# Evaluation of Effective Mass in InGaAsN/GaAs Quantum Wells Using Transient Spectroscopy

^{1}

^{2}

^{*}

## Abstract

**:**

_{0}of charges from the conduction band was 0.093 ± 0.006, while the charges from the conduction band exhibited an effective mass of 0.122 ± 0.018.

## 1. Introduction

## 2. Materials and Methods

_{3}:H

_{2}mixture) were employed as the precursors, while the high-purity hydrogen was used as a carrier gas. The heterostructures consisted of 450 nm thick GaAs buffer layer, followed by triple In

_{y}Ga

_{1−y}As

_{1−x}N

_{x}/GaAs quantum wells region, and capped by 40–50 nm thick GaAs, as depicted in Figure 1 [22]. A family of 15 heterostructures of various InGaAsN thicknesses and indium/nitrogen ratios was fabricated for this study. The InGAsN layer thicknesses $d$ varied from 6 to 19.8 nm. The nitrogen content x ranged from 0 to 1.2%, whereas the indium content y ranged from 0 to 16%. The concentric ring geometry was applied for electrode topology. Here, the voltage pulse was applied at the Pt/Ti/Pt/Au electrode, while the AuGe/Ni/Au provided the ground.

## 3. Results and Discussion

^{−6}K

^{−1}[29]. As a result, the quantum well with a width of 14 nm in a temperature difference of 300 K changes by 0.15% (i.e., 0.02 nm). This difference can be neglected since it is in the range of the experimental error. Furthermore, it is interesting to note that the quantum well eigenvalue energies in Equation (4) are linearly proportional to the square of the quantum number and quantum well width ratio, ${n}^{2}/{d}^{2}$.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Sketch of the energy band diagram of InGaAsN/GaAs quantum well structure. (

**b**) A simplified view of the triple quantum well structure and (

**c**) micrograph (transmission electron microscopy in the bright field) of fabricated heterostructure.

**Figure 2.**(

**a**) Steady-state current-voltage characteristic of heterostructure with $x=0.32\%$, $y=13.3\%$, and $d=16.6\mathrm{nm}$. (

**b**) The spectrum of the Fourier coefficient ${b}_{1}$ together with simulations of various energy states. (

**c**) The Arrhenius plot.

**Figure 3.**Normalised capture cross-section dependence on energy eigenvalues for heterostructure with $x=0.32\%$, $y=13.3\%$, and $d=16.6\mathrm{nm}$ (shown in Figure 2) with the quantum well depth of 289 meV as estimated by energy band offset reports.

**Figure 4.**Eigenvalue energy dependence on ${n}^{2}/{d}^{2}$ ratio for conduction and valence bands. The effective mass is evaluated according to Equation (3).

**Table 1.**Electron effective masses of InGaAsN/GaAs quantum well heterostructures estimated by various techniques.

$\mathbf{Effective}\mathbf{Mass}{\mathit{m}}_{\mathit{n},\mathit{p}}^{*}/{\mathit{m}}_{0}$ | Technique | Reference |
---|---|---|

0.05 ~ 0.09 (n) | RTOP | [12] |

0.06 ~ 0.08 (n) | RTOP | [30] |

0.077 ~ 0.078 (n) | QHE, SdH | [31] |

0.07 ~ 0.12 (p) | SdH | [32] |

0.07 (n) | ODCR | [33] |

0.093 ± 0.006 (n) | Transient spectroscopy | This work |

0.122 ± 0.018 (p) | Transient spectroscopy | This work |

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**MDPI and ACS Style**

Stuchlikova, L.; Sciana, B.; Kosa, A.; Matus, M.; Benko, P.; Marek, J.; Donoval, M.; Dawidowski, W.; Radziewicz, D.; Weis, M. Evaluation of Effective Mass in InGaAsN/GaAs Quantum Wells Using Transient Spectroscopy. *Materials* **2022**, *15*, 7621.
https://doi.org/10.3390/ma15217621

**AMA Style**

Stuchlikova L, Sciana B, Kosa A, Matus M, Benko P, Marek J, Donoval M, Dawidowski W, Radziewicz D, Weis M. Evaluation of Effective Mass in InGaAsN/GaAs Quantum Wells Using Transient Spectroscopy. *Materials*. 2022; 15(21):7621.
https://doi.org/10.3390/ma15217621

**Chicago/Turabian Style**

Stuchlikova, Lubica, Beata Sciana, Arpad Kosa, Matej Matus, Peter Benko, Juraj Marek, Martin Donoval, Wojciech Dawidowski, Damian Radziewicz, and Martin Weis. 2022. "Evaluation of Effective Mass in InGaAsN/GaAs Quantum Wells Using Transient Spectroscopy" *Materials* 15, no. 21: 7621.
https://doi.org/10.3390/ma15217621