Biased Quantum Wells Research Articles

Optical excitation of squeezed longitudinal optical phonon states in an electrically biased quantum well

We present quantum kinetic calculations showing how squeezed phonon states can be generated in a biased quantum well by optical driving. In such states the uncertainty of the lattice displacement or momentum is reduced below its zero-point value. It is shown that quantitative results that are meaningful for real observations require accounting for the inevitably limited spatial resolution. Our simulations yield results for the strength of the squeezing and predict under which conditions it can occur: Optical excitations on the lowest absorption line need at least two pulses to generate squeezing, while a single pulse below the band gap may produce a squeezed state which has an almost minimum-value uncertainty product.

Generation of coherent LO phonons in optically driven biased quantum wells

AbstractWe present a theoretical analysis and numerical simulations of the resonant generation of coherent LO phonons in an electrically biased quantum well. The system is driven by a laser pulse short enough to simultaneously excite two transitions, which leads to a quantum beat that can resonantly create coherent phonons. The generation of incoherent phonons is also calculated on a quantum kinetic level and found to be dominant in terms of the energy transferred to the lattice.The simulations successfully reproduce the main features found in recent experiments [Mizoguchi et al., Appl. Phys. Lett. 94, 171105 (2009)]. Depending on the excitation conditions different generation mechanisms can be discerned. We discuss their characteristics and their relative efficiency in the special case of the quantum well model under consideration. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Resonant generation of coherent LO phonons by charge oscillations in a biased quantum well

A theoretical analysis of the generation of coherent and incoherent LO phonons after optical excitation of an electrically biased quantum well is presented. We show numerical calculations based on the density-matrix formalism where both coherent and incoherent phonons are included on a fully quantum kinetic level. Bulk phonon modes are used as is appropriate for the wide quantum well studied here. The generation of coherent phonons is resonantly enhanced when two exciton lines with the splitting tuned to the phonon energy are simultaneously excited; such a tuning is achievable by the quantum-confined Stark effect, where the exciton lines are shifted by varying the electric bias. However, there is also a strong emission of incoherent LO phonons due to intersubband transitions of the excited carriers; even in the resonant case this by far dominates the energy transfer to the lattice. The different contributions of the impulsive and the resonant coherent phonon generation mechanism are discussed. A good agreement with recent experiments is found.

Interplay between coherent and incoherent phonons in optically excited biased quantum wells

We present numerical simulations of the generation of coherent LO phonons in an electrically biased quantum well. An ultrashort laser pulse is used to simultaneously excite two exciton levels, which leads to an oscillating dipole moment that couples to the polar lattice and drives the phonons. The generation of coherent phonons becomes resonantly enhanced if the splitting of the two exciton levels is tuned to the LO phonon energy. In this case relaxation by emission of incoherent phonons becomes also possible. Our calculation therefore takes into account incoherent phonons on a quantum kinetic level as well. The intersubband relaxation by excitation of incoherent phonons competes with the generation of coherent phonons and is dominant in terms of the energy transferred.

Density of states in an electrically biased quantum well

Density of states in a quantum well has been studied in the presence of an electric field applied perpendicular to the growth direction. We have shown that an extra quantization is introduced to the motion of the electron due to the discrete energy levels known as Wannier-Stark ladder states and the nature of density of electronic states changes from quasi two-dimensional to quasi one-dimensional.

Optical transitions between valley split subbands in biased Si quantum wells

By a tight-binding $s{p}^{3}{d}^{5}{s}^{*}$ model, we study numerically the optical transitions involving the lowest conduction states confined in strained [001] Si quantum wells. These states belong to the fundamental and to the first excited quantum well (QW) subbands, each one split into a doublet by intervalley interaction. Both hard wall and finite SiGe barriers boundary conditions for the QWs are considered. Amplitudes of the doublet splittings as a function of the well width and of a uniform electric field superimposed along the growth direction are first investigated. Then, we study atomic contributions and parity character of the doublet wave functions to derive selection rules for interdoublet optical transitions. Finally, we demonstrate the role of intervalley coupling and the effectiveness of the selection rules here presented, for the interpretation of the absorption spectrum of a $n$-type Si QW between SiGe barriers, evaluated at different temperatures.

Direct determination of ultrafast intersubband hole relaxation times in voltage biased SiGe quantum wells by a density matrix interpretation of femtosecond resolved photocurrent experiments

We report the quantitative and direct determination of hole intersubband relaxation times in a voltage biased SiGe heterostructure using density matrix calculations applied to a four-level system in order to interpret photocurrent (PC) pump–pump experiments. One consistent set of parameters allows the simulation of two kinds of experiments, namely pump–pump photocurrent experiments at a free electron laser (wavelength 7.9 μm) and the laser-power dependence of the PC signal. This strongly confirms the high reliability of these parameter values, of which the most interesting in respect to Si based quantum cascade laser development is the extracted heavy-hole relaxation time. The simulations show that this relaxation time directly determines the experimentally observed decay of the pump–pump photocurrent signal as a function of the delay time. For a heavy hole intersubband spacing of 160 meV, a value of 550 fs was obtained. The experimental method was further applied to determine the LH1–HH1 relaxation time of a second sample with a transition energy below the optical phonon energy. The observed relaxation time of 16 ps is consistent with the value found for the same structure by transmission pump–probe experiments.

Direct monitoring of the excited state population in biased SiGe valence band quantum wells by femtosecond resolved photocurrent experiments

The authors report a direct measurement of the optical phonon intersubband hole relaxation time in a SiGe heterostructure and a quantitative determination of hole relaxation under electrically active conditions. The results were obtained by femtosecond resolved pump-pump photocurrent experiments using a free electron laser (wavelength 7.9μm). Additionally, the intensity dependence of the nonlinear photocurrent response was measured. Both types of experiments were simulated using a density matrix description. With one parameter set, a consistent modeling was achieved confirming the significance of the extracted heavy hole relaxation times. For an intersublevel spacing of 160meV, a value of 550fs was obtained.

Nonlinear excitation kinetics of biased quantum wells: Coherent dynamical screening effect

AbstractIn this paper we describe a strongly nonlinear process of ultrafast photoexcitation of a biased quantum well. This process is governed by coherent dynamical screening, where the instantaneously polarized photoexcited carriers screen initial bias field. This results in a dynamic modification of the bandstructure of the quantum well, which is totally coherent with the temporal intensity distribution in the excitation laser pulse. We developed a time‐resolved theoretical model of coherent dynamical screening, which predicts interesting fundamental consequences, such as nonlinear absorption and ultra‐broadband THz emission. The results of our THz and optical experiments are in good agreement with the theoretical model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ring-shaped luminescence pattern in biased quantum wells studied as a steady-state reaction front

Under certain conditions, focused laser excitation in semiconductor quantum well structures can lead to a charge separation and a circular reaction front, which is visible as a ring-shaped photoluminescence pattern. The diffusion-reaction equations governing the system are studied here with the aim of a detailed understanding of the steady state. The qualitative asymmetry in the sources for the two carriers is found to lead to unusual effects which dramatically affect the steady-state configuration. Analytic expressions are derived for carrier distributions and interface positions for a number of cases. These are compared with steady-state information obtained from simulations of the diffusion-reaction equations.

Two-electron absorption in a biased quantum well

Linear light absorption of 2D electrons confined within a biased quantum well is studied theoretically. We demonstrate that for light polarization perpendicular to the 2D plane, in addition to conventional absorption peak at frequency ℏ ω ≈ Δ , where Δ is the intersubband energy distance, there exists a peak around a double frequency ℏ ω ≈ 2 Δ . This additional peak is entirely due to electron–electron interactions, and corresponds to excitation of two electrons by one photon. The magnitude of two-electron absorption is proportional to U 2 , where U is the applied bias.

Rashba spin splitting in biased semiconductor quantum wells

Rashba spin splitting (RSS) in biased semiconductor quantum wells is investigated theoretically based on the eight-band envelope function model. We find that at large wave vectors, RSS is both nonmonotonic and anisotropic as a function of in-plane wave vector, in contrast to the widely used linear and isotropic model. We derive an analytical expression for RSS, which can correctly reproduce such nonmonotonic behavior at large wave vectors. We also investigate numerically the dependence of RSS on the various band parameters and find that RSS increases with decreasing band gap and subband index, increasing valence band offset, external electric field, and well width. Our analytical expression for RSS provides a satisfactory explanation to all these features.

Role of dynamical screening in excitation kinetics of biased quantum wells: Nonlinear absorption and ultrabroadband terahertz emission

In this work we describe the ultrafast excitation kinetics of a biased quantum well, arising from the optically induced dynamical screening of a bias electric field. The initial bias electric field inside the quantum well is screened by the optically excited polarized electron-hole pairs. This leads to a dynamical modification of the properties of the system within an excitation pulse duration. We calculate the excitation kinetics of a biased quantum well and the dependency of resulting electronic and optical properties on the excitation pulse fluence, quantum well width, and initial bias field strength. Our calculations, in particular, predict the strongly nonlinear dependency of the effective optical absorption coefficient on the excitation pulse fluence, and ultrabroadband terahertz emission. Our theoretical model is free of fitting parameters. Calculations performed for internally biased InGaN∕GaN quantum wells are in good agreement with our experimental observations [Turchinovich et al., Phys. Rev. B 68, 241307(R) (2003)], as well as in perfect compliance with qualitative considerations.

Temperature-dependent polarization characteristics of composite-resonator vertical-cavity lasers

We investigate the output characteristics from 10/spl deg/C to 160/spl deg/C of a monolithic dual-resonator vertical-cavity laser composed of three distributed Bragg reflector mirrors that separate two nominally identical optical cavities. The light output from the top ion-implanted cavity under forward bias is partitioned into two orthogonal polarizations of the fundamental transverse mode. A reverse bias of sufficient magnitude applied to the bottom oxide cavity causes the abrupt suppression of the dominant polarization and simultaneous emergence of the orthogonal polarization, consistent with wavelength dependent electroabsorptive loss in the reverse biased quantum wells of the oxide-confined cavity. We calculate the internal loss as a function of reverse bias and temperature, and characterize the polarization properties of the device based on the temperature dependence of the laser output. The polarization switching is consistent with increasing absorption with increasing temperature and decreasing absorption at longer wavelengths.

Multibandk∙ptheory of carrier escape from quantum wells

A general theory of multichannel coherent particle escape introducing the escape matrix based on the scattering formalism has been developed and applied to the problem of hole escape from biased quantum wells. This approach incorporates band-mixing effects, such as valence-band nonparabolicity and heavy-to-light (light-to-heavy) hole transformations, in the theory of carrier escape from quantxum wells consistently with the principles of multiband effective-mass theory. The numerical calculations, made in the Luttinger approximation, show significant influence of the band-mixing effects on the hole escape time and are in satisfactory agreement with available experimental data. The effective decrease of the heavy-hole tunneling mass (``lightening'') as a result of the light-hole admixture is found to be the major reason for the escape-time decrease, as compared to the simple parabolic-band effective-mass model. The concept of the escape matrix can be used for investigating multichannel coherent escape processes in different systems such as quantum wires, quantum dots, or photonic structures.

Breakdown of optical selection rules in a highly biased quantum well

Optical transitions between electronic states in a quantum well are governed by symmetry of the states. The selection rule and its breakdown in electric fields have been intensively studied. However, most of such studies have concerned with ground states so far. Behavior of transitions between higher states in high electric fields has not been well revealed. In this paper, in order to investigate optical transitions of high-index states in electric fields, we carried out electroreflectance measurement for a quantum well embedded in a p–i–n diode. Measured electroreflectance spectra are rich in structure, indicating that many transitions between high-index states occur. With increasing applied voltage, these signals show significant red-shift as well as modulation of intensity. We show that the modulation of intensities is well understood from shapes of the wave functions and their deformation due to applied electric field.

Optical absorption of THz-field-driven and dc-biased quantum wells

Linear optical absorption in a quantum well driven by a growth-direction-oriented THz electric field is investigated. We show that if in addition to the THz field a dc bias field is applied to the quantum well, the optical absorption becomes much more sensitive to the presence of the THz field. This results in the emergence of multiple replicas in the absorption spectrum of biased quantum wells for a low-frequency (compared with the subband energy spacing) THz field. We consider undoped quantum wells and develop an approach that allows us to treat nonlinear effects in THz field strength. We discuss separately the optical absorption due to free-electron-hole pairs and due to excitons.

Enhanced optical/THz frequency mixing in a biased quantum well

Strong enhancement of the optical emission at THz sidebands from a THz-field driven quantum well in the presence of a dc bias is predicted. The process of the THz/optical mixing is formulated as the interaction of the incident light with THz-dressed excitons. This allows one to find nonperturbative analytic expressions for the conversion efficiency of the fundamental to the THz sidebands. A maximum efficiency of a few percent is predicted for a single GaAs quantum well, and ways for its further enhancement are discussed.

Gigantic Photon–Photon Coupling in Biased Semiconductor Microcavities: A Step toward Single-Photon Blockade

We discuss optical nonlinearities in biased semiconductor microcavities. Optical nonlinearities arise from field screening by spatially separated electron–hole pairs in biased quantum wells (QWs). However, in wide QWs where the spatial separation is large, biasing is accompanied by a drastic decrease of oscillator strength, and has a negative impact on the optical nonlinearity. We show here that in an exciton polariton microcavity in the strong coupling regime, a decrease in oscillator strength only weakly affects the optical nonlinearity. Gigantic enhancement of photon–photon interaction is then realized by biasing, and the single-photon blockade limit can be reached.

Energy spectrum, density of states, and optical transitions in strongly biased narrow-gap quantum wells

We study theoretically the effect of an electric field on the electron states and far-infrared optical properties in narrow-gap lead salt quantum wells. The electron states are described by a two-band Hamiltonian. An application of a strong electric field across the well allows the control of the energy gap between the two-dimensional (2D) states in a wide range. A sufficiently strong electric field transforms the narrow-gap quantum well to a nearly gapless 2D system, whose electron energy spectrum is described by linear dispersion relations \epsilon_{\sigma} (k) ~\pm (k-k_{\sigma}), where k_{\sigma} are the field-dependent 2D momenta corresponding to the minimum energy gaps for the states with spin numbers \sigma. Due to the field-induced shift of the 2D subband extrema away from k=0 the density of states has inverse-square-root divergencies at the edges. This property may result in a considerable increase of the magnitude of the optical absorption and in the efficiency of the electrooptical effect.