Abstract

This paper shows that the experimental results of quantum well energy transitions can be found numerically. The cases of several ZnO-ZnMgO wells are considered and their excitonic transition energies were calculated using the finite difference method. In that way, the one-dimensional Schrodinger equation has been solved by using the BLAS and LAPACK libraries. The numerical results are in good agreement with the experimental ones.

Highlights

  • ZnO is a very abundant material in nature, with very interesting physiochemical properties: it is non-toxic and presents high chemical stability

  • Its exciton binding energy of the order of 60 meV, enables the design of laser devices operating at room temperature

  • This study presents a numerical model that allows retrieving transition energies of excitons measured in a ZnO-ZnMgO or other quantum-well

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Summary

Introduction

ZnO is a very abundant material in nature, with very interesting physiochemical properties: it is non-toxic and presents high chemical stability It possesses a direct and large band gap (3.37 eV) at room temperature. (2016) Numerical Verification of Transition’s Energies of Excitons in Quantum Well of ZnO with the Finite Difference Method. The realistic physics of the Schrödinger equation arises from its equivalence to a tightbiding model for crystalline solid [1], in both the bulk and quantum confinement cases. This study presents a numerical model that allows retrieving transition energies of excitons measured in a ZnO-ZnMgO or other quantum-well. This model is based on the finite difference method [2] [3].

Experimental Details
Structural Characterization and Optical Properties
Use of the Finite Difference Method
Finite Difference Method
Verification and Discussions
Conclusion

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