03959nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001800153072001800171072002300189072001600212100008000228245012500308250001800433264006900451300004400520336002600564337002600590338003600616347002400652490007500676505046700751520160001218650002002818650001702838650002002855650002602875650001302901650002002914650001702934650001902951650003702970650003503007650002103042700007703063710003403140773002603174776003603200776003603236776003603272830007503308856004603383978-3-031-53816-2DE-He21320251030112003.0cr nn 008mamaa240422s2024    sz |    s    |||| 0|eng d  a97830315381627 a10.1007/978-3-031-53816-22doi 4aQC610.9-611.8 7aTJFD52bicssc 7aSCI0770002bisacsh 7aTJFD2thema1 aChowdhury, Sujaul.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aNumerical Exploration of Isolated GaAs-AlGaAs Quantum Wellh[electronic resource] /cby Sujaul Chowdhury, Urmi Talukder.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aVIII, 91 p. 69 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSynthesis Lectures on Engineering, Science, and Technology,x2690-03270 aBackground on Microelectronics -- Background on Semiconductor Nanostructure Physics -- Numerical Calculation of Energy Spectrum of GaAs-AlGaAs Quantum Well Having Abrupt Potential Steps Using Regula Falsi Method -- Numerical calculation of Energy Spectrum of GaAs-AlGaAs Quantum Well Having Abrupt Potential Steps Using Finite Difference Method -- Numerical Calculation of Energy Spectrum of Parabolic Quantum Well of Finite Depth Using Finite Difference Method.  aThis book begins with the eigenvalue equation of energy and presents calculation of the energy spectrum of GaAs-AlGaAs Quantum Well using finite difference method and knowledge of potential energy profile, without using expressions for eigenfunctions, continuity of eigenfunctions, or their spatial derivatives at the two abrupt potential steps. The authors find that the results are almost the same as those obtained by solving numerically using regula falsi method, and transcendental equations that are obeyed by the energy levels, where the transcendental equations are obtained by requiring continuity of eigenfunctions and of their spatial derivatives at the two potential steps. Thus, this book confirms that it is possible to numerically calculate the energy spectrum of Quantum Well by the finite difference method when it is not correct or when it is not possible to use continuity of eigenfunctions and their spatial derivatives at the two abrupt potential steps. The authors also show that it is possible to use the finite difference method in cases where the potential steps are non-abrupt. The book demonstrates this by calculating the energy spectrum of isolated parabolic Quantum Well of finite depth using finite difference method. In addition, this book: Presents innovative research on alternative methods of calculating the energy spectrum of GaAs-AlGaAs Quantum Well Includes confirmation of the authors’ results by comparing them to the standard calculation techniques Highlights the opportunities for further use of the finite difference method in nanostructure physics. 0aSemiconductors. 0aNanoscience. 0aNanotechnology. 0aMathematical physics. 0aPhysics.14aSemiconductors.24aNanophysics.24aNanometrology.24aMathematical Methods in Physics.24aApplied and Technical Physics.24aNanoengineering.1 aTalukder, Urmi.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303153815508iPrinted edition:z978303153817908iPrinted edition:z9783031538186 0aSynthesis Lectures on Engineering, Science, and Technology,x2690-032740uhttps://doi.org/10.1007/978-3-031-53816-2