Time-resolved spectroscopy of semiconductor quantumwell hueterostructures

Physica 127B (1984) 343-3¢~ North-Holland, Amsterdatr.

Tm~-R~OLVF.D SP~L-'Y~OSCOPY O F S ~ C O N D U C T O R WELL ~E~rF.~:OSTRUC~Ig~

QUANTUM

J.F. R Y A N Clarendon Laborato~, Uni~er~it9~[ ~7~[o~, Oxford, UK Reeeta~ progress in transient ahsc,f.~ti~0 .and lumine~enee s|:udies of multiple qu-qr~tumwell (MOW) structures is reviewed. Hot-carrier relaxation h~ haea stud;'cd in both unripped and modulation doped samples. Confine:nero of e~citons in narrow '¢¢ellsh~ recentl?¢hat~ delcetod by measuring a I~ge reduction in the ¢xeitc3nllfctirne. Finally, the evidence for nonradlatlve prOCeSsesi~ djs~tt'l~ed. 1. ~ t m d u e t l o ~ 'The last few years have seen re~aargable advances in the techniques ozed to ~e0vr~te and detect ultrashort optical pulses, anti tl~ application of these techniques to tia/e~r~solved spectroscopy of semiconductors has ftande Doss~ble direct, real-time studies of some ~f ille fundamentally important processes sucl~ ~s.~lvctronelectron and e!ectron-phonon ir~te¢~.at{~C*g.Much progress has b e e n made i~ unders~;~a~liag such properties as the energy relaxatiort r~f ~ptieally generated hot carriers in direct Rap t~aterials [1-3], the screening of exeitons arid bie~cilons in an optically induced dynamic M~tt tl'~ft,~ition [4], a~ad the formation and dv~ay of self~lqcal~zed charge states in the quazi-one,Oi~easional semiconductor (CH)~ [5], just to Clt~t~te a few examples. At present the exper~t~ntal limit of temporal resolution is ~ I0 -in s altla~u#~ much shorter pulses have in fact been generated [6]. Absorption spectroscopy, which t~ses a~ exciteand-probe method, obtains this fes~lotio~ when a sub-picosecond whhe light contiqo~o is used as the p~'obe [7]. Luminescence sp~'etr0~¢~py, on th~~. other hand, can obtain ~10~x:~ whdt~ a fast Ke,rr cell is used [4], but when "~t~lg optical signals are to be studied the synchrotrons streak camera method is more suitable ~tltl~ugh the resoiution is poorer, ~ 1 0 - '~ s. : cletgiled discussion of these techniques is beyoo~5 ~h¢ i~ope of this article, but a complete des~iDtiOt~ oar~ be found in the proceedings of recet,~ co~f~¢ences o.n Picosecond Phenomena [8].

A n increasingly important area in semiconductor physics is the behaviour of two-dimensic,gal (2D) carriers confined at a heterojunetion ,or in a quantum well (QYV) structure. In the G a A s AJ~Gat_xAs system a high-quality interface can be obtained by epita.xial ~.~'owth methods, and the development of modulation doping, which largely eliminates charged defects from the confinement region, has led to the discovery of important new phenomena such as the quant~:adon of ~he Hall effect [9]. Because of the reduced dimensionality of ~he era'fiefs in these structures the relaxation kinetics might be expected to differ from that found in the bulk as a consequence of: (i) modified carrier--carrier scatte.,q-'ng, screening, and inter-subband relaxation; (ii) modified clectron-phonon scattering and so a different rate of energy relmxation of hot carriers; Off) confinement of excitons and a reduced exeiton lifetime. In addition, entirely new effects will arise: (iv) trapping of carriers into the wells from the barriers; ( 0 interface effects In this paper I will show how time-resol':ed spectroscopy applied to the GaAs-AIGaAs system can help to answer some ot these questions. It should be remarked at the outset that these materials are among the purest compound semiconductors that can be grown and that intrinsic properties dominate; for example, the radiative efficiency of electron-hole pairs in a QW is close to unity.

0378-4363/84/$03.00 © Elsevier Sc:iet~e Publishers B.V. (Nor~th-Holland Physics Publishing Oivi~;i~t0

344

J. E Ryan ! Time-resolvedspectroscopy of quantum wells

Furthermore, the experiments described i~elow in which the cleetron gas produced by modulation doping is heated optically and then observed to ¢ool cannot be done in bulk material simply because trapping at defects dominates the carrier kinetics.

.

!

-

5

~

0e

I,..Y/ 151

2. ][-][ot-C~-ier relaxation in qnantmu weUs Time-resolved optical studies of bulk G a A s [1-3] have shown that photoexcited hot carriers ver2, rapidly come to internal equilibrium through carrier--carrier interactions, and then cool towards the lattice temperature principally by LO phonon emission, For carrier densities n ~ 1 0 : ~ c m -a the eleetron-phonon scattering rate r~ ~ is found to be ~10r~s -'~ [2] while at higher densities the rate is reduced by screening: at n ~ 5 × 1 0 ' V e m -'~ a reduction by a factor of five is reported [3]. The motivation for studying these effects in quantum wells, over and above the obvious technological interest in device perrefinance, has been to see if the electrons behave differently when confined in 2D, to see whether the electron-phonon interaction is different, and to see how screening acts in 2D. T h e first detailed study ol" hot-carrier relaxation in u . d o p e d quantum wells was made by Shank et al. [~0] using transient absorption techniques. They used a M Q W structure in which do,,A ~= 205 .~ and dAIG.A~= 224/~, The excitation energy was 1.64eV, so that only the GaAs layer was excited. Their results, reproduced in fig. 1, show most vividly the dramatic changes that occur after intense excitation. Prior to excitation sharp, well-defined subband exciton states are observed superimposed on the steplike density of states that is characteristic of the 2D system. Within 1 p~ of excitation at a pair density n = 2.5 ~: 10~7cm -:~ (fig. la) screening o~ the electron-hole Coulomb interaction has bleached the exci~on absorption, and band gap renormalization due to exchange and correlation effects is observed. After 100ps the absorption profile has recovered more or less to its form before excitation, and the carriers have cooled to the lattice temperature ( T L = 7 7 K ) ; exeiton~,

nl

.... t,~4

1~7

(~NER(;Y [oV)

I t GO (a)

,1 ,," ,%,, ~ 13p~m~ .i 0~=~..~ .....................

08

~NER~Y I~v'~

~b)

F~g. l. Transient a b ~ r p f i o n spectra of an undoped G a A s AI(.~aA.,; MOW s~rueture for c~arrier densities, a/ n ~ 2.5× l O : ~ c m "~" b) n = 5 x l O W e m "'~. From reL 10.

however, remain screened eve~ at this time, A1 the higher density of 5 × 1017 em -a (fig, lb) theJ band filling as carriers cool is qu~te dramatic, and at ~00ps the apparent band gap E g ' . ~ l . 5 4 e V , At ever~ higher densities optical gain is o b s e ~ e d over a wide energy range above and below the energy gap, Extracting carrier temperatures from the data is not straight-forward. The absorption coefficient is, neglecting exciton effects.

i

where ao includes matrix elements and is assumed to be energy independent. The summation is over all electron and hole subbands; D ( E ) is the density of states, S(E) is a Coulomb enhancement factor [11]. a~ci f~ and fl, are the electron and hole Fermi factors. By fittinhz this expression to :he spectra obtained at different times, values of the carrier density, temperature and chemical potential are determined, The resalts of such a fitting procedure are shown in fig. 2, Also shown are values obtained for bulk

J,F. Rytm / Time.resolve:l apeetrOscopy of quantum i¢ells

----MQW

LOW PUMP

4 0 0 1 1 ~ BULK GaAo LOW PUMP

ooi\ ~MOW

NIQ~i laONP

20C ~ x'h,x..,,"

50

•r~¢ (PICOSECONI~S)

400

Fig. 2, Carrier t~:wperatur~ v,~, time for a MQW structure. The data obtalncd from a balk sample are included for comparison. From ref. 10.

Ga/',s. It appears that the temperatures and coo',ing rates in the Q W are similar to those of the bulk; a six-fold increase in ~'o is found at n = 2.5 × 10 t7 cm "s, which compares with a factor" of five in the bulk at nearly the same density. T h e conclusions from this experiment are then that the e l e c t r o n - L O phonon interaction does not s e e m to be significantly modified in 2D as far as energy relaxation is concerrled, flint the presence of higher-lying $ubbands does not appear to significantly modify the dynamics, and that screening has m u c h the same effect as in the bulk. Phototuminescence spectroscopy c~tn in principle yield the same kind of information by measuring hot luminescence from energy states well above the band gap. Because tho density of states i:n 2 D is constant in this region the emitted intensity has the form 1"12]

I( E) -~ to e.xp(-E/k T,),

345

al. [13] who used a synchronous streak camera to detect the weak luminescence. T h e y used a synchronously-pumped R 6 G dye laser (he= 2.01 eV) so that both the barrier regions and the wells were excited. A spectrum is detected every t 3 ns and integrated for ~10ro pulses so that a very high signal-to-noise ratio is achieved. The temporal resolution is - 2 0 ps, and is limited by the spectrometer which ;;s used to disperse the luminescence. T h e results were obtained from a M Q W with d a , ~ = 258/~ and d~ao,~, -- 494 A., with the A I G a A s barrier being $i doped; an electron density no= 2 x 10iTem -'~ exists in the well before photoexcitation. T h e lifetimes were m e a s u r e d at differen~ values of energy for a range of excited carrier densities. Fig. 3 shows the results obtained under intense illumination when the photoexeited carrier density n:-5 × 10~Sem -~a At the highest energy the luminescen,:e~ 'profile is resolution limited, i.e. the times for both the growth and decay of populatior.* in these states are less than 20 ps. A t lower er.ergies a real risetime is resolved, and a]so a rapid increase in lifetime. For states near the band edge the lifetime increases to ~ 7 5 0 p s . These re..;ults, and the data obtained ~or intermediate and low pumping conditions are summarised in fig. 4. At low den:~ity, n ~ - 1 0 ~ s e m -~, (curve (c)) the lifetime is short ~-100ps, a n d practica~ly independent of energy over the small range that m e a s u r e m e n t s could tm :made. At n = 10 ~6 cm -3

i.?

E~

,..2.1

1,576eV

(2)

so that a fime-resolv~d measurement gives To(t) rather move directly than in absorption spectroscopy. This approach has been taken by Ryan et

T~ME

Fig. 3. Time dcpend~nce of the kmfir~r~:nce intensity versus energy for n = 5 × 101~ern "°, From rcf. ;3,

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.L ~. Ryan / Time-resolved spectroscopy of quantum wells 120 Ia }~;

-

80-

/~00 (bl

o

60 -

y- ......

~ ..........

200 I¢I

1,5~.

~,52

I li6

TIHE

ENERgy levi

Fig. 4, Hot luminescen~ Iifctlmes for photoexclted carrier densltic~, a) n=5×10mcm-'~:, b) n = 4 × 1 0 J ~ ' e m - a ; c) n = 9 × 101acre ''~. The carrier density due to modulation doping is n~j= 2:< t0~7em -~. Frora t e l 13.

(curve (b)) the times at low energy are considerably longer, but a sharp decrease is found at high energy, reducing to ~ 2 0 ps. At the ~ a x i m u m density, n = 5 ~10~'cm '-s (curve (a)) ~he lowenergy lifetime is close to ~hat found m bulk GaAs, but now the rapid decrease at high. energy is very dramatic. The short lifetimes measured at high c n e r g i ~ are consistent with the absorption data (fig. 1), and are explained by rapid cooling of the electron distribution. The density-dependent lifetime at low energies, on the other hand, is accounted for by efficient non-radiative trapping processes. I will return to this latter point in section 4. The mean energy relaxation rate of the 2D electron gas is related to the temperature by de

/

7, = kk2

F1

F~\dT

Z"

where the F~ are the Fermi-Dirac integrals. Since the bracketed term is close to unity the classical result is a fairly good approximation. The energy loss rate by LO phonon emission is [a2] dt

=

ELO e x p ( + E L o / k . T ~ ) . -r~

(4)

The relations (~-) and (5) enable a xalue for % to be obtained from the data. The temperatures oblained from the luminescence profiles using {2) are shown in fig. 5. For the lowesx density case the optically heated electron gas is still relatNely co!d and highly degenerate so that relaxation by optical phonon emission is not important [14-], and

Ips)

Fig. 5+ Time dependence of the car~¢f temperature for b~ht~ doped M Q W structure. T h e solid lines represent theoretical fits with v u = 7 ps+ See cq. (4). The carrier densit.',cs arc as in

lig. ~.. From ret. ]3,

relaxation occurs on a much longer time scale by acoustic phonon processes. At the two higher densities the gas cools in about 100ps to a temperature well above the lattice temperature ( T L = 4 K , although the temperature of the illuminated region is not known). A similar effect has been seen for bulk GaAs [2, 3]. The solid lines in fig. 5 are the fitted results using (2) and (3), and the same value of % = 7 ps is obtained in each case, which is an order of magnitude greater than the value obtained for undoped wells. This difference is quite surprising and it is not known yet whetlher the cause is due to a real difference in behaviour of the two structures, different experimental conditions, or the approximations in the fitting methods. The issue, therefore, of whether screening is more effective in 2D remains unresolved. ]~t would appear '.hat the 2D plasma frequency w~o=(2~rneq/m*r) lt2 (where a is the 2 D density), which is enhanced over the 3D frequency w~s~=(4cme~lm*~d) ~t2 by the factor (qdt2) it2, can approach ELO for the wavevectors that are relevant to energy relaxation, so that strong screening of the electron-LO phonon interaction might result. On the face of it the luminescence data suggest that this reduction takes place, but considerably more work both experimental and theoretical is required to elucidate this ma+;ter.

3. Exd~ou c~mSnemeut One of the most important features of O W structures is the ability to control the degree of

347

J,F. R.van / Time-,esolvedspectrolcopy of quantum wells

localization by adjusting the welt thickness. The M O W samples in which hot carrier p h e n o m e n a have been studied to date have dG~.~=2()0 250 A., and dearly the experiments slhould be extended t~;. narrower wells, rn addition to the confinement of free carriers that occurs at interfaces and in QWs, confinement of exeitons also takes place. An~sotropy of fi:~ese bound states becomes significant when the well thickness is reduced below -~2 a n *, where a~ is the bulk exciion radius; i~: G a A s this condition m e a n s that for d ~< 200 A confinement of the excitons states inc,'eases, and so the binding energy and the radiative efficiency increase as :he particle wavef,anction overlap increases [1I, 17]. For the ,~ame reason the cxciton radius is exl~ected to decrease by a factor of two, and the lif~dme :>y a factor of four. GiSbel et el. [15] have recently z-eported timeresolved luminescence measurements of excitons in single q u a n t u m well (do,~,~ = 50/~) and a double weI1 (dG,A~ = 140 ~ ) . In both cases the thickness of the A I G a A s top layer is 1 p,m: carriers were optically excited in this ~ayer and subsequently trapped in the wells. Sharp luminescence lines originating from both the well av.d the barrier regior~ were observed which were attributed to free exciton recombination. The timed e p e n d e n t intensities of these lines are shown in fig. 6. T h e A I G a A s luminescence is short-lived compared to the G a A s luminescence, which is found to d e p e n d on the well thickness: the former effect is attributed to efficient trapping of carriers into the well, while the latter is attributed to confinement of excitons within the well. By ~olving coupled rate equations G6bel et el. [15] obtained a reduction of the e:~citon lifetime by a factor of 2.85. Several questions should be raised at this point. The identification of the states as free excitons requires that complimentary absorption or excitation spectroscopy measurements should be made. T h e existence of bound excitons in such structures is well known, a~id the effect of defects on lifetimes can be dramatic (see section 4 below). T h e interpretation that the risetime of the confined exciton luminescence arises from trapping ot carrier from the barrier region should

, i.A \ :i~ I ~ . . ' ~ _ ~ _ _ ~ _ . ~ ~

.,°,°°v ,

-...I

o

0

I

~,,

~q

zoo

400

600

Boo

! [Psi

Fig. 6. Exciton lifetimes in a) single OW d~.,,~,=50A, r= 350 ps; b) double QW dG,,~.,~ 140 .~. "~= 1 us. Open circles: GaAIAs luminescence: e!losed circles: GaAs luminescence. From ref. 15.

be weighed against the evidence of fig. 3; there, risetimes are energy dependent and near the band edge a value ~ 100 ps is observed (which is similar to the exeitz,n risetime), even w h e n cartiers are ,:x,;ited directly within the we~k Nevertheless, the data show the trend expected for confinement, but t h e case is not complete and substantial further work is required.

4. Non-radiative processes

It has already been mentioned that nonradiative effects become evident in t h e timeresoNed luminescence spectra at low excitation densities. Ryan et aI. 1"13] have studied the total luminescence lifetime over a wide range of carrier densities and obtained the result shown in fig. 7. T h e low-density ( n < 5 × 1 0 ~scm -3) lifetime is n - i n d e p e n d e n t and has a value, of 80 ps which is interpreted as a trapping, t i m e At higher densities the lifetime increases as the traps are saturated, and the lifetime approaches the bulk value, lit is "also observed that tbe total luminescence efficiency scales accurately with the m e a s u r e d lifetime. The origin and nature of the traps responsible for this effect are unknown. Interface recombination centres and residual im-

J.F. Ryan / Time.resolvedspectroscopy of quantum wells

348

60(1

ii

,o~

.......,.

EXCITE[3

C/I~RI[S O[/4$1Ty

Ic~

Fig. 7. Total luminescence decay times versus excited carrier density. From ref. 13. p u r i t i e s s u c h as c a r b o n a n d o x y g e n a r e all p o s sibilities.

5. Conclusions Time-resolved optical studies of QW structures have already given important information about hot carrier dynamics and recombination processes. Although none of the questions posed in section 1 have been answered categorically as yet, it is clear that these techniques have great potential. Only a very few structures have been examined, to date, but a very rapid extension is envisaged. References [1] C.V. Shatlk, R.L. Fork, R.F. I_.chenyand Jal~deep Shah. Phys. Roy. Lctt 42 (19'79) 112.

[2"] D. yon der Linde and R. Lambrieh, Phys. Rest. Lett, 42 (1979) 1090. [3] R.F. Lchony. Jagcleep Shah, R.L. Fork, C.V. Shank and A. Migus, Solid State Commuo 31 (1979) 809. ~4] D. Hulin, A. Antonetti, I..L Chase, J.L. Martin, A. Mig~s, A. Mysyrowicz, .I.P, Lowenau, S, Sehmitt-Rink and F1. Hang, Phys. Roy. Lctt 52 (1984) 779. IS] C.V. Shank. R. Yen, R . L Fork, J'. Orcnsteln and G.L. Baker, Phys, Roy. Lett 69 (1982} 1660. [6] C.V. Shank, R . L Fork, R. Yen, R.H, Stolen and W.J, Tomlinson. Appl. Phys. Left. 40 (1982) 761. [7] R . L Fork, B J , G~eeno and CN. Shank. Appl. Phys. Left. 38 (1982) 671. [8] Picosecond Phenomena: Springer Series in Chemical Physics vols. 4, 14, 23 (Springer, Berlin; 1978, 1980, 1982). [9] D.C. Tsui, H . L Stormer and A.C. Gessard. Phys. Rev. l.,etL 48 (1982) 1559; H.L. Smrmer, A. Chang, D.C, Tsni. J,C,M. Hwang, A.C. Gosszrd arid W. Wiegmann, P h i . Rev. Lett. 50 (1983) 1953. [101 C.V. Shank, R,L Fork, R. Yen, J. Shalh B.L Gxeeno, A.C, Gossard and C, Weisbuch. Solid State Commun. 47 (1983) 981. [11] EL. Ledeman and .;.D, Dow, Phys. Rev, B13 (1976) 1633. [12] Jagdeep Shah, Solid State Electronics 21 (1978) 43, [13] J.F. Ryan. R.A. Taylor, A J . Tarberfield. A. MaeJal. J.M. Worloek, A.C. Gossard and W. Wi,,'gmann, to he pttbli~hed, [14.] E,O. G~bel and O. Hildebrand, Phys. Stat. Sol. (b) 88 (1978) 64-5. [15] E.O. G~bel, H. Jang, J. Kuhl and K. PIoog, Phys. Rev. Lett 51 (1.983) 1588. [16] J.E Ryan, R.A. Taylor, A.J. Turbertield, A. Maeiel, J.M. Worlock. A.C. Gossard and W. Wiegmar, n, to he published. [17] R.C. Miller. D,A, Kleinman, W.T. Tsang and A.C. GOssard, Phys. Reg, B 24 (1981) 1134.