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The excitation-dependent photoluminescence (PL) of ZnSe nanocrystals (NC) grown on GaAs (100) substrate was studied. The PL spectra observed corroborate previous observations of a bimodal size distribution of NC grown, and, in addition, evidence the existence of spectral diffusion with extend dependent on excitation power. Besides, it was also shown that at relatively intense excitation an extra band has arose in luminescence spectra due to biexcitons confined in NC of 3.5-4.0 nm size. The binding energy of these biexcitons was as large as 23 meV. In recent years the properties of highly excited semiconductor nanocrystals (NC) widely referred to as semiconductor quantum dots (QD) have gained much attention largely due to advance in application development motivated by the demonstration of effective lasing in CdSe-based QD [1]. At the same time the semiconductor compound which has received the most intense interest in previous years has been ZnSe known to have a room temperature direct band gap of 2,7 eV that corresponds to emission in the blue region of the spectrum. Properly tailored ZnSe-based QD are well suited for short wavelength light emitters, a fact recognized worldwide by research groups several of whom have expanded a great deal of effort attempting to produce ZnSe NC of high quality [2,3]. However properties of extremely small ZnSe crystals under intense optical excitation remain unexplored and require better insight.Recently, a vapor phase technique has been utilized to grow ZnSe nanocrystals atop GaAs (100) substrate [4]. The distinguishing feature of applied technique was the use of horizontal type quartz reactor exploiting a large (~250°C/cm) temperature gradient in the deposition zone just in front of substrate on which ZnSe NC were collected. Applied characterization techniques indicated the formation of two distinct sets of nanocrystals on the same substrate. The average characteristic sizes of NC in these sets have been estimated to be in the ranges of 36.6-41.2 and 3.5-4.0 nm while the effective Bohr radius ( ) a B of the free exciton in bulk ZnSe is known to be~50 C [5]. From these facts one can easily realize that samples described in Ref. 4 are unique since they provide chance to compare behavior of carriers confined in sub-excitonic and superexcitonic volumes of ZnSe by studying photoluminescence (PL) just from the same single sample. The present work extends research on those samples with the aim to investigate their emission spectra under high level of optical excitation.The excitation source was N 2 laser (337.1 nm) with optical pulses of 10 -8 s and 100 Hz repetition rate. In our case this excitation can be treated as a quasi-continuous-wave (qCW) excitation as the pulses used were long enough compared to all characteristic times known for nonequilibrium e-h system in direct-gap semiconductors.
The excitation-dependent photoluminescence (PL) of ZnSe nanocrystals (NC) grown on GaAs (100) substrate was studied. The PL spectra observed corroborate previous observations of a bimodal size distribution of NC grown, and, in addition, evidence the existence of spectral diffusion with extend dependent on excitation power. Besides, it was also shown that at relatively intense excitation an extra band has arose in luminescence spectra due to biexcitons confined in NC of 3.5-4.0 nm size. The binding energy of these biexcitons was as large as 23 meV. In recent years the properties of highly excited semiconductor nanocrystals (NC) widely referred to as semiconductor quantum dots (QD) have gained much attention largely due to advance in application development motivated by the demonstration of effective lasing in CdSe-based QD [1]. At the same time the semiconductor compound which has received the most intense interest in previous years has been ZnSe known to have a room temperature direct band gap of 2,7 eV that corresponds to emission in the blue region of the spectrum. Properly tailored ZnSe-based QD are well suited for short wavelength light emitters, a fact recognized worldwide by research groups several of whom have expanded a great deal of effort attempting to produce ZnSe NC of high quality [2,3]. However properties of extremely small ZnSe crystals under intense optical excitation remain unexplored and require better insight.Recently, a vapor phase technique has been utilized to grow ZnSe nanocrystals atop GaAs (100) substrate [4]. The distinguishing feature of applied technique was the use of horizontal type quartz reactor exploiting a large (~250°C/cm) temperature gradient in the deposition zone just in front of substrate on which ZnSe NC were collected. Applied characterization techniques indicated the formation of two distinct sets of nanocrystals on the same substrate. The average characteristic sizes of NC in these sets have been estimated to be in the ranges of 36.6-41.2 and 3.5-4.0 nm while the effective Bohr radius ( ) a B of the free exciton in bulk ZnSe is known to be~50 C [5]. From these facts one can easily realize that samples described in Ref. 4 are unique since they provide chance to compare behavior of carriers confined in sub-excitonic and superexcitonic volumes of ZnSe by studying photoluminescence (PL) just from the same single sample. The present work extends research on those samples with the aim to investigate their emission spectra under high level of optical excitation.The excitation source was N 2 laser (337.1 nm) with optical pulses of 10 -8 s and 100 Hz repetition rate. In our case this excitation can be treated as a quasi-continuous-wave (qCW) excitation as the pulses used were long enough compared to all characteristic times known for nonequilibrium e-h system in direct-gap semiconductors.
Using the Vakarchuk formulae for the density matrix, we calculate the number N k of atoms with momentumhk for the ground state of a uniform one-dimensional periodic system of interacting bosons.We obtain for impenetrable point bosons N0 ≈ 2is no condensate or quasicondensate on low levels at large N . For almost point bosons with weak. In this case, the quasicondensate exists on the level with k = 0 and on low levels with k = 0, if N is large and β is small (e.g., for N ∼ 10 10 , β ∼ 0.01). A method of measurement of such fragmented quasicondensate is proposed.
According to the well-known analysis by Noziéres, the fragmentation of the condensate increases the energy of a uniform interacting Bose system. Therefore, at T = 0 the condensate should be nonfragmented. We perform a more detailed analysis and show that the result by Noziéres is not general. We find that, in a dense Bose system, the formation of a crystal-like structure with a fragmented condensate is possible. The effect is related to a nonzero size of real atoms. Moreover, the wave functions studied by Noziéres are not eigenfunctions of the Hamiltonian and, therefore, do not allow one to judge with confidence about the structure of the condensate in the ground state. We have constructed the wave functions in such a way that they are eigenfunctions of the Hamiltonian. The results show that the fragmentation of the condensate (quasicondensate) is possible for a finite one-dimensional uniform system at low temperatures and a weak coupling.Keywords: interacting bosons, fragmented condensate, quasicondensate.for the Bose gas in a double-well potential of a trap, the state with two condensates, which are localized at different minima of a trap, is energy-gained [19,20]. The other examples of a fragmented condensate and the references can be found in [7,21]. The solutions with a fragmented condensate were obtained for one-dimensional (1D) and two-dimensional (2D) Bose gases in a trap [22,23,24,25,26,27,28,29]. The fragmentation of the condensate of quasiparticles is discussed in review [30].In the present work, we will analyze the problem of fragmentation of the condensate in more details than in [17,18]. We will show that the fragmentation of the condensate is possible even for a uniform system (analogous result was obtained previously [31] without general analysis of the problem of fragmentation). In this case, the condensates are not separated in the r-space, in contrast to the solutions in [19,20,22,23,24,25,26,27,29].We will consider the problem step by step, by passing from a more crude description to an accurate one. Periodic Bose system: quasi-single-particle approachIn this section, we will carry on the analysis similar to the analysis by Pollock [16] and by Noziéres [17,18] and will take into account the nonpointness (nonzero intraction radius) of real particles. Consider the periodic system of N bosons with repulsive interaction (ν(0) > 0).
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