Phonon satellites and time-resolved studies of carrier recombination dynamics in InGaN quantum wells

We have studied the photoluminescence and time-resolved photoluminescence of a set of InGaN quantum wells with well thickness from 1 to 7.5 nm. An analysis of the phonon satellites at 5 K shows Huang–Rhys factors from 0.32 to 0.44. The increase of this factor is caused by the electron–hole separation induced by the piezoelectric field. The time-resolved photoluminescence at room temperature shows that the decay time of the 1 and 2 nm wells does not depend on the wavelength. The maximum decay time is around 600 ps for the 2, 3 and 4 nm wells. However, for the 3 and 4 nm wells a decrease of the photoluminescence decay time is observed at the highest wavelengths. This suggest the onset of a non-radiative process in these samples. The optimum well width for efficient emission for these single quantum wells was found to be 2 nm.     

Unstructured Adiabatic Quantum Search

In the adiabatic quantum computation model, a computational procedure is described by the continuous time evolution of a time dependent Hamiltonian. We apply this method to the Grover's problem, i.e., searching a marked item in an unstructured database. Classically, the problem can be solved only in a running time of order O(N) (where N is the number of items in the database), whereas in the quantum model a speed up of order has been obtained. We show that in the adiabatic quantum model, by a suitable choice of the time-dependent Hamiltonian, it is possible to do the calculation in constant time, independent of the the number of items in the database. However, in this case the initial time-complexity of is replaced by the complexity of implementing the driving Hamiltonian.     

Micro-photoluminescence of GaN quantum dots embedded in 100 nm wide cylindrical AlN pillars

Individual pillars were etched from a sample embedding a single plane of GaN/AlN quantum dots, deposited by molecular beam epitaxy on a sapphire substrate. Pillars with diameters ranging from 0.1 to 5 μm were fabricated by electron-beam lithography and SiCl₄ reactive ion etching. The PL from a single pillar could be measured by using a confocal microscope, with a spatial resolution of 600 nm. We report an intense PL signal from pillar diameters as small as 0.1 μm at room temperature. By increasing the power of the excitation laser from 0.05 to 200 μW, we induced a blue-shift of the PL energy peak from 2.38 to 2.86 eV, accompanied by a substantial broadening of the PL line. This is explained by the photo-induced screening of the internal electric field, which is close to 10 MV/cm in GaN/AlN heterostructures. Finally we report and tentatively explain a photodarkening effect, i.e., the progressive decrease of the PL intensity over two orders of magnitude, after one hour of continuous laser excitation. However, this effect does not seem to be correlated to the etching process.     

Infrared photodetection with semiconductor self-assembled quantum dots

Semiconductor self-assembled quantum dots are potential candidates to develop a new class of midinfrared quantum photodetectors and focal plane arrays. In this article, we present the specific midinfrared properties of InAs/GaAs quantum dots associated with the intersublevel transitions. The electronic structure, which accounts for the strain field in the islands, is obtained within the framework of a three-dimensional 8 band k.p formalism. The midinfrared intersublevel absorption in n-doped quantum dots is described. We show that the carrier dynamics can be understood in terms of polarons which result from the strong coupling regime for the electron–phonon interaction in the dots. The principle of operation of vertical and lateral quantum dot infrared photodetectors is described and discussed by comparison with quantum well infrared photodetectors. We review the performances of different type of detectors developed to date and finally give some orientation to realize high performance quantum dot infrared photodetectors. To cite this article: P. Boucaud, S. Sauvage, C. R. Physique 4 (2003).     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

Quantum principal commutative subalgebra in the nilpotent part ofU_q \widehat{sl}_2 and lattice KdV variables

We propose a quantum lattice version of B. Feigin and E. Frenkel's constructions, identifying the KdV differential polynomials with functions on a homogeneous space under the nilpotent part of . We construct an action of the nilpotent part of on their lattice counterparts, and embed the lattice variables in a , coinduced from a quantum version of the principal commutative subalgebra, which is defined using the identification of with its dual algebra.     

Quantum affine algebras

We classify the finite-dimensional irreducible representations of the quantum affine algebra in terms of highest weights (this result has a straightforward generalization for arbitrary quantum affine algebras). We also give an explicit construction of all such representations by means of an evaluation homomorphism , first introduced by M. Jimbo. This is used to compute the trigonometricR-matrices associated to finite-dimensional representations of .     

Isomorphism of two realizations of quantum affine algebraU_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})

We establish an explicit isomorphism between two realizations of the quantum affine algebra given previously by Drinfeld and Reshetikhin-Semenov-Tian-Shansky. Our result can be considered as an affine version of the isomorphism between the Drinfield/Jimbo and the Faddeev-Reshetikhin-Takhtajan constructions of the quantum algebra .     

About some optical properties of AlxGa1−xN /GaN quantum wells grown by molecular beam epitaxy

Wurtzitic nitride quantum wells grown along the (0001) axis experience a large Stark effect induced by the differences of spontaneous and piezoelectric polarizations between the well and barrier materials. In Al_xGa_1−xN/GaN quantum wells, due to the adverse actions of quantum confinement, that blue-shifts transition energies, and of the Stark field, that red-shifts them, the transition energies are nearly independent of barrier compositions at a particular well thickness (L₀2.6 nm), at least for x≤0.3. The effect of alloy fluctuations is then minimal, as reflected by a minimum in the quantum well luminescence linewidth when LL₀ for wells grown by molecular beam epitaxy on silicon or sapphire substrates. We use this effect to estimate the average variances of well widths and alloy composition fluctuations. Both results are in good agreement with, respectively, a scanning tunneling microscopy study of GaN (0001) surfaces, and estimates based on the lateral extent of the quantum well excitons.We then discuss the optical properties of the Al_xGa_1−xN barrier material, with particular emphasis on the symmetry of the valence band maximum (Γ₉ or Γ₇). We show that it may play an important role in the apparent barrier luminescence efficiency. We analyse the possible consequences of the barrier Γ₉–Γ₇ crossover on the Al_xGa_1−xN/GaN quantum well properties.     

Spinor Representations of $${U}_q (\hat {\mathfrak{o}}(N))$$ )

This Letter concerns an extension of the quantum spinor construction of . We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, and construct quantum spinor representations of .     

Generalization of the $$\mathcal{U} $$ q (gl(N)) Algebra and Staggered Models

We develop a technique for the construction of integrable models with a ₂ grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang–Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group , with a matrix deformation parameter q such that (q )² = q ². The symmetry behind these models can also be interpreted as the tensor product of the (–1)-Weyl algebra by an extension of _q (gl(N)) with a Cartan generator related to deformation parameter –1.     

Quantum action principle in curved space

Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianL _c( , x)=(M/2)g_ij(x) ^{i j}–v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that an arbitrary point transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian.     

Uncertainty principle and the horizon size of our universe

Quantum uncertainties prevent simultaneous measurement of the expansion factor S(t) and its time derivative . Consequently the Hubble size has an inherent uncertainty in the quantum state that describes the semiclassical evolution of the universe. We show that the quantum uncertainty in the Hubble size of the universe is amplified to unacceptably large values in any inflationary process.This essay received an honorable mention from the Gravity Research Foundation, 1986-Ed.     

Nitride-based ultraviolet Schottky barrier photodetectors with LT-AlN cap layers

We present the characteristics of novel GaN-based ultraviolet (UV) Schottky barrier photodetectors (PDs) with a low-temperature (LT-)AlN cap layer. Comparing them with conventional Schottky barrier PDs, it was found that we achieved smaller dark current and larger UV to visible rejection ratio from the PDs with the LT-AlN cap layer. The dark leakage current for the Schottky barrier PDs with the LT-AlN cap layer was shown to be about four orders of magnitude smaller than that for the conventional Schottky barrier PDs. With −5 V applied bias, the measured responsivity and UV to visible rejection ratio are 0.16 A /W and 7.74×10² for the Schottky barrier PDs with the LT-AlN cap layer, respectively. This result can be attributed to the thicker and higher potential barrier when the LT-AlN cap layer was inserted.     

MBE growth of nitride-based photovoltaic intersubband detectors

In this work, we present the plasma-assisted molecular-beam epitaxial growth of quantum well infrared photodetector (QWIP) structures, including the Si-doped GaN/AlN short-period superlattice of the active region, conductive AlGaN claddings and integration of the final device. The growth of Si-doped GaN/AlN multiple quantum well (QW) structures is optimized by controlling substrate temperature, metal excess and growth interruptions. Structural characterization confirms a reduction of the interface roughness to the monolayer scale. P-polarized intersubband absorption peaks covering the 1.33–1.91 μm wavelength range are measured on samples with QW thickness varying from 1 to 2.5 nm. The absorption exhibits Lorentzian shape with a line width around 100 meV in QWs doped 5×10¹⁹ cm⁻³. To prevent partial depletion of the QWs owing to the internal electric field, we have developed highly-conductive Si-doped AlGaN cladding layers using In as a surfactant during growth. Complete ISB photodetectors with 40 periods of 1 nm-thick Si-doped GaN QWs with 2 nm-thick AlN barriers have been grown on conductive AlGaN claddings, the Al mole fraction of the cladding matching the average Al content of the active region. Temperature-dependent photovoltage measurements reveal a narrow (90 meV) detection peak at 1.39 μm.     

New GaN Schottky barrier diode employing a trench on AlGaN/GaN heterostructure

A new GaN Schottky barrier diode employing a trench structure, which is proposed and fabricated, successfully decreases a forward voltage drop without sacrificing any other electric characteristics. The trench is located in the middle of Schottky contact during a mesa etch. The Schottky metal of Pt/Mo/Ti/Au is e-gun evaporated on the 300 nm-deep trench as well as the surface of the proposed GaN Schottky barrier diode. The trench forms the vertical Au Schottky contact and lateral Pt Schottky contact due to the evaporation sequence of Schottky metal. The forward voltage drops of the proposed diode and conventional one are 0.73 V and 1.25 V respectively because the metal work function (5.15 eV) of the vertical Au Schottky contact is considerably less than that of the lateral Pt Schottky contact (5.65 eV). The proposed diode exhibits the low on-resistance of 1.58 mΩ cm² while the conventional one exhibits 8.20 mΩ cm² due to the decrease of a forward voltage drop.     

Integrals of Vertex Operators and uantum Shuffles

Given a braided vector space , we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on . Using the quantum shuffle construction of the 'upper triangular part' of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of .     

Quantum fluctuations in atomistic semiconductor devices

Atomistic Green function simulations of model 25 nm×25 nm Si MOSFETs predict strong fluctuation effects derived from mode fluctuations in the quantum transport through the inhomogeneous 2DEG channel caused by the spatial distribution of non-self-averaged discrete dopants.     

Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model

We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group on a space E. We define the algebra of smooth complex valued functions on , with convolution as multiplication, in terms of which the groupoid geometry is developed. Owing to the fact that the group G is finite the model can be computed in full details. We show that by suitable averaging of noncommutative geometric quantities one recovers the standard space-time geometry. The quantum sector of the model is explored in terms of the regular representation of the algebra , and its correspondence with the standard quantum mechanics is established.