InP quantum wells

Solid-State Electronics Vol. 31, No. 3/4, pp. 431-434, 1988 Printed in Great Britain

0038-1101/88 $3.00+0.00 Pergamon Journals Ltd

H O T C A R R I E R E N E R G Y LOSS R A T E S IN GalnAS/InP Q U A N T U M WELLS

D . J . Westland, J . F . Ryan, M.D. Scott*, J . l . Davies* a n d J . R . Riffat*

Clarendon Laboratory, Parks Road, O x f o r d OX1 3PU United Kingdom. *Plessey Research (Caswell) Limited, Allen Clark Research Centre, Caswell Towcester, Northants United Kingdom.

ABSTRACT We have measured the energy loss rates of hot carriers in bulk Ga.47In.53A.s a n d in Ga.47In.53As/InP quantum wells of widths 154 A a n d 14 A. We find that the energy loss rates are considerably lower than predicted by the unscreened c a r r i e r - L O p h o n o n interaction. We show that the discrepancy m a y be resolved, at least in part, by invoking the presence of a non-equilibrium p h o n o n distribution, the magnitude of the effect depending on the well width.

KEYWORDS Hot carrier energy photoluminescence

loss;

hot

phonons;

GalnAs/InP

quantum

wells;

Ga.47In.53As;

picosecond

time-resolved

Picosecond time-resolved photolumlnescence measurements of bulk GaInAs have shown that the energy loss rate (ELR) of photoexcited carriers at high carrier temperatures (~ 500K) and densities (nex ~ l x l 0 1 8 cm 3) is lower by a factor of ~ I0 than the value estimated for e l e c t r o n - L O p h o n o n emission (Kash and Shah, 1984) assuming an unscreened Frolich interaction. F u r t h e r m o r e , our measurements of the E L R in a GaInAs/InP multiple quantum well ( M Q W ) structure, again obtained from picosecond photolumineseence studies, show a further reduction of a factor ~ 3 with respect to the bulk (Westland and others, 1987a); a similar effect was found previously in G a A s / A I G a A s M Q W structures (Ryan a n d others, 1984; Ryan a n d others,1986). However, energy loss rates of both bulk a n d M Q W G a l n A s structures measured by cw carrier heating methods (Lobentanzer and others, 1987) are m u c h higher than the picosecond photoluminescence values. We show here that " h o t " phonon effects can account for these a p p a r e n t discrepancies. The samples used in our experiments were (i) a bulk l a t t i c e - m a t c h e d epilayer of G a . 4 7 I n . 5 3 A s grown on InP, (ii) a 3 0 - p e r i o d M Q W with 154A Ga.47In.53As. wells a n d 160,4, InP barriers (Westland a n d others, 1987b), and (iii) a 1 3 0 - p e r i o d M Q W with 14A wells a n d 82A barriers. Carriers were excited using 3ps pulses from a synchronously p u m p e d , m o d e - l o c k e d Rhodamine 6G dye laser operating at 607 rim. T h e samples were held at 4K in a He cryostat. Photoluminescence was time resolved by means of a frequency upconversion technique (Kash and Shah, 1984; Westland a n d others, 1987a), the time resolution being laser pulse limited. Spectral resolution was obtained using a 30cm m o n o c h r o m a t o r , giving an energy resolution of 3meV. The luminescence spectrum was measured at various time delays with respect to the excitation pulse; typical spectra obtained f r o m the 14,~ M Q W for nex = 6x101 7 c m - 3 are shown in Fig. 1. We observe a large energy shift of the luminescence due to q u a n t u m confinement from = 810 meV in the bulk to 1130 meV for the well. The decrease in intensity at higher energies with increasing time is due to the relaxation (cooling) of the hot carriers. The t i m e - d e p e n d e n t carrier t e m p e r a t u r e was obtained as described previously (I(ash a n d Shah, 1984) from the slope of the h i g h - e n e r g y region of the luminescence spectrum. Figure 2 shows the carrier temperature for the bulk sample as a function of time at a carrier density of = 3x101~8 c m -3. T h e r e is a n initial fast cooling to a t e m p e r a t u r e of a b o u t 50K, due mainly to the emission of polar optic phonons f r o m the electron-hole plasma. As noted above, the E L R is considerably smaller than that for the bare e a r r i e r - L O interaction: for T c * 500K the slope of the experimental cooling curve in Fig. 2 is equivalent to an E L R of = 7 meV ps - 1 , whereas the theoretical value for a F e r m i - D i r a e carrier distribution is 85 meV ps -1 . In o r d e r to obtain a more complete model of the cooling we have used the method due to P~itz and Kocevar (1983), which includes the effect of a n o n - e q u i l i b r i u m p h o n o n population created by the cooling carriers.

431 S.S.E. 31/2~4--1

432

F F

6O0

E

'l

0

s~ I I

1060

1100 llL~O 11B0 ENERGY (rneV)

0

1220

20

40

60 TIME

Fig. 1. Time resolved spectra from the 14 ,~ M Q W . (A) at 1.4 ns, (B) at 500 ps and (C) at 20 ps after excitation,

80

100

120

(ps)

Fig. 2. Cooling curve for bulk InGaAs. (A) with no hot phonons, (B) using a hot phonon model at a carrier density of lxl01 8cm-3, and (C) with a carrier density of 5x10~ acre-3" The dots are experimental points for a density of =3x10 ~a c m - 3 .

Emission of phonons by the relaxing carriers causes the population of the vibrational modes of the lattice to increase according to : dNq

27r

2

dt

I

> t 2

Nq-N T

(1)

710 where N q is the population of an LO mode of wavevector q and energy $i¢00 (assumed dispersionless), N T is the equilibrium thermal population. The c a r r i e r - p h o n o n matrix element Hcp is given by the well-known Frolich interaction (Seeger, 1985). r i o is the LO phonon lifetime, which is assumed to be wavevector independent. The summation in eq.(1) includes electrons and holes Integration of (1) gives the energy lost by the carriers and allows the carrier temperature to be determined as a function of time. The integration interval includes the generation of carriers by the laser pulse, which was assumed to be Gaussian in shape. The results of this calculation are shown by the solid curves in Fig. 2, performed at carrier densities of l xl0 ~a cm - 3 and 5x10 ~ a c m - 3 , which represent the limits of the experimental uncertainty in this quantity. There is very good agreement between theory and experiment. For comparison, a cooling curve calculated using an equilibrium phonon distribution is also shown; the result is an increased ELR and rapid cooling to a t e m p e r a t u r e of about 30K. It should be stressed that the calculation does not include a n y variable parameters which can be used to fit theory and experiment. However, some of the quantities appearing in eq.(1) are not well known. The value of rio in Gain.as is uncertain at present, and we used the G a A s value of 26ps (Klemens 1966). Poiz and Kocevar (1983) showed that the calculated cooling curve was not very sensitive to this parameter. There is an added complication, due to the t w o - m o d e behaviour of phonons in GaInAs, however R a m a n scattering experiments by Pearsall, Carles and Portal (1982) have shown that only the G a A s - l i k e p h o n o n behaves as an LO phonon. Screening effects are not important in a h o t - p h o n o n analysis; the inclusion of screening reduces the phonon emission rate, but this in turn reduces the effectiveness of the p h o n o n 'bottlenecking'. We conclude from this analysis that, as in bulk GaAs, the hot phonon effect can account for the reduced E L R in bulk GalnAs. Extending the hot p h o n o n analysis to a quasi-two-dimensional ( 2 - D ) system is more problematical as the interaction of a 2 - D electron-hole gas with the vibrational modes of a M Q W system is not well understood.

433

1200

600 O •

1000

500

800

400

v w

300

,•60C O-

t~

tsa

400

f-- 20c

200

I0C

o

2'0

0'0

o'o

I

,oo

I

I

' 2'0' ~o

,20

I

6'o' 8'o

TIME (ps)

TIME (ps)

Fig. 4. Cooling curve for the 14 A MQW at a carrier density =6x101 7cm - a . The dots are experimental points. The solid line is the hot phonon calculation.

Fig. 3. Cooling curve for the 154 ./~ MQW at a carrier density =3x101 Scm-3. The dots are experimental points. The solid line is the hot phonon calculation.

We have adopted the model of Riddoch and Ridley (1983), which assumes that the carriers are confined but that the phonons are bulk-like. The matrix element in (1) is then given by : 2

I < 'Hcp'

where

and

> I

e 2~icO

2 ~ °Q2 [ e ~ ° - l -

2

es-l]

(sk" ' k t " q l G ( q z ) [

(Nq'qz+~±½)

C ( q z ) - -~ (G++ + C_+- G+_- G__)

G +-+

= sinC[qz±(kz±kz)]

L ~..

e x p i [ q z t ( k z ±.k z ) ]

(2)

(3)

~L

(4)

The phonon wavevector Q has an in-plane component g and a perpendicular component qz" As pointed out by Cai and Marchetti (1986) this model leads to an unphysical dependence on the sample size: this is because the carriers are localised in the quantum well but the phonon modes may extend throughout the sample. Thus, any hot phonon effect will be reduced by increasing the sample size, since this will produce more phonon modes to which the carriers couple more weakly. We resolve this difficulty by assuming that the confined carrier - lattice 'interaction length' is greater than the MQW period. This then enables us to take the volume of a well-barrier period as the sample volume f~, and L as the MQW period. The results of the analysis for the 154 ,~ MQW are shown in Fig. 3. To make the calculation tractable we considered only relaxation within the first sub-band. It can be seen that the calculation gives a considerable improvement over the equilibrium phonon model. The origin of the slower cooling in the MQW compared with the bulk lies in an enhanced hot phonon effect, since the number of modes with momentum perpendicular to the 2D plane to which the carriers can couple is reduced. The calculated cooling rates are slightly lower than the measured rates because the contribution from the higher sub-bands is not included. When this effect is integrated over the entire relaxation process we see from Fig. 3 that the calculated temperature is systematically higher than the measured value.

434

The calculation applied to the 14 ,~ well, which contains only one electron and one heavy hole sub-band, gives an improved agreement with experiment at early times (Fig. 4). At longer times, however, the calculated ELR is faster than the experimental value, so that the temperature is lower than measured. The cause of this latter effect is not known. It is quite evident from recent calculations, however, that proper account must be taken of the 2D nature of the phonons of the quantum well (Riddoch and Ridley, 1985; Sawaki, 1986). The population of hot phonons will be reduced in a cw measurement and this can account for the 60 fs carrier-phonon scattering time observed by Lobentanzer and colleagues (1987). It also explains why no difference was found between the bulk and MQW, if the slower cooling for the MQW observed by us is due to an enhancement in the hot phonon effect (c.f.Shah and others, 1985 for cw measurements of ELR in GaAs quantum wells).

REFERENCES Cai, W., M. C. Marchetti and M. Lax (1986). Nonequilibrium electron-phonon scattering in semiconductor heterojunctions. Phys. Rev. B, 34, 8573-8580. Kash, K. and J. Shah (1984). Carrier energy relaxation in In.53Ga 47As determined from picosecond luminescence studies. AppI. PhTs. Lett., 45, 401-403. Klemens, P. G. (1966). Anharmonic decay of optical phonons. Phys. Rev., 148, 845-848. Lobentanzer, H., W. W. Rhtile, W. Stoltz and K. Ploog (1983). Hot carrier-phonon interaction in t h r e e - and two-dimensional Ga0.47In0.53As. Solid State Comm. 62, 53-56. Pearsall, T. P., R. Caries and J. C. Portal (1983). Single longitudinal-mode optical phonon scattering in Ga.47In.53As. Appl. Phys. Lett., 42, 436-438 P~tz, W. and P. Kocevar (1983). Electronic power transfer in pulsed laser excitation of polar semiconductors. Phys. Rev. B, 28, 7040-7407. Riddoch, F. A. and B. K. Ridley (1983). On the scattering of electrons by polar optical phonons in quasi-2D quantum wells. J. Phys. C: Solid State Physics, 16, 6971-6982. Riddoch, F. A. and B. K. Ridley (1985). Electron scattering rates associated with the polar optical phonon interaction in a thin ionic slab. Ph'csica, 134 B+C, 342-346. Ryan, J. F., R. A. Taylor, A. J. Turberfield, A. Maciel, J. M. Worlock, A. C. Gossard and W. Wiegmann (1984). Time-resolved photoluminescence of two-dimensional hot carriers in GaAs-A1GaAs heterostructures. Phys. Rev. Lett., 53, 1841-1844. Ryan, J. F., R. A. Taylor, A. J. Turberfield and J. M. Worlock (1986). Time-resolved photoluminescence from hot two-dimensional carriers in GaAs-GaAIAs multiple quantum wells. Surface Science. 170, 511-514. Sawaki, N. (1986). On the reduction of the electron-LO phonon scattering in a semiconductor superlattiee. J. Phys. C: Solid State Physics, 19, 4965-4975. Shah, J., A. Pinczuk, A. C. Gossard and W. Wiegmann (1985). Energy loss rates for hot electrons and holes in GaAs quantum wells. Phys. Rev. Lett., 54, 2045-2048. Seeger, K. (1985). Scattering processes in a spherical one-valley model. In M. Cardona and Hans-Joachim Queisser (Eds.), Semiconductor Physics, an Introduction, 3rd ed. Springer Verlag, Berlin. Chap. 6, pp153-213. Westland, D. J., D. Mihailovi~, J. F. Ryan, M. D. Scott and P. A. Claxton (1987). Energy relaxation and recombination of hot carriers in GaInAs/InP quantum wells using picosecond time-resolved luminescence spectroscopy. In O. EngstrOm (Ed.), Proc. 18 th Int. Conf. on the Physics of Semiconductors. World Scientific, Singapore. pp465-468. Westland, D. J., A. M. Fox, A. C. Maciel, J. F. Ryan, M. D. Scott, J. I. Davies and J. R. Riffat (1987). Optical studies of excitons in Ga.47In 53As/InP multiple quantum wells. Appl. Phys. Lett., 50, 839-841.