# Combining in-situ measurements in molecular beam epitaxy: Study of AlGaAs properties at growth temperature

Pierre Gadras, Léo Bourdon, Antoine Fées, Karim Ben Saddik, Guilhem Almuneau, Alexandre Arnoult, Quentin Gravelier

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Pierre Gadras, Léo Bourdon, Antoine Fées, Karim Ben Saddik, Guilhem Almuneau, et al.. Combining in-situ measurements in molecular beam epitaxy: Study of AlGaAs properties at growth temperature. VCSEL Day 2024, Sep 2024, Toulouse, France., 2024. [hal-04710142](https:// HAL Id: hal-04710142 )

HAL Id: hal-04710142

https://cnrs.hal.science/hal-04710142v1

Submitted on 27 Sep 2024

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## Motivations

Better control over epitaxy process is a key element for the realization of high performances VCSELs. However, no universal practical tool has been implemented to date.

With EpiCentre, joint lab with Riber, we're working on combining in-situ measurements in molecular beam epitaxy (MBE) to achieve advanced materials growth control in real time.

In-situ tools:

* Reflection high-energy electron diffraction (RHEED)

* Atomic Absorption of fluxes

* Spectral reflectance

* Curvature measurement

* Band-edge measurement

* ✓ Surface morphology

* ✓ Cells fluxes

* ✓ Growth rates

* ✓ Compositions

* ✓ Substrate temperature

<figure><img src="image_1.png" /></figure>

Feed-back control

Optical constants

<figure><img src="image_2.png" /></figure>

Band-gap, Doping

<figure><img src="image_3.png" /></figure>

## How to precisely measure optical indices at growth temperature ?

### In-situ measurement : Spectral Reflectometry

To measure optical indices, we grow a layer of **known composition** and measure **in-situ in real time the spectral reflectance**.

In the same time, we determine the **growth temperature** through **band-edge thermometry** (BandiT)

<figure><img src="image_4.png" /><figcaption>Normalized in-situ measured spectral reflectance</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Example of In-situ reflectance oscillations of GaAs layer at 600°C at λ = 500 nm. Model curve is based on optical indices values derived from [3].</figcaption></figure>

Simple model of optical reflectance oscillations [1]:

$$R(t) = \left| \frac{r_{\infty} + r_i e^{-i\delta t}}{1 + r_{\infty} r_i e^{-i\delta t}} \right|^2, \quad \delta \approx \frac{4\pi \tilde{n} G}{\lambda} * \cos(\theta)$$

with, $r_{\infty}$ : reflectance coefficient between the layer/air

$r_i$ : reflectance coefficient between the layer/substrate

$\tilde{n}$ : complex optical index of the growing film

$G$ : growth rate

$\theta$ : Angle of incidence of the light

Approximation in case of similar high refractive index film substrate:

$$R(t) = R_{\infty} - 2\sqrt{R_{\infty}R_{i}}(1 - R_{\infty})e^{-\gamma t} * \cos(\omega t - \sigma)$$

with,

$$n = \frac{\omega \lambda}{4\pi G \cos(\theta)}, \quad k = \frac{\gamma \lambda}{4\pi G \cos(\theta)}$$

### Ex-situ measurement : X-Ray Reflectivity

Measurement method of GaAs, AlAs and AlₓGa₁-ₓAs growth rates:

* Ga/Al cell shutter kept open to prevent burst effect,

* Layer thicknesses by fitting the oscillations of X-ray reflectometry with a model [2],

* Estimation of the uncertainty on the fitted thickness, using Gaussian approximation of $\chi^2$ loss function

<figure><img src="image_6.png" /><figcaption>X-ray Reflectivity measurement of sample A1592 and fit.</figcaption></figure>

High resolution X-ray diffraction (004) to determine AlₓGa₁-ₓAs composition.

<figure><img src="image_7.png" /><figcaption>Variation of $\chi^2$ around the minima and estimation of the measurement accuracy for sample A1592</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>HRXRD measurement around (004) of sample A1595 and fit.</figcaption></figure>

## Calculation of the spectral dispersion of the refractive indices at 600°C

<figure><img src="image_9.png" /><figcaption>GaAs</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>AlAs</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Al₀.₅₃Ga₀.₄₇As</figcaption></figure>

Optical indices of GaAs, AlAs and Al₀.₅₃Ga₀.₄₇As at growth temperature :

* Very good agreement with the scarce available data in the literature at high temperature,

* Refractive indices measured over the full spectral range available with the spectrometers (400-1400 nm)

* Measurement accuracy assessment (work in progress):

$$\Delta n = \frac{\omega}{4\pi G} \sqrt{(\Delta\lambda)^2 + \left(\frac{\lambda \omega}{2\pi} \Delta\Lambda\right)^2 + \left(\frac{\lambda}{G} \Delta G\right)^2}$$

with: $\Delta\lambda = \pm 4$ nm, $\Delta\Lambda = \pm 5$ s, $\frac{\Delta G}{G} \sim 1\%$ + Temperature measurement accuracy: $\Delta T = \pm 1$°C

## Perspectives

* **Mid-term objective:** generate n and k database for all AlₓGa₁-ₓAs compositions and at various growth temperatures.

* **Long-term objective:** Combining in-situ measurements:

* Using $n(\lambda, T, x_{Al})$ database to deduce growth rate from reflectance measurement

* With in-situ curvature measurement to extract alloy composition

<figure><img src="image_12.png" /></figure>

Feed-back control on the process parameters for VCSEL epitaxy

<figure><img src="image_13.png" /><figcaption>Normalized in-situ spectral reflectance of a VCSEL at 940 nm</figcaption></figure>

More
informations

<figure><img src="image_14.png" /></figure>

## References:

[1] W. G. Breiland et K. P. Killeen, J. Appl. Phys. 1995 (doi: 10.1063/1.360496)

[2] Leptos software, https://www.bruker.com/

[3] P. Lautenschlager, M. Garriga, S. Logothetidis, et M. Cardona, Phys. Rev. B 1987 (doi: 10.1103/PhysRevB.35.9174)

[4] H. Yao, P. G. Snyder, et J. A. Woollam, J. Appl. Phys. 1991 (doi: 10.1063/1.349285)

[5] C. H. Kuo & al., et G. N. Maracas, JVST B. 1995 (doi: 10.1116/1.587941)

[6] H. Kawai, & al, J. Appl. Phys. 1987 (doi: 10.1063/1.338825)

[7] J.-H. Shin et Y.-H. Lee, J. Appl. Phys. 1994, (doi: 10.1063/1.357874)

[8] V. Bardinal, R. Legros, et C. Fontaine», Appl. Phys. Lett. 1995 (doi: 10.1063/1.114681)

cnrs

## Acknowledgments:

RENATECH (French Network of Technology Platforms) at LAAS-CNRS
Epicentre, RIBER LAAS-CNRS joint lab

Laboratoire conventionné avec