NANO LETTERS
Markovian and Non-Markovian Light-Emission Channels in Strained Quantum Wires
2009 Vol. 9, No. 9 3129-3136
V. Lopez-Richard,*,† J. C. Gonza´lez,‡ F. M. Matinaga,‡ C. Trallero-Giner,§ E. Ribeiro,| M. Rebello Sousa Dias,† L. Villegas-Lelovsky,†,¶ and G. E. Marques† Departamento de Fı´sica, UniVersidade Federal de Sa˜o Carlos, 13.565-905, Sa˜o Carlos, Sa˜o Paulo, Brazil, Departamento de Fı´sica, UniVersidade Federal de Minas Gerais, 30.123-970, Belo Horizonte, Minas Gerais, Brazil, Faculty of Physics, HaVana UniVersity, 10400 HaVana, Cuba, Departamento de Fı´sica, UniVersidade Federal do Parana, 81.531-990, Curitiba, Parana, Brazil, and Departamento de Fı´sica, UniVersidade Federal de Sa˜o Carlos, 13.565-905, Sa˜o Carlos, Sa˜o Paulo, Brazil Received April 15, 2009; Revised Manuscript Received July 1, 2009
ABSTRACT We have achieved conditions to obtain optical memory effects in semiconductor nanostructures. The system is based on strained InP quantum wires where the tuning of the heavy-light valence band splitting has allowed the existence of two independent optical channels with correlated and uncorrelated excitation and light-emission processes. The presence of an optical channel that preserves the excitation memory is unambiguously corroborated by photoluminescence measurements of free-standing quantum wires under different configurations of the incoming and outgoing light polarizations in various samples. High-resolution transmission electron microscopy and electron diffraction indicate the presence of strain effects in the optical response. By using this effect and under certain growth conditions, we have shown that the optical recombination is mediated by relaxation processes with different natures: one a Markov and another with a non-Markovian signature. Resonance intersubband light-heavy hole transitions assisted by optical phonons provide the desired mechanism for the correlated non-Markovian carrier relaxation process. A multiband calculation for strained InP quantum wires was developed to account for the description of the character of the valence band states and gives quantitative support for light hole-heavy hole transitions assisted by optical phonons.
The transmission, storage, and detection of quantum information on the nanometer scale is the focus of recent experimental and theoretical endeavors. Particular attention has been paid to the study and growth1,2 of semiconductor quantum wires (QWr’s) for their potential use in quantum information processing and photonic applications. The studies of linearly polarized emission from QWr’s have been carried out for a long time. The combination of two effects has been ascribed as the source of the peculiar anisotropic optical response: (i) a classical electrostatic effect due to the difference between the dielectric constants of the wire and the surrounding medium3-5 and (ii) the quantum anisotropy of the dipole matrix element involved in the optical transitions.6-8 Classically, without taking into consideration quantum effects and the selection rules for the optical transitions and * Corresponding author. E-mail:
[email protected]. † Departamento de Fı´sica, Universidade Federal de Sa˜o Carlos. ‡ Universidade Federal de Minas Gerais. § Havana University. | Universidade Federal do Parana. ¶ Permanent Address: Instituto de Fisica, Universidade Federal de Uberlandia, 38.400-902, Uberlandia, Minas Gerais, Brazil. 10.1021/nl9012024 CCC: $40.75 Published on Web 08/10/2009
2009 American Chemical Society
considering the polarizability tensor to be diagonal and independent of the frequency, εij - I ) (ε - 1)δij, it can be proven that the ratio of the absorption coefficients of light polarized along and perpendicular to the wire axis, R| and R⊥, is given by R⊥/R| ) δ ) (2ε0(ε + ε0))2, where ε and ε0 are the dielectric constants of the QWr and the surrounding medium, respectively.5,9 The Rayleigh scattering holds the same anisotropic response in a dielectric cylinder for the perpendicular, I⊥, and parallel, I|, scattered light intensities (i.e., I⊥/I| ) δ).9,10 However, for inelastic processes the polarizability tensor of the nanostructure is no longer diagonal and cannot be considered frequency-independent. In any discussion of inelastic processes, the relaxation mechanisms must be considered. This is the case for nonresonant photoluminescence (PL) in systems under strain and quantization effects, for which the simplified classical picture of elastic scattering cannot be applied without considering the carrier-energy distribution before photon emission. The lack of validity of the elastic scattering model used in previous work3-5 is particularly evident in the case of strained QWr’s where different relaxation channels
subbands can be identified by the degree of linear polarization of the out-coming photons, as will be shown below. To characterize the recombination process, we shall label the intensity of the emission as IR,β, where R and β represent the polarization of the detected photons (outgoing) and the excitation (incoming photons), respectively. In general, the emission rate intensity at which the PL occurs in a semiconductor can be written as11,12 IR,β )
∑ ∫ n (E)P β i
out i (E;R, pωS)
dE
(1)
i,j
Figure 1. Schematic diagram of E-H pair excitation, relaxation, and recombination in a wire under a strain field. (i) Incoming light creates simultaneously E-H pairs in the E-HH and E-LH subbands. (ii) Fast relaxation takes place through LO-phonon emission. (iii) At the bottom of the subbands, the thermalization is via an acoustic phonon, leading to an uncorrelated light absorption and emission processes. (iv) If the splitting between the LH and HH subbands is tuned to be equal to the energy of an LO phonon, then a fast mechanism through an optical deformation potential, connecting E-LH and E-HH subbands, will occur.
contribute to the carrier distribution responsible for the PL process. In this letter, we will show how to master the correlation loss between excitation and light-emission channels in quantum systems such as a strained, free-standing InP QWr. A detailed discussion, based on experimental and theoretical results, of the Markov and non-Markovian nature of relaxation processes associated with the optical response of the QWr’s will be presented. The discussion will address the interplay between anisotropic absorption and emission, with respect to the polarization of light, on one side, and the electronic structure and elementary excitations, on the other, that ultimately lead to the modulation of the optical response. Because we are assuming low concentration of impurities, the inherent electron-hole distribution for the description of the PL intensity (eq 1) is mainly dictated by the interaction with optical and acoustical phonons. In the following discussion, we will show how a manipulation of the QWr synthesis allows us to master the correlation loss between excitation and light emission. A diagram illustrating the electron-hole (E-H) pair excitation, relaxation, and emission processes in a strained QWr is shown in Figure 1. The presence of strain leads to the breakdown of degeneracy at the top of the valence band between heavy-hole (HH) and light-hole (LH) subbands and, ultimately, to the blue shift in the PL spectrum. In our case and because of the presence of biaxial compressive strain, the HH subband will lie at the top of the valence band. However, the HH and LH states will have hybrid character as a result of strong intersubband mixing. Although the character of the holes in the valence band is hybrid as a result of interband coupling, we shall retain the notation HH and LH for the topmost and lower subbands, respectively. It is important to point out that the hybrid character of the valence 3130
where nβi (E) dE is the number of E-H pairs within the kinetic energy interval (E,E + dE) in subband i, which depends on the polarization excitation conditions (β), and Pout is the i probability per unit time of electron-hole annihilation with the emission of a photon with energy pωS and polarization R. It is implicit in eq 1 that the PL intensity is ruled by the E-H distribution function nβi (E). Following the relaxation and optical recombination processes sketched in Figure 1, we must consider the interplay between radiative processes, the scattering by phonons, and other nonradiative mechanisms. The E-H pair relaxation occurs via two main steps: first, fast scattering mechanisms based on LO phonon emission and second, thermalization near the bottom of the subbands. Because of energy conservation, the thermalization process can take place through the assistance of acoustical phonons or by any other nonradiative mechanism. This slower scattering process, if compared to the faster Fro¨hlich LO-phonon emission, destroys the correlation between E-H pair creation and annihilation probabilities associated with incident and emitted light. Thus, the energy distribution function at the bottom of the subbands corresponds to a nonequilibrium condition and must depend on the relative contribution of acoustical phonons and nonradiative scattering rates. For kinetic energy E < pωLO (with pωLO being the optical phonon energy), the number of E-H pairs can be described by a distribution function of the type n(E) ≈ exp(-E/(kBTe)), with a certain effective temperature Te given by (kBTe)-1 ) (kBT)-1 - [τac/ (4mu2τ)]. (See ref 12 for a detailed discussion.) Here, u is the speed of sound in the material, T is the absolute temperature, and τac (τ) is the relaxation time due to acoustic mechanisms (radiative and nonradiative processes). The ratio between τac and τ determines two different regimes: (i) if τ . τac, then a thermal quasi-equilibrium is reached with Te f T and n(E) approaching the Maxwell-Boltzman distribution function leading to the thermalized luminescence and (ii) a strong nonequilibrium distribution of carriers once τ , τac. Thus, an impoverishment of the correlation between the emitted and incoming light will take place in case (i), whereas correlated excitation and emission is expected in case (ii). This physical picture suggests that a slow relaxation mechanism would provoke memory loss with respect to the initial condition of E-H pair creation. In turn, a faster relaxation channel may improve the correlation between the incoming and outgoing photons. Therefore and according to the discussed relaxation processes shown in Figure 1, it Nano Lett., Vol. 9, No. 9, 2009
Figure 2. (a) SEM micrographs of free-standing InP QWr’s grown on a (001) InP substrate. (b) TEM image of an InP QWr with the characteristic catalytic particle at the end. (c) Electron diffraction pattern from the QWr. (d) High-resolution TEM image of a lateral part of the QWr.
is expected that the time τ associated with the E-HH pair (τHH) should be larger than that for the E-LH (τLH))(i.e., under the condition τHH . τLH, the PL spectrum should present a better correlation between the incoming and emitted light for the E-LH subband than for the E-HH). Moreover, when the energy difference between the valence bands approaches the energy of an optical phonon, pωLO, a resonance scattering process will take place and the rate, 1/τLH, is ruled by the optical deformation potential interaction, which couples the LH and HH subbands. The relaxation time by acoustical phonons in III-V semiconductors is τac ≈ 10-11-10-12 s, and that for optical phonons is τ0 ≈ 10-13-10-14 s (i.e., τ0 , τac). Under resonance conditions, when the splitting between HH and LH subbands approaches pωLO, the E-LH distribution function is drastically reduced β and nLH ≈ Pin(E; β, pωl), where Pin is the creation rate of E-LH pairs by a quantum of light pωl with polarization β.13 We shall note that, for the processes displayed in Figure 1, the intraband LO-phonon relaxation takes place simultaneously for electrons in the conduction band and holes in the valence band through the Fro¨hlich interaction, yet a much slower interband transition assisted by the optical deformation potential is also allowed between HH and LH subbands.14,15 According to the discussion before and following eq 1, we can characterize the PL in strained QWr’s within two limiting situations: (i) if the detected frequency, ωS, corresponds to the E-HH transition (ωBS shown in Figure 1), then emission line B responds as thermalized luminescence and Nano Lett., Vol. 9, No. 9, 2009
an uncorrelated absorption and emission process is expected; (ii) for ωS = ωSC under the resonance condition, where the energy difference between the E-LH and E-HH subbands approaches pωLO, the PL intensity can be characterized by the product of probabilities IR,β ∝ Pin(β) Pout(R), leading to a certain correlation between incoming and emitted light. Hence, the PL spectra will present two channels with different natures: one Markovian process and another with a non-Markovian signature. It is important to note that in bulk zinc blende semiconductors the relaxation process at the bottom of the E-HH and E-LH bands, degenerated at the Γ point of the Brillouin zone, occurs via interaction with acoustic phonon plus other nonradiative slower mechanisms. Hence, the optical memory effects are suppressed, and typical thermalized PL spectra in the InP substrate should be expected.12 As reported in ref 16, the engineering of strain effects in QWr’s can become an effective tool for the modulation of electronic properties that are useful for potential applications as nanoscopic devices. Towards this goal, we have synthesized free-standing strained InP QWr’s, as shown in Figure 2a, by the vapor-liquid-solid growth method in a chemical beam epitaxy (CBE) reactor.17 Colloidal Au nanoparticles of 20 nm diameter were deposited on (001) InP substrates by spin coating and were used as catalitic seeds (Figure 2b) for the formation of QWr’s at a growth temperature of 450 °C using thermally cracked PH3 and trimethylindium as chemical beam precursors for 20 min. The morphology and 3131
crystal structure of the samples were examined by scanning electron microscopy (SEM, Jeol JSM-6330F) (Figure 2a) and transmission electron microscopy (TEM, Jeol JEM-3010) (Figure 2b). Selected-area electron diffraction (SAED) and high-resolution TEM (HRTEM) of our samples, as displayed in Figure 2c,d, allowed us to confirm that the InP QWr’s grow uniformly from the base to the top along the [001] direction, despite their alignment with the [111]B direction of the substrate, and present a zinc blend structure (with cubic symmetry). Unlike the InP QWr’s grown by other techniques,18-20 no evidence was found of structural changes in our samples with signatures of wurzite crystal structure. Strain fields were experimentally identified in these QWr’s by analyzing the Fourier transform of HRTEM images and SAED patterns of several nanowires. Two sources of strain have been identified: surface oxidation and the lattice mismatch at the QWr-catalyst interface. (Note that the InP Qwr’s are lattice matched to the InP substrate.) A large density of extended defects could also produce strain fields, but they were not detected in our QWr’s. Figure 3a shows a TEM image of the top part of an InP QWr surrounded by an ∼1-nm-thick oxide layer along with a clear mismatch at the interface with the catalytic particle. In thicker QWr’s, the oxide layer should be the main cause of the strain observed,22,23 as represented in Figure 3b, whereas in thinner QWr’s the mismatch at the QWr-catalyst interface can play a role similar to that of the lattice mismatch between QWr’s and the substrates.24,25 The experiments reveal an enhancement of the spacing between the planes perpendicular to the QWr and a shortening of the interplane distance along the QWr axis if compared to the bulk InP parameters, as displayed in Figure 3b. By analyzing HRTEM images and SAED patterns of several QWr X-ray diffractograms of the QWr, the wire axis is εzz ) (1.00 ( 0.25)% and the biaxial strain is ε| ) (-0.9 ( 0.25)%. The measured mismatch ratio εzz/ε| ) -1.111 is close to the value εzz/ε| ) -2c12/c11 = -1.110 that corresponds to compressive biaxial strain in the (001) plane (the elastic moduli, c11 ) 10.11 and c12 ) 5.61, in units of 1011 dyn cm-2 were taken from ref 21). The optical properties were investigated by polarizationresolved PL spectroscopy carried out using a T64000 Jobin Yvon spectrometer with a liquid-nitrogen-cooled chargecoupled device (CCD) Si detector and a linearly polarized He-Ne laser (632.8 nm) at 5.5 mW. The sample was mounted in a coldfinger liquid-helium cryostat, and a quarter wave plate and a Glan-Taylor polarizer were used to rotate the linearly polarized laser excitation and to analyze the QWr emissions. To clarify unambiguously the nature of the observed PL lines, we deposited a few InP QWr’s over the surface of a Si substrate (with weak PL ∼1.1 eV) and then mounted this sample in a cryostat. The corresponding SEM micrograph is reported in Figure 4a. PL measurements of a single QWr were carried out by using an Olympus BX51 optical microscope with a 100× long-working-distance objective lens. It focused the power excitation of the unpolarized He-Ne laser operating at 5.5 mW in a region of ap3132
Figure 3. (a) TEM image of the tip of an InP QWr showing an oxide layer surrounding the wire and the structural mismatch at the QWr-catalyst interface. (b) HRTEM image of a lateral region of the InP QWr illustrating the enhancement of the spacing between the planes perpendicular to the QWr and a shortening of the interplane distance parallel to the QWr axis, when compared to the bulk InP parameters.
proximately 1 µm. The PL spectrum of a single QWr is shown in Figure 4b, and the emission leading to peaks B and C, above the InP bulk gap energy of Eg ) 1.4236 eV,21 are attributed to the wire electronic structure produced by the strain fields within the QWr, which breaks the degeneracy of the HH and LH valence bands at the Γ point in the Brillouin zone. The nature of emission lines B and C can be identified by their relative positions with respect to the bulk gap energy. The valence band electronic structure of such InP strained QWr’s is represented in Figure 5b, which can be compared to the unstrained case displayed in Figure 5a. These calculations were carried out by considering the anisotropy of the Γ8 valence bands using the 4 × 4 Luttinger-Kohn Hamiltonian. The valence band levels more effectively involved in the optical recombination from the conduction band ground state are denoted here as HH(0) and LH(0). They are defined by the optical selection rules determined by the polarization of the emitted photons. Note that, for an unstrained QWr (Figure 5a), the top valence band at kz ) 0 Nano Lett., Vol. 9, No. 9, 2009
Figure 6. PL spectra, at 77 K, for four incoming and outgoing configurations of polarized photons in a sample as grown on the InP substrate. The PL configurations are shown in Figure 4a.
hole subband energies at the Γ point represent a small fraction of the total energy shift that includes those produced by the strain field. The energy shifts for the E-H subbands (with respect to the energy gap) due to the presence of biaxial strain are given by26 ∆EHH ) -P - Q Figure 4. (a) SEM micrograph of a free-standing InP QWr deposited onto a Si substrate. (b) PL measurements of a single QWr. (Solid lines) Linearly polarized recorded PL spectra with unpolarized incoming light. (Circles) Degree of linear polarization, as discussed later (eq 6). The polarization configurations used are specified by arrows in panel a.
(2)
for the HH and ∆ELH ) -P + Q +
2Q2 ∆SO
(3)
)
(4)
for the LH, where
(
P ) 2(av + ac)
c11 - c12 ε| c11
and
(
Q ) -b
Figure 5. (a) Energy dispersion of the light-hole and heavy-hole subbands in an unstrained InP QWr with 37 nm diameter. (b) Energy dispersion for the light-hole and heavy-hole subbands in a strained InP QWr with ε| ) -0.9%. The states with predominant HH(0) and LH(0) character are highlighted as black and gray curves, respectively.
is occupied by a level with strong LH character, whereas the compressive strain promotes the first HH levels to the top. Given the large values of the QWr diameter, within the range of 37 ( 6 nm, the spatial confinement effects on the Nano Lett., Vol. 9, No. 9, 2009
)
c11 + 2c12 ε| c11
(5)
Using the mean value of the biaxial strain, ε| ) -0.9%, obtained by electron diffraction, the corresponding energy shifts for both valence subbands are |∆EHH| ) 28.61 meV and |∆ELH| ) 73.87 meV. After the introduction of the effects of confinement and intersubband coupling, the relative shifts of the valence subbands are 32.83 meV for the HH and 76.05 meV for the LH, which match the experimental observations for PL peaks B and C as shown in Figure 6: 31.31 and 72.54 meV, respectively. These PL spectra correspond to emissions from multiple QWr’s, thus the peak positions can be attributed to the contribution from the predominant QWr configurations as used in the calculations. The energy separation shown in Figure 5 between both valence subbands, 43.20 meV = |∆ELH| - |∆EHH| ) 45.26 meV, displays a 3133
small contribution due to the electronic confinement. In these calculations, we have used the values ac ) -7.0 eV,27 av ) -0.6 eV,27 and b ) -1.7 eV 21 for the deformation potentials and ∆SO ) 0.108 eV 21 for the spin-orbit split-off energy. To test the conditions for recording Markovian and nonMarkovian light-emission channels, we have studied the degree of linear polarization of the emitted light and the degree of correlation between the creation and the annihilation of E-H pairs by performing polarization-resolved PL measurements on the strained InP QWr samples: (i) for a single QWr on the Si substrate and (ii) as grown on the InP substrate. For these measurements, we used the configurations indicated in Figure 4a where the photon wavevectors are taken perpendicular to the z axis of the wire. Thus, two independent linear polarizations can be tested: polarizations perpendicular and parallel to the wire. Given the intensities of linearly polarized photons emitted along the QWR axis, I|,β, and perpendicular to it, I⊥,β, the degree of linear polarization (DLP) for a certain polarization β of the incoming photons can be defined as DLP(β) )
I|,β - I⊥,β I|,β + I⊥,β
(6)
We shall use the index β ) 0 for unpolarized excitation. DLP(0) for a single QWr is shown in Figure 4b. Note that the emission channel labeled C is more polarized along the QWr axis than emission B. This contrast between DLP(0) from peaks B and C denotes a qualitative difference in the nature of the valence band states involved in the optical transitions given the isotropic nature of the conduction band wave function. According to the optical selection rules, a higher degree of linear polarization of peak C corroborates the character of an E-LH recombination. (See the electronic structure in Figure 5b.) Thus, by fixing the outgoing polarization we are scanning the degree of admixture of valence states involved in the corresponding transitions. The positive value of DLP for both emission lines also corroborates the zinc blende structure of the QWr’s as determined by electron diffraction. Observations of DLP signal inversion is a known signature of the formation of the wurzite structure in the QWr’s,18 a feature that is not observed in our QWr’s. A question to be answered is whether the degree of linear polarization is affected by the polarization of incoming photons. Knowledge of the correlation between the emission intensities for the independent linear polarizations and the polarization of incident photons will allow the characterization of memory retention for each channel. Four combinations of outgoing and incoming polarizations were tested, as represented in Figure 6, in as-grown samples of QWr’s on the InP substrate. Here, peak A corresponds to emissions from the bulk InP. From these results, the DLP(β) detected from QWr’s is shown in Figure 7a for incoming photons polarized along the QWr axis, β ) ||, and polarized perpendicular to it, β ) ⊥. The emissions from the InP substrate can serve as a reference, in this case. For convenience and in order to avoid the overlapping of experimental 3134
Figure 7. (a) Degree of linear polarization (eq 6) for two conditions of incoming photon polarization (the DLP, obtained with incoming polarization perpendicular to the QWr axis, has been multiplied by -1). (b) Shadowed region: PL spectrum for linearly polarized light along the QWr axis for both the incoming and outgoing photons. Circles denote the correlation degree (eq 7) between the excitation and the emission processes.
points, the results for DLP(⊥) have been multiplied by -1. Note in Figure 7a the symmetry of the DLP function with respect to the horizontal axis. In this case, we can conclude that the degree of polarization is independent of incoming light polarization. However, according to Figure 6, there is a correlation in the optical response with respect to the polarization of the excitation. To characterize this “memory effect”, we have introduced the correlation degree (CD) as CD )
I|,| + I⊥,⊥ - I|,⊥ - I⊥,| I|,| + I⊥,⊥ + I|,⊥ + I⊥,|
(7)
Following the above definition, if I|,| ) I|,⊥ and I⊥,⊥ ) I ⊥,| (i.e., if the emission is independent of the excitation; uncorrelated process: IR,β ∝ Pout(R)), then CD ) 0. This condition characterizes the signature of a memoryless channel or Markovian process, which is directly linked to the thermalized luminescence. Yet, if the emission and the excitation were correlated so that the PL intensity could be characterized by the product of the probabilities of each process (Pout(R) for the emission and Pin(β) for the excitation, IR,β ∝ Pout(R) Pin(β)), then the PL line would present non-Markovian signatures with the correlation degree given by CD )
(
)
Pin(|) - Pin(⊥) DLP Pin(|) + Pin(⊥)
(8)
Moreover, if the condition I⊥,| ) I|,⊥ is fulfilled (peak C in Figure 6), then CD ) DLP2. In Figure 7b, we have displayed the correlation degree as a function of the emission energy. It can be seen from the Figure that CD ) 0 over the region of peak A, corresponding to the emission from bulk Nano Lett., Vol. 9, No. 9, 2009
InP, and CD ≈ 0 for line B associated with emission for the QWr. Thus, emission B loses its memory of the initial excitation process and can be characterized as a Markovian event. For peak C, CD = 0.1. This coincides with the value of DLP2 in this energy region where DLP = 0.3, as shown in Figure 7a. In this sense, the photon emission with energy pωCS can be classified as a non-Markovian process that retains the memory of the E-H creation by incident light. As stated above, the reason for the memory loss of PL line B lies is that the relaxation process on the bottom of the E-HH subband is mainly assisted by acoustic phonons. The corresponding PL intensity is described by the product of a Maxwell-Boltzman distribution function and the recombination rate Pout(pωS ) pωSB). For line C, the nonMarkovian nature is explained by the tuning, as a result of the strain field, the LH and HH valence subband splitting, which equals the InP LO-phonon energy, pωLO ) 43 meV.28 Under this condition, optical phonon emission is allowed and the relaxation from the bottom of the E-LH subband (Figure 1) takes place by the deformation potential mechanism (i.e., by an interband process involving transitions between LH and HH bands).14 Notice that energy conservation and low temperature, at the bottom of the E-LH or E-HH subbands, forbid relaxation assisted by Fro¨hlich interaction.15 Thus, the deformation-potential-assisted transition from the LH to the HH subband corresponds to a faster cascadelike process that inhibits thermalization, thus preserving the information about the initial creation conditions that correlates both excitation and emission rates. Under stationary conditions, when the E-H population is established, transitions between the lowermost E-LH states become independent of the occupation of lower-lying E-HH levels. Under the resonance condition, as shown in Figure 1, the population in the E-LH subband depends on the excitation probability, leading to emission C that is strongly dependent on the polarization of incoming photons. If the resonance condition when the LH-HH splitting equals the LO-phonon energy pωLO is not fulfilled, then we will recover the thermalized PL situation and emission C will become a memoryless channel independent of the incoming photon polarization. In summary, thermalization cannot be achieved if there is a fast nonradiative relaxation mechanism that allows the carriers to leave the bottom of the given subband. Under the resonance condition, when the separation between the two valence subbands approaches the energy of one LO phonon, this conditions is fulfilled. In this case, the nonradiative mechanism that inhibits the thermalization in the lower-lying valence subband (involved in transition C) is the optical-phonon interaction assisted by the deformation potential. The application of a magnetic field could be a method for tuning the correlation degree and looking for optimal conditions for correlated excitation and emission.14,15 Although the focus of this work has been the study of an unreported effect of a simultaneously correlated and uncorrelated nanoscopic emission source, the coexistence of mechanisms that preserve the excitation memory along Nano Lett., Vol. 9, No. 9, 2009
with memoryless channels makes strained QWr’s attractive candidates for building optical devices and photonic circuits. The interest in biphoton sources31 created by the modulated growth conditions of nanoparticles and their potential use as elements of quantum cryptography,32 in correlated or uncorrelated emitters, might certainly offer opportunities for the search for applications of these strained QWR’s. Note Added after ASAP Publication: This article was published ASAP on August 10, 2009. Figures 4 and 7 have been modified. The correct version was published on September 9, 2009. Acknowledgment. We acknowledge financial support from the Brazilian agencies and institutions FAPESP, CNPq, FAPEMIG, CAPES and LME - LNLS. The sample was grown in the CBE system at Instituto de Fı´sica “Gleb Wataghin”, Universidade Estadual de Campinas (UNICAMP, BRAZIL). The authors also thank J. Bettini, H. R. Gutie´rrez, M. A. Cotta and D. Ugarte for their authorization to use unpublished images on the nanowire electron microscopy characterization. Finally, GEM and CT-G are grateful to the visiting scholar program from the ICTP/Trieste. References (1) Duam, X. F.; Lieber, C. M. AdV. Mater. 2000, 12, 298. (2) Bjo¨rk, M. T.; Ohlsson, B. J.; Sass, T.; Persson, A. I.; Thelander, C.; Magnusson, M. H.; Deppert, K.; Wallenberg, L. R.; Samuelson, L. Nano Lett. 2002, 2, 870. (3) Ils, P.; Gre´us, Ch.; Forchel, A.; Kulakovskii, V. D.; Gippius, N. A.; Tikhodeev, S. G. Phys. ReV. B 1995, 51, 4272. (4) Muljarov, E. A.; Zhukov, E. A.; Dneprovskii, V. S.; Masumoto, Y. Phys. ReV. B 2000, 62, 7420. (5) Wang, J.; Gudiksen, M. S.; Duan, X.; Cui, Y.; Lieber, C. M. Science 2001, 293, 1455. (6) Bockelmann, U.; Bastard, G. Phys. ReV. B 1992, 45, 1688. (7) Akiyama, H.; Someya, T.; Sakaki, H. Phys. ReV. B 1996, 53, R4229. (8) Vouilloz, F.; Oberli, D. Y.; Dupertuis, M.-A.; Gustafsson, A.; Reinhardt, F.; Kapon, E. Phys. ReV. B 1998, 57, 12378. (9) Landau, L. D.; Lifshitz, E. M.; Pitaevskii, L. P. Electrodynamics of Continuous Media; Pergamon: Oxford, U.K., 1984; p 319. (10) Landau, L. D.; Lifshitz, E. M. The Classical Theory of Fields; Pergamon: Oxford, U.K., 1984; p 189. (11) Been H.; Williams, E. W. In Semiconductors and Semimetals; Willardson, R. K., Beer, A. C., Eds.; Academic: New York, 1972; Vol. 8, p 182. (12) Trallero Giner, K.; Sotolongo Costa, O.; Lang, I. G.; Pavlov, S. T. SoV. Phys. Solid State 1986, 28, 1160. [Fiz. TVerd. Tela 1986, 28, 2075]Trallero Giner, K.; Sotolongo Costa, O.; Lang, I. G.; Pavlov, S. T. SoV. Phys. Solid State 1986, 28, 1774. [Fiz. TVerd. Tela 1986, 28, 3152]. (13) If E > pωLO, then the energy distribution is dictated by the simultaneous scattering by LO phonons as a result of the strong Fro¨hlich interaction. In this “cascade-like model”, E is proportional to Pin.29 For the relaxation process shown in Figure 1, the last step is mediated by the optical deformation potential. Very recently, it was shown that LHHH-phonon optical deformation potential interaction becomes important in InP nanostructures. This mechanism is responsible for the appearance of unussual TO-phonon lines in InP and InAs emission spectra.30 (14) Lopez, V.; Marques, G. E.; Drake, J.; Trallero-Giner, C. Phys. ReV. B 1997, 56, 15691. (15) Lopez-Richard, V.; Marques, G. E.; Trallero-Giner, C.; Drake, J. Phys. ReV. B 1998, 58, 16136. (16) Hong, K.-H.; Kim, J.; Lee, S.-H.; Shin, J. K. Nano Lett. 2008, 8, 1335. (17) Gonzalez, J. C.; da Silva, M. I. N.; Lozano, X. S.; Zanchet, D.; Ugarte, D.; Ribeiro, E.; Gutierrez, H. R.; Cotta, M. A. J. Nanosci. Nanotechnol. 2006, 6, 2182. (18) Mishra, A.; Titova, L. V.; Hoang, T. B.; Jackson, H. E.; Smitha, L. M.; Yarrison-Rice, J. M.; Kim, Y.; Joyce, H. J.; Gao, Q.; Tan, H. H.; Jagadish, C. Appl. Phys. Lett. 2007, 91, 263104. 3135
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