Fermi sea shake-up in quantum well luminescence spectra

Solid-State Electronics Vol. 37, Nos 4-6, pp. 825-829, 1994

Copyright © 1994ElsevierScienceLtd Printed in Great Britain.All rights reserved 0038-1101/94 $6.00+0.00

Pergamon

FERMI SEA SHAKE-UP IN QUANTUM WELL LUMINESCENCE SPECTRA M. S. SKOLNICK 2, K. J. NASH 2, D. J. MOWBRAY l, M. K. SAKER 2, T. A. FISHER l, D. M. WHITTAKER I, D. W. PEGGS~, N. MIURA 3, S. SASAKI 3, R. S. SMITH4 and S. J. BASS2 tDepartment of Physics, University of Sheffield, Sheffield $3 7RH, England, 2DRA, St Andrew's Road, Malvern, Worcs WRI4 3PS, England, 31nstitutefor Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan and 4GEC-Marconi Materials Technology Ltd, Caswell, Towcester, Northants NN23 8EQ, England Abstract--Evidence for many body shake-up in the magneto-luminescencespectra of quantum wells is presented. Results for both lattice matched InGaAs-InP and strained layer AIGaAs-InGaAs~3aAs structures, covering a wide range of carrier densities, are presented. In all the structures coupling between shake-up and LO phonon excitations is observed. Strong enhancement of the shake-up satellite of the Ne = 1 Landau level (LL) recombination, due to resonant coupling with the N, = 0 LL is presented.

Fermi sea shake-up is a fundamental many body effect in which excitations of the Fermi sea arise during the recombination between a photocreated hole and a high density electron system[I-3]. Shakeup corresponds to the creation of an electron-hole quasi-particle pair on either side of the Fermi energy during recombination. The energy of the photon which is emitted in the presence of shake-up is lower than in its absence; the difference in the energies corresponds to the energy of the electron-hole quasiparticle pair created during shake-up. Such pair excitations across the Fermi level have a continuous range of energies and thus give rise to a broad low energy tail to recombination spectra. For this reason, until very recently[4], the only evidence for shake-up processes in semiconductor spectra was obtained from lineshape analyses[5] or from the observation of anomalously strong photoluminescence (PL) in the forbidden k _l_zgeometry in GaAs-AIGaAs quantum well (QW) spectra[6,7]. However, we have shown within the last few months that definite observations of shake-up can be obtained from the study of the PL spectra of QWs in magnetic field[4]. In magnetic field the electron states are quantized into Landau levels, with the consequence that the only possible shake-up excitations are to unfilled Landau levels (LLs) above the Fermi level. As a result the broad low energy tail in the PL spectra is transformed into a series of discrete shake-up satellites. Comparison of the zero and finite magnetic field spectra then shows that the B = 0 tail is also due to shake-up. The work of Ref. [4] was carried out from 0 to 10T on a lattice matched InGaAs-InP QW containing 1.15 x 10~ cm -2 electrons. In the present paper these results are extended up to 20T. Interaction between the shake-up satellites and LO phonon lattice excitations is observed, of very similar form to that reported recently for an A!,Ga I _,.As-ln~Ga~_ ~As-GaAs strained layer QW

containing a relatively high density (7.2 x 10It cm -2) of carriers[8,9]. New results for the strained layer QW up to higher field are also reported. Strong evidence for the enhancement of the satellites due to resonant inter-LL coupling will be presented. Finally, the satellite behaviour for the strained layer QW will be shown to be of very similar form to that observed in an InGaAs-InP QW also containing a high density of carriers (9.2 x l0 II cm-2). Details of the InGaAs-InP and A1GaAsInGaAs-GaAs samples are given in Refs [4, 8, 10]. The PL experiments were carried out at 4.2 or 2 K in either a 14 T superconducting or 20 T Bitter magnet. PL was excited with ~25 mW/cm 2 of 633 nm radiation from a He-Ne laser, dispersed by a grating spectrometer and detected using a cooled Ge photodiode. The PL spectra for the lattice-matched In0.~3Ga047As-InP (50 ,~ wide QW (nS= 1.15 x l0 N cm -2) were presented in Ref. [4] and will not be repeated here. At B = 0, the spectrum consists of a zero phonon line (ZPL) at 847.4 meV and LO phonon satellite structure in the 800-820 meV region to lower energy. Above 2.0 T the phonon satellites are resolved into contributions from the GaAs and InAslike LO modes of the InGaAs QW material and from the InP modes of the barrier. This behaviour is summarized in the fan diagram of transition energies against magnetic field shown in Fig. 1. Splitting of the ZPL into n = 0 and n = ILLs is seen with the n = 1 LL depopulating at 2.4T at a filling factor v = 2 , corresponding to n~= 1.15 x 10~ cm -2. The ZPL variation with B is replicated at 27, 33 and 43 meV to lower energy by the "InAs", "GaAs" and lnP LO modes mentioned above. In addition, lower energy Tj, /'2 and T3 shake-up satellites are visible. The T, satellites correspond to inter-Landau-level Fermi sea excitations in which an additional electron is promoted from the

825

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M.S. SKOLNICKet al.

Are = 0 state to N~ = 1, 2 or 3 higher LLs. The spacing of the T, satellites below the ZPL is close to integral multiples of ht~¢, the inter-LL separation. Closer inspection of Fig. I shows that the ZPL-T~ separation is greater than the T~-T.,, T,-T3 splittings, and that the TI energy varies in a non-linear fashion with B. The ZPL-T~ spacing (AE) can be expressed in terms of an apparent effective mass m-~, using the expression AE = h e B / m * . The variation of m ~with B is shown in the inset to Fig. I. m * varies from 0.037 m 0 at 2.3 T to 0.047 m0 at 9.6 T, close to the Q W band edge effective mass m * of 0.05 m 0 in these I n G a A s - I n P QWs[8]. This behaviour was explained in Ref. [4] by noting that the shake-up excitations correspond to inter-LL magneto-plasmon excitations of the Fermi sea. The energy of the magneto-plasmon excitations is only equal to hto¢ for in-plane wave-vector q =0111-13]. At v = I, the departure from h~o¢ of the maximum in the magnetoplasmon density of states is given by E l ~ 0.17 ve 2/d o, where 10 = (h/eB)) is the magnetic length. The factor v/lo in E 1 varies as B-½, and as a result the apparent effective mass m * is expected to tend towards m * with increasing B, as observed in the inset to Fig. 1. The Tj satellite intensities decrease with increasing B in the low field range (0-10 T). As shown in Fig. 2, T l decreases in intensity by a factor of ~ 5 from 8.5 to 10 T, where it is only barely visible with ~ 0 . 0 1 % of the intensity of the ZPL. F r o m 10.5 to 17.5 T, T~ is not observed, but it then re-appears in the 18 to 195T range, as shown in Fig. 2(c). For B > 17T, T 1 is at lower energy than the LO phonon satellites (see

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Figs 1 and 2). Its re-appearance in the high field range arises from resonant mixing between T~ and the much stronger LO phonon satellites of the ZPL. Very similar resonant interactions are discussed below for the high density A I G a A s - I n G a A s - G a A s and InG a A s - I n P QWs. In those cases the resonant interactions are observed at much lower field since higher LLs are populated to relatively higher fields. As a result the LO phonon satellites of n/> l LLs interact with the T, satellites at lower magnetic field. The B = 0PL spectrum of the strained layer AlvGa ~_,,As-InxGa ~_xAs-GaAs (y ~ 0.23, x ~ 0.10)150 A wide Q W with ns = 7.2 x 10u c m - : (EF = 25.4 meV) is shown in Fig. 3(a). It consists of a peak at !.417 eV, corresponding to recombination of electrons at q = 0 at the bottom of the Q W conduction band, together with a broad high energy tail extending to the electron Fermi energy at E~. The q ~ 0 transitions up to the Fermi wavevector (2 x 106cm -~) are made allowed by the weak disorder in the system. In magnetic field the spectrum breaks up into LL transitions (N~,Nh). At 10 T (v = 3) only the N c = 0 and 1 LLs are populated. Recombination of N~ = ! electrons with holes in both the N h = 0, I L L s is observed due to the non-thermal distribution of the photo-created holes. The intensity of the N e = 1 transitions decreases with increasing field from 10 to 14 T [Fig. 3(b) to (e)] as the Nc = 1 LL depopulates towards v = 2 (14.9T). To lower energy below the (0,0) principal recombination line T, shake up satellites and N L LO phonon satellites of the Are'th LL are observed. These results are summarized in the fan diagram of Fig. 4. Spectra below 10 T were presented in Ref. [7], together with a discussion of oscillations

Fermi sea shake-up in quantum well luminescence spectra of intensity of the NL satellites with B which occur at crossing points with the 7", satellites. In the present paper we will concentrate on the new results above 10T, in particular the resonant anticrossing between ! L and T~ in the 9 to 13 T region and the behaviour of the T ~' feature with B. As for the I n G a A s - I n P sample of Figs 1 and 2 the (0,0)-T~ separation is greater than ht~c. The dashed line representing the variation of the T~ energy with B is drawn at an energy of 1.25 ho9c, with the corresponding T2 and T3 energies at 2.25 and 3.25 hto¢ below (0,0)

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Fig. 3. PL spectra at B =0, 10, 11, 12 and 14T in Fig. 3(a)-(e) for AlGaAs-InGaAs-GaAs 150A wide, modulation doped strained layer quantum well. Landau level transitions (N,, NL) are observed in Fig. 3(b)--(e), with Ti shake-up and IL, 0L LO phonon satellite lines to lower energy. The resonant exchange of intensities between 1Land T~ in the l I - 1 2 T region is seen in Fig. 3(c) and (d). Away from resonance the LO phonon 1L line is the dominant satellite. The inset shows the variation of the intensity of T~', the shake-up satellite of (1,0), relative to that of (i,0). The near constant intensity ratio of T ~*/(1,0) shows that T is a satellite of (1,0), resonantly enhanced by interaction with (0,0).

827

as expected from the magneto-plasmon theory of Kallin and Halperin[ll,4,8]. For this sample the variation of the T~ energy with B is strongly perturbed by resonant anticrossings with the N L satellites, thus precluding any determination of the variation of the departure of the Tr(O,O) energy from a linear variation with B (equivalent to the variation of m ~- with B in the inset to Fig. l). The resonant interaction between 1L and T~ is clearly seen in the fan diagram of Fig. 4, where anti-crossing is observed in the 9-14 T region. Away from resonance the I L satellite is dominant, as seen in the spectra of Fig. 3(b, c) at l0 and 14 T, respectively. In the intermediate region T~ gains intensity due to resonant mixing with 1L, with the two satellites having equal intensity at l l . 5 T. The variation of intensities between the two sides of the resonance is shown in the l l and 12T spectra of Fig. 3(c,d) respectively. The variation of the intensity of T ~' the low energy shoulder ~ 5 meV below (0,0) at 10 T is particularly interesting. In Ref. [8], this feature was tentatively ascribed to a shake-up satellite of (1,0) enhanced in intensity by resonant mixing with (0,0). This attribution is given strong support by the higher field data presented in the inset to Fig. 4, where the intensity of T ~' relative to that of the (1,0) transition is presented. If T* is a satellite of (1,0), the ratio of the two intensities is expected to be a constant, independent of magnetic field. This is exactly the behaviour observed in the inset to Fig. 4, where the intensity ratio of ~7.5 is seen to vary by less than 15% from 9 to 14T (v = 3.3-2.1). This observation provides strong support to the attribution of the T* feature to shake-up satellite of (1,0). The shake-up excitation corresponds to the promotion of an additional electron from N e = 0 to N e = 1. T* occurs ~1.3 htac below (1,0) consistent with the separation observed between (0,0) and T~, as required since both T~ and T ? arise from ANe = i inter-LL excitations. The high intensity of T~ relative to (1,0) is also noteworthy. (I,0) is relatively weak compared to (0,0), even when N~ = i is filled at 7.4 T (v = 4), since (1,0) is a ANe = 1 transition observed only due to the presence of weak disorder in the system[14]. T~' is ,-, 7.5 times stronger than its parent line (1,0) since it is nearly degenerate with the d o m i n a n t recombination transition (0,0), and is strongly enhanced in intensity by resonant mixing with (0,0). Finally, we describe briefly magneto-PL results for an I n G a A s - I n P QW with high ns of 9.2 x 10 n cm -2, which shows very similar LO p h o n o n and shake-up satellites to those described above for the AiG a A s - I n G a A s - G a A s structure. This sample exhibits a strong Fermi energy edge singularity[15] in its PL spectrum, due to the strong localization of photocreated holes in alloy fluctuations in the I n G a A s QW. This contrasts with the behaviour for the more perfect AIGaAs-InGaAs--GaAs QW of Figs 3 and 4 where only a weak feature at E F is observed in

828

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Fig. 4. Transition energies against magnetic field for AIGaAs-InGaAs~aAs quantum well. LL filling factors (v) are indicated. The dashed lines to indicate the shake-up transitions (T~, T:, T3) are drawn at energies 1.25h~¢, 2.25 hco~, 3.25 hto¢ below (0,0). The fields indicated by the indices in the lower part of the figure correspond to the crossing points of T~ with the N~ satellites, at fields corresponding to the resonance condition (m + 0.25)h~o~= ho~to, as discussed in Ref.[7]. Fig. 3(a). In this paper we present only the variation of the transition energies against magnetic field, a discussion of the spectra in the satellite region being reserved for a separate publication. PL spectra for the principal LL transitions up to 10 T can be found in Ref. [10]. The transition energies against magnetic field are shown in Fig. 5. An # 0 LL transitions (N~,0) are observed for Are from 0 to 8. The straight lines through the experimental points correspond to (N, + ½) hco¢ variations with m * = 0.05 m0[10]. Two points in particular should be noted concerning the (N~, 0) transitions. Firstly, the main transitions exhibit oscillations around the linear (N~ + ½) hco¢ variation as a function of filling factor. These oscillations have been attributed to oscillations of exchange and correlation energies or to variations in the self-consistent potential with filling factor[16-18]. Secondly, the (3,0), (2,0) and (1,0) transition energies deviate to lower energy below the linear fits as soon as the respective LL begins to empty with increasing B [e.g. (I,0) above v = 4 where N~ = 1 begins to empty][19]. This deviation probably arises due to the finite width of the distribution of LL energies. As the filling factor is reduced, recombination from the tail of the broadened distribution dominates the PL spectrum to a progressively greater extent, with the result that the observed LL transition energies deviate increasingly below (N~ + ½) ho9,:. To lower energy, NL LO phonon satellites and T~ shake-up satellites are observed, in a very similar manner to that reported in Figs 3 and 4. The dominant LO phonon satellites 2 L, 1L and 0 L arise from the

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33 meV GaAs-like LO p h o n o n modes of the l n G a A s QW, as seen for the low density l n G a A s - I n P Q W in Figs I and 2. The satellite labelled IA arises 43 meV below the (!,0) transition and is due to emission of an InP barrier LO phonon (the InP LO phonon energy is 43 meV). The attribution of 1A to an LO p h o n o n satellite of (1,0) is supported by the very similar intensity variation of lg and (1,0) with field as N, = 1 depopulates towards v = 2. The straight lines representing the Tj and ~ transitions which give the best fits to the experimental points, are drawn hco¢ and 2hco~ below the (0,0) energies. The difference between these splittings and the 1.25 hto¢, 2.5 hco¢ splittings of Fig. 4 may arise from the greater distribution of Landau level energies in this case, as shown already by the departure below (N~ + ½) hco~ of the (N~,0) transitions for partially filled LLs. The results for the principal (N,,0) transitions show that tail states dominant the recombination for small LL filling; such a distribution of LL energies may also perturb the observed shake-up energies and thus lead to the ~hco¢ and ~ 2 hco¢ energies observed. As discussed for the strained layer QW of Fig. 4, anti-crossing between the LO phonon and shake-up satellites is observed in Fig. 5, between the 0L and T t satellites from 12 to 19 T. The splitting of the two branches at resonance is 10meV, fairly

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Fermi sea shake-up in quantum well luminescence spectra close to t h a t observed for the T~, I t anti-crossing of Figs 3 and 4. In conclusion, shake-up a n d LO p h o n o n satellites in the m a g n e t o - P L spectra o f lattice m a t c h e d a n d strained Q W structures covering a wide range of carrier density have been presented. I n t e r a c t i o n between the Fermi-sea a n d lattice excitations has been observed in all the samples investigated. E n h a n c e m e n t of the shake-up satellite intensity by r e s o n a n t coupling with the d o m i n a n t Are = 0 LL r e c o m b i n a t i o n line has been d e m o n s t r a t e d .

Acknowledgement--We thank J. C. Maan for collaboration at the Max Planck Institut, Grenoble where the experiments up to 20 T were carried out.

REFERENCES

1. See e.g., G. D. Mahan Many Particle Physics, Chap. 8. Plenum Press, New York (1990). 2. Y. A. Byshkov and E. I. Rashba. Zh Eksp Teor Fiz. 96, 757 (1989) [Sot. Phys JETP 69, 430 (1989)]. 3. T. Uenoyama and L. 1. Sham. Phys. Rer. Lett. 65, 1048 (1990). 4. K.J. Nash, M. S. Skolnick, M. K. Saker and S. J. Bass, Phys. Rev. Lett. 70, 3115 (1993). 5. See, for example, J. H. Collet, W. W. Ruhle, M. Pugnet, K. Leo and A. Million, Phys. Rer. B 40, 12296 (1989) and references therein.

829

6. R. Sooryakumar, A. Pinczuk, A. C. Gossard, D. S. Chemta and L. J. Sham, Phys. Rer. Lett. 58, 1150 (1987). 7. G. D. Sanders and Y. C. Chang, Phys. Rer. B 32, 5521 (1985). 8. M. S. Skolnick, D. J. Mowbray, D. M. Whittaker and R. S. Smith, Phys. R~. B 47, 6823 (1993). 9. Similar interaction phenomena between LO phonon and shake-up satellites has also been reported by L. V. Butov, V. I. Grinev. V. D. Kulakovskii and T. G. Andersson, Phys. Rer. B 46, 13627 (1992). 10. M. S. Skolnick, K. J. Nash, S. J. Bass, P. E. Simmonds and M. J. Kane, Solid State Commun. 67, 637 (1988). I 1. C. Kallin and B. Halperin, Phys. Ret,. B 31, 3635 (1985). 12. A. H. Macdonald, J. Phys. C18, 1003 (1985). 13. A. Pinczuk, J. Valladares. D. Heiman, A. C. Gossard, J. H. English, C. W. Tu, L. Pfeiffer and K. West. Phys. Rer. Lett. 61, 2701 (1988). 14. At 10 T, the ratio of the (1,0) to (0,0) intensity is 1: 20. 15. M. S. Skolnick, J. M. Rorison, K. J. Nash, D. J. Mowbray, P. R. Tapster, S. J. Bass and A. D. Pitt. Phys. Rer. Lett. 58, 2130 (1987). 16. S. Katayama and T. Ando, Solid State Commun. 70, 97 (1989). 17. T. Uenoyama and L. J. Sham, Phys. Rev. B39, 11044 (1989). 18. R. Stepniewski, W. Knap, A. Raymond, G. Martinez, T. Rotger, J. C. Maan and J. P. Andre. In High Magnetic Fields in Semiconductor Physics (Edited by G. Landwehr), p. 62. Springer-Verlag, Berlin (1989). 19. Similar but smaller deviations of the (1,0) and (2,0) transitions from linearity when the N, = 1 and 2 LLs are partially filled, are visible in Fig. 3.