Intersubband scattering as a tool to study the symmetry properties of a parabolic quantum well

The electron mobility in parabolic quantum wells is measured as a function of carrier density at low temperatures. The curves display pronounced maxima that indicate the onset of intersubband scattering, i.e. the population of another subband. We find that the population of a given subband only depends on the total carrier density almost independent of the position of the wavefuntion within the well which can be tuned via a front and back gate electrode. This is in agreement with predictions for a perfect parabolic potential. If a potential spike is inserted in the center of the PQW we find a complicated behavior for the mobility versus carrier density maxima which reflects the changed symmetry of the potential.     

Intersubband relaxation of hot carriers in quantum well systems

We use an ensemble Monte Carlo simulation of coupled electrons, holes and nonequilibrium polar optical phonons in multiple quantum well systems to model the intersubband relaxation of hot carriers measured in ultra-fast optical experiments. We have investigated the effect of various models of confined photon modes on the energy relaxation and intersubband transition rate in single quantum well and coupled well systems. In particular, the symmetry of the atomic displacement with respect to the quantum well has a marked effect on the relative intersubband versus intrasubband scattering rates, depending on whether one considers electrostatic boundary conditions(slab modes) or mechanical boundary conditions(guided modes). In single quantum wells systems, the overall intersubband relaxation time is not found to be strongly dependent on the confined mode model used due to competing effects of hot phonons and the relative intrasubband scattering rates. For coupled well systems, the relaxation rate is much more dependent on the exact nature of the phonon amplitude. Large effects are found associated with localized AlAs interface modes which dominate the intersubband relaxation time.     

Intersubband transitions in band gap engineered parabolic potential wells

Intersubband transitions in spike-inserted wide parabolic quantum wells are investigated. A thin potential barrier within the pure parabola devides the electron system in two well separated but strongly coupled layers, which in turn drastically changes the collective excitations scheme. In contrast to a pure parabolic quantum well where according to the generalised Kohn's Theorem only one fixed resonance is observed, the collective intersubband transitions recover the complex coupling and splitting scheme of the single particle states of a strongly coupled system. We interpret our experimental findings in terms of resonant tunnel processes and discuss them using simple model calculations.     

Electric field effect on the linear and nonlinear intersubband refractive index changes in asymmetrical semiparabolic and symmetrical parabolic quantum wells

By using the displacement harmonic variant method and the compact density matrix approach, the linear and nonlinear intersubband refractive index changes (RICs) in a semiparabolic quantum well (QW) with applied electric field have been investigated in detail. The simple analytical formulae for the linear and nonlinear RICs in the system were also deduced. The symmetrical parabolic QWs with applied electric fields were taken into account for comparison. Numerical calculations on typical GaAs QWs were performed. The dependence of the linear and nonlinear RICs on the incident optical intensity, the frequencies of the confined potential of the QWs and the strength of the applied electric field were discussed. Results reveal that the RICs in the semiparabolic quantum well system sensitively depend on these factors. The calculation also shows that the semiparabolic QW is a more ideal nonlinear optical system relative to the symmetric parabolic QW systems.     

Edge state equilibration in a two-subband system

In order to honor Jörg Kotthaus, I present unpublished experimental results which were obtained in 1994 when I was a postdoc in Munich.The scattering between edge states in the quantum Hall regime is strongly reduced compared to scattering in the bulk of a two-dimensional electron gas. For edge states with different Landau quantum numbers an equilibration length as long as 100μm has been determined. In the case of Landau levels with different spin quantum numbers this length may reach values of 1 mm. Here we set out to explore the equilibration between edge states with different subband quantum numbers. Using parabolic quantum wells as a tunable multi-subband system we find that intersubband scattering can reduce the equilibration length to values below 5μm.     

Effects of intersubband interaction on multisubband electron transport in single and double quantum wells

The multisubband electron transport properties are studied for doped single quantum well and gated double asymmetric quantum well structures. The effects due to intersubband interaction and screening of the ionized impurity scattering are also investigated. We show that intersubband coupling plays an essential role in describing the screening properties as well as the effect of ionized impurity scattering on the mobility in a doped single quantum well. For coupled double quantum well structures, negative transconductance is found theoretically which is due to resonant tunneling between the two quantum wells.     

Intersubband optical absorption of electrons in double parabolic quantum wells of Al_xGa_(1-x)As/Al_yGa_(1-y)As

Some realizable structures of double parabolic quantum wells(DPQWs) consisting of Al_xGa_(1-x)As/Al_yGa_(1-y)As are constructed to discuss theoretically the optical absorption due to the intersubband transition of electrons for both symmetric and asymmetric cases with three energy levels of conduction bands. The electronic states in these structures are obtained using a finite element difference method. Based on a compact density matrix approach, the optical absorption induced by intersubband transition of electrons at room temperature is discussed. The results reveal that the peak positions and heights of intersubband optical absorption coefficients(IOACs) of DPQWs are sensitive to the barrier thickness, depending on Al component. Furthermore, external electric fields result in the decrease of peak, and play an important role in the blue shifts of absorption spectra due to electrons excited from ground state to the first and second excited states. It is found that the peaks of IOACs are smaller in asymmetric DPQWs than in symmetric ones. The results also indicate that the adjustable extent of incident photon energy for DPQW is larger than for a square one of a similar size. Our results are helpful in experiments and device fabrication.     

Microscopic Many-Body Effects on Intersubband Resonance in Quantum Well

Considering the Coulomb many-body interactions, we investigate the intersubband optical processes of the quantum well by using the semiconductor Bloch equations. We calculate the evolution of intersubband absorption spectral line shape as a function of lattice temperature and electron density. It is found that the coupling of intersubband plasmons can reduce and red-shift the lower energy resonance, simultaneously enhance and blue-shift the higher energy resonance. The dependence of cascading resonances on temperature and electron density is also discussed.     

Electronic structure and nonlinear optical properties of a two-dimensional hexagonal quantum dot

In this work electronic structure, the linear and the third-order nonlinear refractive index changes as well as optical absorption coefficients of a two-dimensional hexagonal quantum dot are investigated. Energy eigenvalues and eigenfunctions of the system are calculated by the matrix diagonalization technique, and optical properties are also obtained using the compact density matrix approach. As our results indicate, both the dot size and the confinement potential have a great influence on the intersubband energy intervals, the transition probability and consequently, the linear and the third-order nonlinear refractive index changes and optical absorption coefficients.     

Polaron effect on linear and nonlinear intersubband optical absorption of a wurtzite GaN-based nanowire

Based on the density matrix approach and the perturbation treatment, the polaronic effect on the linear and nonlinear intersubband optical absorption coefficients in quasi-one-dimensional wurtzite nanowires (NWs) is investigated. The simple analytical formulas for polaronic states and the linear and nonlinear optical absorption coefficients in the NW systems are also deduced. Numerical calculation on a freestanding wurtzite GaN NW is performed. The polaronic effect and quantum size effect as well as the influence of incident optical intensity on the optical absorption properties are analyzed and discussed. The results show that, the polaronic effect results in significant increase of the absorption coefficients, and obvious decrease of saturation absorption intensity. In order to observe strong optical absorption, a nitride NW with relative small radius should be chosen. Moreover, a comparison with the situation of GaN-based quantum well systems is also done, and the profound physics is analyzed reasonably.     

Terahertz field-induced modulations of intersubband absorptions in quantum wells

Nonlinear optical properties of intersubband electrons in a 3-level quantum well under intense terahertz field are investigated by using a density matrix approach. The results show that the terahertz fields with different frequencies cause the distinct modulations of the intersubband absorptions. The terahertz-induced sideband and Autler--Towns splitting in the absorption spectrum are obtained, respectively for the terahertz-photon energy below and close to the transition energy between the ground and first excited state.     

Intersubband transition in quantum wells and triple-barrier diode infrared detector concepts

We present effective mass theory results for intersubband transition energies, oscillator strengths, and other quantities which are relevant to the design of quantum well devices. Results are presented in the form of contour plots for easy reference. Theory gives good agreement with existing experimental data by various research groups. In addition, a new quantum well infrared detector is proposed, which employs resonant tunneling in a triple-barrier diode. The device has a narrow bandwidth controlled by the resonance width and a very low dark current making high temperature (> 77 K) operation possible.     

Nonlinear optical properties of an exciton bound to an ionized donor impurity in quantum dots

In this study, a detailed investigation of the nonlinear optical properties of the (D⁺,X) complex in a disc-like parabolic quantum dot has been carried out by using the matrix diagonalization method and the compact density-matrix approach. First, the numeric calculations and analysis of the oscillator strength of intersubband quantum transition from the ground state into the first excited state at the varying confinement frequency have been performed. Second, the linear, third-order nonlinear, and total absorption coefficients and refractive indices have been investigated. It is observed that the confinement frequency of QDs and the intensity of the illumination have drastic effects on the nonlinear optical properties. In addition, we find that all kinds of absorption coefficients and refractive indices of an exciton in QDs shift to lower energies and their peak values have considerably decreases induced by the impurity.     

Intersubband transitions from the second subband in a coupled quantum wells structure

Asymmetrical coupled quantum wells structures with energy separation between the first two subbands of the order of 10–50 meV are key structures in the design of optically pumped intersubband lasers. In these structures the population of the second subband is not negligible and intersubband transitions from the second to higher excited subbands can be observed. In this work we investigate the temperature dependency of the intersubband transitions from the second subband in an asymmetrical coupled quantum wells structure. We show that this approach provides a direct way to measure the energy separation between the second subband and the Fermi energy which is a crucial parameter in the design of optically pumped intersubband lasers.     

Linear and nonlinear intersubband optical absorption in symmetric double semi-parabolic quantum wells

The linear and the nonlinear intersubband optical absorption in the symmetric double semi-parabolic quantum wells are investigated for typical GaAs/AlxGa1−xAs. Energy eigenvalues and eigenfunctions of an electron confined in finite potential double quantum wells are calculated by numerical methods from Schrödinger equation. Optical properties are obtained using the compact density matrix approach. In this work, the effects of the barrier width, the well width and the incident optical intensity on the optical properties of the symmetric double semi-parabolic quantum wells are investigated. Our results show that not only optical incident intensity but also structure parameters such as the barrier and the well width really affect the optical characteristics of these structures.     

Intersubband optical absorption coefficients and refractive index changes in a parabolic cylinder quantum dot

Optical absorption coefficients and refractive index changes associated with intersubband transition in a parabolic cylinder quantum dot are theoretically investigated. In this regard, the electronic structure of the dot is studied using the one band effective mass theory, and by means of the compact-density matrix approach the linear and nonlinear optical absorption coefficients and refractive index changes are calculated. The effects of the size of the dot, optical intensity and electromagnetic field polarization on the optical absorption coefficient and refractive index changes are investigated. It is found that absorption and refractive index changes are strongly affected not only by the size of the dot but also by optical intensity and the electromagnetic field polarization.     

Electron Raman scattering in single and multilayered spherical quantum dots: Effects of hydrogenic impurity and geometrical size

Based on the effective mass and parabolic one-band approximations, the differential cross-section for the intersubband electron Raman scattering process in a single and multilayered spherical quantum dots is investigated. The influence of an on-center hydrogenic impurity and geometrical parameters such as the well and barrier widths on the differential cross-section is studied. Results show that the number, the position and the magnitude of the peaks of emission spectra, considerably depend on the presence of the hydrogenic impurity as well as geometrical parameters. Results also reveal that the magnitude of the peaks significantly depend on the polarization vectors of incident and scattered lights.     

Morse势阱中子带间的光吸收

研究了Morse势阱中子带间的光吸收,并且利用密度矩阵算符理论和迭代方法,推导出了线性和三阶非线性子带间的光吸收系数的解析表达式,然后以GaAs/AlGaAsMorse势阱为例进行数值计算。结果表明,线性吸收系数是正的,为总吸收系数作出积极的作用,而三阶非线性吸收为负,抵消了一部分线性吸收,进而得到总的吸收系数;吸收系数随着入射光强度的增大而减小,即出现吸收饱和现象;当势阱参数a增大时,吸收系数增大,即阱宽较窄时,系统吸收的能量较多。若要获得较大的光学吸收系数,就要输入较小的光场强度,并选择适当的势阱参数a和入射光频率。     

Ultrafast interband pumping of quantum‐cascade structures: A feasibility study of a THz pulse amplifier

Gain spectra of a three‐well GaAs/AlGaAs quantum‐cascade structure under interband pumping by ultrashort optical pulses are studied within the framework of the density matrix theory. A mathematical model for intersubband kinetics is derived taking into account many‐body interactions and ultrafast interband optical pumping. It is found that pulsed interband pumping leads to an increase in intersubband gain by an order of magnitude, which is characterised by 1 ps rise time and 8 ps recovery time under pumping by 100 fs pulses with a peak intensity of 100 MW/cm². Possible implementations of the concept are highlighted. The results uncover a new possibility for ultrafast switching of the material gain in quantum‐cascade structures.     

Laser-induced quantum coherence in a semiconductor quantum well

The phenomenon of electromagnetically induced quantum coherence is demonstrated between three confined electron subband levels in a quantum well which are almost equally spaced in energy. Applying a strong coupling field, two-photon resonant with the 1-3 intersubband transition, produces a pronounced narrow transparency feature in the 1-2 absorption line. This result can be understood in terms of all three states being simultaneously driven into "phase-locked" quantum coherence by a single coupling field. We describe the effect theoretically with a density matrix method and an adapted linear response theory.