- Email: [email protected]
Magneto-optics on single quantum dots
Physica B 298 (2001) 239}245
Magneto-optics on single quantum dots A. Zrenner*, F. Findeis, M. Baier, M. Bichler, G. Abstreiter Walter Schottky Institut, Technische Universita( t Mu( nchen, Am Coulombwall, D-85748 Garching, Germany
Abstract We report about magneto-optical experiments on single self-assembled InGaAs quantum dots. In the "rst part of our contribution we concentrate on phonon assisted absorption studied by photoluminescence excitation spectroscopy. We observe phonon assisted absorption via InGaAs and GaAs LO phonons, as well as sequential phonon assisted biexciton generation followed by sequential biexciton decay. The magnetic "eld dependence of the observed phonon resonances exhibits distinct di!erences between exciton and biexciton lines, which are caused by spin conservation and decay statistics. In the second part, we report about controlled single electron charging of a single quantum dot investigated by magneto-photoluminescence spectroscopy on electric "eld tunable structures. We observe the emission lines of neutral, single, and double charged exciton states for di!erent bias conditions. The application of high magnetic "elds results in fully resolved Zeeman splittings and diamagnetic shifts. The upper Zeeman component of the single charged exciton is found to be quenched at higher electric "elds. This behavior is explained in terms of an enhanced tunneling probability of the triplet versus the singlet con"guration. 2001 Elsevier Science B.V. All rights reserved. PACS: 78.55.!m; 78.66.Fd; 73.23.!b; 78.60.Hk; 85.30.V Keywords: Quantum dots; Magneto-optics; Phonons; Charged excitons
1. Introduction A lot of interest is currently focused on semiconductor quantum dots (QDs), which are often referred to as arti"cial atoms. Self-assembled QDs formed by Stranski}Krastanow growth belong to the most promising and most widely studied systems today (see for example Ref. [1] for review). As almost defect free, coherently strained islands with large band o!set to the surrounding matrix material, they are interesting systems both for basic research and future device applications. * Corresponding author. Tel.: #49-89-289-12772; fax: #4989-320-6620. E-mail address: [email protected] (A. Zrenner).
In optical experiments the emission spectra of self-assembled QDs typically consist of various groups of peaks, which correspond to optically allowed transitions between di!erent shells with equal principal quantum numbers n (n"1, 2, 2"s, p, 2). In a simple picture the single particle spectrum of self-assembled QDs can be described by transitions between those Fock}Darwin levels in the conduction and valence band, as sketched in Fig. 1a [2]. For disc-shaped QDs with parabolic con"nement potential, the degeneracy in each shell is given by 2n. Since the single particle energy spacing in selfassembled QDs is comparable to typical Coulomb energies in the system, distinct and fundamental modi"cations to the single particle model are
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 0 3 1 0 - 6
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Fig. 1. (a) Schematic view of a QD shell structure. The QD is shown for the condition of completely "lled s-shells (biexciton); (b) typical arrangement for optical access to a single QD by means of a metallic shadow mask.
observed as the number of electrons and holes in the QD is increased [3}8]. Di!erent neutral occupancies in the QD can be obtained by power dependent optical excitation. The associated few particle states have been intensively studied in the past years by multi-exciton photoluminescence (PL) spectroscopy and corresponding theoretical investigations. In the current contribution, we report our results on two new and related problems in the "eld of single QD spectroscopy. In the following section we discuss the in#uence of phonons on the absorption properties of QDs. Finally, we present our results on charged occupancies in a single QD.
2. Phonon assisted absorption The bare eigenstates of `emptya QDs can be inferred by PL-excitation spectroscopy (PLE) or related methods like photocurrent spectroscopy. Results on QD ensembles and single self-assembled QDs show the expected, resonant absorption from higher shells, but also comparably strong phonon assisted absorption lines [9}11]. The enhancement of the phonon coupling was recently investigated for both intraband [12] and interband [13,14] processes in QDs. We performed our experiments on an In Ga As QD, which was optically accessed by a low temperature confocal microscope via an Al-shadow mask as indicated in Fig. 1b. Further details on the sample under investigation can be found elsewhere [15]. In the following, we concentrate on the phonon assisted absorption processes
Fig. 2. MPLE overview spectrum of a single self-assembled In Ga As QD under high excitation conditions. It covers excitation energy between the QD and the 2D wetting layer (WL). The many bodylines vanish below the WL absorption edge and strong phonon resonances appear on the 1X line. Even on the biexciton line 2X weak resonances can be seen. A basic energy diagram for phonon assisted absorption is shown in the inset.
of a single InGaAs QD with a ground state energy of 1320 meV. Corresponding data are shown in Fig. 2. The displayed energy range covers the GaAs LO phonon resonance at about 1356 meV for the single exciton (1X) and biexciton (2X) line. In such multichannel-PLE data (MPLE), PL-spectra are contained along the x-axis for each resonant excitation energy displayed on the y-axis, whereas PLEdata is contained along the y-axis for each detection energy displayed on the x-axis. The most important features in the MPLE spectra are the sharp absorption resonances, which appear on decrease of the laser energy from 1360 to 1352 meV. Those resonances are found at laser energies of 1356 and 1360 meV, above the PL energy of the single exciton ground state E of the investigated QD at .* 6 1320 meV. With respect to the ground state the corresponding resonance energies (E !E ) * .* 6 appear at 32, 36 and 40 meV. The strongest peak is detected at a resonance energy of 36 meV, matching nicely the GaAs LO phonon energy within the accuracy of our measurement. A weaker resonance at 32 meV is assigned to an InGaAs phonon mode related with the QD. Phonon assisted absorption, as observed here, is schematically sketched in the
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inset of Fig. 2. The resonance around 40 meV falls into the region of the QD d-shell of the investigated QD and shows a doublet "ne structure which would be expected for a slightly asymmetric QD shape. As shown in Fig. 3a and b and discussed more in detail further on, the most intense resonances on the 1X line are observed also on the 2X line. Between the resonances a weak continuum like absorption is observed as a function of excitation energy. Such a background absorption has also been reported by other groups for single selfassembled QDs [16]. In Fig. 3a and b, we discuss MPLE data of the 1X and 2X GaAs LO phonon resonance peaks for B"0 T and B"12 T. With increasing magnetic "eld (not shown), we observe for both lines a pure diamagnetic shift of 8.3 eV/T and a Zeeman splitting of 104 eV/T, as expected for s-shell states of a QD with zero angular momentum. Phonon resonances lead to a constant o!set between absorption and emission energy independent of magnetic "eld. For the GaAs LO phonon resonance we get a variation in energy o!set of only 0.2 meV for "ve di!erent magnetic "elds. Since the GaAs LO energy is constant as a function of magnetic "eld, but the energies of both Zeeman components change, the resonance conditions for the laser excitation energies have to change as well. This magnetic "eld induced detuning of the resonance condition results in a twofold, diagonal splitting of the 1X GaAs LO phonon resonance with exact amount of the Zeeman energy E . 8 The observed diagonal splitting of the resonance conditions in the MPLE plot is a consequence of exciton spin conservation during the phonon assisted absorption process and the successive recombination process (see Fig. 3b). So far we only discussed the resonances of the 1X line, where one exciton at a time is generated and annihilated in the QD. However, there are additional features contained in the MPLE data shown in Fig. 3a and b, which clearly go beyond this scenario. In particular we "nd, that for all resonant laser energies which lead to strong emission on the 1X line, also weaker emissions appear at the position of the biexciton line 2X. The above described twofold, diagonal splitting of the 1X resonance at "nite magnetic "elds leads therefore to a fourfold,
241
Fig. 3. Multi-channel PLE spectra from a single quantum dot in the region of the LO-phonon assisted absorption for B"0 T (a) and B"12 T (b). The resonance energies on the single exciton line 1X show Zeeman splitting and diamagnetic shift, but the resonance energies with respect to the ground state remain una!ected by magnetic "eld. The weaker biexciton resonances 2X show a distinctly di!erent behavior. (c) Model for sequential LO-phonon assisted generation of a biexciton (1, 2) and the following decay (3, 4) as described in the text.
symmetrical splitting of the 2X resonance. Based on the observation that the marked GaAs-LO resonance in the 1X PLE spectrum is observed also in the 2X PLE spectrum, we discuss now a model for
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sequential phonon assisted generation of a biexciton and the following sequential decay in Fig. 3c. For the resonant laser energy E " (1), an * * exciton with energy E in the QD and a phonon 6 with energy E are generated at a "xed rate. As *long as the dot is occupied with one exciton, successive transitions should be renormalized by the amount of the biexciton binding energy and hence, blocked at the given excitation energy. However, for unchanged excitation energy E " (2), * * a second exciton (with opposite spin) can be generated by absorption under participation of a di!erent phonon with energy E #E , where E *6 6 is the biexciton binding energy. This second absorption process, generating the biexciton with energy E #E in the QD, is enabled by the 6 6 previously discussed weak background absorption. Each absorption process leading from the single to the two exciton state can contribute here and does not have to be phonon assisted in general. The biexciton decays sequentially and we expect "rst the emission of a photon at the position of the 2X line at E" (3) followed by the 1X emission at 6 E" (4). As a function of magnetic "eld the 2X 6 resonance performs a fourfold, symmetric splitting (marked in Fig. 3b) in contrast to the twofold, diagonal splitting of the 1X resonances. This behavior "rmly con"rms the above discussed model of sequential phonon assisted generation of a biexciton and the following sequential decay. Each of the Zeeman components of the 1X resonance can be a starting point for biexciton generation, resulting after the second phonon assisted absorption process of course in the same biexciton eigenstate. Now two excitons with opposite spin orientations are in the QD, whose statistic probability for radiative decay is the same. Depending on which of them decays "rst, either the or the compo nent of the 2X line is observed. This means that independent of the "rst absorbed spin orientation (upper or lower Zeeman-branch of the 1X phonon resonance), both Zeeman-levels of the 2X line are observed with the same probability. Hence we obtain a fourfold, symmetric splitting for a 2X resonance, which is unambiguously connected with the phonon assisted sequential generation and decay of a biexciton state. Related results in terms of equally strong biexciton Zeeman components under the
condition of strongly spin polarized exciton injection have already been observed previously in QDs formed by well width #uctuations [17].
3. Charged excitons Di!erent occupation numbers for electrons and holes result in charged exciton complexes. In analogy to QDs with neutral occupancy } arti,cial atoms, charged exciton complexes may be considered as artixcial ions. Charged excitons have been studied in ensembles of QDs by PL [18] as well as in interband transmission experiments [19] and recently also in single quantum rings by PL [20]. Theoretical analyses of few-particle e!ects in optical spectra predict binding energies for charged excitons in the order of some meV [21}23]. Here, we report on charging of a single InGaAs QD in a controlled way with an increasing number of electrons probed by magneto-PL. For controlled charging of individual QDs, a special electric "eld tunable n}i structure has been grown by molecular beam epitaxy. The In Ga As QDs are embedded in an i-GaAs region 40 nm above the n-doped GaAs layer (5;10 cm\). The growth of the QDs is followed by 270 nm i-GaAs, a 40 nm thick Al Ga As blocking layer, and a 10 nm i-GaAs cap layer. As a top Schottky gate we use a 5 nm thick semitransparent Ti layer (T+50%). The samples were processed as photodiodes combined with electron beam structured shadow masks with apertures ranging from 200 to 800 nm. Schematic overviews of the sample arrangement and the band diagram are shown in Fig. 4a and b. The occupation of the QD with electrons can be controlled by applying an external bias voltage V on the Schottky gate with respect to the back contact. For positive V , the band #attens and the electron levels of the QD are dipped into the Fermi sea of the n-GaAs back contact. In our experiments excitons are generated optically at low rate, relax into the QD, and form charged excitons together with the V induced extra electrons. We used a HeNe laser (632.8 nm) for optical excitation and a cooled CCD camera for detection of the PL. The sample was mounted in
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Fig. 4. (a) Photodiode combined with a near "eld shadow mask; (b) schematic band diagram of the structure for zero bias.
a confocal low-temperature microscope (see Ref. [24] for details). In Fig. 5a and b, we present PL spectra as a function of V in the range of !550 to #400 mV with respect to the back contact corresponding to electric "elds of 37.5 to 11.1 kV/cm. The PL intensity is displayed as gray scale plot for B"0 T in Fig. 5a and for B"12 T in Fig. 5b. As a function of V we "nd a series of lines with discrete jumps in the emission energy. These lines can be assigned to emissions from s-shell transitions of X, X\ and X\ (marked in Fig. 5a and b) as discussed more in detail further on starting with B"0 T. For large negative < (< (!0.5 V) the electron levels are far above the Fermi energy and the QD is neutral. Optically generated excitons can relax into the QD, but before radiative recombination (+1 ns), the carriers tunnel out of the QD due to the high applied electric "eld and PL emission is quenched. For V "!0.5 V the QD is still uncharged, but in the smaller electric "eld radiative recombination gets more likely and the X emission line appears at 1307 meV. In fact this line is a doublet with a weak sideline separated by about 0.4 meV attributed to an asymmetric shape of the QD [25].
Fig. 5. Gray scale plot of PL intensity as a function of PL energy and < . The series of lines can be assigned to emissions from s-shell transitions of X, X\ and X\. At zero magnetic "eld (a) and at B"12 T (b).
With increasing V , the X line shifts to higher energies due to the quantum con"ned Stark e!ect in the decreasing electric "eld. For V "!0.35 V a new emission line appears below the X line at 1302.5 meV, indicating the occupation of the QD by the "rst electron. The X\ binding energy with respect to the X is determined to be E \ "4.6 meV by the measured di!erence in 6 emission energies. For !0.35 V(< (0 V, the X and the X\ lines coexist, which is a consequence of the statistical nature of non-resonant optical excitation. In the presence of one extra electron, the capture and subsequent decay of an electron hole pair leads to the emission of a X\ photon. If only a single hole is captured we expect a X photon, and if a single electron is captured we expect no photon but electron back transfer to the n> region. In the PL experiment we average over a time
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interval of 40 s, hence, we collect X\ as well as X photons. At < "0 V the QD is charged with a second electron, leading to a further small red shift of the main emission line, but also to the appearance of an additional weaker line at 1298.1 meV. This additional line, 4.6 meV below the main line, is characteristic for the X\ decay. The energy di!erence between the two X\ lines corresponds to the difference in the s}p exchange energies between the two possible "nal states with parallel or antiparallel spin orientation of the two remaining electrons [21]. Again X\ and X\ can be observed simultaneously over a certain range in < . At < '0.19 V, only one broad emission line remains. This indicates the "lling of the wetting layer (WL) states with electrons. Here, in the x}y plane weakly con"ned electrons are interacting with only one hole in the QD causing a broadening of the detected s-shell decay in the QD. A rough estimation of the external voltage needed to bring the WL states below the Fermi energy, taking charging energy and the electrostatics of the structure into account, results in a reasonable value of 531 mV. From the inset of the X\ line to the inset of the broadened emission we measure < +540 mV. Finally, we discuss the magnetic "eld dependence of the neutral and charged excitons. Corresponding data for B"12 T are shown in Fig. 5b. From comparison of the B"0 T data shown in Fig. 5a, it is clear that single electron charging versus V is mostly una!ected by magnetic "eld. The centers of s-shell emission for X, X\, and X\ are shifted to higher energies due to diamagnetic shift and each emission line splits into two lines, separated by the Zeeman energy. In Fig. 6 we show an overview of the Zeeman splittings and diamagnetic shifts observed for X, X\, and X\ as a function of magnetic "eld. The observed weak di!erences between the Zeeman energies of the neutral and charged excitons seem to indicate, that the spin orientation of extra charges in the QD does not change during the radiative decay from the s-shell. Taking a closer look on the high magnetic "eld data shown in Fig. 5b some more features attract attention. Within the scope of this contribution we concentrate here only on the experimentally
Fig. 6. Diamagnetic shift of the X, X\, and X\ line as a function of magnetic "eld. Inset: Zeeman splitting of the X, X\, and X\ line as a function of magnetic "eld.
observed asymmetry in the PL-intensity of the two Zeeman branches of the X\ line for !0.35 V(< (!0.13 V. This phenomenon is observed only for the X\ line, not for the X and X\ lines. The explanation of this phenomenon involves spin polarization, Pauli blocking, and state selective tunneling as summarized in Fig. 7a and b. At B"12 T a single electron in a QD is spin polarized in thermal equilibrium. The optical excitation of (bright) excitons can happen with two di!erent spin orientations, which results in the charged exciton states shown in Fig. 7a and b. Due to Pauli blocking in the conduction band, parallel electron spin orientation results in a metastable triplet state with one electron in the s-shell and one in the p-shell (see Fig. 7a). If the tunneling time from the p-shell is shorter as the electron spin #ip time (which is expected for the applied V ), an electron is lost and we end up with a neutral exciton and hence with a contribution to one Zeeman component of the X line, i.e. we loose one Zeeman component of the X\ line. The introduction of an exciton with opposite spin orientation however produces a singlet state as shown in Fig. 7b. Radiative decay of this con"guration results in a contribution to the other Zeeman component of the X\ line. Which of the Zeeman levels will be on the low energy side is an issue of sign and magnitude of the associated electron and hole g-factors, which
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Fig. 7. X\ triplet (a) and singlet (b) con"gurations. The triplet state is subjected to tunnel decay from the p-shell.
are (independently and for the present structure) unknown so far. Our "ndings also imply that the associated heavy hole spin #ip time should be at least of the same order or longer than the e}h lifetime.
4. Summary In summary, we have studied phonon assisted processes and controlled single electron charging in single InGaAs QDs by spatially resolved magnetooptic techniques.
Acknowledgements This work was supported "nancially by the Deutsche Forschungsgemeinschaft via SFB 348 and by the BMBF via 01BM917. References [1] A. Zrenner, J. Chem. Phys. 112 (2000) 7790. [2] V. Fock, Z. Phys. 47 (1928) 446. [3] E. Deckel, D. Gershoni, E. Ehrenfreund, D. Spector, J.M. Garcia, P.M. Petro!, Phys. Rev. Lett. 80 (1998) 4991.
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[4] L. Landin, M.S. Miller, M.-E. Pistol, C.E. Pryor, L. Samuelson, Science 280 (1998) 262. [5] F. Findeis, A. Zrenner, G. BoK hm, G. Abstreiter, Solid State Commun. 114 (2000) 227. [6] P. Hawrylak, Phys. Rev. B 60 (1999) 5597. [7] U. Hohenester, F. Rossi, E. Molinari, Solid State Commun. 111 (1999) 187. [8] M. Bayer, O. Stern, P. Hawrylak, S. Fafard, A. Forchel, Nature 405 (2000) 923. [9] S. Fafard, R. Leon, D. Leonard, J.L. Merz, P.M. Petro!, Phys. Rev. B 52 (1995) 5752. [10] R. Heitz, M. Veit, N.N. Ledentsov, A. Ho!mann, D. Bimberg, V.M. Ustinov, P.S. Kop'ev, Zh.I. Alferov, Phys. Rev. B 56 (1997) 10435. [11] A. Zrenner, M. Markmann, E. Beham, F. Findeis, G. BoK hm, G. Abstreiter, J. Electron. Mater. 28 (1999) 542. [12] S. Hameau, Y. Guldner, O. Verzelen, R. Ferreira, G. Bastard, J. Zeman, A. Lemam( tre, J.M. Ge`rard, Phys. Rev. Lett. 83 (1999) 4152. [13] R. Heitz, I. Mukhametzhanov, O. Stier, A. Madhukar, D. Bimberg, Phys. Rev. Lett. 83 (1999) 4654. [14] V.M. Fomin, V.N. Gladilin, S.N. Klimin, J.T. Devreese, P.M. Koenraad, J.H. Wolter, Phys. Rev. B 61 (2000) R2436. [15] F. Findeis, A. Zrenner, G. BoK hm, G. Abstreiter, Phys. Rev. B 61 (2000) R10579. [16] Y. Toda, O. Moriwaki, M. Nishioka, Y. Arakawa, Phys. Rev. Lett. 82 (1999) 4114. [17] A. Schaller, A. Zrenner, G. Abstreiter, G. BoK hm, Physica E 2 (1998) 609. [18] K.H. Schmidt, G. Medeiros-Ribeiro, P.M. Petro!, Phys. Rev. B 58 (1998) 3597. [19] R.J. Warburton, C.S. DuK rr, K. Karrai, J.P. Kotthaus, G. Medeiros-Ribeiro, P.M. Petro!, Phys. Rev. Lett. 79 (1997) 5282. [20] R.J. Warburton, C. SchaK #ein, D. Haft, F. Bickel, A. Lorke, K. Karrai, J.M. Garcia, W. Schoenfeld, P. Petro!, Nature 405 (2000) 926. [21] A. Wojs, P. Hawrylak, Phys. Rev. B 55 (1997) 13066. [22] A. Hartmann, Y. Ducommun, E. Kapon, U. Hohenester, C. Simserides, E. Molinari, Phys. Stat. Sol. A 178 (2000) 283. [23] G.A. Narvaez, P. Hawrylak, Phys. Rev. B 61 (2000) 13753. [24] A. Zrenner, M. Markmann, A. Paassen, A.-L. Efros, M. Bichler, W. Wegscheider, G. BoK hm, G. Abstreiter, Physica B 256}258 (1998) 300. [25] D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, D. Park, Phys. Rev. Lett. 76 (1996) 3005.
Magneto-optics on single quantum dots A. Zrenner*, F. Findeis, M. Baier, M. Bichler, G. Abstreiter Walter Schottky Institut, Technische Universita( t Mu( nchen, Am Coulombwall, D-85748 Garching, Germany
Abstract We report about magneto-optical experiments on single self-assembled InGaAs quantum dots. In the "rst part of our contribution we concentrate on phonon assisted absorption studied by photoluminescence excitation spectroscopy. We observe phonon assisted absorption via InGaAs and GaAs LO phonons, as well as sequential phonon assisted biexciton generation followed by sequential biexciton decay. The magnetic "eld dependence of the observed phonon resonances exhibits distinct di!erences between exciton and biexciton lines, which are caused by spin conservation and decay statistics. In the second part, we report about controlled single electron charging of a single quantum dot investigated by magneto-photoluminescence spectroscopy on electric "eld tunable structures. We observe the emission lines of neutral, single, and double charged exciton states for di!erent bias conditions. The application of high magnetic "elds results in fully resolved Zeeman splittings and diamagnetic shifts. The upper Zeeman component of the single charged exciton is found to be quenched at higher electric "elds. This behavior is explained in terms of an enhanced tunneling probability of the triplet versus the singlet con"guration. 2001 Elsevier Science B.V. All rights reserved. PACS: 78.55.!m; 78.66.Fd; 73.23.!b; 78.60.Hk; 85.30.V Keywords: Quantum dots; Magneto-optics; Phonons; Charged excitons
1. Introduction A lot of interest is currently focused on semiconductor quantum dots (QDs), which are often referred to as arti"cial atoms. Self-assembled QDs formed by Stranski}Krastanow growth belong to the most promising and most widely studied systems today (see for example Ref. [1] for review). As almost defect free, coherently strained islands with large band o!set to the surrounding matrix material, they are interesting systems both for basic research and future device applications. * Corresponding author. Tel.: #49-89-289-12772; fax: #4989-320-6620. E-mail address: [email protected] (A. Zrenner).
In optical experiments the emission spectra of self-assembled QDs typically consist of various groups of peaks, which correspond to optically allowed transitions between di!erent shells with equal principal quantum numbers n (n"1, 2, 2"s, p, 2). In a simple picture the single particle spectrum of self-assembled QDs can be described by transitions between those Fock}Darwin levels in the conduction and valence band, as sketched in Fig. 1a [2]. For disc-shaped QDs with parabolic con"nement potential, the degeneracy in each shell is given by 2n. Since the single particle energy spacing in selfassembled QDs is comparable to typical Coulomb energies in the system, distinct and fundamental modi"cations to the single particle model are
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 0 3 1 0 - 6
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Fig. 1. (a) Schematic view of a QD shell structure. The QD is shown for the condition of completely "lled s-shells (biexciton); (b) typical arrangement for optical access to a single QD by means of a metallic shadow mask.
observed as the number of electrons and holes in the QD is increased [3}8]. Di!erent neutral occupancies in the QD can be obtained by power dependent optical excitation. The associated few particle states have been intensively studied in the past years by multi-exciton photoluminescence (PL) spectroscopy and corresponding theoretical investigations. In the current contribution, we report our results on two new and related problems in the "eld of single QD spectroscopy. In the following section we discuss the in#uence of phonons on the absorption properties of QDs. Finally, we present our results on charged occupancies in a single QD.
2. Phonon assisted absorption The bare eigenstates of `emptya QDs can be inferred by PL-excitation spectroscopy (PLE) or related methods like photocurrent spectroscopy. Results on QD ensembles and single self-assembled QDs show the expected, resonant absorption from higher shells, but also comparably strong phonon assisted absorption lines [9}11]. The enhancement of the phonon coupling was recently investigated for both intraband [12] and interband [13,14] processes in QDs. We performed our experiments on an In Ga As QD, which was optically accessed by a low temperature confocal microscope via an Al-shadow mask as indicated in Fig. 1b. Further details on the sample under investigation can be found elsewhere [15]. In the following, we concentrate on the phonon assisted absorption processes
Fig. 2. MPLE overview spectrum of a single self-assembled In Ga As QD under high excitation conditions. It covers excitation energy between the QD and the 2D wetting layer (WL). The many bodylines vanish below the WL absorption edge and strong phonon resonances appear on the 1X line. Even on the biexciton line 2X weak resonances can be seen. A basic energy diagram for phonon assisted absorption is shown in the inset.
of a single InGaAs QD with a ground state energy of 1320 meV. Corresponding data are shown in Fig. 2. The displayed energy range covers the GaAs LO phonon resonance at about 1356 meV for the single exciton (1X) and biexciton (2X) line. In such multichannel-PLE data (MPLE), PL-spectra are contained along the x-axis for each resonant excitation energy displayed on the y-axis, whereas PLEdata is contained along the y-axis for each detection energy displayed on the x-axis. The most important features in the MPLE spectra are the sharp absorption resonances, which appear on decrease of the laser energy from 1360 to 1352 meV. Those resonances are found at laser energies of 1356 and 1360 meV, above the PL energy of the single exciton ground state E of the investigated QD at .* 6 1320 meV. With respect to the ground state the corresponding resonance energies (E !E ) * .* 6 appear at 32, 36 and 40 meV. The strongest peak is detected at a resonance energy of 36 meV, matching nicely the GaAs LO phonon energy within the accuracy of our measurement. A weaker resonance at 32 meV is assigned to an InGaAs phonon mode related with the QD. Phonon assisted absorption, as observed here, is schematically sketched in the
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inset of Fig. 2. The resonance around 40 meV falls into the region of the QD d-shell of the investigated QD and shows a doublet "ne structure which would be expected for a slightly asymmetric QD shape. As shown in Fig. 3a and b and discussed more in detail further on, the most intense resonances on the 1X line are observed also on the 2X line. Between the resonances a weak continuum like absorption is observed as a function of excitation energy. Such a background absorption has also been reported by other groups for single selfassembled QDs [16]. In Fig. 3a and b, we discuss MPLE data of the 1X and 2X GaAs LO phonon resonance peaks for B"0 T and B"12 T. With increasing magnetic "eld (not shown), we observe for both lines a pure diamagnetic shift of 8.3 eV/T and a Zeeman splitting of 104 eV/T, as expected for s-shell states of a QD with zero angular momentum. Phonon resonances lead to a constant o!set between absorption and emission energy independent of magnetic "eld. For the GaAs LO phonon resonance we get a variation in energy o!set of only 0.2 meV for "ve di!erent magnetic "elds. Since the GaAs LO energy is constant as a function of magnetic "eld, but the energies of both Zeeman components change, the resonance conditions for the laser excitation energies have to change as well. This magnetic "eld induced detuning of the resonance condition results in a twofold, diagonal splitting of the 1X GaAs LO phonon resonance with exact amount of the Zeeman energy E . 8 The observed diagonal splitting of the resonance conditions in the MPLE plot is a consequence of exciton spin conservation during the phonon assisted absorption process and the successive recombination process (see Fig. 3b). So far we only discussed the resonances of the 1X line, where one exciton at a time is generated and annihilated in the QD. However, there are additional features contained in the MPLE data shown in Fig. 3a and b, which clearly go beyond this scenario. In particular we "nd, that for all resonant laser energies which lead to strong emission on the 1X line, also weaker emissions appear at the position of the biexciton line 2X. The above described twofold, diagonal splitting of the 1X resonance at "nite magnetic "elds leads therefore to a fourfold,
241
Fig. 3. Multi-channel PLE spectra from a single quantum dot in the region of the LO-phonon assisted absorption for B"0 T (a) and B"12 T (b). The resonance energies on the single exciton line 1X show Zeeman splitting and diamagnetic shift, but the resonance energies with respect to the ground state remain una!ected by magnetic "eld. The weaker biexciton resonances 2X show a distinctly di!erent behavior. (c) Model for sequential LO-phonon assisted generation of a biexciton (1, 2) and the following decay (3, 4) as described in the text.
symmetrical splitting of the 2X resonance. Based on the observation that the marked GaAs-LO resonance in the 1X PLE spectrum is observed also in the 2X PLE spectrum, we discuss now a model for
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sequential phonon assisted generation of a biexciton and the following sequential decay in Fig. 3c. For the resonant laser energy E " (1), an * * exciton with energy E in the QD and a phonon 6 with energy E are generated at a "xed rate. As *long as the dot is occupied with one exciton, successive transitions should be renormalized by the amount of the biexciton binding energy and hence, blocked at the given excitation energy. However, for unchanged excitation energy E " (2), * * a second exciton (with opposite spin) can be generated by absorption under participation of a di!erent phonon with energy E #E , where E *6 6 is the biexciton binding energy. This second absorption process, generating the biexciton with energy E #E in the QD, is enabled by the 6 6 previously discussed weak background absorption. Each absorption process leading from the single to the two exciton state can contribute here and does not have to be phonon assisted in general. The biexciton decays sequentially and we expect "rst the emission of a photon at the position of the 2X line at E" (3) followed by the 1X emission at 6 E" (4). As a function of magnetic "eld the 2X 6 resonance performs a fourfold, symmetric splitting (marked in Fig. 3b) in contrast to the twofold, diagonal splitting of the 1X resonances. This behavior "rmly con"rms the above discussed model of sequential phonon assisted generation of a biexciton and the following sequential decay. Each of the Zeeman components of the 1X resonance can be a starting point for biexciton generation, resulting after the second phonon assisted absorption process of course in the same biexciton eigenstate. Now two excitons with opposite spin orientations are in the QD, whose statistic probability for radiative decay is the same. Depending on which of them decays "rst, either the or the compo nent of the 2X line is observed. This means that independent of the "rst absorbed spin orientation (upper or lower Zeeman-branch of the 1X phonon resonance), both Zeeman-levels of the 2X line are observed with the same probability. Hence we obtain a fourfold, symmetric splitting for a 2X resonance, which is unambiguously connected with the phonon assisted sequential generation and decay of a biexciton state. Related results in terms of equally strong biexciton Zeeman components under the
condition of strongly spin polarized exciton injection have already been observed previously in QDs formed by well width #uctuations [17].
3. Charged excitons Di!erent occupation numbers for electrons and holes result in charged exciton complexes. In analogy to QDs with neutral occupancy } arti,cial atoms, charged exciton complexes may be considered as artixcial ions. Charged excitons have been studied in ensembles of QDs by PL [18] as well as in interband transmission experiments [19] and recently also in single quantum rings by PL [20]. Theoretical analyses of few-particle e!ects in optical spectra predict binding energies for charged excitons in the order of some meV [21}23]. Here, we report on charging of a single InGaAs QD in a controlled way with an increasing number of electrons probed by magneto-PL. For controlled charging of individual QDs, a special electric "eld tunable n}i structure has been grown by molecular beam epitaxy. The In Ga As QDs are embedded in an i-GaAs region 40 nm above the n-doped GaAs layer (5;10 cm\). The growth of the QDs is followed by 270 nm i-GaAs, a 40 nm thick Al Ga As blocking layer, and a 10 nm i-GaAs cap layer. As a top Schottky gate we use a 5 nm thick semitransparent Ti layer (T+50%). The samples were processed as photodiodes combined with electron beam structured shadow masks with apertures ranging from 200 to 800 nm. Schematic overviews of the sample arrangement and the band diagram are shown in Fig. 4a and b. The occupation of the QD with electrons can be controlled by applying an external bias voltage V on the Schottky gate with respect to the back contact. For positive V , the band #attens and the electron levels of the QD are dipped into the Fermi sea of the n-GaAs back contact. In our experiments excitons are generated optically at low rate, relax into the QD, and form charged excitons together with the V induced extra electrons. We used a HeNe laser (632.8 nm) for optical excitation and a cooled CCD camera for detection of the PL. The sample was mounted in
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Fig. 4. (a) Photodiode combined with a near "eld shadow mask; (b) schematic band diagram of the structure for zero bias.
a confocal low-temperature microscope (see Ref. [24] for details). In Fig. 5a and b, we present PL spectra as a function of V in the range of !550 to #400 mV with respect to the back contact corresponding to electric "elds of 37.5 to 11.1 kV/cm. The PL intensity is displayed as gray scale plot for B"0 T in Fig. 5a and for B"12 T in Fig. 5b. As a function of V we "nd a series of lines with discrete jumps in the emission energy. These lines can be assigned to emissions from s-shell transitions of X, X\ and X\ (marked in Fig. 5a and b) as discussed more in detail further on starting with B"0 T. For large negative < (< (!0.5 V) the electron levels are far above the Fermi energy and the QD is neutral. Optically generated excitons can relax into the QD, but before radiative recombination (+1 ns), the carriers tunnel out of the QD due to the high applied electric "eld and PL emission is quenched. For V "!0.5 V the QD is still uncharged, but in the smaller electric "eld radiative recombination gets more likely and the X emission line appears at 1307 meV. In fact this line is a doublet with a weak sideline separated by about 0.4 meV attributed to an asymmetric shape of the QD [25].
Fig. 5. Gray scale plot of PL intensity as a function of PL energy and < . The series of lines can be assigned to emissions from s-shell transitions of X, X\ and X\. At zero magnetic "eld (a) and at B"12 T (b).
With increasing V , the X line shifts to higher energies due to the quantum con"ned Stark e!ect in the decreasing electric "eld. For V "!0.35 V a new emission line appears below the X line at 1302.5 meV, indicating the occupation of the QD by the "rst electron. The X\ binding energy with respect to the X is determined to be E \ "4.6 meV by the measured di!erence in 6 emission energies. For !0.35 V(< (0 V, the X and the X\ lines coexist, which is a consequence of the statistical nature of non-resonant optical excitation. In the presence of one extra electron, the capture and subsequent decay of an electron hole pair leads to the emission of a X\ photon. If only a single hole is captured we expect a X photon, and if a single electron is captured we expect no photon but electron back transfer to the n> region. In the PL experiment we average over a time
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interval of 40 s, hence, we collect X\ as well as X photons. At < "0 V the QD is charged with a second electron, leading to a further small red shift of the main emission line, but also to the appearance of an additional weaker line at 1298.1 meV. This additional line, 4.6 meV below the main line, is characteristic for the X\ decay. The energy di!erence between the two X\ lines corresponds to the difference in the s}p exchange energies between the two possible "nal states with parallel or antiparallel spin orientation of the two remaining electrons [21]. Again X\ and X\ can be observed simultaneously over a certain range in < . At < '0.19 V, only one broad emission line remains. This indicates the "lling of the wetting layer (WL) states with electrons. Here, in the x}y plane weakly con"ned electrons are interacting with only one hole in the QD causing a broadening of the detected s-shell decay in the QD. A rough estimation of the external voltage needed to bring the WL states below the Fermi energy, taking charging energy and the electrostatics of the structure into account, results in a reasonable value of 531 mV. From the inset of the X\ line to the inset of the broadened emission we measure < +540 mV. Finally, we discuss the magnetic "eld dependence of the neutral and charged excitons. Corresponding data for B"12 T are shown in Fig. 5b. From comparison of the B"0 T data shown in Fig. 5a, it is clear that single electron charging versus V is mostly una!ected by magnetic "eld. The centers of s-shell emission for X, X\, and X\ are shifted to higher energies due to diamagnetic shift and each emission line splits into two lines, separated by the Zeeman energy. In Fig. 6 we show an overview of the Zeeman splittings and diamagnetic shifts observed for X, X\, and X\ as a function of magnetic "eld. The observed weak di!erences between the Zeeman energies of the neutral and charged excitons seem to indicate, that the spin orientation of extra charges in the QD does not change during the radiative decay from the s-shell. Taking a closer look on the high magnetic "eld data shown in Fig. 5b some more features attract attention. Within the scope of this contribution we concentrate here only on the experimentally
Fig. 6. Diamagnetic shift of the X, X\, and X\ line as a function of magnetic "eld. Inset: Zeeman splitting of the X, X\, and X\ line as a function of magnetic "eld.
observed asymmetry in the PL-intensity of the two Zeeman branches of the X\ line for !0.35 V(< (!0.13 V. This phenomenon is observed only for the X\ line, not for the X and X\ lines. The explanation of this phenomenon involves spin polarization, Pauli blocking, and state selective tunneling as summarized in Fig. 7a and b. At B"12 T a single electron in a QD is spin polarized in thermal equilibrium. The optical excitation of (bright) excitons can happen with two di!erent spin orientations, which results in the charged exciton states shown in Fig. 7a and b. Due to Pauli blocking in the conduction band, parallel electron spin orientation results in a metastable triplet state with one electron in the s-shell and one in the p-shell (see Fig. 7a). If the tunneling time from the p-shell is shorter as the electron spin #ip time (which is expected for the applied V ), an electron is lost and we end up with a neutral exciton and hence with a contribution to one Zeeman component of the X line, i.e. we loose one Zeeman component of the X\ line. The introduction of an exciton with opposite spin orientation however produces a singlet state as shown in Fig. 7b. Radiative decay of this con"guration results in a contribution to the other Zeeman component of the X\ line. Which of the Zeeman levels will be on the low energy side is an issue of sign and magnitude of the associated electron and hole g-factors, which
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Fig. 7. X\ triplet (a) and singlet (b) con"gurations. The triplet state is subjected to tunnel decay from the p-shell.
are (independently and for the present structure) unknown so far. Our "ndings also imply that the associated heavy hole spin #ip time should be at least of the same order or longer than the e}h lifetime.
4. Summary In summary, we have studied phonon assisted processes and controlled single electron charging in single InGaAs QDs by spatially resolved magnetooptic techniques.
Acknowledgements This work was supported "nancially by the Deutsche Forschungsgemeinschaft via SFB 348 and by the BMBF via 01BM917. References [1] A. Zrenner, J. Chem. Phys. 112 (2000) 7790. [2] V. Fock, Z. Phys. 47 (1928) 446. [3] E. Deckel, D. Gershoni, E. Ehrenfreund, D. Spector, J.M. Garcia, P.M. Petro!, Phys. Rev. Lett. 80 (1998) 4991.
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[4] L. Landin, M.S. Miller, M.-E. Pistol, C.E. Pryor, L. Samuelson, Science 280 (1998) 262. [5] F. Findeis, A. Zrenner, G. BoK hm, G. Abstreiter, Solid State Commun. 114 (2000) 227. [6] P. Hawrylak, Phys. Rev. B 60 (1999) 5597. [7] U. Hohenester, F. Rossi, E. Molinari, Solid State Commun. 111 (1999) 187. [8] M. Bayer, O. Stern, P. Hawrylak, S. Fafard, A. Forchel, Nature 405 (2000) 923. [9] S. Fafard, R. Leon, D. Leonard, J.L. Merz, P.M. Petro!, Phys. Rev. B 52 (1995) 5752. [10] R. Heitz, M. Veit, N.N. Ledentsov, A. Ho!mann, D. Bimberg, V.M. Ustinov, P.S. Kop'ev, Zh.I. Alferov, Phys. Rev. B 56 (1997) 10435. [11] A. Zrenner, M. Markmann, E. Beham, F. Findeis, G. BoK hm, G. Abstreiter, J. Electron. Mater. 28 (1999) 542. [12] S. Hameau, Y. Guldner, O. Verzelen, R. Ferreira, G. Bastard, J. Zeman, A. Lemam( tre, J.M. Ge`rard, Phys. Rev. Lett. 83 (1999) 4152. [13] R. Heitz, I. Mukhametzhanov, O. Stier, A. Madhukar, D. Bimberg, Phys. Rev. Lett. 83 (1999) 4654. [14] V.M. Fomin, V.N. Gladilin, S.N. Klimin, J.T. Devreese, P.M. Koenraad, J.H. Wolter, Phys. Rev. B 61 (2000) R2436. [15] F. Findeis, A. Zrenner, G. BoK hm, G. Abstreiter, Phys. Rev. B 61 (2000) R10579. [16] Y. Toda, O. Moriwaki, M. Nishioka, Y. Arakawa, Phys. Rev. Lett. 82 (1999) 4114. [17] A. Schaller, A. Zrenner, G. Abstreiter, G. BoK hm, Physica E 2 (1998) 609. [18] K.H. Schmidt, G. Medeiros-Ribeiro, P.M. Petro!, Phys. Rev. B 58 (1998) 3597. [19] R.J. Warburton, C.S. DuK rr, K. Karrai, J.P. Kotthaus, G. Medeiros-Ribeiro, P.M. Petro!, Phys. Rev. Lett. 79 (1997) 5282. [20] R.J. Warburton, C. SchaK #ein, D. Haft, F. Bickel, A. Lorke, K. Karrai, J.M. Garcia, W. Schoenfeld, P. Petro!, Nature 405 (2000) 926. [21] A. Wojs, P. Hawrylak, Phys. Rev. B 55 (1997) 13066. [22] A. Hartmann, Y. Ducommun, E. Kapon, U. Hohenester, C. Simserides, E. Molinari, Phys. Stat. Sol. A 178 (2000) 283. [23] G.A. Narvaez, P. Hawrylak, Phys. Rev. B 61 (2000) 13753. [24] A. Zrenner, M. Markmann, A. Paassen, A.-L. Efros, M. Bichler, W. Wegscheider, G. BoK hm, G. Abstreiter, Physica B 256}258 (1998) 300. [25] D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, D. Park, Phys. Rev. Lett. 76 (1996) 3005.