying out many of the measure-
ments and to D. High and J. McNeely for the ms, terial
preparations work.
P H VSI CAL REVE EW VOLUME 133, NUMBER 3A 3 FEBRUAR Y 1964
Conduction Band Minima of Ga(gs, .p,) t
%. G. SpxrzER
P/eotrioa/ irngineereng Department, University of Sonthern California, Los Ange/es, Ca/ifornia
C. A. MEAD
Ca/ffornia institnte of Teottno/ogy, Pasadena, Ca/~fornia
(Received 21 August 1963)
Photoresponse of surface barriers on samples of Ga(As&, P,) covering the range 0(z &I has been meas-
ured. ThreshoMs corresponding to both direct and indirect, band-to-band excitations within the semicon-
ductor and also photoinjection from the metal have been identified. The threshold of the direct transition
varies with composition from 1.37 eV in GaAs to 2.65 eV in GaP. The indirect transition was followed for
g &0.38 and again varied linearly from 2.2 eV in GaP to an extrapolated value in 1.62 eV in GaAs. The energy
separation of the two conduction band minima in GaAs is in disagreement with previously reported values,
I. INTRODUCTION
'T has been demonstrated in recent work, that when
~ ~ the photovoltaic response is measured for a Schottky
barrier at a clean metal-semiconductor interface, the
response has two distinct spectral regions. The 6rst
region is where the photon energy exceeds E, the energy
gap of the semiconductor, and electron transitions take
place from the valence to the conduction band. The
second region, where hs &E, is generally a region where
t This work was supported in part by the U. S. OfIjlce of Naval
Research under contract NONR 220(42) and the International
Telephone and Telegraph Corporation.
the response per photon is much smaller, and a number
of recent studies' ' have attributed this response to
'C. R. Crowell, W. G. Spitzer, L. E. Howarth, and E. E.
LaBate, Phys. Rev. 127, 2006 (1962).
2 C. A. Mead and W. G. Spitzer, Appl. Phys. Letters 2, f4 (1963).
3 G. W. Mahlman, Phys. Rev. Letters 7, 408 (1961).' R. Williams, Phys. Rev. Letters 8, 402 (1962).' W. G. Spitzer and C. A. Mes, d, J. Appl. Phys. (to be pub-
lished).
6 W. G. Spitzer, C. R. Crowell, and M. M. Atalla, Phys Rev.
Letters 8, 57 (1962).
7 C. R. Crowell, W. G. Spitzer, and H. G. White, Appl. Phys.
Letters 1, 3 (1962).' H. G. White and R. A. Logan, J. Appl. Phys. 34, 1990 (1963).
I D. Kahng, Solid State Electron. 6, 281 (1963).
CONDUCTION BAND MINIMA OF Ga(As, , P, ) A873
photoemission of electrons (or holes) from the metal
over the Schottky barrier. The present work consists of
the application of this experimental method to the
Ga(As&, P,) system. The photoresponse has been meas-
ured on samples covering the range from x=0 to x= 1.
Of particular interest is the range where hv&E, . For
x&0.38, the response is resolved into two distinct re-
gions, one due to indirect or phonnn aided transitions
and the second due to direct transitions, The threshold
of the direct process could be followed across the entire
composition range and the indirect process from x=0.38
to x=1.0.
II. BACKGROUND
Considerable effort has been devoted to the study of
the structure of the conduction band in elemental and
compound semiconductors. Of particular interest in the
present study, is the work which has attempted to iden-
tify the relative positions of the (000) and (100) minima
in GaAs and GaP.
Khrenreich' "and Paul" have reviewed most of the
experimental evidence for the position of these minima.
Ehrenreich concludes that the (100) minima are 0.36 eV
above the R=O minimum in GaAs while in GaP the two
minima reverse positions with an energy separation of
about 0.35 eV. In each case the deeper of the two
minima forms the bottom of the conduction band.
That the conduction band minimum is not at k=0
in GaP can be concluded from the spectral shape of the
absorption edge" and the large value of the electron
effective mass. ' The pressure dependence of E, and
resistivity suggest (100) minima. """ Experimental
evidence for the higher k=0 minimum comes from
optical measurements where the interpretation has been
shown to be questionable. Absorption edge measure-
ments indicate the beginning of a rapidly rising absorp-
tion starting approximately 0.35 eV above the indirect
threshold. "However, Paul" points out that the pressure
dependence of the absorption edge leads to a separation
of 1 eV for the two minima if a speci6c functional
form is assumed for the pressure dependence of the
indirect transition. An infrared absorption band ob-
served in n-type GaP had been tentatively assigned"
to interband transitions between the two minima.
However, later work" showed that the absorption band
position had a much smaller pressure dependence than
was expected from the pressure coefficient of the two
minima. It has also been suggested" that the band is
due to a 0.4 deep oxygen impurity level.
' H. Ehrenreich, Phys. Rev. 120, 1951 (1960)."H. Ehrenreich. J. Appl. Phys. 32, 21559 (1961).
"W. Paul, J. Appl. Phys. 32, 2082S (1961).
"W. G. Spitzer, M. Gerhsenson, C. J. Frosch, and D. F. Gibbs,
Phys. Chem. Solids 11, 339 (1959).
'4T. S. Moss, Report of the International Conference on The
Physecs of Serrtecortdlctors (The Institute of Physics and The
Physical Society, London, 1962), p. 295."A. Sagar and R. C. Miller, J. Appl. Phys. Suppl. 32, 2073
(1961).' M. Gershenzon and R. M. Milkulyak, Solid State Electron.
5, 313 (1962).
The primary evidence for the energy separation of the
two minima in GaAs comes from the analysis of the
temperature dependence of the Hall coefficient. ' '~
There is considerable evidence that the k=0 minimum
is the bottom of the conduction band; however, the
exact value of E, appears to be in question. Numerous
absorption edge measurements' show the room tem-
perature absorption to start at 1.37&0.02 eV. However,
theoretical 6ts to the data"" in the high absorption
regions give values for E, of 1.41 eV and 1.43 eV. The
absorption curves of one of these studies" also shows
evidence for direct exciton formation. Recent measure-
Inents" of electroluminescent band-to-band recombina-
tion radiation in shallow p-ss junctions show peaks near
1.36 eV and 1.39 eV. The authors interpret these emis-
sion bands as the indirect and direct transitions, respec-
tively, where the indirect transition arises from the
splitting of the heavy hole band degeneracy via spin-
orbit interaction. There has been recent evidence" that
E, is impurity concentration-dependent. There is also
an infrared absorption band' in e-type GaAs which had
been interpreted in terms of interband transitions, but
in view of the GaP results, this interpretation must be
regarded as suspect. It has been indicated" that there
is some difhculty with the interpretation of the pressure
dependence of the GaAs resistivity when the 0.36-eV
separation is assumed.
Much of the justification for Ehrenreich's analysis"
comes from absorption edge data on Ga(Ass,. P,) solid
solutions. These measurements indicate an abrupt
change in the variation of the intrinsic absorption edge
with composition near @=0.5. Linear extrapolations of
the two portions of the curve gave energy separations
in the cases x=O and @=1which were in general agree-
ment with the above quoted values. However, examina-
tion of the results show that the scatter in the experi-
Inental data and the necessity of extrapolating over a
50%%uz composition range introduces a substantial uncer-
tainty (tenths of an eV) into the position of the higher
lying minimum in each case.
III. EXPERIMENTAL
Samples were prepared on material obtained from
several industrial laboratories. Surface received various
chemical treatments depending upon condition but
were always cleaned in HF for at least 15 min prior to
placing in an oil-free vacuum system. Gold 6lms up to
1000 A thick were deposited on the surface by evap-
'7 L. W. Aukerman, and R. K. Willardson, J. Appl Phys. 31,
939 (1960).' T. S. Moss, J. Appl. Phys. 32, 2136S (1961)."I.Kudman and T. Seidel, J. Appl. Phys. 33p 771 (1962).
) W. G. Spitzer and J. M. Whelan, Phys. Rev. 114, 59 (1959)."R. Braunstein, J. I. Pankove, and H. Nelson, Appl. Phys.
Letters 3, 31 (1963).
ss M. V. Hobden and M. D. Sturge, Proc. Phys. Soc. (London)
78, 615 (1961).
2g D. N. Nasledov, A. A. Rogachev, S. M. Ryvkin, V. E. Khar-
tsiev, and B. V. Tsarenkov, Fiz. Tverd. Tela 4, 3346 (1962)
Ltranslation: Soviet Phys. —Solid State 4, 2449 (1963)j.
~ g I $ I
}.5 RD
h~ (ev)
Fzo. t. The rootn-tempersture (photovoltsge)'Is versus photon
energy for bvo samples of Ga(As&, P,). Where the data points
are for hg &1.7 ey, the sample has &=0.20. The other sample has
g=0.78.
oration in the form of 0.0i in. diam. dots at a residual
were gaspressure of &10 ' Torr. The photoresponse data
taken gsj.ng a quartz prism monochromator equipped
with a 50-cps shopping system Rnd synchronous
detection. The units were illuminated from the metal
side (front wall configuration). Several samples were
made with aluminum dots in addition to the goM. , and
in these cases the results were essentially identical. The
form of the response for hr &E, was found to be inde-
pendent of the thickness of the metal layer.
In most cases the composition values were obtained
from x-ray fluorescence measurements by comparison
of the As E and Ga Ep lines which occur at close to the
same energy. The estimated over-all accuracy in the
composition determined by this method is +2%. In the
few cases for which fIuorescence Ineasurements were not
made, the composition was supplied by the laboratory
in which the sample was grown. These values were
determined by lattice constant measurements.
Neglecting phonon energies the absorption coefFicient,
0,, for indirect transitions is given by
curves for two samples of widely different compositions
are shown in Fig. j..The left curve shows emission from
the metal into the semiconductor followed at higher
photon energy by an abrupt increase in response due to
semiconductor band-to-band excitation. The second
curve shows low energy response from the metal fol-
lowed by two well-resolved intrinsic excitation processes
within the semiconductor. The lower of these follows a
second power dependence as expected for an indirect
transition. The increase in response due to the higher
transition is sufEciently rapid that its functional form
ls difIIcult to determine Rnd Rs will be shown is Rs"
cribed to a direct transition. The fact that changes in
O. up to a level of j.0' cm ' are observed in the photore-
sponse indicates a very short I.which is consistent with
the small minority carrier lifetimes in these materials. "
The photothresholds for each region were taken from
the zero response after subtracting out the extrapola-
tion of the response due to the lower energy processes.
The error in the photothresholds is largely due to this
extrapolation procedure and is estimated to be at most
+0.02 eV. The measurements themselves were taken
with a resolution of better than 0.01 eV.
For samples in which x&0.38, the indirect transition
occurs at lower energy than the direct and the position
of both minima could be followed across the entire com-
position range to x= i. %hen x+0.38, the direct tran-
sition occurs at the lower energy and only the k =0 mini-
mum could be followed. The results of these measure-
ments are shown in detail in Fig. 2. The photothresholds
measured by this technique on the terminal compounds
are in good agreement with those obtained from optical
absorption data.
In the present case the photovoltaic technique has
advantages over optical absorption measurements. The
direct edge can be seen on top of the indirect edge with-
out the necessity of preparing micron thick-samples.
& a.o
where hag is the threshold energy and I is close to 2.0.
A value of m=2.2 has been reported" for GaP. If the
optical attenuation length I/o. is large compared to the
minority carrier diffusion length I., and the width of the
depletion layer, then the number of electrons per inci-
dent photon is proportional to 0,.If hv is dose to he~ then
the photoresponse will be proportional to (hv —hp, )'.
Therefore, under these assumptions, a (photovoltage)'"
versus hu plot may be expected to show a linear region
where indirect transitions are dominant. Photoresponse
0 O.l 0.2 0.5 04 05 0.8 ' 0.7 0.8 0.9 l.P
GaAs MOL FRACTION PHOSPHORUS GOP
Fxo. 2. A plot of the threshold energies as a function of the mole
fraction of phosphorus. The dark points indicate samples vrhere the
composition vms measured by x-ray Quorescence. Triangles cor-
respond to the direct transition and circles to the indirect.
~C. Hilsum and A. C. Rose-Innes. Semiconducf~ng III—V
CwePogwd (Pergamon Press, Inc. , Neve York, 1961),p. 182.
CONDUCTION BAND MINIMA OF Ga(As, P, )
Also the composition of the Ga(As~, P,) often varies
through the thickness of the sample making direct ab-
sorption measurements unreliable. Many of the samples
were only very thin epitaxial layers on GaAs, and could
not have been used for studying the lower absorption.
cocKcicnt regions.
In view of the results given in Fig. 2 the linear extra-
polation procedure used by Khrenreich is well justified.
There is no question that the rapid risc in the absorption
edge of GaP near 2.65 eV is due to the same type of
optical transitions which are responsible for the absorp-
tion edge in GaAs; direct transitions to the conduction
band minimum at k= 0. It may be noted that the energy
separations for the two minima for x=0 and x= j. are
are not the same as those previously reported. " For
GaP it was pointed out that the value of this separation
(~0.35 eV) as well as the identification of the minima
involved was not on a very sound basis, The value from
Fig. 2 is 0.45&0.04 CV. It should be pointed out, how-
ever, that this value is the difference in photothrcsholds.
Assuming previously reported phonon energies for the
indirect transition" the energy separation could be as
low Rs 0.40~0.04 cV assuTDing no contribution to thc
photorcsponsc f1oID direct cxclton for IDatlon. ' In
GaAs the separation of the thresholds is smaller since
the crossover is at x=0.38 rather than at @=0.55 as
previously reported. The higher threshold was obtained
by extrapolation but should be accurate within &0.03
eV. Accounting for the maximum GaAs phonon en-
ergy'~" the separation of the minima could be as large
as 0.28&0.05 eV. This result is in disagreement with
the 0.36-CV value deduced from Hall data. It should be
noted that it is assumed that the response near the
1.37-CV threshold, which is a region of low-absorption
coeKcient, arises from direct transitions to the R=O
m1nnnum. If the Eg values deduced froID thc high-ab-
sorption region"" are used, then the energy separation
wonld be reduced by 0.04 to 0.06 eV. Care was exercised
to use nondegenerate samples to eliminate band filling29
effects.
Careful photomcasurcments were made on GaAs in
25 D. Kleinman and %. G. Spider, Phys. Rev. 11&, 110 (1960)."D. G. Thomas, M. Gershenzon, and J. J. Hop6eld (to be
published).
2'%. Coehran, S. J. Fray, F. A. Johnson, J. E. Quarrington,
and W. Williams, J. Appl. Phys. Suppl. 32, 2136 {1961),
~8 W. G. Spitzer, J. Appl. Phys. 32, 792 (1963)."E.Burnstein, Phys. Rev. 93, 632 (1954).
the 1.5- to 1.8-CV region in an attempt to observe struc-
ture due to the presence of the indirect transitions. A
small increase was noted near 1.7 eV. If one assumes the
indirect transitions follow the same spectral form as in
GaP and that the increase corresponds to an additional
absorption coeKcient of 100 cm ' according to ~/R
=hn/n, where R= response, then. the indirect threshold
would be near 1.6 CV in rough agreement with 1.62-CV
value of Fig. 2. However, the spin-orbit splitting of thc
valence band" "is 0.33 CV and the structure could also
be due to direct transitions from the split OG band. The
absorption threshold here would be 1.68 eV. No evi-
dence was seen for the spin-orbit sphtting of the degen;
crate heavy-hole band"; however, this would appear as
only a slight rounding at the bottom of the direct edge
and would be dificult to separate from the metal
photoresponse.
Note added iN proof. After the completion of this work,
there appeared a note by N. Holonyak, S. F. Bevacqua,
C. V. Bielan, and S.J.Lubowsio, AppL Phys. Letters 3,
47 (1963), in which emission from laser diodes of
Ga(As-P) was studied. The conclusions drawn concern-
ing the onset of the indirect transition are a striking
confirmation of our results. Also, a very recent study of
optical absorption in e-type GA(As~, P ) in the 3p
region has been reported by J. W. Allen and J. W.
Hodby, Proc. Phys. Soc. (London) 82, 315 (1963).They
conclude that below room temperature the 3p the GAP
absorption band is associated with vertical transitions
from hydrogen-like donor states near the conduction
band minimum to a higher conduction band. Above
room temperature transitions from the lowest conduc-
tion band must also be considered. These results tend
to confirm a proposal previously made by %. PauP2 for
thc origin of this band. The authors wish to thank
R. Zallen for bringing this later work to their attention.
ACKNO%'I EDGMENTS
The authors wish to express their gratitude to T.
Benedict of Merc Chemical Company, R. A. Ruehr-
wein of Monsanto Chemical Company, and L. Bailey
of Texas Instruments for supplying the samples of
Ga(As-P); A. Chodos for the x-ray fluorescence meas-
urements and H. M. Simpson, for fabrication of the
samples.
O' R. Braunstein, Phys. Chem. Solids 8, 280 (1959)."R.Braunstein and E.O. Kane, Phys. Chem. Solids 23, 1423
(1962).


English

Conduction Band Minima of Ga(As_(1−x)P_x)

A872 DALE E. HILL
These results indicate that the 300'K fluorescence
for p-type GaAs does not involve the acceptor states.
The fluorescence for lightly doped n an-d p-type GaAs
occurs at nearly the same energy as the energy gap.
However, for heavily doped m-type GaAs, the recom-
bination leading to the fluorescence seems to originate
at an energy 1 to 2 kT below the Fermi level as com-
puted from the absorption measurements.
IV. SUMMARY AND CONCLUSIONS
From the absorption measurements it can be seen
that in general the shifts of the absorption edge with
increased doping level occur in either direction and
can be divided into two components. The shifts to
higher energy predominate in e-type GaAs at 77'K and
the shifts to lower energy predominate in p-type GaAs
at 300'K. The shifts to higher energy are caused by
the change of the Fermi level with doping. The shifts
to lower energy can probably be explained as an
eA'ective decrease in the band gap. An additional phe-
nomena which should be taken into account is the
change in energy gap which occurs when the lattice
parameter changes with doping level. The Burstein
type shifts are not satisfactorily explained in detail by
Eq. (1). This is not too surprising for such a simple
theory, but it is of interest to know where the principal
difhculties lie. Part, but not all of the problem lies in
not accounting for the nonparabolic nature of the con-
duction band. The eGect of impurities in decreasing
the band gap mentioned in the previous paragraph if
understood and properly accounted for may explain
most of the remaining differences. The shifts observed
for heavily sulfur-doped GaAs are anamolous and not
understood at the present time.
From the fluorescence measurements we see that the
acceptor state is involved in the recombination which
leads to fluorescence at 77'K, but not at 300'K. In
addition we have seen that Ge as a dopant in GaAs
produces a deep level, presumably an acceptor state
roughly 0.08 eV above the valence band edge. The
e-type fluorescence occurs essentially at the band gap
energy for low doping levels and although the Quo-
rescence energy increases at the highest doping levels,
the recombination resulting in this emission does not
primarily involve carriers in the neighborhood of the
Fermi level.
ACKNOWLEDGMENTS
The author would like to express his appreciation
to R. Dalrymple for carrying out many of the measure-
ments and to D. High and J. McNeely for the ms, terial
preparations work.
P H VSI CAL REVE EW VOLUME 133, NUMBER 3A 3 FEBRUAR Y 1964
Conduction Band Minima of Ga(gs, .p,) t
%. G. SpxrzER
P/eotrioa/ irngineereng Department, University of Sonthern California, Los Ange/es, Ca/ifornia
C. A. MEAD
Ca/ffornia institnte of Teottno/ogy, Pasadena, Ca/~fornia
(Received 21 August 1963)
Photoresponse of surface barriers on samples of Ga(As&, P,) covering the range 0(z &I has been meas-
ured. ThreshoMs corresponding to both direct and indirect, band-to-band excitations within the semicon-
ductor and also photoinjection from the metal have been identified. The threshold of the direct transition
varies with composition from 1.37 eV in GaAs to 2.65 eV in GaP. The indirect transition was followed for
g &0.38 and again varied linearly from 2.2 eV in GaP to an extrapolated value in 1.62 eV in GaAs. The energy
separation of the two conduction band minima in GaAs is in disagreement with previously reported values,
I. INTRODUCTION
'T has been demonstrated in recent work, that when
~ ~ the photovoltaic response is measured for a Schottky
barrier at a clean metal-semiconductor interface, the
response has two distinct spectral regions. The 6rst
region is where the photon energy exceeds E, the energy
gap of the semiconductor, and electron transitions take
place from the valence to the conduction band. The
second region, where hs &E, is generally a region where
t This work was supported in part by the U. S. OfIjlce of Naval
Research under contract NONR 220(42) and the International
Telephone and Telegraph Corporation.
the response per photon is much smaller, and a number
of recent studies' ' have attributed this response to
'C. R. Crowell, W. G. Spitzer, L. E. Howarth, and E. E.
LaBate, Phys. Rev. 127, 2006 (1962).
2 C. A. Mead and W. G. Spitzer, Appl. Phys. Letters 2, f4 (1963).
3 G. W. Mahlman, Phys. Rev. Letters 7, 408 (1961).
' R. Williams, Phys. Rev. Letters 8, 402 (1962).
' W. G. Spitzer and C. A. Mes, d, J. Appl. Phys. (to be pub-
lished).
6 W. G. Spitzer, C. R. Crowell, and M. M. Atalla, Phys Rev.
Letters 8, 57 (1962).
7 C. R. Crowell, W. G. Spitzer, and H. G. White, Appl. Phys.
Letters 1, 3 (1962).
' H. G. White and R. A. Logan, J. Appl. Phys. 34, 1990 (1963).
I D. Kahng, Solid State Electron. 6, 281 (1963).
CONDUCTION BAND MINIMA OF Ga(As, , P, ) A873
photoemission of electrons (or holes) from the metal
over the Schottky barrier. The present work consists of
the application of this experimental method to the
Ga(As&, P,) system. The photoresponse has been meas-
ured on samples covering the range from x=0 to x= 1.
Of particular interest is the range where hv&E, . For
x&0.38, the response is resolved into two distinct re-
gions, one due to indirect or phonnn aided transitions
and the second due to direct transitions, The threshold
of the direct process could be followed across the entire
composition range and the indirect process from x=0.38
to x=1.0.
II. BACKGROUND
Considerable effort has been devoted to the study of
the structure of the conduction band in elemental and
compound semiconductors. Of particular interest in the
present study, is the work which has attempted to iden-
tify the relative positions of the (000) and (100) minima
in GaAs and GaP.
Khrenreich' "and Paul" have reviewed most of the
experimental evidence for the position of these minima.
Ehrenreich concludes that the (100) minima are 0.36 eV
above the R=O minimum in GaAs while in GaP the two
minima reverse positions with an energy separation of
about 0.35 eV. In each case the deeper of the two
minima forms the bottom of the conduction band.
That the conduction band minimum is not at k=0
in GaP can be concluded from the spectral shape of the
absorption edge" and the large value of the electron
effective mass. ' The pressure dependence of E, and
resistivity suggest (100) minima. """ Experimental
evidence for the higher k=0 minimum comes from
optical measurements where the interpretation has been
shown to be questionable. Absorption edge measure-
ments indicate the beginning of a rapidly rising absorp-
tion starting approximately 0.35 eV above the indirect
threshold. "However, Paul" points out that the pressure
dependence of the absorption edge leads to a separation
of 1 eV for the two minima if a speci6c functional
form is assumed for the pressure dependence of the
indirect transition. An infrared absorption band ob-
served in n-type GaP had been tentatively assigned"
to interband transitions between the two minima.
However, later work" showed that the absorption band
position had a much smaller pressure dependence than
was expected from the pressure coefficient of the two
minima. It has also been suggested" that the band is
due to a 0.4 deep oxygen impurity level.
' H. Ehrenreich, Phys. Rev. 120, 1951 (1960).
"H. Ehrenreich. J. Appl. Phys. 32, 21559 (1961).
"W. Paul, J. Appl. Phys. 32, 2082S (1961).
"W. G. Spitzer, M. Gerhsenson, C. J. Frosch, and D. F. Gibbs,
Phys. Chem. Solids 11, 339 (1959).
'4T. S. Moss, Report of the International Conference on The
Physecs of Serrtecortdlctors (The Institute of Physics and The
Physical Society, London, 1962), p. 295.
"A. Sagar and R. C. Miller, J. Appl. Phys. Suppl. 32, 2073(1961).
' M. Gershenzon and R. M. Milkulyak, Solid State Electron.
5, 313 (1962).
The primary evidence for the energy separation of the
two minima in GaAs comes from the analysis of the
temperature dependence of the Hall coefficient. ' '~
There is considerable evidence that the k=0 minimum
is the bottom of the conduction band; however, the
exact value of E, appears to be in question. Numerous
absorption edge measurements' show the room tem-
perature absorption to start at 1.37&0.02 eV. However,
theoretical 6ts to the data"" in the high absorption
regions give values for E, of 1.41 eV and 1.43 eV. The
absorption curves of one of these studies" also shows
evidence for direct exciton formation. Recent measure-
Inents" of electroluminescent band-to-band recombina-
tion radiation in shallow p-ss junctions show peaks near
1.36 eV and 1.39 eV. The authors interpret these emis-
sion bands as the indirect and direct transitions, respec-
tively, where the indirect transition arises from the
splitting of the heavy hole band degeneracy via spin-
orbit interaction. There has been recent evidence" that
E, is impurity concentration-dependent. There is also
an infrared absorption band' in e-type GaAs which had
been interpreted in terms of interband transitions, but
in view of the GaP results, this interpretation must be
regarded as suspect. It has been indicated" that there
is some difhculty with the interpretation of the pressure
dependence of the GaAs resistivity when the 0.36-eV
separation is assumed.
Much of the justification for Ehrenreich's analysis"
comes from absorption edge data on Ga(Ass,. P,) solid
solutions. These measurements indicate an abrupt
change in the variation of the intrinsic absorption edge
with composition near @=0.5. Linear extrapolations of
the two portions of the curve gave energy separations
in the cases x=O and @=1which were in general agree-
ment with the above quoted values. However, examina-
tion of the results show that the scatter in the experi-
Inental data and the necessity of extrapolating over a
50%%uz composition range introduces a substantial uncer-
tainty (tenths of an eV) into the position of the higher
lying minimum in each case.
III. EXPERIMENTAL
Samples were prepared on material obtained from
several industrial laboratories. Surface received various
chemical treatments depending upon condition but
were always cleaned in HF for at least 15 min prior to
placing in an oil-free vacuum system. Gold 6lms up to
1000 A thick were deposited on the surface by evap-
'7 L. W. Aukerman, and R. K. Willardson, J. Appl Phys. 31,
939 (1960).
' T. S. Moss, J. Appl. Phys. 32, 2136S (1961).
"I.Kudman and T. Seidel, J. Appl. Phys. 33p 771 (1962).) W. G. Spitzer and J. M. Whelan, Phys. Rev. 114, 59 (1959).
"R. Braunstein, J. I. Pankove, and H. Nelson, Appl. Phys.
Letters 3, 31 (1963).
ss M. V. Hobden and M. D. Sturge, Proc. Phys. Soc. (London)
78, 615 (1961).
2g D. N. Nasledov, A. A. Rogachev, S. M. Ryvkin, V. E. Khar-
tsiev, and B. V. Tsarenkov, Fiz. Tverd. Tela 4, 3346 (1962)
Ltranslation: Soviet Phys. —Solid State 4, 2449 (1963)j.
~ g I $ I
}.5 RD
h~ (ev)
Fzo. t. The rootn-tempersture (photovoltsge)'Is versus photon
energy for bvo samples of Ga(As&, P,). Where the data points
are for hg &1.7 ey, the sample has &=0.20. The other sample has
g=0.78.
oration in the form of 0.0i in. diam. dots at a residual
were gaspressure of &10 ' Torr. The photoresponse data
taken gsj.ng a quartz prism monochromator equipped
with a 50-cps shopping system Rnd synchronous
detection. The units were illuminated from the metal
side (front wall configuration). Several samples were
made with aluminum dots in addition to the goM. , and
in these cases the results were essentially identical. The
form of the response for hr &E, was found to be inde-
pendent of the thickness of the metal layer.
In most cases the composition values were obtained
from x-ray fluorescence measurements by comparison
of the As E and Ga Ep lines which occur at close to the
same energy. The estimated over-all accuracy in the
composition determined by this method is +2%. In the
few cases for which fIuorescence Ineasurements were not
made, the composition was supplied by the laboratory
in which the sample was grown. These values were
determined by lattice constant measurements.
Neglecting phonon energies the absorption coefFicient,
0,, for indirect transitions is given by
curves for two samples of widely different compositions
are shown in Fig. j..The left curve shows emission from
the metal into the semiconductor followed at higher
photon energy by an abrupt increase in response due to
semiconductor band-to-band excitation. The second
curve shows low energy response from the metal fol-
lowed by two well-resolved intrinsic excitation processes
within the semiconductor. The lower of these follows a
second power dependence as expected for an indirect
transition. The increase in response due to the higher
transition is sufEciently rapid that its functional form
ls difIIcult to determine Rnd Rs will be shown is Rs"
cribed to a direct transition. The fact that changes in
O. up to a level of j.0' cm ' are observed in the photore-
sponse indicates a very short I.which is consistent with
the small minority carrier lifetimes in these materials. "
The photothresholds for each region were taken from
the zero response after subtracting out the extrapola-
tion of the response due to the lower energy processes.
The error in the photothresholds is largely due to this
extrapolation procedure and is estimated to be at most
+0.02 eV. The measurements themselves were taken
with a resolution of better than 0.01 eV.
For samples in which x&0.38, the indirect transition
occurs at lower energy than the direct and the position
of both minima could be followed across the entire com-
position range to x= i. %hen x+0.38, the direct tran-
sition occurs at the lower energy and only the k =0 mini-
mum could be followed. The results of these measure-
ments are shown in detail in Fig. 2. The photothresholds
measured by this technique on the terminal compounds
are in good agreement with those obtained from optical
absorption data.
In the present case the photovoltaic technique has
advantages over optical absorption measurements. The
direct edge can be seen on top of the indirect edge with-
out the necessity of preparing micron thick-samples.
& a.o
where hag is the threshold energy and I is close to 2.0.
A value of m=2.2 has been reported" for GaP. If the
optical attenuation length I/o. is large compared to the
minority carrier diffusion length I., and the width of the
depletion layer, then the number of electrons per inci-
dent photon is proportional to 0,.If hv is dose to he~ then
the photoresponse will be proportional to (hv —hp, )'.
Therefore, under these assumptions, a (photovoltage)'"
versus hu plot may be expected to show a linear region
where indirect transitions are dominant. Photoresponse
0 O.l 0.2 0.5 04 05 0.8 ' 0.7 0.8 0.9 l.P
GaAs MOL FRACTION PHOSPHORUS GOP
Fxo. 2. A plot of the threshold energies as a function of the mole
fraction of phosphorus. The dark points indicate samples vrhere the
composition vms measured by x-ray Quorescence. Triangles cor-
respond to the direct transition and circles to the indirect.
~C. Hilsum and A. C. Rose-Innes. Semiconducf~ng III—V
CwePogwd (Pergamon Press, Inc. , Neve York, 1961),p. 182.
CONDUCTION BAND MINIMA OF Ga(As, P, )
Also the composition of the Ga(As~, P,) often varies
through the thickness of the sample making direct ab-
sorption measurements unreliable. Many of the samples
were only very thin epitaxial layers on GaAs, and could
not have been used for studying the lower absorption.
cocKcicnt regions.
In view of the results given in Fig. 2 the linear extra-
polation procedure used by Khrenreich is well justified.
There is no question that the rapid risc in the absorption
edge of GaP near 2.65 eV is due to the same type of
optical transitions which are responsible for the absorp-
tion edge in GaAs; direct transitions to the conduction
band minimum at k= 0. It may be noted that the energy
separations for the two minima for x=0 and x= j. are
are not the same as those previously reported. " For
GaP it was pointed out that the value of this separation(~0.35 eV) as well as the identification of the minima
involved was not on a very sound basis, The value from
Fig. 2 is 0.45&0.04 CV. It should be pointed out, how-
ever, that this value is the difference in photothrcsholds.
Assuming previously reported phonon energies for the
indirect transition" the energy separation could be as
low Rs 0.40~0.04 cV assuTDing no contribution to thc
photorcsponsc f1oID direct cxclton for IDatlon. ' In
GaAs the separation of the thresholds is smaller since
the crossover is at x=0.38 rather than at @=0.55 as
previously reported. The higher threshold was obtained
by extrapolation but should be accurate within &0.03
eV. Accounting for the maximum GaAs phonon en-
ergy'~" the separation of the minima could be as large
as 0.28&0.05 eV. This result is in disagreement with
the 0.36-CV value deduced from Hall data. It should be
noted that it is assumed that the response near the
1.37-CV threshold, which is a region of low-absorption
coeKcient, arises from direct transitions to the R=O
m1nnnum. If the Eg values deduced froID thc high-ab-
sorption region"" are used, then the energy separation
wonld be reduced by 0.04 to 0.06 eV. Care was exercised
to use nondegenerate samples to eliminate band filling29
effects.
Careful photomcasurcments were made on GaAs in
25 D. Kleinman and %. G. Spider, Phys. Rev. 11&, 110 (1960).
"D. G. Thomas, M. Gershenzon, and J. J. Hop6eld (to be
published).2'%. Coehran, S. J. Fray, F. A. Johnson, J. E. Quarrington,
and W. Williams, J. Appl. Phys. Suppl. 32, 2136 {1961),
~8 W. G. Spitzer, J. Appl. Phys. 32, 792 (1963).
"E.Burnstein, Phys. Rev. 93, 632 (1954).
the 1.5- to 1.8-CV region in an attempt to observe struc-
ture due to the presence of the indirect transitions. A
small increase was noted near 1.7 eV. If one assumes the
indirect transitions follow the same spectral form as in
GaP and that the increase corresponds to an additional
absorption coeKcient of 100 cm ' according to ~/R
=hn/n, where R= response, then. the indirect threshold
would be near 1.6 CV in rough agreement with 1.62-CV
value of Fig. 2. However, the spin-orbit splitting of thc
valence band" "is 0.33 CV and the structure could also
be due to direct transitions from the split OG band. The
absorption threshold here would be 1.68 eV. No evi-
dence was seen for the spin-orbit sphtting of the degen;
crate heavy-hole band"; however, this would appear as
only a slight rounding at the bottom of the direct edge
and would be dificult to separate from the metal
photoresponse.
Note added iN proof. After the completion of this work,
there appeared a note by N. Holonyak, S. F. Bevacqua,
C. V. Bielan, and S.J.Lubowsio, AppL Phys. Letters 3,
47 (1963), in which emission from laser diodes of
Ga(As-P) was studied. The conclusions drawn concern-
ing the onset of the indirect transition are a striking
confirmation of our results. Also, a very recent study of
optical absorption in e-type GA(As~, P ) in the 3p
region has been reported by J. W. Allen and J. W.
Hodby, Proc. Phys. Soc. (London) 82, 315 (1963).They
conclude that below room temperature the 3p the GAP
absorption band is associated with vertical transitions
from hydrogen-like donor states near the conduction
band minimum to a higher conduction band. Above
room temperature transitions from the lowest conduc-
tion band must also be considered. These results tend
to confirm a proposal previously made by %. PauP2 for
thc origin of this band. The authors wish to thank
R. Zallen for bringing this later work to their attention.
ACKNO%'I EDGMENTS
The authors wish to express their gratitude to T.
Benedict of Merc Chemical Company, R. A. Ruehr-
wein of Monsanto Chemical Company, and L. Bailey
of Texas Instruments for supplying the samples of
Ga(As-P); A. Chodos for the x-ray fluorescence meas-
urements and H. M. Simpson, for fabrication of the
samples.
O' R. Braunstein, Phys. Chem. Solids 8, 280 (1959).
"R.Braunstein and E.O. Kane, Phys. Chem. Solids 23, 1423
(1962).


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Conduction Band Minima of Ga(As_(1−x)P_x)

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