Exciton states in wurtzite InGaN/GaN quantum wells: Strong built-in electric field and interface optical-phonon effects

Considering the strong built-in electric field (BEF) effects and large exciton–phonon interactions, we investigate the exciton states confined in an InGaN/GaN single quantum well (QW) by using the Lee–Low–Pines variational method. We find that the exciton state modification caused by the exciton–phonon interactions is remarkable. The exciton energy shift due to exciton–phonon interactions increases monotonically if the well width increases. With increasing the In fraction, the exciton energy shift firstly increases to a maximum, then decreases. The BEF has a significant influence on the exciton states in a QW with large well width. The physical reasons have been analyzed in detail. Good agreement for the zero-phonon peak energies and the Huang–Rhys factor has been obtained between our numerical results and the corresponding experimental measurements.     

Effects of laser field and electric field on impurity states in zinc-blende GaN/AlGaN quantum well

Based on the effective-mass approximation, the competition effects between the laser field and applied electric field on impurity states have been investigated variationally in the ZB GaN/AlGaN quantum well (QW). Numerical results show that for any laser field, the electric field makes the donor binding energy present asymmetric distribution with respect to the center of the QW. Moreover, when the laser field is weak, the electric field effects are obvious on the donor binding energy; however, the electric field effects are insensitive to the variation of donor binding energy in the ZB GaN/AlGaN QW with strong laser field.     

Influence of quantum well inhomogeneities on absorption,spontaneous emission,photoluminescence decay time,and lasing in polar InGaN quantum wells emitting in the blue-green spectral region

It is shown that in polar InGaN QWs emitting in the blue-green spectral region a Stokes shift between spontaneous emission (SE) and optical transition observed in contactless electroreflectance (CER) spectrum (absorption-like technique) can be observed even at room temperature, despite the fact that the SE is not associated with localized states. Time resolved photoluminescence measurements clearly confirm that the SE is strongly localized at low temperatures whereas at room temperature the carrier localization disappears and the SE can be attributed to the fundamental transition in this QW. The Stokes shift is observed in this QW system because of the large built-in electric field, i.e., the CER transition is a superposition of all optical transitions with non-zero electron-hole overlap integrals and, therefore, the energy of this transition does not correspond to the fundamental transition of InGaN QW. Lasing from this QW has been observed at the wavelength of 475 nm, whereas the SE was observed at 500 nm. The 25 nm shift between the lasing and SE is observed because of a screening of the built-in electric field by photogenerated carriers. However, our analysis shows that the built-in electric field inside the InGaN QW region is not fully screened under the lasing conditions.     

Donor impurity states in direct-gap SiGe quantum well: Applied electric field and quantum size effects

Within the framework of the effective-mass approximation and variational procedure, competition effects between applied electric field and quantum size on donor impurity states in the direct-gap Ge/SiGe quantum well (QW) have been investigated theoretically. Numerical results show that the applied electric field (quantum size) dominates electron and impurity states in direct-gap Ge/SiGe QW with large (small) well width. Moreover, the competition effects also induce that the donor binding energies show obviously different behaviors with respect to electric field in the QW with different well widths. In particular, when the impurity is located at left boundary of the QW, the donor binding energy is insensitive to the variation of well width when well width is large for any electric field case.     

An exciton in a quantum well in the presence of crossed electric and magnetic fields

An analytical approach to the problem of the Wannier–Mott exciton in a semiconductor quantum well (QW) in the presence of external magnetic and electric fields is developed. The magnetic field is taken to lie in the heteroplanes while the electric field is directed perpendicular to the heteroplanes. Explicit dependencies of the energy levels and wave-functions of the exciton on the magnitudes of the fields for a wide range of the width of the QW are obtained. For the narrow QW, the results are valid for arbitrary electron and hole effective masses. In the case of intermediate and wide QWs, the adiabatic approximation implying the extreme difference of the electron and hole masses is used. In the intermediate QW, the states of the relative motion are the standard Coulomb states affected by the external fields while the states of the centre of mass are the size-quantized states in the QW. We focus particularly on the delocalized states caused by the external electric field and the motion of the excitons centre of mass in the magnetic field. These states are localized far away from the Coulomb centre. A strong influence of the boundaries of the wide QW on the delocalized exciton states is found to occur. Estimates of the expected values are made using typical parameters associated with GaAs QW.     

Bound States and the Third Harmonic Generation in an Electric Field Biased Semi-parabolic Quantum Well

Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems.     

Size-dependent surface states of strained cobalt nanoislands on Cu(111)

Low-temperature scanning tunneling spectroscopy over Co nanoislands on Cu(111) showed that the surface states of the islands vary with their size. Occupied states exhibit a sizable downward energy shift as the island size decreases. The position of the occupied states also significantly changes across the islands. Atomic-scale simulations and ab initio calculations demonstrate that the driving force for the observed shift is related to size-dependent mesoscopic relaxations in the nanoislands.     

Alternating layer and island growth of Pb on Si by spontaneous quantum phase separation

Real-time in situ x-ray studies of continuous Pb deposition on Si(111)-(7x7) at 180 K reveal an unusual growth behavior. A wetting layer forms first to cover the entire surface. Then islands of a fairly uniform height of about five monolayers form on top of the wetting layer and grow to fill the surface. The growth then switches to a layer-by-layer mode upon further deposition. This behavior of alternating layer and island growth can be attributed to spontaneous quantum phase separation based on a first-principles calculation of the system energy.     

外电场下BN分子的结构及性质

采用QCISD方法研究了BN基态分子在不同场强条件下的稳定构型及激发态性质。分析了外电场对BN分子键长、总能量、能级、谐振频率和红外谱强度以及对BN分子前10个激发态的激发能、振子强度等的影响。结果表明随着正向电场的逐渐增大, BN分子键长先减小后增大;分子总能量则先增大后减小;分子电偶极矩μ增大;费米能级和能隙均减小。谐振频率及红外谱强度均随正向电场的增大而增大。由基态到第1激发态的波长减小,激发能增大,而基态至第2－10激发态的波长增大而激发能减小。     

外电场下BN分子的结构及性质

采用QCISD方法研究了BN基态分子在不同场强条件下的稳定构型及激发态性质。分析了外电场对BN分子键长、总能量、能级、谐振频率和红外谱强度以及对BN分子前10个激发态的激发能、振子强度等的影响。结果表明随着正向电场的逐渐增大, BN分子键长先减小后增大;分子总能量则先增大后减小;分子电偶极矩 增大;费米能级和能隙均减小。谐振频率及红外谱强度均随正向电场的增大而增大。由基态到第1激发态的波长减小,激发能增大,而基态至第2-10激发态的波长增大而激发能减小。     

Influence of exciton energy on intersubband transition of chirped superlattice GaAs/AlGaAs quantum cascade laser

The influence of exciton energy on intersubband transition was simulated for a chirped supperlattice quantum cascade laser of GaAs/Al_xGa_1-xAs. Exciton energy was modelled as a function of QW width for alloys of various percentages of constituent elements. The results showed that the exciton energy decreased proportionally with increasing QW width. Models were also generated to study exciton energy as a function of the percent alloy contents of Al_xGa_1-xAs barriers for QWs of various widths. Exciton energy showed characteristics of higher discrete energy when QW width was narrower. Transition energy was also simulated from e₁ and e₂ to the 1s exciton state as functions of applied electric field at various QW widths. Our simulation results showed that the transition energy from e₂ to the 1s exciton state increased proportionally to the increasing strength of the electric field. This transition energy was indicative of THz range radiation.     

Shake-up intersubband transitions observed in GaAs/AlGaAs quantum wells

Shake-up transitions involving QW hole subbands have been observed as satellites in selective photoluminescence spectra of undoped GaAs/AlGaAs QWs. These shake-up transitions are explained in terms of an interaction between localized exciton and valence-band hole states attached to the QW subbands, in which holes are shaken up from the n=1 heavy hole subband to higher subbands, either the n=1 light hole subband or the n=2 heavy hole subband. The required localization is due to the interface roughness; thus these new transitions are of intrinsic origin. From the observation of the intersubband shake-up processes we derive direct information about the hole inter-subband energies. Furthermore, the satellite intensity is strikingly enhanced in the presence of a magnetic field due to an increasing exciton localization related to the compression of its wave function in the field. The exciton wave function compression continues until its radius in the plane of the well is comparable with the radius of the "flat island" characterized by constant QW width. Accordingly, from the magnetic field dependence of the shake-up satellite intensity we can roughly estimate the size of the "flat islands" and consequently probe the interface roughness.     

Electric field effects on the states of an exciton in square cross-section quantum well wires

The Letter studies the role of the external electric field on the binding energy of the exciton states in square cross-section quantum well wires. Using the effective-mass approximation within a variational scheme and expanding the wave function into Fourier series, we calculate the binding energies of the ground state as well as that of the excited states as the functions of the geometry and the strength of the applied electric field. In the presence of an electric field, it is found that for the ground state the Stark effect is redshift, and for the first and the second excited state the binding energy are split into two levels which will change in contrary situation along with the increasing of the strength of the applied electric field.     

Exciton states in asymmetric GaInNAs/GaAs coupled quantum wells in an applied electric field

The electronic and optical properties of exciton states in GaInNAs/GaAs coupled quantum well (CQW) structure have been theoretically investigated by solving the Schrödinger equation in real space. The effect of well width on the exciton states has been also studied by varying the well width from 5?nm to 10?nm in asymmetric structures. The electron, hole and exciton states are calculated in the presence of an applied electric field. It is found that there are two direct (bright) exciton states with the largest oscillator strengths. Their energies weakly depend on the electric field due to the compensation between the blue shift and red shift of the electron–hole pair states. In addition, these two states are overlap in the case of symmetric CQWs and one of them is then shifted to higher energy in asymmetric CQWs. The ground state exciton has the binding energy of approximately 7.3?meV and decrease to around 3.0?meV showing the direct to indirect transition of the ground state. The direct–indirect crossover is observed at different electric field for different structure. It happens at the electric field when the e1–e2 electron anticrossing or h1–h2 hole anticrossings is observed, so that the crossover can be controlled by the well width of CQWs structure.     

Bound States and the Third Harmonic Generation in an Electric Field Biased Semi-parabolic Quantum Well

Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic Q W have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic Q W systems.     

Lateral electric field effects on quantum size confinement in cylindrical quantum dot under parabolic potential

Within the effective mass approximation, we investigated theoretically the ground-state energy of a single particle and the binding energy of the neutral donor impurity (D⁰) affected by a lateral electric field in a parabolic quantum dot (QD). The results show that the electron and the hole ground-state energy and the band to band transition energies shift to lower values (red shift) by increasing the field intensity. The quantum Stark shift (QSS) for the electron increases rapidly in the quasi spherical QD (QSQD) by increasing the lateral field, whereas for the hole it increases monotony. In the cylindrical QDs (CQDs), we found that the QSS for electron and hole increase monotonically. The quantum size, lateral electric field and impurity position effect on the binding energy of neutral donor (D⁰) is studied. Unexpected behavior of D⁰ in quantum well limit (QW), the binding energy of D⁰ is increasing (blue shift) with increasing QD radius R$R$ at the presence of a lateral electric field. It appears that for a fixed size of the QD, the off-center binding energy decreases when the impurity ion is displaced from the center to the QD borders, while it is shifted to lower energy with increasing the field.     

Evidence for Fermi level shift in GaInAs/GaAs quantum wells upon nitrogen incorporation

GaInAs/GaAs and GaInNAs/GaAs quantum well (QW) structures grown by metalorganic vapor phase epitaxy have been studied by contactless electroreflectance spectroscopy. In addition to the N-related redshift of QW transitions, an increase in the electric field in the GaAs cap layer has been observed after the incorporation of nitrogen atoms into the GaInAs QW. This observation is associated with the tendency of the Fermi level shift to a given energy in the GaInNAs QW region due to N-related defects.     

Finite barrier width effects on exciton states and optical properties in wurtzite InGaN/GaN quantum well

Exciton states and optical properties in wurtzite (WZ) InGaN/GaN quantum well (QW) are investigated theoretically, considering finite barrier width and built-in electric field effects. Numerical results show that when the barrier width increases, the ground-state exciton binding energy, the interband transition energy and the integrated absorption probability increase first and then they are insensitive to the variation of the barrier width. For any barrier width, the ground-state exciton binding energy and the integrated absorption probability have a maximum when the well width is 1 nm; moreover, the integrated absorption probability goes to zero when the well width is larger than 6 nm. In addition, the competition effects between the built-in electric field and quantum confinement are also investigated in the WZ InGaN/GaN QW.     

The origin of spectral distortion in electric field modulation spectroscopy based on scanning tunneling microscopy

Electric field modulation spectroscopy using scanning tunneling microscopy (STM-EFMS) measurements were performed for a Si(1 1 1) surface with epitaxially-grown β-FeSi₂ islands. STM-EFMS spectra acquired around the indirect energy gap of Si reproduced the photon energy peak position observed in conventional macroscopic EFMS experiments. However, a considerable discrepancy was found in the energy position of the accompanying spectral dip. We examined two possibilities for the cause of this discrepancy. The first interpretation is that the STM-‘EFMS’ spectra may simply reflect the local density of states based on essentially the same principle as that of tunneling spectroscopy. However, this interpretation is ruled out by the facts that almost identical STM-EFMS spectra are obtained also out of the regime of tunneling. The second interpretation is a spectral distortion due to a large electric field steadily built in the sample surface, which is supported experimentally by a spectral shift of the dip energy that is induced by altering the tip-induced band bending.     

施加电场的半抛物量子阱中的电光效应

利用量子力学中的紧致密度矩阵方法，研究了施加电场的半抛物量子阱中的电光效应。通过位移谐振子变换，得到了系统中的电子态的精确解。对典型的GaAs材料进行数值计算的结果表明，随着电场强度的增加，电光效应系数几乎线性随之增加；但是随着半抛物量子阱受限势频率的增加，电光效应系数单调地减小；而且在同样的电场强度及抛物束缚势频率作用下，半抛物量子阱模型中的电光效应系数比抛物量子阱模型中的值大两个数量级，这是由于我们所选模型本身的非对称性以及电场进一步使这种非对称性增强的缘故。