A simpler graphical solution and an approximate formula for energy eigenvalues in finite square quantum wells

2020 ◽  
Vol 88 (11) ◽  
pp. 1019-1022
Author(s):  
F. M. S. Lima
Keyword(s):  
Quantum Wells ◽  
Approximate Formula ◽  
Graphical Solution ◽  
Energy Eigenvalues

LINEAR AND NONLINEAR INTERSUBBAND OPTICAL ABSORPTION OF FINITE AND INFINITE SEMI-PARABOLIC QUANTUM WELLS

2011 ◽  
Vol 25 (07) ◽  
pp. 497-507 ◽  
Author(s):  
M. J. KARIMI ◽  
A. KESHAVARZ ◽  
A. POOSTFORUSH
Keyword(s):  
Refractive Index ◽  
Optical Properties ◽  
Optical Absorption ◽  
Quantum Well ◽  
Quantum Wells ◽  
Resonant Peak ◽  
Energy Eigenvalues ◽  
Finite Case ◽  
Infinite Case ◽  
Index Changes

In this work, the optical absorption coefficients and the refractive index changes for the infinite and finite semi-parabolic quantum well are calculated. Numerical calculations are performed for typical GaAs / Al x Ga 1-x As semi-parabolic quantum well. The energy eigenvalues and eigenfunctions of these systems are calculated numerically. Optical properties are obtained using the compact density matrix approach. Results show that the energy eigenvalues and the matrix elements of the infinite and finite cases are different. The calculations reveal that the resonant peaks of the optical properties of the finite case occur at lower values of the incident photon energy with respect to the infinite case. Results indicate that the maximum value of the refractive index changes for the finite case are greater than that of the infinite case. Our calculations also show that in contrast to the infinite case, the resonant peak value of the total absorption coefficient in the case of the finite well is a non-monotonic function of the semi-parabolic confinement frequency.

IMPROVED ARBITRARY l-STATE SOLUTIONS OF THE HULTHÉN POTENTIAL

2009 ◽  
Vol 24 (28n29) ◽  
pp. 5523-5529 ◽  
Author(s):  
WEN-CHAO QIANG ◽  
WEN LI CHEN ◽  
KAI LI ◽  
HUA-PING ZHANG
Keyword(s):  
Analytical Solutions ◽  
Approximate Formula ◽  
Approximation Scheme ◽  
Wave Functions ◽  
Centrifugal Term ◽  
Hulthén Potential ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Radial Schrödinger Equation ◽  
Numerical Integration Methods

We developed a new and simple approximation scheme for centrifugal term. Using the new approximate formula for 1/r2 we derived approximately analytical solutions to the radial Schrödinger equation of the Hulthén potential with arbitrary l-states. Normalized analytical wave-functions are also obtained. Some energy eigenvalues are numerically calculated and compared with those obtained by C. S. Jia et al. and other methods such as the asymptotic iteration, the supersymmetry, the numerical integration methods and a Mathematica program, schroedinger, by W. Lucha and F. F. Schöberl.

Optical properties in GaAs/AlGaAs semiparabolic quantum wells by the finite difference method: Combined effects of electric field and magnetic field

2018 ◽  
Vol 32 (13) ◽  
pp. 1850159 ◽  
Author(s):  
Ru-Yu Yan ◽  
Jian Tang ◽  
Zhi-Hai Zhang ◽  
Jian-Hui Yuan
Keyword(s):  
Magnetic Field ◽  
Optical Properties ◽  
Electric Field ◽  
Quantum Wells ◽  
Applied Electric Field ◽  
Differential Method ◽  
Optical Rectification ◽  
Intersubband Transitions ◽  
Energy Eigenvalues ◽  
Device Applications

In the present work, the optical properties of GaAs/AlGaAs semiparabolic quantum wells (QWs) are studied under the effect of applied electric field and magnetic field by using the compact-density-matrix method. The energy eigenvalues and their corresponding eigenfunctions of the system are calculated by using the differential method. Simultaneously, the nonlinear optical rectification (OR) and optical absorption coefficients (OACs) are investigated, which are modulated by the applied electric field and magnetic field. It is found that the position and the magnitude of the resonant peaks of the nonlinear OR and OACs can depend strongly on the applied electric field, magnetic field and confined potential frequencies. This gives a new way to control the device applications based on the intersubband transitions of electrons in this system.

Characterization of GaAs/AlGaAs quantum wells and quantum wires by chemical lattice imaging

1994 ◽  
Vol 52 ◽  
pp. 736-737
Author(s):  
A. Carlsson ◽  
J.-O. Malm ◽  
A. Gustafsson
Keyword(s):  
Quantum Well ◽  
Quantum Wells ◽  
Quantum Wires ◽  
Vapour Phase ◽  
Quantitative Information ◽  
Lattice Imaging ◽  
Vapour Phase Epitaxy ◽  
Metalorganic Vapour Phase Epitaxy ◽  
High Resolution Images

In this study a quantum well/quantum wire (QW/QWR) structure grown on a grating of V-grooves has been characterized by a technique related to chemical lattice imaging. This technique makes it possible to extract quantitative information from high resolution images.The QW/QWR structure was grown on a GaAs substrate patterned with a grating of V-grooves. The growth rate was approximately three monolayers per second without growth interruption at the interfaces. On this substrate a barrier of nominally Al0.35 Ga0.65 As was deposited to a thickness of approximately 300 nm using metalorganic vapour phase epitaxy . On top of the Al0.35Ga0.65As barrier a 3.5 nm GaAs quantum well was deposited and to conclude the structure an additional approximate 300 nm Al0.35Ga0.65 As was deposited. The GaAs QW deposited in this manner turns out to be significantly thicker at the bottom of the grooves giving a QWR running along the grooves. During the growth of the barriers an approximately 30 nm wide Ga-rich region is formed at the bottom of the grooves giving a Ga-rich stripe extending from the bottom of each groove to the surface.

Characterisation of multilayer materials using a position-sensitive atom probe

1990 ◽  
Vol 48 (4) ◽  
pp. 624-625
Author(s):  
RAD Mackenzie ◽  
G D W Smith ◽  
A. Cerezo ◽  
J A Liddle ◽  
CRM Grovenor ◽  
...  
Keyword(s):  
Quantum Well ◽  
Quantum Wells ◽  
Spatial Information ◽  
Chemical Vapour ◽  
Atom Probe ◽  
Organic Chemical ◽  
Growth Stages ◽  
Multiple Quantum ◽  
Quartz Wool ◽  
Position Sensitive

The position sensitive atom probe (POSAP), described briefly elsewhere in these proceedings, permits both chemical and spatial information in three dimensions to be recorded from a small volume of material. This technique is particularly applicable to situations where there are fine scale variations in composition present in the material under investigation. We report the application of the POSAP to the characterisation of semiconductor multiple quantum wells and metallic multilayers.The application of devices prepared from quantum well materials depends on the ability to accurately control both the quantum well composition and the quality of the interfaces between the well and barrier layers. A series of metal organic chemical vapour deposition (MOCVD) grown GaInAs-InP quantum wells were examined after being prepared under three different growth conditions. These samples were observed using the POSAP in order to study both the composition of the wells and the interface morphology. The first set of wells examined were prepared in a conventional reactor to which a quartz wool baffle had been added to promote gas intermixing. The effect of this was to hold a volume of gas within the chamber between growth stages, leading to a structure where the wells had a composition of GalnAsP lattice matched to the InP barriers, and where the interfaces were very indistinct. A POSAP image showing a well in this sample is shown in figure 1. The second set of wells were grown in the same reactor but with the quartz wool baffle removed. This set of wells were much better defined, as can be seen in figure 2, and the wells were much closer to the intended composition, but still with measurable levels of phosphorus. The final set of wells examined were prepared in a reactor where the design had the effect of minimizing the recirculating volume of gas. In this case there was again further improvement in the well quality. It also appears that the left hand side of the well in figure 2 is more abrupt than the right hand side, indicating that the switchover at this interface from barrier to well growth is more abrupt than the switchover at the other interface.

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