# Linear and Nonlinear Intersubband Optical Properties of Direct Band Gap GeSn Quantum Dots

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Intersubband Transition Energies

^{*}is the corresponding effective mass, $r$ is the coordinate vector in Cartesian coordinates and $V$ is the confining potential barrier. The Schrödinger equation has been solved for the electrons in Г and L bands taking into account the lattice mismatch induced strain. The calculation procedure and material parameters are detailed elsewhere [21,22].

## 3. Linear and Nonlinear Optical Properties

_{x}- and s-like electron states in the QD’s $\mathsf{\Gamma}$ valley.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

QD | Quantum Dots |

AC | absorption coefficient |

RIC | refractive index change |

CMO | Complementary Metal Oxide Semiconductor |

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**Figure 2.**Intersubband transition energy $({E}_{p}^{\mathsf{\Gamma}}-{E}_{s}^{\mathsf{\Gamma}})$ and energy difference between p-like electron energy level in Г-valley and s-like electron energy levels in L valley $({E}_{s}^{\mathrm{L}}-{E}_{p}^{\mathsf{\Gamma}})$ as a function of the QD diameter.

**Figure 3.**In plane-normalized s (

**a**,

**d**), p

_{x}(

**b**,

**e**) and p

_{y}(

**c**,

**f**) electron envelope wave function for a QD with diameter 40 nm and 20 nm respectively.

**Figure 4.**Calculated linear (

**a**), 3rd order nonlinear (

**b**) and total refractive index changes (RIC) (

**c**) as a function of the photon energy for different QD sizes: D = 20 nm (red), D = 26 nm (blue), D = 32 nm (green), D = 40 nm (pink).

**Figure 5.**Calculated linear (solid lines), 3rd order nonlinear (dotted lines) and total absorption coefficient (AC) (filled area curves) as a function of photon energy for a selection of QD sizes: D = 20 nm (red), D = 26 nm (blue), D = 32 nm (green), D = 40 nm (pink).

**Figure 6.**Incident optical intensity dependence of total optical AC (

**a**) and RIC (

**b**) as a function of the photon energy for D = 40 nm.

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**MDPI and ACS Style**

Baira, M.; Salem, B.; Madhar, N.A.; Ilahi, B. Linear and Nonlinear Intersubband Optical Properties of Direct Band Gap GeSn Quantum Dots. *Nanomaterials* **2019**, *9*, 124.
https://doi.org/10.3390/nano9010124

**AMA Style**

Baira M, Salem B, Madhar NA, Ilahi B. Linear and Nonlinear Intersubband Optical Properties of Direct Band Gap GeSn Quantum Dots. *Nanomaterials*. 2019; 9(1):124.
https://doi.org/10.3390/nano9010124

**Chicago/Turabian Style**

Baira, Mourad, Bassem Salem, Niyaz Ahmad Madhar, and Bouraoui Ilahi. 2019. "Linear and Nonlinear Intersubband Optical Properties of Direct Band Gap GeSn Quantum Dots" *Nanomaterials* 9, no. 1: 124.
https://doi.org/10.3390/nano9010124