# Degree of Polarization of Cathodoluminescence from a GaAs Facet in the Vicinity of an SiN Stripe

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## Abstract

**:**

## 1. Introduction

#### 1.1. DOP as a Function of Strain

#### 1.2. Least Squares Fits

## 2. Sample and SEM Measurements

#### 2.1. SiN Stripes on GaAs

_{4}, N

_{2}, and He as precursors. After deposition, a stress of $-220$ MPa was measured at the wafer level through the measurement of the wafer bow. Wafers were then processed with standard UV contact lithography to define the stripes of various widths and groupings by the reactive ion etching of the SiN layers and the removal of the photoresist. Bars of 3 mm width in the $\widehat{\mathit{n}}$ direction and of 368 $\mathsf{\mu}$m thickness in the $\widehat{\mathit{v}}$ direction were cleaved for scanning electron microscope (SEM) and CL analysis. The backside of the wafer was not polished.

#### 2.2. SEM Data

## 3. Fits to the CL Yield

## 4. Fits of FEM Simulations to the DOP and ROP Data

#### 4.1. Some Details on the FEM Simulations

#### 4.2. Fits to the Data

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**CL yield as calculated from ${P}_{1}$ and ${P}_{2}$ (top panel), DOP (middle panels), and ROP (bottom panels), displayed using a false color mapping. The same DOP and ROP data are displayed in the two columns but for different thresholds of $0.04\times C{L}_{\mathrm{max}}$ and $0.6\times C{L}_{\mathrm{max}}$. The color bar (

**g**) shows the false color mapping that was used to display the data.

**Figure 4.**Fits of complementary error functions to the $C{L}_{\mathrm{DOP}}$ data as a function of v for: (

**a**) near the mid-point of the SiN stripe, $h=102$; and (

**b**), far from the SiN stripe, $h=18$.

**Figure 5.**Fits of complementary error functions to the $C{L}_{\mathrm{DOP}}$ and $C{L}_{\mathrm{ROP}}$ data as a function of v near the mid-point of the stripe, i.e., at $h=102$, and on an expanded scale.

**Figure 6.**DOP and ROP data, the fits to the data, and $5\times $ the residues. The same area of $208\times {v}_{step}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}5.46\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m by $204\times {h}_{step}=8.92\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m is displayed in each panel. The colour bar (

**g**) shows the false colour mapping that was used to display the data and has the same explanation as the colour bar of Figure 3.

**Figure 7.**From top to bottom, residues for fits with 1, 2, 3, and 4 basis functions plus background functions. A $3\times 3$ point smoothing (unit-area convolution) was used to reduce the noise and thus enhance the ability to see patterns in the residue. Compare panels (

**c**,

**f**) of Figure 6 with panels (

**d**,

**h**) to observe the noise reduction caused by the smoothing. The colour bar (

**i**) shows the false colour mapping that was used to display the data and has the same explanation as the colour bar of Figure 3.

**Table 1.**Fit parameters for fits of Equation (17) to the CL yields, $C{L}_{DOP}$ and $C{L}_{ROP}$, for vertical planes specified by h. The SiN stripe is in the interval $57\le h\le 156$.

File | h | $\mathit{\chi}$ | A | ${\mathit{v}}_{\mathit{e}}$ | ${\mathit{v}}_{\mathit{e}}$ (nm) | ${\mathit{\sigma}}_{\mathit{v}}$ (nm) | FWHM (nm) |
---|---|---|---|---|---|---|---|

$C{L}_{\mathrm{DOP}}$ | 18 | 464 | 20,817.0 | $28.45$ | 747 | 201 | 473 |

$C{L}_{\mathrm{DOP}}$ | 98 | 630 | 19,465.2 | $29.87$ | 785 | 203 | 477 |

$C{L}_{\mathrm{DOP}}$ | 102 | 630 | 19,463.4 | $29.76$ | 782 | 203 | 478 |

$C{L}_{\mathrm{DOP}}$ | 106 | 673 | 19,452.2 | $28.46$ | 748 | 205 | 482 |

$C{L}_{\mathrm{DOP}}$ | 190 | 480 | 20,990.3 | $29.18$ | 766 | 204 | 480 |

$C{L}_{\mathrm{ROP}}$ | 18 | 464 | 21,549.1 | $26.87$ | 705 | 204 | 481 |

$C{L}_{\mathrm{ROP}}$ | 98 | 664 | 20,073.7 | $28.24$ | 740 | 203 | 479 |

$C{L}_{\mathrm{ROP}}$ | 102 | 659 | 20,087.5 | $28.13$ | 737 | 203 | 478 |

$C{L}_{\mathrm{ROP}}$ | 106 | 705 | 20,268.2 | $26.92$ | 706 | 207 | 487 |

$C{L}_{\mathrm{ROP}}$ | 192 | 461 | 21,603.6 | $27.70$ | 727 | 206 | 486 |

**Table 2.**$\chi $ values for fits of the DOP and ROP data to FEM simulations for a $4.35\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m-wide SiN stripe on GaAs for ${R}_{a}=1.2$.

Elements | Influence | ${\mathit{\chi}}_{\mathit{T}}$ | ${\mathit{\chi}}_{\mathbf{DOP}}$ | ${\mathit{\chi}}_{\mathbf{ROP}}$ | $\mathit{\delta}{\mathit{\chi}}_{\mathit{T}}/\mathbf{CI}$ |
---|---|---|---|---|---|

$0+1$ | 1: biaxial SiN stress | $1.0943$ | $1.1248$ | $1.0633$ | $-258.4$ |

$0+1+2$ | 2: uniaxial $\widehat{\mathit{n}}$ stress | $1.0485$ | $1.0757$ | $1.0210$ | $-8.9$ |

$0+1+2+3$ | 3: biaxial interface stress | $1.0290$ | $1.0498$ | $1.0082$ | $-3.8$ |

$0+1+2+3+4$ | 4: biaxial etch stress | $1.0274$ | $1.0513$ | $1.0033$ | $-0.3$ |

0 | 0: background only | $2.43$ | $3.20$ | $1.28$ |

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**MDPI and ACS Style**

Cassidy, D.T.; Landesman, J.-P.; Mokhtari, M.; Pagnod-Rossiaux, P.; Fouchier, M.; Monachon, C. Degree of Polarization of Cathodoluminescence from a GaAs Facet in the Vicinity of an SiN Stripe. *Optics* **2023**, *4*, 272-287.
https://doi.org/10.3390/opt4020019

**AMA Style**

Cassidy DT, Landesman J-P, Mokhtari M, Pagnod-Rossiaux P, Fouchier M, Monachon C. Degree of Polarization of Cathodoluminescence from a GaAs Facet in the Vicinity of an SiN Stripe. *Optics*. 2023; 4(2):272-287.
https://doi.org/10.3390/opt4020019

**Chicago/Turabian Style**

Cassidy, Daniel T., Jean-Pierre Landesman, Merwan Mokhtari, Philippe Pagnod-Rossiaux, Marc Fouchier, and Christian Monachon. 2023. "Degree of Polarization of Cathodoluminescence from a GaAs Facet in the Vicinity of an SiN Stripe" *Optics* 4, no. 2: 272-287.
https://doi.org/10.3390/opt4020019