Numerical simulation of a coupling effect on electronic states in quantum dots

Lasers operating at 1.3 μm have attracted considerable attention owing to their potential to provide efficient light sources for next-generation high-speed communication systems. InAs/GaAs quantum dots (QDs) were pointed out as a reliable low-cost way to attain this goal. However, due to the lattice mismatch, the accumulation of strain by stacking the QDs can cause dislocations that significantly degrade the performance of the lasers. In order to reduce this strain, a promising method is the use of InAs QDs embedded in InGaAs layers. The capping of the QD layer with InGaAs is able to tune the emission toward longer and controllable wave-lengths between 1.1 and 1.5 μm. In this work, using the effective-mass envelope-function theory, we investigated theoretically the optical properties of coupled InAs/GaAs strained QDs based structures emitting around 1.33 μm. The calculation was performed by the resolution of the 3D Schrödinger equation. The energy levels of confined carriers and the optical transition energy have been investigated. The oscillator strengths of this transition have been studied with and without taking into account the strain effect in the calculations. The information derived from the present study shows that the InGaAs capping layer may have profound consequences as regards the performance of an InAs/GaAs QD based laser. Based on the present results, we hope that the present work make a contribution to experimental studies of InAs/GaAs QD based structures, namely the optoelectronic applications concerning infrared and mid-infrared spectral regions as well as the solar cells.     

Investigation of gain recovery for InAs/GaAs quantum dot semiconductor optical amplifiers by rate equation simulation

The gain recoveries in quantum dot semiconductor optical amplifiers (QD SOAs) are numerically studied by rate equation simulation. Similar to the optical pump-probe experiment, the injection of double 150 fs optical pulses is used to simulate the gain recovery of a weak continuous signal under different injection levels, inhomogeneous broadenings, detuning wavelengths, and pulse signal energies for the QD SOAs. The obtained gain recoveries are then fitted by a response function with multiple exponential terms to determine the response times. The gain recovery can be described by three exponential terms with the time constants, which can be explained as carrier relaxation from the excited state to the ground state, carrier captured by the excited state from the wetting layer, and the supply of the wetting layer carriers. The fitted lifetimes decrease with the increase of the injection currents under gain unsaturation, slightly decrease with the decrease of inhomogeneous broadening of QDs, and increase with the increase of detuning wavelength between continuous signal and pulse signal and the increase of the pulse energy.     

Effect of inter-level relaxation and cavity length on double-state lasing performance of quantum dot lasers

Double-state lasing phenomena are easily observed in self-assembled quantum dot (QD) lasers. The effect of inter-level relaxation rate and cavity length on the double-state lasing performance of QD lasers is investigated on the basis of a rate equation model. Calculated results show that, for a certain cavity length, the ground state (GS) lasing threshold current increases almost linearly with the inter-level relaxation lifetime. However, as the relaxation rate becomes slower, the ratio of excited state (ES) lasing threshold current over the GS one decreases, showing an evident exponential behavior. A relatively feasible method to estimate the inter-level relaxation lifetime, which is difficult to measure directly, is provided. In addition, fast inter-level relaxation is favorable for the GS single-mode lasing, and leads to lower wetting layer (WL) carrier occupation probability and higher QD GS capture efficiency and external differential quantum efficiency. Besides, the double-state lasing effect strongly depends on the cavity length.     

Effect of inter-level relaxation and cavity length on double-state lasing performance of quantum dot lasers

Double-state lasing phenomena are easily observed in self-assembled quantum dot (QD) lasers. The effect of inter-level relaxation rate and cavity length on the double-state lasing performance of QD lasers is investigated on the basis of a rate equation model. Calculated results show that, for a certain cavity length, the ground state (GS) lasing threshold current increases almost linearly with the inter-level relaxation lifetime. However, as the relaxation rate becomes slower, the ratio of excited state (ES) lasing threshold current over the GS one decreases, showing an evident exponential behavior. A relatively feasible method to estimate the inter-level relaxation lifetime, which is difficult to measure directly, is provided. In addition, fast inter-level relaxation is favorable for the GS single-mode lasing, and leads to lower wetting layer (WL) carrier occupation probability and higher QD GS capture efficiency and external differential quantum efficiency. Besides, the double-state lasing effect strongly depends on the cavity length.     

Wavelength and polarization selective multi-band tunnelling quantum dot detectors

The reduction of the dark current without reducing the photocurrent is a considerable challenge in developing far-infrared (FIR)/terahertz detectors. Since quantum dot (QD) based detectors inherently show low dark current, a QD-based structure is an appropriate choice for terahertz detectors. The work reported here discusses multi-band tunnelling quantum dot infrared photo detector (T-QDIP) structures designed for high temperature operation covering the range from mid-to far-infrared. These structures grown by molecular beam epitaxy consist of a QD (InGaAs or InAlAs) placed in a well (GaAs/AlGaAs) with a double-barrier system (AlGaAs/InGaAs/AlGaAs) adjacent to it. The photocurrent, which can be selectively collected by resonant tunnelling, is generated by a transition of carriers from the ground state in the QD to a state in the well coupled with a state in the double-barrier system. The double-barrier system blocks the majority of carriers contributing to the dark current. Several important properties of T-QDIP detectors such as the multi-colour (multi-band) nature of the photoresponse, the selectivity of the operating wavelength by the applied bias, and the polarization sensitivity of the response peaks, are also discussed.     

Nanostructure model and optical properties of InAs/GaAs quantum dot in vertical cavity surface emitting lasers

We apply 8-band k.p model to study InAs/GaAs quantum dots (QDs). The strain was calculated using the valence force field (VFF) model which includes the four nearest-neighbour interactions. For the optical properties, we take into account both homogeneous and non-homogeneous broadening for the optical spectrum. Our simulation result is in good agreement with the experimental micro-photoluminescence (μ-PL) result which is from InAs/GaAs QD vertical cavity surface emitting lasers (VCSELs) structure wafer at room temperature. Accordingly, our simulation model is used to predict the QD emission from this QD-VCSELs structure wafer at different temperature ranging from 200–400 K. The simulation results show a decrease of 41 meV of QD ground state (GS) transition energy from 250–350 K. The changes of QDGS transition energy with different temperature indicate the possible detuning range for 1.3-μm wave band QD-VCSELs applications without temperature control. Furthermore, QD differential gain at 300 K is computed based on this model, which will be useful for predicting the intrinsic modulation characteristics of QD-VCSELs.     

GaAs pyramidal quantum dot coupled to wetting layer in an AlGaAs matrix: A strain-free system

In this contribution, the electronic and linear and nonlinear optical properties of pyramid-shaped GaAs quantum dots (QDs) coupled to wetting layer (WL) in an Al_0.3Ga_0.7As matrix have been investigated. This nanostructure is relaxed from strain effects due to very small lattice-mismatching. Three transitions of P-to-S, WL-to-P, and WL-to-S were considered and the corresponding transition dipole moments, oscillator strengths, and linear and nonlinear optical properties regarding to these transitions were investigated as a function of the QD height. The results showed that for P-to-S transition, which is a purely in-plane-polarized transition, the dependence of electronic and optical properties on the size is moderate and can be neglected. But for WL-to-P and WL-to-S transitions, which are in-plane- and z-polarized transitions, respectively, the electronic as well as optical properties are strongly size-dependent. Furthermore, a competition between WL-to-S and WL-to-P transitions was observed when the QD size changed.     

Quantum dot semiconductor laser with optoelectronic feedback

The optoelectronic feedback (OEF) in quantum dot semiconductor lasers (QD SLs) is studied theoretically where a model includes wetting layer ground state and excited state for QDs are included separating electrons and holes in their dynamics. Both positive and negative OEF are studied. The time series of photon density, the phase portraits of carriers in the states are studied. The parameters affecting OEF are examined where an excitability is seen. The QD SL is found to be more sensitive to the changes in time delay compared with other SLs and a complicated routs are seen in the behavior of QD SL.     

The transition mechanisms of quantum-dot/quantum-well mixed-mode infrared photodetectors

The transition mechanisms of a 10-period quantum-dot (QD)/quantum-well (QW) mixed-mode infrared photodetector is investigated in this paper. Both mid-wavelength infrared (MWIR) and long-wavelength infrared (LWIR) responses are observed for the device. The lower normal incident absorption of the LWIR peak suggests that the QW intra-band transition is responsible for the response while the QD intra-band transition for the MWIR response. Due to the coexistence of MWIR and LWIR responses, the MWIR response should be resulted from one-photon transition while the LWIR response from the two-photon transition. To explain the transition mechanisms of the MMIP device, a model is proposed in this paper. The increases of both MWIR and LWIR responses with increasing measurement temperatures observed for the device are attributed to the increase of electrons in the QW ground state/wetting layer state resulted from the increase of one-photon absorption process with increasing temperatures.     

Dynamics of optical pulse amplification and saturation in multiple state quantum dot semiconductor optical amplifiers

We have developed a novel analytical model, which describes the dynamic characteristics of optical pulse amplification and saturation in three state quantum dot (QD) semiconductor optical amplifiers (SOAs). The model takes into account the effect of the ground state, the excited state and the 2-dimensional wetting layer. The model is simple, accurate and fast, which makes it suitable for device design and characterization. The derived model has been utilized to study large-signal cross-gain modulation and crosstalk in multi-channel QD-SOA. Analytical expressions for large signal cross-gain modulation and crosstalk in multichannel SOA are derived. The effect of the dot relaxation/escape lifetimes and energy separation between QD states on cross-gain modulation and crosstalk are also studied. Our calculations show that by reducing QD energy state separation, via engineering the dot size and composition, one can reduce the cross-gain modulation efficiency and reduce crosstalk in multi-channel QD-SOAs.     

Polarization-dependent carrier dynamics in a passive InAs/InP quantum dot waveguide

We investigate carrier dynamics in a passive InAs/InP quantum dot (QD) waveguide using 255 fs optical pulses at a central wavelength of 1568 nm. We observe strong anisotropy of absorption saturation for different polarizations. Pump-probe measurements indicate the presence of carrier relaxation dynamics on a timescale in the order of tens of picoseconds due to cascaded relaxation of carriers generated by two-photon absorption (TPA) from the bulk region to the QDs via the wetting layer. These relaxation timescales are much longer than in QD amplifiers. Our observations are supported by a rate-equation model which includes TPA, showing good agreement with the pump-probe measurements.     

Morphology response to strain field interferences in stacks of highly ordered quantum dot arrays

Twofold stacked InGaAs/GaAs quantum dot (QD) layers are grown on GaAs(001) substrates patterned with square arrays of shallow holes. We study the surface morphology of the second InGaAs QD layer as a function of pattern periodicity. Comparing our experimental results with a realistic simulation of the strain energy density E(str) distribution, we find that the second InGaAs QD layer sensitively responds to the lateral strain-field interferences generated by the buried periodic QD array. This response includes the well-known formation of vertically aligned QDs but also the occurrence of QDs on satellite strain energy density minima. Our calculations show that base size and shape as well as lateral orientation of both QD types are predefined by the E(str) distribution on the underlying surface.     

Carrier capture and relaxation through a continuum background in InAs quantum dots

Carrier capture and relaxation in self-assembled InAs/GaAs quantum dots (QDs) have been studied, using bleaching rise time measurements for both the ground state (GS) and the first excited state (ES) transition, as a function of temperature (5, 77 and 293 K) and excitation density. We surprisingly observe that the bleaching rise time is longer for the ES than for the GS, indicating that the ES does not act as an intermediate state. At intermediate excitation density where the carrier relaxation is usually explained by Auger scattering, we still observe a temperature dependence pointing towards a single phonon emission process. For high excitation density, we observe a temperature-dependent plateau in the initial bleaching rise time, contradicting an Auger scattering-based relaxation model. Both these experimental results point towards a relaxation through the continuum background, followed by a single LO-phonon emission towards the QD GS.     

Spin coherence during optical excitation of a single nitrogen-vacancy center in diamond

We examine the quantum spin state of a single nitrogen-vacancy (NV) center in diamond at room temperature as it makes a transition from the orbital ground state (GS) to the orbital excited state (ES) during nonresonant optical excitation. While the fluorescence readout of NV-center spins relies on conservation of the longitudinal spin projection during optical excitation, the question of quantum phase preservation has not been examined. Using Ramsey measurements and quantum process tomography of the optical excitation process, we measure a trace fidelity of F=0.87±0.03, which includes ES spin dephasing during measurement. Extrapolation to the moment of optical excitation yields F≈0.95. This result provides insight into the interaction between spin coherence and nonresonant optical absorption through a vibronic sideband.     

Theoretical analysis of the electronic structure of truncated-pyramidal GaN/AlN quantum dots

We present a theoretical analysis of the electronic structure of GaN/AlN quantum dots (QD) with a hexagonal, truncated-pyramidal shape. We use a Fourier-transform technique that we had previously developed to calculate the 3D strain and built-in electric fields due to the QD structure. The electron and hole energy levels and wavefunctions are then calculated in the framework of an 8-band k·P model (with zero spin–orbit splitting), using an efficient plane-wave expansion method. We show that because of the large built-in piezoelectric and spontaneous polarization fields, the calculated transition energy is sensitive to variations in the wetting layer width, pyramid top diameter and also to the values chosen for the piezo-electric constants and spontaneous polarization values of bulk GaN and AlN. Numerical results are presented for a set of GaN/AlN QD structures that have been studied experimentally and described in the literature. We find that the calculated value of the ground-state optical transition energy for these structures is in good agreement with experiment.     

Fabrication and characterization of a vertical pillar structure including a self-assembled quantum dot and a quantum well

We fabricate and characterize a novel vertical pillar structure including a self-assembled InAs quantum dot (QD) and an InGaAs quantum well (QW). The vertical current through both the InAs QD and an electrostatically defined QD made in the InGaAs QW can be measured by adjusting the position of the InGaAs QD in the QW plane relative to the InAs QD with two side-gate voltages applied independently. We study optical response of the current through the vertical double QD by irradiating light, which is assumed to be mainly absorbed in the InAs QDs. We successfully probe a time-dependent energy level shift due to the Coulomb interaction from holes trapped in the vicinity of the pillar.     

Optical characterization of individual quantum dots

Optical characterization of single quantum dots (QDs) by means of micro-photoluminescence (μPL) will be reviewed. Both QDs formed in the Stranski–Krastanov mode as well as dots in the apex of pyramidal structures will be presented. For InGaAs/GaAs dots, several excitonic features with different charge states will be demonstrated. By varying the magnitude of an external electric or magnetic field and/or the temperature, it has been demonstrated that the transportation of carriers is affected and accordingly the charge state of a single QD can be tuned. In addition, we have shown that the charge state of the QD can be controlled also by pure optical means, i.e. by altering the photo excitation conditions. Based on the experience of the developed InAs/GaAs QD system, similar methods have been applied on the InGaN/GaN QD system.     

Stress evolution during growth of bilayer self-assembled InAs/GaAs quantum dots

We investigated the stress evolution during molecular-beam epitaxy of bilayer InAs/GaAs(001) quantum dot (QD) structures in real time and with sub-monolayer precision using an in-situ cantilever beam setup. During growth of the InAs at 470 °C a stress of 5.1 GPa develops in the wetting layer, in good agreement with the theoretical misfit stress. At a critical thickness of 1.5 monolayers the strain is relieved by the QD formation. In the case of InAs/GaAs bilayer structures, the second InAs layer grows identical to the first for GaAs spacer thicknesses exceeding ∼13 nm. For thinner spacers the critical thickness for the 2D/3D transition in the second layer decreases. The stress of the second InAs layer does not reach the value of the first, indicating that InAs QDs grow on partially strained areas due to the strain field of the previous InAs layer. PACS 68.35.-p; 68.35.Gy; 68.65.Hb; 81.07.Ta; 81.10.Aj     

Large Signal Modulation Characteristics in the Transition Regime for Two-State Lasing Quantum Dot Lasers

Large-signal modulation capability,as an important performance indicator,is directly related to the high-speed optical communication technology involved.We experimentally and theoretically investigate the large-signal modulation characteristics of the simultaneous ground-state(GS) and the excited-state(ES) lasing in InAs/GaAs quantum dot laser diodes.The large-signal modulation capability of total light intensity in the transition regime from GS lasing to two-state lasing is unchanged as the bias-current increases.However,GS and ES large-signal eye diagrams show obvious variations during the transition.Relaxation oscillations and large-signal eye diagrams for GS,ES,and total light intensities are numerically simulated and analyzed in detail by using a rate-equation model.The findings show that a complementary relationship between the light intensities for GS and ES lasing exists in both the transition regime and the two-state lasing regime,leading to a much smaller overshooting power and a shorter settling time for the total light intensity.Therefore,the eye diagrams of GS or ES lasing are diffuse whereas those of total light intensity are constant as the bias-current increases in the transition regime.     

Enhancement of the photoluminescence intensity of a single InAs/GaAs quantum dot by separate generation of electrons and holes

It is demonstrated that the microphotoluminescence (μPL) spectrum of a single InAs/GaAs self-assembled quantum dot (QD) undergoes considerable changes when the primary laser excitation is complemented with an additional infrared laser. The primary laser, tuned slightly below the GaAs band gap, provides electron-hole pairs in the wetting layer (WL), as well as excess free electrons from ionized shallow acceptors in the GaAs barriers. An additional IR laser with a fixed energy well below the QD ground state transition generates excess free holes from deep levels in GaAs. The excess electron and hole will experience diffusion separately, due to the time separation between the two events of their generation, to eventually become captured into the QD. Although the generation rates of excess carries are much lower than that of the electron-hole pair generation in the WL, they considerably influence the QD emission at low temperatures. The integrated PL intensity increases by several times as compared to single-laser excitation, and the QD exciton spectrum is redistributed in favor of a more neutral charge configuration. The dependence of the observed phenomenon on the powers of the two lasers and the temperature has been studied and is consistent with the model proposed. The concept of dual excitation could be successfully applied to different low-dimensional semiconductor structures in order to manipulate their charge state and emission intensity. The text was submitted by the authors in English.