Model Solid Theory Research Articles

Computation of the electronic structure and direct-gap absorption spectra in Ge-rich Si1−x Gex/Ge/Si1−xGex type-I quantum wells

This paper presents the results of conduction band discontinuities calculation for strained/relaxed Si1−x Ge x /Si1−y Ge y heterointerfaces in Γ 15C , Γ 2′C and L upper bands minima, as well as the room-temperature strained (vs. relaxed) band gaps deduced from the classical model-solid theory. Based upon the obtained data, we propose a type-I W-like Si1−y Ge y /Si1−x Ge x /Ge/Si1−x Ge x /Si1−y Ge y quantum wells heterostructure optimized in terms of compositions and thicknesses. Electronic states and wave functions are found by solving Schrodinger equation without and under applied bias voltage. An accurate investigation of the optical properties of this heterostructure is done by calculating the energies of the interband transitions and their oscillator strengths. Moreover, a detailed computation of the bias-voltage evolution of the absorption spectra is presented. These calculations prove the existence of type-I band alignment at Γ 2′C point in compressively strained Ge quantum wells grown on relaxed Ge-rich Si1−y Ge y buffers. The strong absorption coefficient (> 8 × 103 cm-1) and the large Stark effect (0.1 eV @ 2 V) of the Γ 2′C transitions thresholds open up perspectives for application of these heterostructures for near-infrared optical modulators.

The effect of dilute nitrogen on nonlinear optical properties of the InGaAsN/GaAs single quantum wells

In this study, we investigate the linear and third order nonlinear optical properties of InGaAsN/GaAs depending on nitrogen content and laser dressing parameter. As theoretical models, band anticrossing and model solid theory are used. In order to obtain the electronic properties of the quantum well, the finite difference method is used. The laser beam affects the electronic properties of the quantum well by changing the shape of the confinement potential. This modification of the potential is determined by laser dressing parameter. By using dilute amount of nitrogen, conduction band and the depth of quantum well can be controlled. The strain which is introduced due to the presence of nitrogen can be compensated by using indium atoms. The electronic and the linear and third order nonlinear optical properties of InGaAsN/GaAs quantum well structure are obtained.

Dielectric confinement on exciton binding energy and nonlinear optical properties in a strained Zn1−xinMgxinSe/Zn1−xoutMgxoutSe quantum well

The band offsets for a Zn1−xinMgxinSe/Zn1−xoutMgxoutSe quantum well heterostructure are determined using the model solid theory. The heavy hole exciton binding energies are investigated with various Mg alloy contents. The effect of mismatch between the dielectric constants between the well and the barrier is taken into account. The dependence of the excitonic transition energies on the geometrical confinement and the Mg alloy is discussed. Non-linear optical properties are determined using the compact density matrix approach. The linear, third order non-linear optical absorption coefficient values and the refractive index changes of the exciton are calculated for different concentrations of magnesium. The results show that the occurred blue shifts of the resonant peak due to the Mg incorporation give the information about the variation of two energy levels in the quantum well width.

Effects of band offsets and the dielectric confinement on exciton binding energy in a strained [formula omitted] quantum dot

On the basis of model solid theory, the band offsets for a Zn1-xinMgxinSe/Zn1-xoutMgxoutSe quantum dot structure are determined. The exciton binding energies due to heavy and light holes with the variation of Mg alloy are reported. The effect of mismatch between the dielectric constants between the dot and the barrier is taken into account. The exciton transition energy as functions of dot radius and Mg content is computed. The dependence of the excitonic transition energies on the geometrical confinement and the Mg alloy is brought out.

A theoretical study of band structure properties for III–V nitrides quantum wells

Reliable and precise knowledge about the strain and composition effects on the band structure properties is crucial for the optimization of InGaN based heterostructures for electronic and optoelectronic device applications. AlInGaN as quaternary barrier material permits to control the band gap and the lattice constant independently. Using the model solid theory and the multi-band k.p interaction model, we investigate the composition effects on band offsets and band structure for pseudomorphic Ga 1− x In x N/Al zIn yGa 1− y − z N (0 0 1) heterointerfaces having zinc-blende structure. The results show that both conduction and valence band states are strongly modified while varying In and Al contents in the well and barrier materials. Furthermore, it is found that using AlInGaN as the barrier material allows the design of heterostructures including InGaN wells with tensile, zero or compressive strain. Such results give new insights for III-nitride compounds based applications and especially may guide the design of white-light emission diodes.

The comparison of the band alignment of GaInAsN quantum wells on GaAs and InP substrates for (0 0 1) and (1 1 1) orientations

The aim of this paper is to examine the effect of growth orientation and dilute nitride on the band alignment of GaInAs quantum wells on GaAs and InP substrates by means of model solid theory. The study provides a comparison of the band alignment and the strained band gap of the related GaInAsN QWs in (1 1 1) and (0 0 1) orientation. Our calculated results show that although 111-oriented GaInAsN QWs enables to reach the longer wavelengths, the conduction band offset gets shallow than that of the 001-oriented ones.

Engineering of Ga1−xInxAsySb1−y/GaSb quantum well for III-V based devices emitting near 2.7 μm

The present investigation is focused on the electronic band parameters for Ga1−xInxAsySb1−y/GaSb quantum wells. Strain effects on heavy holes (hh), light holes (lh) and split off (so) bands are investigated as a function of indium and arsenic compositions in the hole range 0 ≤ x, y ≤ 1. The valence band offsets are calculated using the model solid theory. Taking into account these results and based on a one dimensional Schrödinger equation, we report a calculation of the quantum confinement of electron and heavy-hole levels for Ga1−xInxAsySb1−y/GaSb quantum well (QW). Our results provide useful information for the design of heterostructure emitting near 2.7 μm.

A convenient band-gap interpolation technique and an improved band line-up model for InGaAlAs on InP

The band-gap energy and the band line-up of InGaAlAs quaternary compound material on InP are essential information for the theoretical study of physical properties and the design of optoelectronics devices operating in the long-wavelength communication window. The band-gap interpolation of In1−x−y Ga x Al y As on InP is known to be a challenging task due to the observed discrepancy of experimental results arising from the bowing effect. Besides, the band line-up results of In1−x−y Ga x Al y As on InP based on previously reported models have limited success by far. In this work, we propose an interpolation solution using the single-variable surface bowing estimation interpolation method for the fitting of experimentally measured In1−x−y Ga x Al y As band-gap data with various degree of bowing using the same set of input parameters. The suggested solution provides an easier and more physically interpretable way to determine not only lattice matched, but also strained band-gap energy of In1−x−y Ga x Al y As on InP based on the experimental results. Interpolated results from this convenient method show a more favourable match to multiple independent experiment data sets measured under different temperature conditions as compared to those obtained from the commonly used weighted-sum approach. On top of that, extended framework of the model-solid theory for the band line-up of In1−x−y Ga x Al y As/InP heterostructure is proposed. Our model-solid theory band line-up result using the proposed extended framework has shown an improved accuracy over those without the extension. In contrast to some previously reported works, it is worth noting that the band line-up result based on our proposed extended model-solid theory has also shown to be more accurate than those given by Harrison’s model.

Identification of candidate material systems for quantum dot solar cells including the effect of strain

AbstractHeterostructures that include self‐assembled quantum dots (SAQDs) have been suggested as model systems for the realization of novel high efficiency solar cells such as those based on intermediate bands (IBs). The lattice mismatch in the epitaxial growth of these structures, necessary for the formation of SAQDs, introduces strain throughout the structure, making the selection of materials systems with appropriate physical parameters problematic. The model solid theory is used to calculate the energy band edge alignment at Γ point of such quantum dot (QD) heterostructures including the effects of strain. With the modified band gaps due to strain, a materials search was performed for high efficiency QD solar cells among III‐V binaries and ternaries with negligible valence band offsets. This requirement of the valence band offset along with the limited band gap ranges for optimum efficiency results in only a few feasible materials systems being identified. The optimum barrier/dot material system found was Al0.57In0.43As/InP0.87Sb0.13 grown on lattice matched metamorphic buffer layer, but due to miscibility gap concerns it is suggested that the Al0.50In0.50As/InAs0.41P0.59 fully strained system may be preferred. Copyright © 2010 John Wiley & Sons, Ltd.

On detection wavelength and electron-hole wave function overlap of type Ⅱ InAs/InxGa1－xSb superlattice infrared photodetector

摘要 运用包络函数模型和传输矩阵方法计算了二类超晶格的能级结构.考虑到InAs与InxGa1-xSb结合存在应变,在计算中InAs/InxGa1-xSb二类超晶格的带阶采用模型固体理论处理.因为吸收系数与电子-空穴波函数交叠成正比，所以研究了InAs/InxGa1-xSb二类超晶格红外探测器的吸收波 关键词: 二类超晶格 / 红外探测器 / 波函数的交叠 / 传输矩阵 Abstract In this paper, the detection wavelength and the electron-hole wave function overlap of InAs/InxGa1-xSb type Ⅱ superlattice photodetectors are numerically calculated by using the envelope function and the transfer matrix methods. The band offset is dealt with by employing the model solid theory, which already takes into account the lattice mismatch between InAs and InxGa1-xSb layers. Firstly, the detection wavelength and the wave function overlap are investigated in dependence on the InAs and InxGa1-xSb layer thicknesses, the In mole fraction, and the periodic number. The results indicate that the detection wavelength increases with increasing In mole fraction, InAs and InxGa1-xSb layer thicknesses, respectively. When increasing the periodic number, the detection wavelength first increases distinctly for small periodic numbers then increases very slightly for large period numbers. Secondly, the wave function overlap diminishes with increasing InAs and InxGa1-xSb layer thicknesses, while it enhances with increasing In mole fraction. The dependence of the wave function overlap on the periodic number shows the same trend as that of the detection wavelength on the periodic number. Moreover, for a constant detection wavelength, the wave function overlap becomes greater when the thickness ratio of the InAs over InxGa1-xSb is larger. Keywords: type Ⅱ superlattice / infrared photodetector / wave function overlap / transfer matrix method 作者及机构信息 黄建亮, 卫炀, 马文全, 杨涛, 陈良惠 1. 中科院半导体研究所纳米光电实验室，北京 100083 基金项目: 国家重点基础研究发展计划(973项目)(批准号: 2010CB327602)资助的课题. Authors and contacts Huang Jian-Liang, Wei Yang, Ma Wen-Quan, Yang Tao, Chen Liang-Hui 1. 中科院半导体研究所纳米光电实验室，北京 100083 参考文献 [1] ［1］Rogalski A 2007 Infrared Phys. Technol. 50 240 [2] ［2］Becker L 2006 Proc. SPIE 6127 61270S [3] ［3］Ashley T, Gordon N T 2004 Proc. SPIE 5359 89 [4] ［4］Youngdale E R, Meyer J R, Hoffman C A, Bartoli F J, Grein C H, Young P M, Ehrenreich H 1994 Appl. Phys. Lett. 64 3160 [5] ［5］Grein C H, Yang P M, Platte M E, Ehrenreich H 1995 J. Appl. Phys.78 7143 [6] ［6］Plis E, Rodriguez J B, Kim H S，Bishop G, Sharma Y D, Dawson L R, Krishna S 2007 Appl. Phys. Lett. 91 133512 [7] ［7］Li J V, Hill C J, Mumolo J, Gunapala S, Mou S, Chuang S L 2008 Appl. Phys. Lett. 93 163505 [8] ［8］Delaunay P Y, Nguyen B M, Razeghi M 2009 Proc. SPIE 7298 72981 [9] ［9］Hoffman D, Nguyen B M, Huang E K, Delaunay P Y, Bogdanov S, PManukar P, Razeghi M, Nathan V 2009 Proc. SPIE 7222 722215 [10] ］Schneider H, Liu H C 2006 Quantum Well Infrared Photodetectors (Germany: Springer) p11 [11] ］Chang Y C, Schulman J N 1985 Phys. Rev. B 31 2069 [12] ］Xia J B, Zhu B F 1995 Semiconductor Superlattice Physics (ShangHai: Science and technology Press) p388(in Chinese) ［夏建白、朱邦芬 1995 半导体超晶格物理(中国上海：上海科学技术出版社)第388页］ [13] ］Smith D L, Maihiot C 1987 J.Appl.Phys. 62 2545 [14] ］Vurgaftman I, Meyer J R, Ram-Mohan L R 2001 J. Appl. Phys. 89 5815 [15] ］Chuang S L 1995 Physics of Optoelectronic Devices (USA：John Wiley & Sons. Inc. ) p157 施引文献

Tailoring of Optoelectronic Properties of InAs/GaAs Quantum Dot Nanosystems by Strain Control

Full three-dimensional numerical analysis based on continuum elasticity and model solid theory has been carried out to evaluate some possible means of tailoring the optoelectronic properties of InAs/GaAs quantum dot (QD) nanosystems. Numerical results predicted that while the stacking period control leads to the shifts in valence band edges, incorporation of In x Ga1−x As ternary strain relief layer (SRL) causes composition-dependent shifts in conduction band edges. On the other hand, modification of the SRL shape itself did not yield significant changes in the confinement potentials. It is therefore suggested that strain control by incorporation of ternary intermediate layers combined with geometry controls, would allow greater flexibility in the tailoring of the opto-electronic characteristics of QD-based systems.

Comment on “Theory and Experiment of ${\hbox{In}}_{1-{x}}{\hbox {Ga}}_{x}{\hbox {As}}_{y}{\hbox{P}}_{1-{y}}$ and ${\hbox{In}}_{1-{x}-{y}}{\hbox {Ga}}_{x}{\hbox {Al}}_{y}{\hbox {As}}$ Long-Wavelength-Strained Quantum-Well Lasers”

Minch [IEEE J. Quantum Electron., vol. 35, no. 5, pp. 771-782, May 1999] compared the theoretical conduction band offset ratio of In <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x-y</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> As/InP heterostructure calculated from Harrison's model and model-solid theory to the empirical results obtained from experimental measurement. We wish to point out that the comparison was not appropriate as the calculated results were the band offset ratio, whereas the reference empirical result was the band offset energy. The corrected comparison graph is presented in this comments.

Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers

InGaAs strained quantum wells (QWs) with GaAs, AlGaAs, and GaAsP barriers are widely used in optically pumped vertical-external-cavity surface-emitting lasers operating at 1 μm wavelength band. Compared with the reported data, the model-solid theory, which is more suitable for the studied materials, is selected to calculate the band offset. The band structures and the gain characteristics of the three different QWs are computed and compared, and the theoretical results are in good agreement with the recent experimental reports. The numerical simulation shows that the QW with the GaAs barrier has the highest absorption but the lowest peak gain, while for the AlGaAs barrier, it has the lowest absorption but the highest peak gain, and for the GaAsP barrier, it has a moderate absorption and peak gain. GaAsP is the most appropriate candidate for the barrier of InGaAs strained QW when the low-threshold, large-gain, and high-temperature characteristics are demanded simultaneously.

Photoluminescence Properties of Tensile-Strained GaAsP/GaInP Single Quantum Wells Grown By Metal Organic Chemical Vapor Deposition

Tensile-strained GaAsP/GaInP single quantum well (QW) laser diode (LD) structures have been grown by low-pressure metal organic chemical vapor deposition (LP-MOCVD) and related photoluminescence (PL) properties have been investigated in detail. The samples have the same well thickness of 16 nm but different P compositions in a GaAsP QW. Two peaks in room-temperature (RT) PL spectra are observed for samples with a P composition larger than 0.10. Temperature- and excitation-power-dependent PL spectra have been measured for a sample with a P composition of 0.15. It is found that the two peaks have a 35 meV energy separation independent of temperature and only the low-energy peak exists below 85 K. Additionally, both peak intensities exhibit a monotonous increase as excitation power increases. Analyses indicate that the two peaks arise from the intrinsic-exciton recombination mechanisms of electron–heavy hole (e–hh) and electron–light hole (e–lh). A theoretical calculation based on model-solid theory, taking into account the spin–orbit splitting energy, shows good agreement with our experimental results. The temperature dependence of PL intensity ratio is well explained using the spontaneous emission theory for e–lh and e–hh transitions, from which the ratio can be characterized mainly by the energy separation between the hh and lh states.

Type-II behavior in wurtzite InP/InAs/InP core-multishell nanowires

We study optical transitions from a periodic array of InP/InAs/InP core-multishell nanowires (CMNs) having a wurtzite crystal structure by using photoluminescence (PL) and PL excitation (PLE) spectroscopy. Observing a large Stokes shift between PL and PLE spectra, a blueshift of the PL peak with a cube-root dependence on the excitation power and a slow and nonexponential decay of PL with an effective decay time of 16 ns suggest a type-II band alignment. Band-offset calculation based on the “model-solid theory” of Van de Walle [Phys. Rev. B 39, 1871 (1989)] supports type-II band lineup if the InAs layer in the wurtzite CMNs is assumed to sustain compressive strain in all directions.

Calculations of electronic structure, elastic properties for YxGa1−xN and band offsets of YxGa1−xN/ScyGa1−yN heterointerfaces

Using the pseudopotential scheme under the virtual crystal approximation combined with the Harrison bond-orbital model, we report a theoretical investigation of the electronic and elastic properties of YxGa1−xN ternary alloys in the zinc-blende structure. Besides, band offsets calculations for pseudomorphically strained YxGa1−xN/ScyGa1−yN interfaces have been performed on the basis of the model solid theory. Our results agree generally well with the available experimental and previously published theoretical data. The composition dependence of the selected features of YxGa1−xN such as energy band gaps, effective masses, elastic constants, bulk modulus, shear modulus, internal strain parameter, and valence and conduction band offsets has been examined. To the author's best knowledge, there had been no reported work on these properties for the material under load.

Evolution of valence-band alignment with nitrogen content in GaNAs∕GaAs single quantum wells

We report on experimental evidence for the transition of valence-band alignment from type I to type II in GaNxAs1−x∕GaAs single quantum wells by photoreflectance measurements. The substitutional nitrogen content covers a range of 1.4%–5.9%. The turning point of the type I–type II transition occurs at x≳4.7%. The experimental observations can be well interpreted by a combination of band anticrossing model and model-solid theory when nonlinear behavior of either the shear deformation potential or the average valence-band energy is taken into account. The effect of dilute nitrogen on the valence-band offset of GaNAs∕GaAs quantum well structure is hence clarified.

化合物半導体界面におけるバンドアラインメントとフェルミ準位ピンニング

Metal-semiconductor, semiconductor-semiconductor and insulator-semiconductor interfaces are basic constituent elements of semiconductor devices. How energy bands align at these interfaces and how well carriers are controlled through these interfaces have been important research topics of surface science as well as basic design issues for semiconductor devices. This paper attempts to review the historical evolution of various models concerning the alignments of energy bands and related Fermi level pinning phenomena at inorganic crystalline semiconductor interfaces, mainly focusing on those of compound semiconductors. The topics discussed include the natural band line-up, surface state model, charge neutrality level, interfacial model, MIGS model, UDM, DIGS model, interface bond polarization model, IFIGS model and model solid theory. It is suggested as a result of reviewing that, by sufficiently removing bond disorder and defects, the natural band line-ups may become realizable after all with feasibility of their artificial modifications by polarization of interface chemical bonds. The strong Fermi level pinning at metal-semiconductor interfaces may be removed in nano-scale structures.

Band offset calculations of ZnSxSe1−x/ZnSySe1−y heterostructures

In order to design devices based on II–VI materials, it is necessary to know the potential across the interface between two materials. Following our recent calculations which prove that the band gap energy of ZnSxSe1−x alloy has a nonlinear behaviour versus the sulphur composition x, it appears that an accurate knowledge of band offsets for ZnSxSe1−x/ZnSySe1−y structures will be useful to model devices based on this heterostructure. On the basis of a model-solid theory, we report in this work the band offset calculations for zinc blende pseudomorphically strained ZnSxSe1−x/ZnSySe1−y interface. From the results obtained, we have calculated the band gap energies of ZnSxSe1−x layers pseudomorphically strained on ZnSySe1−y substrate as a function of compositions x and y in the whole range 0≤x,y≤1. Also, the band gaps of bulk ZnSxSe1−x deposed on ZnSySe1−y for several values of y have been calculated versus the sulphur content x. Analytical formulas fitting these bands have been obtained. In view of the lack of theoretical calculations, our results seem likely to be useful especially in the design of ZnSxSe1−x structures for optoelectronic devices applications.

Theoretical investigation of the conduction and valence band offsets of GaAs 1 −x N x/GaAs 1− yN y heterointerfaces

Theoretical investigations of the conduction band offset (CBO) and valence band offset (VBO) of the relaxed and pseudo-morphically strained GaAs 1− x N x /GaAs 1− y N y heterointerfaces at various nitrogen concentrations ( x and y) within the range 0–0.05 and along the [0 0 1] direction are performed by means of the model-solid theory combined with the empirical pseudopotential method under the virtual crystal approximation that takes into account the effects of the compositional disorder. It has been found that for y < x, the CBO and VBO have negative and positive signs, respectively, whereas the reverse is seen when y > x. The band gap of the GaAs 1− x N x over layer falls completely inside the band gap of the substrate GaAs 1− y N y and thus the alignment is of type I (straddling) for y < x. When y > x, the alignment remains of type I but in this case it is the band gap of the substrate GaAs 1− y N y which is fully inside the band gap of the GaAs 1− x N x over layer. Besides the CBO, the VBO and the relaxed/strained band gap of two particular cases: GaAs 1− x N x /GaAs and GaAs 1− x N x /GaAs 0.98N 0.02 heterointerfaces have been determined.