# Plasma wave resonances in Graphene channels under controlled gate for high frequency applications

Abdelhamid Mahi, Fatima Zohra Mahi, Luca Varani

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## To cite this version:

Abdelhamid Mahi, Fatima Zohra Mahi, Luca Varani. Plasma wave resonances in Graphene channels under controlled gate for high frequency applications. Materials Research Express, 2023, 10 (7), pp.076303. 10.1088/2053-1591/ace4a0. hal-05252258

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# Plasma wave resonances in Graphene channels under controlled gate for high frequency applications

To cite this article: AbdelHamid Mahi et al 2023 *Mater. Res. Express* 10 076303

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# Plasma wave resonances in Graphene channels under controlled gate for high frequency applications

AbdelHamid Mahi¹, Fatima Zohra Mahi² and Luca Varani³

¹ Institute of Sciences, Instrumentation and Advanced Materials Laboratory, Nour Bashir University Center of El Bayadh, Algeria

² Department of Materials Sciences, University of Bechar, Algeria

³ University of Montpellier, CNRS, Montpellier, France

E-mail: mido.mahi@gmail.com

**Keywords:** graphene high electron mobility transistors, Bilayer and monolayer Graphene, resonances, dielectric substrates, voltage gain

## Abstract

Several devices based on 2D materials have become interesting for high-frequency applications especially sensors, amplifiers and modulators of Terahertz frequencies. Moreover, High Electron Mobility Transistors (HEMTs) have emerged as important competitors owing to the high quality of resonances associated with plasma-wave oscillations in the channel. In this study, the plasma wave resonances in a Graphene channel of High Electron Mobility Transistors (HEMTs) were studied. The calculations were based on our small-signal model and therefore can determine the resonances and voltage gain of the Monolayer and Bilayer graphene channels. The influence of the dielectric substrates between the gate and the channel, impurity depth positions and channel materials (InGaAs, Bilayer and Monolayer graphene) on the dynamic behavior of the Graphene transistor was investigated. This analysis can extract the high performance conditions of HEMTs Graphene amplifiers.

## 1. Introduction

In recent years, several studies have shown that two-dimensional (2D) materials are the best candidates for terahertz devices [1–5], particularly for optical communications devices [6], nanodetectors coupled with THz antennas [7] and phototransistors based on black phosphorus materials [8]. The superior properties of 2D materials lie in the oscillations of plasma waves under conditions of high carrier mobility [2–5]. One of the 2D material and most important then the 2D electron gas is because of its high electronic mobility, unique structure of massless Dirac fermions, weak electron-phonon interactions and unique ballistic transport [9, 10]. This makes graphene a good candidate for saturable absorption in different optical devices [11, 12], infrared devices, electro-optic devices, and field effect transistors (FETs) for radio frequency applications [13].

Furthermore, High Electron Mobility Transistors (HEMT) have important electrical properties for several terahertz applications, such as detectors, emitters and amplifiers [14–16]. The study of HEMTs based on InGaAs material shows the existence of THz plasma-wave oscillations in the channel which leads to the appearance of terahertz resonances in the small-signal admittance spectrum as refered [17–20]. High resonances in the small-signal response appeared at frequencies up to 7 THz when a short gate covered the total nano-channel length of the transistor [21, 22]. For the THz antenna and detection, the analytical [17, 23] and experimental [24, 25] studies demonstrate the possibility of amplifying some terahertz frequencies (no more than 2 THz) by the InGaAs HEMTs when the resonant plasma frequency coincides with the frequency of the incoming monochromatic THz radiation. The analysis of HEMTs based on InGaAs material has been described in [14, 17] and focus their behavior on terahertz frequencies. Several high-frequency HEMTs applications, sensing and amplification require the performance of resonances based on strong plasma mode oscillations in the transistor channel. Therefore, we seek to improve the quality of the resonances by using Graphene as a channel to provide multiple choices for HEMTs applications in the high-frequency domain.

In this study, analytical calculations are proposed to describe the behavior of HEMTs with graphene channels. The calculations were based on the small-signal model developed for InGaAs HEMTs in [17]. The
<figure><img src="image_11.png" /><figcaption>Figure 1. Graphene channel HEMTs with SiO$_{2}$ dielectric substrate.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 2. Structure of graphene channel HEMTs connected to Y$_{C}$ real charge.</figcaption></figure>

model was used to determine the response and voltage gain spectra in THz frequencies for different scenarios of Graphene materials (Graphene Monolayer (GML) and Graphene Bilayer (GBL)) and dielectric substrates (H$_{2}$O, Ethanol (160K), HfO$_{2}$ and SiO$_{2}$). The effects of different graphene parameters (relaxation rate, effective mass and dielectric permittivity) and the impurity position in the dielectric substrate were investigated.

## 2. Analytical model

We consider the HEMTs as a channel of bulk Graphene entirely covered by the gate where the channel is separated from the gate by a dielectric substrate. The structure is schematically shown in figure 1 where the dielectric of distance d between the channel and gate is SiO$_{2}$. The transistor channel is characterized by a length L, thickness δ = 15 nm, gate-to-channel distance d and electron concentration n$_{0}$.

As a reference, the source potential is zero ΔV$_{s}$ = 0 where the drain-source and gate-source voltages are ΔV$_{d}$ and ΔV$_{g}$, respectively.

The carrier oscillations behavior in the channel is controlled by the gate voltage ΔV$_{g}$ which leads to the control of the voltage amplification in the following calculations. A numerical description of the transistor was obtained using a one-dimensional analytical equations when we neglect the dependence of any physical phenomenon on the thickness of Graphene (one-dimensional Graphene structure).

The admittance elements Y$_{dd}$ and Y$_{dg}$ were determined using the hydrodynamic model coupled with a pseudo-two-dimensional (P2D) Poisson equation developed in [23, 26, 27]. The admittances spectra are obtained through the relation of drain current-to- ΔV$_{d}$ and ΔV$_{g}$ voltages:

$$ \Delta j_d = Y_{dd} \Delta V_d + Y_{dg} \Delta V_g \quad (1) $$

According to [28], the expressions of the admittance elements are given by: Y$_{dd}$ = γβ cos βl / sin βl, Y$_{dg}$ = Y$_{gd}$ = γβ 1 − cos βl / sin βl where γ = −ε$_{c}$ω$_{3D}^{2}$ / (iω + ν) − iωε$_{c}$, ω$_{3D}$ = √e$^{2}$n$_{0}$/ε$_{c}$m* is the free-carrier 3D plasma frequency, k$_{y}$ = √ε$_{d}$/ (ε$_{c}$dδ) is a parameter describing the transverse geometry of the device, β$^{2}$= k$_{y}^{2}$[(ω$^{2}$ − iων) / (ω$_{3D}^{2}$ + iω(iω + ν))] where ν is the relaxation rate, m* is the effective mass, d is the distance between the channel-gate and ε$_{c,d}$ is the dielectric constants in the channel and in the dielectric between the channel and the gate, respectively.

As that studied in [17], the voltage gain spectrum is determined when the transistor is loaded with an external charge Y$_{C}$ introduced between the source and drain contacts. The spectral voltage gain was studied for a real Graphene device characterized in [29] for Terahertz range as shown in figure 2.
<figure><img src="image_13.png" /><figcaption>Figure 3. Admittance modulus $Y_{dd}$ and $Y_{dg}$ of HEMTs graphene with the dielectric SiO$_2$.</figcaption></figure>

In this case, the drain current is given by the equivalent electronic transistor-load circuit as:

$$ \Delta j_d = Y_C \Delta V_d \quad (2) $$

The voltage gain was obtained using equations (1) and (2), respectively:

$$ G = \frac{\Delta V_d}{\Delta V_g} = \frac{Y_{dg}}{Y_C - Y_{dd}} \quad (3) $$

In this article, the analysis of the Graphene HEMTs response is based on Graphene parameters such as relaxation rate $\nu$, effective mass $m^*$ and permittivity constants $\epsilon_{c,d}$.

### 3. Admittances and voltage gain of HEMTs graphene

In this section, we analyze the Terahertz behavior of HEMTs Graphene channels with the dielectric substrate SiO$_2$. The results of figure 3 are obtained for the graphene-SiO$_2$ where the effective mass $m^* = 0.021 m_0$ [30], the relaxation rate $\nu = 0.5 \times 10^{12} s^{-1}$ [31], the permittivity constants of the dielectric SiO$_2$ and the graphene are $\epsilon_c = 4$ and $\epsilon_d = 2.3823$ [32], respectively.

Figure 3 shows a series of resonance peaks appearing at frequencies up to 20 THz. The resonances in the admittances spectra $Y_{dd}$ and $Y_{dg}$ are associated with the excitation of plasma modes in channel of HEMTs. The admittance $Y_{dd}$ presents all resonances corresponding to all excitation modes when only the odd resonance appears in the $Y_{dg}$ spectrum. Therefore, resonances originating from the oscillations modes in the channel can be controlled by the gate.

The voltage gain spectrum calculated using equation (3) and reported in figure 4 for different real charge $Y_C$.

The voltage gain exhibits resonances at frequencies up to 20 THz. Graphene HEMTs can be used as a voltage amplifier in a high range of terahertz frequencies where the amplification is assisted by plasma resonances. For the high admittance $Y_C$, the gain spectrum exhibits resonances of odd modes corresponding to $Y_{dg}$ behavior; therefore, the potential is fixed at the channel extremities and symmetrical boundary conditions are achieved. In the absence of charge load and approaching open-circuit conditions ($Y_C \approx 0$), a shift of the resonance frequencies is observed, and the case of an asymmetrically in the channel appears.

### 4. Effect of dielectric substrates on HEMTs graphene response

We will focus in this section the behavior of graphene HEMTs on different dielectric substrates: H$_2$O, Ethanol (160K), HfO$_2$ and SiO$_2$. The change in dielectric substrates introduces a variation in two physical terms: relaxation rate and permittivity according to tables 1 and 2, respectively [31, 32].

Scattering time for different dielectric graphene extracted from [31].

In order to analyze the effect of the dielectric substrates on the admittances $Y_{dd}$ and $Y_{dg}$, we kept all the Graphene parameters constants (relaxation rate $\nu = 10^{13} s^{-1}$, effective mass $m^* = 0.192 \times 10^{-31} Kg$, dielectric
<figure><img src="image_14.png" /><figcaption>**Figure 4.** The voltage gain of graphene HEMTs channels reported for different real charge values $Y_c$.</figcaption></figure>

<table><caption>**Table 1.** Permittivity of graphene for different dielectric substrates.</caption><thead><tr><th>Dielectric</th><th>ε<sub>c</sub> (dielectric permittivity)</th><th>ε<sub>d</sub> (graphene)</th></tr></thead><tbody><tr><td>H<sub>2</sub>O</td><td>80</td><td>1.0853</td></tr><tr><td>Ethanol (160 K)</td><td>55</td><td>1.1234</td></tr><tr><td>Ethanol (300K)</td><td>25</td><td>1.2658</td></tr><tr><td>HfO<sub>2</sub></td><td>25</td><td>1.2658</td></tr><tr><td>SiO<sub>2</sub></td><td>4</td><td>2.3823</td></tr></tbody></table>

<table><caption>**Table 2.** Scattering time of different dielectric substrates.</caption><thead><tr><th>Dielectric</th><th>Scattering time τ (s)</th></tr></thead><tbody><tr><td>HfO<sub>2</sub></td><td>10<sup>-13</sup></td></tr><tr><td>SiO<sub>2</sub></td><td>2 × 10<sup>-12</sup></td></tr></tbody></table>

constants in the channel and the length L) and we modified separately the dielectric constant values of H₂O, Ethanol (160K), HfO₂ and SiO₂ (table 1).

Figure 5 illustrates the modification introduced by different dielectric substrates on admittances $Y_{dd}$ and $Y_{dg}$. As shown in figure 3, we observe a series of resonance peaks caused by plasma wave oscillations along the channel where the resonant frequency depends on the free-carrier 3D plasma frequency $\omega_{3D}$. It can also be noticed that the amplitude of the resonance peaks decreases and can disappear when the dielectric between the channel and the gate is changed (see the solid lines in figures 5(a) and (b)). Therefore, high-quality resonances were obtained in the case of SiO₂ between the channel and gate. The appearance of this quality of resonances is related to the decrease in the SiO₂ dielectric constant $\epsilon_c$ and therefore the increase in bowth: the gate control and the free-carrier 3D plasma frequency are given by the analytical terms $k_y$ and $\omega_{3D}$, respectively.

However, the resonances disappeared when the Graphene channel was coupled with dielectric substrates H₂O, Ethanol (160K), HfO₂. Therefore, all the dielectrics H₂O, Ethanol (160K), HfO₂ present the same behavior effect on the terahertz Graphene HEMTs response (absence of plasma oscillations modes).

For a real study, the results are extracted for the relaxation rate and the dielectric constants of HfO₂ and SiO₂ according to tables 1 and 2. The choice of HfO₂ had the same effect as that shown by H₂O and Ethanol (160K) on the admittance spectra in figure 5.

The response of HEMTs Graphene-HfO₂ and Graphene-SiO₂ is reported in figure 6.

We observed a high amplitude of resonances associated with the high oscillations plasma modes in the Graphene channel with SiO₂ substrate. Therefore, good gate control is obtained by the effective substrate SiO₂ (see figure 6(b)). The dielectric SiO₂ presents a low value for both the permittivity $\epsilon_c$ and the relaxation rate $\nu$, compared to HfO₂ (see tables 2 and 3), which can produce a high free-carrier 3D plasma frequency (resonances
<figure><img src="image_15.png" /><figcaption>Figure 5. Admittance modulus of HEMTs graphene for different dielectric. (a) $Y_{dd}$ and (b) $Y_{dg}$.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 6. Admittance modulus $Y_{dd}$ and $Y_{dg}$ of HEMTs SiO$_2$-graphene and HfO$_2$-graphene.</figcaption></figure>

<table><caption>Table 3. The scattering time for different impurity distance Z.</caption><thead><tr><th>Z (nm)</th><th>τ (s) for E = E<sub>f</sub></th><th>τ (s) for E/E<sub>f</sub> = 0.2</th><th>τ (s) for E/E<sub>f</sub> = 2</th></tr></thead><tbody><tr><td>0</td><td>4 × 10<sup>-13</sup></td><td>2 × 10<sup>-12</sup></td><td>4 × 10<sup>-13</sup></td></tr><tr><td>1</td><td>7 × 10<sup>-13</sup></td><td>2 × 10<sup>-12</sup></td><td>10<sup>-12</sup></td></tr><tr><td>5</td><td>4 × 10<sup>-12</sup></td><td>2.8 × 10<sup>-12</sup></td><td>2.8 × 10<sup>-11</sup></td></tr><tr><td>10</td><td>1.8 × 10<sup>-11</sup></td><td>4 × 10<sup>-12</sup></td><td>6 × 10<sup>-11</sup></td></tr></tbody></table>

appearing at high frequency) and high carrier mobility (significantly increasing the quality of the resonance), respectively.

## 5. Impurity effect on the graphene HEMTs response

In this section, we consider that the impurity located at a distance Z in SiO$_2$ substrate is the highest in the Graphene region as shown in figure 7.

The scattering time is given in table 3 for monolayer n-type Graphene with a surface electronic density $n = 10^{12} \text{ cm}^{-2}$ according to the [33].

In other hand, the effective mass of monolayer graphene is calculated by:

$$m^* = \frac{E_F}{v_F^2} \qquad (4)$$

Where $v_F$ is the Fermi velocity estimated as $1.1 \times 10^6 \text{ m/s}$ [34], and $E_F = 0.12 \text{ eV}$ is the Fermi energy. The effective mass of monolayer Graphene depends on the Fermi energy which significantly depends on the impurity
<figure><img src="image_17.png" /><figcaption>**Figure 7.** Ionized impurity located at distance Z between the graphene and the gate.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 8.** Admittances of graphene channels HEMTs reported for different position values Z. (a) $|Y_{dd}|$ and (b) $|Y_{dg}|$.</figcaption></figure>

position. Below, we analyze the influence of position Z on the Graphene HEMTs response by considering the case $E = E_f$ in table 3.

By using the constants $\epsilon_d = 4$, $\epsilon_d = 2.3823$ and the effective mass $m^* = 0.192 \times 10^{-31}$ Kg [34], the response of HEMTs graphene reported for different impurity position values is reported in figure 8.

High-quality resonances were obtained when the impurity was far from the SiO₂-graphene interface. Therefore, a low amplitude of resonances appears for a decrease in the position Z by conserving the oscillations plasma modes (the odd and all resonances). A significant variation in the scattering time $\tau$ was observed when the impurities were located at several positions. The scattering time decreases with increasing of the position Z ($\tau$ decreases when the impurities are far from the interface SiO₂-Graphene). The impurity position Z effect relies on the influence of the relaxation rate which directly depends on the variation in the scattering time.

## 6. Response of graphene Bilayer channels HEMTs

From the graphene Monolayer (GML) to the graphene Bilayer (GBL), the effective mass of electrons changes from $m_e^* = 0.012 m_0$ Kg to $m_e^* = 0.041 m_0$ Kg, respectively [35]. The relaxation rate calculated by the formula $\nu = \frac{e}{m_e^* \mu_e}$ where the electron mobility of GBL is $\mu_e = 2.5 \times 10^5$ cm²V⁻¹s⁻¹ and the mobility of GML is $1.43 \times 10^6$ cm²V⁻¹s⁻¹ [34]. Therefore, the exact value of the relaxation rate of the Graphene bilayer considered in this section is $\nu = 0.17 \times 10^{12}$ s⁻¹ [35].

The responses of the Graphene Bilayer (GBL) and Graphene Monolayer (GML) channel HEMTs are shown in figure 9.

We observe a slight displacement of resonances towards the low terahertz frequencies for the GBL channels associated with the decreases in the 3D plasma frequency modes which depends on the effective mass. A significant decrease in the amplitude of the resonances corresponds to a decrease in the relaxation rate of the GBL compared to that of the GML (see figure 9). In $|Y_{dg}|$ spectrum, the control of the gate decreases at a high terahertz frequency, therefore the frequency positions and the amplitude of resonances decrease.

Figure 10 illustrates the voltage gains of the HEMTs with InGaAs, GML and GBL channels. The results in figure 10 can be used to analyze the material effect on HEMTs amplification through the physical parameters $m^*$, $\nu$, $\epsilon_d$ and $\epsilon_r$ of InGaAs, GML and GBL materials.
<figure><img src="image_19.png" /><figcaption>**Figure 9.** Admittances module $|Y_{dd}|$ and $|Y_{dg}|$ of HEMTs with graphene bilayer and graphene monolayer channel. The substrate is $SiO_2$.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 10.** Voltage gain of HEMTs with different channel materials: InGaAs, GML and GBL. The dielectric substrate is $SiO_2$.</figcaption></figure>

The results in figure 10 show the amplifier process realized by different materials considered as channels of the HEMTs. An ideal amplifier can be obtained by a Graphene Bilayer for low terahertz frequencies (less than 2 THz) and by a Graphene Monolayer for high Terahertz frequencies (greater than 5 THz). The importance of InGaAs material for terahertz applications is negligible compared to Graphene with mono/Bi layers.

## 7. Comparison of InGaAs and graphene channels HEMTs response

In this section, we describe the study of the Terahertz response obtained using the parameters of the InGaAs and graphene materials. We do not consider the terahertz behavior of the HEMTs on an InGaAs material which was studied in [17].

The parameters of graphene and InGaAs material are illustrated in table 4.

Figure 11 shows the admittance and voltage gain of the InGaAs and Graphene channel HEMTs. The voltage gain was calculated in the absence of any real charge $Y_C$ connected between the source and drain of the HEMT terminals.

According to the response discussion in section 3, we note that a high amplitude of resonances is obtained by the Graphene-SiO₂ owing to the high electron mobility in the channel. Indeed, as discussed in several sections the frequency range of resonances is controlled by the 3D free-carrier plasma mode which is related to the dielectric constant in the channel and in the dielectric between the channel and the gate.

An inevitable consequence of the Graphene parameters is that the Graphene channel presents a series of resonances with an amplitude 10 times greater than the resonances of the InGaAs channel. Moreover, a series of resonances appeared at high terahertz frequencies (up to 20 THz) for the Graphene material when an InGaAs
<figure><img src="image_21.png" /><figcaption>**Table 4.** Permittivity of graphene for different dielectric substrates.</figcaption></figure>

<table><thead><tr><th>Parameters</th><th>Graphene</th><th>InGaAs</th></tr></thead><tbody><tr><td>ε<sub>c</sub></td><td>4</td><td>13.38</td></tr><tr><td>ε<sub>d</sub></td><td>2.3823</td><td>13.38</td></tr><tr><td>m<sup>*</sup> (kg)</td><td>0.021 m<sub>0</sub></td><td>0.048 m<sub>0</sub></td></tr><tr><td>ν (s<sup>-1</sup>)</td><td>0.5 × 10<sup>12</sup></td><td>10<sup>13</sup></td></tr></tbody></table>

channel was generated resonances in the frequency range limited to 6 THz. For the voltage gain comparaison, the high-frequency resonances obtained by the Graphene channel HEMTs lead to improved amplifier quality to tens of terahertz (see figure 11(c)). These results show the Terahertz frequency domain of amplification of several material-channel HEMTs.

## 8. Conclusion

Analytical calculations have been proposed to determine the terahertz response of Graphene-channels HEMTs. This study characterizes the HEMTs for the graphene Monolayer, graphene Bilayer and graphene with different dielectric substrates: H₂O, Ethanol (160K), HfO₂ and SiO₂. The calculation considers the small-signal model of HEMTs developed in [17] where the results were extracted for the Graphene parameters as the effective mass, relaxation rate and permittivity constants.

The results can lead to a real comparaison between the Terahertz efficiency of the InGaAs and the Graphene channels HEMTs. The influence of the Graphene parameters, Graphene type (Monolayer and Bilayer) and various materials (InGaAs, GBL and GML) have been shown.

The admittances $Y_{dd}$ and $Y_{gd}$ spectra show high resonances quality at the frequency range up to 17 THz. Similar to the InGaAs channels HEMTs, the $Y_{dd}$ of Graphene HEMTs exhibits all the oscillations modes in the channel where the gate-drain admittance $Y_{gd}$ presents only the odd resonances due to the control of the gate.
According to the results of the voltage gain spectra, a high amplification can be obtained by the Graphene channels HEMTs at frequencies from 1 THz to 17 THz.

The InGaAs and Graphene channels responses show that resonances with high amplitudes in the high terahertz frequency range are generated by the Graphene channel compared with InGaAs. Indeed, high-quality resonances in high terahertz frequencies are also obtained by the SiO₂ dielectric substrate which is associated with an increase in the plasma frequency and relies on the long scattering time.

Analysis of the impurity position in the dielectric substrate shows that good resonance peaks appear when the impurities are far from the Graphene-dielectric interface.

A significant increase in the resonances can be obtained by Monolayer Graphene (GML) compared to Bilayer Graphene (GBL) and InGaAs materials. Therefore, amplification is guaranteed by the GML channel HEMTs and allowed in the frequency range $f < 20$ THz corresponding to their electronic parameters.

These results can be useful for adjusting the material in HEMTs devices for nanometric terahertz amplifiers based on plasmonic oscillations modes in the channel of HEMTs.

## Acknowledgments

This work is partly supported by the Algerian ministry of higher education and research.

## Data availability statement

All data that support the findings of this study are included within the article (and any supplementary files).

## Conflicts of interest

* **Funding:** The author(s) warrant that any financial interests, direct or indirect, that exist or may be perceived to exist by individual contributors in connection with this manuscript have been disclosed in the covering letter. Furthermore, the support of the project is named in the covering letter as well as the in Acknowledgement. Finally, the authors declare that no funds, grants, or other support was received during the preparation of this manuscript.

* **Conflict of interest:** None of the authors have received research support from any university or research grants from the company.

* **Ethics approval:** We confirm that the manuscript has been read and approved by all named authors, and that there are no other persons who satisfied the criteria for authorship but are not listed. We have further confirmed that all of us have approved the order of the authors listed in the manuscript.

* **Consent for contribution:** The users are free to use the work, subject to proper attribution of authorship and ownership of the rights. Authors may use their material in presentations and subsequent publications they write or edit themselves, provided that the Journal of Electronic Materials is referenced in writing and acknowledged as the original publication.

* **Consent for publication:** We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property.

* **Code availability:** This study was partly supported by the Algerian Ministry of Higher Education and Research.

* **Authors' contributions:** All authors have made substantial contributions to the manuscript and are willing to take public responsibility for its content. The authors attest that all persons designated as authors qualify for authorship and all those who qualify are listed.

## ORCID iDs

Fatima Zohra Mahi https://orcid.org/0000-0003-4238-8181
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