Solid State Communications, VoL8, pp. 1089—1093, 1970.
Pergamcrn Press.
Printed in Great Britain
PHOTOEXCITED HOT LO PTIuNONS IN GaAs Jagdeep Shah, R.C.C. Leite and J.F.. Scott Bell Telephone Laboratories, Incorporated Holmdel, New Jersey
(Received 5 tlav 1970 h’ R. Loudon)
We report the observation of photoexcited “hot” LO phonons in GaAs. We also obtain an order of magnitude estimate of LO phonon lifetime which agrees reasonably well with the estimate from the linewidth in Raman scattering. Finally we compare our results with the recent experiments by VellaColeiro in which a large magnetic field is essential for the observation of “hot” LO phonons.
NONTHERMAL equilibrium population of acoustic phonons has been investigated in some 1 Recently G. VellaColeiro detail in the past. has reported2 that a large nonthermal equilibrium population of LO phonons can be created by photoexcited carriers in CdS when the magnetic field applied to the sample is such that the energy difference between two Landau levels in the conduction band equals ~ LO the LO phonon energy. We report here our results on GaAs which show that the application of magnetic field is not essential for the creation of “hot”
phonon lifetime 7 is sufficiently long, this would lead to a large population of hot LO phonons. Most of the observations were made on two relatively pure epitaxially grown samples about 5mm square. One sample had (111) face a~d carrier concentration ~ 1 >. 10’~cm~at 300 K. The other sample had (110) face and carrier concentration 5 ~. 10~at 300K. The hot phonons were detected by observing surface Raman scattering. The same laser used to produce the hot phonons was also used for
LO phonons by photoexcited carriers. (By’ “hot” phonons, we mean nonthermal population of phonons.) We also obtain an estimate of the phonon lifetime under the assumptions that the photoexcited carriers decay by emitting LO phonons and that the LO phonons decay before they equilibrate within the LO phonon branch, This estimate is in good agreement with the lifetime deduced from phonon linewidths in Raman scattering.3
Raman scattering. The Raman spectra were analyzed with a double monochromator and detected by an S20 photomultiplier and an electrometer. The sample was mounted on a copper block to insure good thermal contact. For room temperature measurements, dry He gas was blown on it continuously. For measurements at lower temperatures, the copper block was in a dewar in the atmosphere of cold He vapor. The Raman scattering spectra were obtained for different laser intensities. Calibrated neutral density filters were used to vary the laser intensity.
In our experiments, a I W Ar + laser was sharply focussed (~75dm in dia.) on epitaxial GaAs. This laser creates a high density of electrons and holes which cascade down to the
Figure 1 shows the room temperature Raman spectra obtained in this manner for two different laser intensities for the sample with (Ill) face.
bottom of the band by emitting LO phonons. This provides an intense source of phonons. If the 1089
1090
PHOTOEXCITED HOT LO PHONONS IN GaAs
‘00
STOKES
T~f\\

Vol. 8, No. 14
ANTISTOKES
‘1’AT0~1~’~ P.O2F~I
Il
I0~
I
I
~L I
(Il
4
Al ~ I
300
2e0
I
‘
2W “ 0 ~AMAN SHIFTS
260
260
300
cm’)
FIG.1. Reflection Raman spectra of GaAs at 300°K for two laser intensities. Note that the ratio (S/A) of Stokes to antiStokes scattering intensity decreases significantly for LO and only slightly for TO as the laser intensity is increased. Notice that the ratio (S/A) of the Stokes to antiStokes intensity for LO decreases significantly as the laser intensity is increased, There is also a slight decrease in S/A for TO, which is consistent with an increase in the
S/A for TO implies that the shift in phonon frequencies is related not to the phonon temperature but to the lattice temperature.
lattice temperature as determined from (i) the position of the peak and the slope of the high energy tail of the luminescence spectra and (ii) the 3 However, shift in the LO and TO frequencies. the decrease in (S/A) for the LO is too large to be accounted for by the estimated increase in the lattice temperature. We conclude therefore that the major cause of the reduction in S/A for the LO is the creation of hot LO phorions by photoexcitation. The LO phonon temperature T can be deduced from S/A at each intensity. The
magnitude estimate of the LO phonon lifetime T. The basic premise of our calculation is that the product of the phonon generation rate and T equals the difference between the nonequilibrium (i.e., in the presence of exciting light) and equilibrium population of LO phonons. In order to estimate G~,the density of phonons generated per second, we assume’ that the photoexcited electron loses nearly all of its excess energy (~\E 1 eV) by emitting LO phonons, i.e.,
LO phonon and the lattice temperatures are 800°Kand ~..420~K respectively at the highest laser intensity used in our experiments.
We can use our results to obtain an order of
(~E/hw~ 0)G~ where G~ electrons generated per second = p ~ P
( ~
.
~
density of
.~
A side remark may be of interest here. The fact that the temperature rise of the lattice
Here P is the. laser power, P the maximum laser . power used in our experiments, ?iw (‘2.5 eV)
estimated from the shift in ~S~0 agrees well with that estimated from luminescence studies and
is the laser photon energy, d (~.0.1~) is the penetration depth of laser into the sample and A is the area of the laser beam at the sample.
Vol. 8, No. 14
PHOTOEXCITED HOT LO PHONONS IN GaAs
GaAs ‘s., 300K ~ EXPERIMENTAL ACORRECTED FOR To
4
1091
f
1.2
0,,~,,,, P/p.
FIG.2. (S/A
—
i)’
vs. P/P
0 for GaAs at ~300cK. The arrow on the ordinate scale indicates the expected value of (S/A — 1)’ at the ambient temperature. The deviation from linearity at high P/P0 is due to lattice heating. The corrected points are indicated on the figure.
Since surtace Raman scattering provides us with information on population of phonons at only 2k~,where k~is the photon wavevector, we now calculate the kphonon given phonon vector.generation rate 6(k) at a
a
=
I g
G(k) 4rrk2dk
where
2 x electron wavevector 2.8 x iO~cm ‘for AE~.1 eV and electron effective mass m’~ 0.07 in 0. G(k) depends on the form of electron—phonon interaction. Assuming type interaction, 2 whereFrohlich a is a constant which can be
G(k)
2(2mAE/h2)2
=
a/k
determined from above. Thus we have
2dk = (G,,/k,,,) dk G(k)4~’rk
is the lattice temperature and the
dispersion of LO phonons is neglected. Similar
where km ke
The equilibrium density of LO phonons between k and k  dk is 1 2dk = 1 4—k2 dk / r10(k)47~k 8 ~ exp(h~LO/kTO)—1
(1)
expression can be written down for nonequilibrium density n(k)4Tlk2dk by replacing 7 with the phonon temperature 1. For k 2k,,, T is determined by the ratio S/A of Fig. 1. The rate equation now be written as G(k)7 = can n(k)—n 0(k) ~inder the assumption that the LO phonons decay before they equilibrate within the LO branch. From the above, we have
1092
PHOTOEXCITED HOT LO PHONONS IN GaAs
=
~
~
Nhere
~ 
1
exp (~‘Lo~ kT
25P~ ~2 ~ 24dk,,,k~
0)
2
7
~
1 )(2) sec
itT’
for values previously given and ~ = 1W. Equation 2 states that if f3 and 7 are independent of P/1~ and if variations of the second term in the bracket are small compared to those of the first term then a plot of (S,/A— 1)’ vs. P/P 0 should be linear with a slope /3/7 and its intercept should equal the second term in the sample bracket.with We show plot inthat Fig.it 2 isfor the (110) such face. aNotice a
Vol 8, No. 14
found300°K. Tat to be of the same order of magnitude as The phonon lifetime T~ 5 x 10~2sec obtained above compares favorably with the lifetime of = 3 x 10_12 sec obtained from Raman linewidths.3 Although ours is only a crude, order of magnitude estimate, the fact that it agrees reasonably well with a generally accepted value of 7 supports our assumptions.
We have also performed this analysis for experiments at 2600 K and 150~K.The maximum LO phonon temperatures obtained were 370 K
It is perhaps 2instructive to note hot thatphonons the fact did not observe that in theVellaColeiro absence of magnetic field may be due to his much smaller phonon generation rate (approximately seven orders of magnitude smaller than ours). It is, however, not clear why the application of certain magnetic fields leads to the observation of hot phonons at such low generation rates. The agreement of LO lifetimes calculated here with those determined from Raman linewidths shows that intrabranch scattering (:~E  0, ~ ~ 0) of LO phonons is not important, despite the lack of dispersion near k o.~Our results also show that electron— phonon interaction is much stronger for LO than for TO phonons. This result may be of interest in view of the controversy in the case of lnSb.7’8
and ~ 3100 K respectively and the maximum lattice temperatures were ~ 260K and 160:K respectively. The intercept gave the correct ambient temperature in each case. Phonon lifetimes were also estimated as above and
.lcknon ledgernents — We acknowledge helpful discussions with Drs. J.M. Worlock, J.P.thank We Gordon, A.E.C.K.N. DiGiovanni Patel for andable G. VellColeiro. technical assistance.
straight line at low laser powers but begins to deviate at larger P/P . However, this deviation is directly attributable to the rise in the lattice temperature. If this is taken into account, then the linear behavior is observed over the entire range of laser powers used in our experiments, From the slope of this straight line in Fig. 2., we obtain 7  5 10’ sec. The intercept gives T 0K, in reasonably close 0 ~with 290the ambient temperature. agreement
REFERENCES 1.
See, for example, CONWELL E.M., Hi~~’li Fi’~ Truiispc~riin Seinicondiiciors, Solid State Physics Suppi. 9, (edited by SEITZ F. and TURNBULL D.) Academic Press, (1967).
2.
VELLACOLEIRO G.P., Pliys. Re~.Leit. 23. 697 (1969).
3.
CHANG R.K., RALSTON J.M. and KEATING D.E., Paper E—3 in Light Scattering (edited by WRIGHT GB.) Springer, New York, (1969).
4.
This is a good assumption in view of the fact that EHRENREICH H. (Phys. Rc~.120, 1951 (1960)) has concluded that polar optical scattering in predominant in relatively pure GaAs between 200° and 500°K.
5.
PARK Y.S. and LANGER D.W., Phys. Ret’. Leji. 13, 392 (1964).
6.
NUSIMOVICI M.A. and BIRMAN
7.
DICKEY D.H. and LARSEN D.M., Plus. Re~.Len. 20. 65 (1968).
8.
McCOMBE B.D., WAGNER R.J. and PRINZ G.A., Solid State Conumun. 7, 1381 (1969).
J.,
in
Spectra of Solids
Phys. Re~. 156. 925 (1967).
Vol 8, No. 14
PHOTOEXCITED HOT LO PHONONS IN GaAs Nous avons observ~des fonons chaud excit~ par la lumi~reen GaAs. Nous avons aussi oblem~an ordre de grandeur pour Ia dur~e de vie des fonons optiques longitudinaux qui est en bonaccord avec celle dériv~par intermediaire de la larg~’urde bande Raman. Non resultats sont contrastés avec ceux de VellaColeiro qui a ttouv~ essentiel la presence de champ magnetic pour produire des fonons chauds.
1093