# Physical and electrical characterizations of low n-doped MOCVD GaN-on-sapphire layers for power electronics applications

Ndembi Ignoumba-Ignoumba, Camille Sonneville, Adrien Bidaud, Pierre Brosselard, Eric Frayssinet, Florian Bartoli, Yvon Cordier, Farid Medjdoub, Dominique Planson, Cyril Buttay

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To cite this version:

Ndembi Ignoumba-Ignoumba, Camille Sonneville, Adrien Bidaud, Pierre Brosselard, Eric Frayssinet, et al.. Physical and electrical characterizations of low n-doped MOCVD GaN-on-sapphire layers for power electronics applications. Power Electronic Devices and Components, 2025, 11, pp.100100. 10.1016/j.pedc.2025.100100. hal-05099383

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# Physical and electrical characterizations of low n-doped MOCVD GaN-on-sapphire layers for power electronics applications

Ndembi Ignoumba-Ignoumba<fnref n="1" />, Camille Sonneville<fnref n="1" />, Adrien Bidaud<fnref n="2" />, Pierre Brosselard<fnref n="1" />, Eric Frayssinet, Florian Bartoli<fnref n="3" />, Yvon Cordier<fnref n="3" />, Farid Medjdoub<fnref n="2" />, Dominique Planson<fnref n="1" />, Cyril Buttay<fnref n="1" />

**Abstract** — This work presents the physical and the electrical characterizations of low n-doped MOCVD GaN-on-sapphire layers and the associated quasi-vertical Schottky Barrier Diodes (SBDs). Samples display overall homogeneous crystalline structure and concentration as examined by C-V measurements, Raman spectroscopy, IV characteristics, XRD and AFM. Turn-on voltage and specific on-resistance are found to be influenced by surface defects density. Cristal defects of the GaN layer are identified by Raman spectroscopy and SEM, and their effect on the electrical characteristics of the diodes is assessed. Most of the SBDs have similar ideality factors of ~1.4, Schottky barrier height of ~0.80 eV, turn-on voltages between 0.6 – 1.1 V and reverse current densities < 0.5 mA/cm<fnref n="2" /> at -100 V. Forward and reverse current characteristics of most SBDs are comparable to some of the best vertical GaN-on-GaN SBDs.

Keywords: GaN-on-sapphire, MOCVD growth, Schottky barrier diode, Power electronic device.

## 1. INTRODUCTION

GaN is a promising material for power devices due to its higher critical electric field, bandgap, and electron mobility compared to those of silicon (Fatahilah et al., 2019). Power devices based on this material show great performance. For instance, GaN-based high electron mobility transistors (HEMTs) with lateral current flow through a so-called “2-DEG” channel are already commercialized, sustaining up to 650 V in their off-state (STmicroelectronics, 2021). Vertical devices enable to reach even higher breakdown voltages ($V_{BD}$) without increasing the device area (He et al., 2021). In vertical configuration, the voltage is sustained across the entire GaN drift layer. Therefore, increasing the drift layer thickness directly enhances $V_{BD}$ but degrades the specific on-resistance ($R_{on,sp}$) so that a trade-off has to be found. The electrical performance of a vertical power device can be expressed using Baliga’s figure of merit (BFOM), which is the ratio $\frac{V_{BD}^2}{R_{on,sp}} = \frac{1}{4}\epsilon_s\mu_nE_C^3$ (Sun et al., 2019), with $\epsilon_s$ being the dielectric constant of the semi-conductor, $\mu_n$ the electron mobility, and $E_C$ the critical electric field.

Baliga’s figure of merit was initially developed to evaluate

the potentialities of a drift layer in a vertical Schottky barrier diode (SBD) configuration. In this configuration, to achieve the highest BFOM, the GaN drift layer must exhibit homogeneously low biaxial stress, a low dislocation density, and a uniformly low n-carrier density (Raja et al., 2022), (N’Dohi et al., 2022), (Schenk et al., 2011). Indeed, the best electrical performances for vertical SBDs are obtained with low biaxial stressed, low n-doped ($n < 10^{16} \text{ cm}^{-3}$) GaN-on-GaN layers having dislocation densities in the range of $10^6 \text{ cm}^{-2}$ (Saitoh et al., 2010), (Cao et al., 2016), (Ozbek & Baliga, 2011), (Han et al., 2018), (Liu et al., 2017). In the publications above, $V_B$ varies from 800 to 1650 V, and $R_{on,sp}$ from 0.71 to 9 mΩ·cm<fnref n="2" />. Despite the high electrical performances of GaN-on-GaN devices, the lack of low cost GaN bulk substrates makes them less commercially viable compared to GaN-on-foreign substrates devices (Amano et al., 2018). In the meantime, foreign substrates such as sapphire, SiC or silicon increase the drift layer internal biaxial stress and the dislocation density up to $10^{10} \text{ cm}^{-2}$ (Amano et al., 2018). Therefore, fabricating SBDs using foreign substrates while achieving electrical performances similar to those made out of GaN substrates is still a challenge.

In this work, we report low n-doped (1.4 to 5.5 × $10^{15} \text{ cm}^{-3}$) GaN-on-sapphire epitaxial layers grown by MOCVD. Most of the quasi-vertical SBDs fabricated from these layers exhibit electrical characteristics which are similar to some of the best reported vertical GaN-on-GaN SBDs. We attribute these characteristics to a uniformly low n-doping concentration and to the low density of screw-type dislocations. The epitaxial layers are characterized through micro-Raman spectroscopy, in order to assess the internal biaxial stress distribution and the n-carrier density homogeneity. Scanning electron microscopy (SEM), atomic force microscopy (AFM) and X-ray diffraction (XRD) analysis are conducted to evaluate surface quality and dislocation density. The above physical characterizations are correlated with the electrical characteristics of the quasi-vertical SBDs through the extraction of key parameters such as Schottky barrier height, ideality factor, turn-on voltage, specific on-resistance and reverse current density. An analysis of

<footnote n="1">¹ N. Ignoumba-Ignoumba (corresponding author), C. Sonneville, P. Brosselard, D. Planson and Cyril Buttay are with Univ. Lyon, INSA Lyon, Univ. Claude Bernard Lyon 1, Ecole Centrale Lyon, CNRS, Ampère, 69621, France, (e-mail: ndembi.ignoumba-ignoumba@insa-lyon.fr) (Phone number: +33614616427), (e-mail: camille.sonneville@insa-lyon.fr), (e-mail: pierre.brosselard@insa-lyon.fr), (e-mail: dominique.planson@insa-lyon.fr) and (e-mail: cyril.buttay@insa-lyon.fr).</footnote>

<footnote n="2">² A. Bidaud and F. Medjdoub are with I.E.M.N - CNRS, 59652 Villeneuve d'Ascq, France, (e-mail: adrien.bidaud@univ-lille.fr) and (e-mail: farid.medjdoub@univ-lille.fr).</footnote>

<footnote n="3">³ E. Frayssinet, F. Bartoli and Y. Cordier are with Université Côte d'Azur, CNRS, CRHEA, F-06560 Valbonne, France, (e-mail: eric.frayssinet@crhea.cnrs.fr), (e-mail: florian.bartoli@crhea.cnrs.fr) and (e-mail: yvon.cordier@crhea.cnrs.fr).</footnote>
<table><caption>Table 1. Summary of samples growth parameters and primary physical characterizations.</caption><thead><tr><th>Sample</th><th>Growth temperature (° C)</th><th>n- GaN Thickness (µm)</th><th>N<sub>D</sub> – N<sub>A</sub> (× 10<sup>15</sup> cm<sup>-3</sup>)</th><th>RMS Roughness on 10 x 10 µm<sup>2</sup> (nm)</th><th>FWHM (002) / (302) (arcsec)</th></tr></thead><tbody><tr><td><b>1</b></td><td>997</td><td>5.0</td><td>1.4</td><td>0.30</td><td>558 / 356</td></tr><tr><td><b>2</b></td><td>1000</td><td>4.1</td><td>2.5</td><td>0.29</td><td>529 / 367</td></tr><tr><td><b>3</b></td><td>993</td><td>4.0</td><td>5.5</td><td>0.48</td><td>522 / 367</td></tr></tbody></table>

surface defects that significantly impact forward and reverse current characteristics is also conducted.

## 2. EXPERIMENTAL METHOD

### 2.1. Epitaxial growth

In this study, three lightly Si-doped drift layers (n- GaN) are grown by Metal Organic Chemical Vapor Deposition (MOCVD) at temperatures ranging from 993° C up to 1000° C with a SiH₄ flow rate ranging from 0.05 to 0.06 sccm, at a pressure of ~13 kPa. All samples are grown on 50.8 cm sapphire substrates and are made of a non-intentionally doped GaN layer (nid GaN) used as a buffer layer, a highly Si n-doped GaN layer stack (n⁺ GaN ~ 5×10¹⁸ – 10¹⁹ cm⁻³, also used to serve as bottom contact), and the Si n-doped drift layer. The n-carrier concentration of n- GaN layers are measured by mercury probe capacitance-voltage technique (C-V). The growth parameters of each drift layer are summarized in Table 1 and a schematic view of the samples structure is presented in Fig. 1a.

<figure><img src="image_4.png" /><figcaption>Fig. 1. Schematic views of samples: after growth (a), after etching (b), and after metal deposition (c).</figcaption></figure>

### 2.2. Physical characterizations

After growth, primary physical characterizations using X-rays diffraction (XRD) and atomic force microscopy (AFM) are done to evaluate the crystal quality, the surface morphology and the dislocations density of the n- GaN layers. XRD characterizations are performed using a triple axis PANalytical X'Pert Pro MRD high-resolution diffractometer allowing the evaluation of the full width at half maximum (FWHM) of (302) and (002) GaN diffraction peaks using omega scans. AFM characterizations are also performed at room temperature using tapping mode with a Nanoscope IV Dimension system. A summary of these primary characterizations is presented in Table 1, with RMS roughness being the Root Mean Square roughness. All samples have a roughness < 0.5 nm. Dislocations densities are similar for all samples and are estimated to be approximately 3 × 10⁸ cm⁻² as obtained by AFM images and confirmed by the relation published in (Schenk et al., 2011) using the FWHM of (002) and (302). Note that the density of pure screw-type dislocations as observed in AFM images is between 10⁴ – 10⁵ cm⁻². Therefore, most of the dislocations are edge-type and mixed-type dislocations. After these primary characterizations, the n- GaN layers are patterned with photolithography and etched using Cl₂ and argon dry etching technique (see Fig. 1b). This forms the circular mesa structures defined in the etching mask (Fig. 2).

After etching, micro-Raman spectroscopy is performed on the n- GaN layers by using a confocal spectrometer (Renishaw Invia model) in back scattering geometry with a 532 nm excitation laser source. For each sample, 4 regions are selected containing each 3 mesa structures of 80, 154 and 308 µm diameter, see Fig. 2. For each mesa structure, a mesh is defined using the spectrometer software (Wire Software 5.4) with a step size between 2 and 4 µm, depending on the diameter of the mesa. At each step, the spectrometer shines light on the n- GaN layers and collects the Raman backscattered spectrum. To

<figure><img src="image_5.png" /><figcaption>Fig. 2. On the left, optical view of selected regions of a sample. Black dots are the mesa structures analyzed through micro-Raman spectroscopy, SEM, and I-V characterizations. On the right, the zoom of the region 7. In gray, the n⁺ GaN layer and in white the n- GaN layer. All regions have been processed with the same etching mask.</figcaption></figure>
assess $E_2^H$ and $A_1(LO)$ peaks values, a Gaussian-Lorentzian fit is applied to the Raman spectrum.

In order to investigate the surface morphology of the mesa structures, SEM analyzes are also conducted on the same mesa structures that were characterized by Raman spectroscopy. The total number of mesa structures analyzed by Raman spectroscopy and SEM technique is 36 and they are spread across 10 regions displayed in Fig. 2.

### 2.3. SBDs fabrication

Following the physical characterizations, quasi-vertical SBDs are formed on the mesas by the deposition of metallic contacts using e-beam evaporation technique. First, Ti(12 nm)/Ni(40 nm)/Al(200 nm)/Au(100 nm) are deposited on $n^+$ GaN and annealed to form the ohmic contact. Then, Ni(20 nm)/Au(200 nm) are deposited on the n-GaN layer to form the Schottky contact, as shown in Fig. 1c.

### 2.4. Electrical characterization

Electrical characterizations are performed on 22 diodes per sample, chosen randomly in the 10 regions shown in Fig. 2, with mesas diameter of 154, 288 and 308 µm.

Firstly, direct current analysis (I-V) is carried out at room temperature using a B2902A (Keysight) source measurement unit (SMU). The forward voltage applied to the anode ranges from 0 to 4 V. The source compliance is adjusted between 1 and 75 mA according to the size of the diode. Each measurement is repeated three times and we keep the third I-V curve, since current stabilizes after the 2^nd^ measurement. Secondly, after approximately one month, reverse I-V analysis is carried out re-using the same SMU B2902A. The reverse voltage ranges from 0 to -100 V with a compliance fixed at 1 µA and steps of 500 mV. As previously mentioned, measurement is repeated and only the third reverse I-V curve is kept when possible. Linear transfer length method (TLM) measurements are also conducted to obtain the specific contact resistance as well as the resistivity of the $n^+$ GaN layer.

## 3. RESULTS

### 3.1. Physical characterization

#### SEM

A SEM analysis of the mesa structures reveals several surface defects. The main ones tend to be aggregates of small particles (diameter < 5 µm) and holes (diameter < 2 µm) as shown in Fig. 3. The origin and the nature of these defects are still unknown but one can expect that aggregates or impurities may occur during the MOCVD growth. Some of the holes may be related to peculiar dislocations or nanopipes. We estimate the density of surface defects for each sample by dividing the total number of aggregates and holes by the total area characterized. The surface defects density of sample 1, 2 and 3 is approximately $7 \times 10^3 \text{ cm}^{-2}$, $9 \times 10^4 \text{ cm}^{-2}$ and $1.7 \times 10^5 \text{ cm}^{-2}$, respectively. Therefore, sample 1 has the best surface quality. We will discuss in Section 4 the effects of these surface defects on Raman results and on the electrical properties of SBDs.

#### Raman spectroscopy

Micro-Raman spectroscopy is a powerful non-destructive optical technique that gives information about the crystalline

<figure><img src="image_6.png" /><figcaption>Fig. 3. SEM image of a mesa structure (top view). Mesa structure of 308 µm diameter. On the right, a zoom of the identified surface defects.</figcaption></figure>

structure of GaN by probing its phonon modes. In the backscattering configuration for wurtze GaN structures, with light propagating along the c-axis, two primary phonon modes cause a positive shift in the wavenumber of the collected light relative to that of the incident one. Those phonons are named $E_2^H$ and $A_1(LO)$ (N'Dohi, 2023), see Fig. 4.

<figure><img src="image_7.png" /><figcaption>Fig. 4. Typical Raman spectrum of a GaN-on-sapphire layer, in backscattering configuration, with light travelling along GaN hexagonal c-axis.</figcaption></figure>

The $E_2^H$ Raman shift peak is widely used to probe biaxial stress in GaN (Kozawa et al., 1995), (Wagner & Bechstedt, 2002), (Lu et al., 2011) due to its lattice displacements being perpendicular to the c-axis (Wieser et al., 1997). Under compressive stress, the peak value shifts positively, while tensile stress induces a negative shift. Conversely, the $A_1(LO)$ Raman shift peak is typically employed to determine n-carrier density because of the coupling between $A_1(LO)$ phonon mode and free n-carriers. When the n-carrier density increases, the peak value shifts positively and its intensity decreases (N'Dohi et al., 2022), (Wieser et al., 1997), (Harima et al., 1998), (Jegathanath et al., 2009).

It worth noting that the $A_1(LO)$ Raman shift peak is also influenced by biaxial stress (Demangeot et al., 1996). For lightly n-doped layers ($n < 10^{17} \text{ cm}^{-3}$) under biaxial stress, the peak shift caused by n-carrier density variations can overlap with the shift induced by biaxial stress, leading to incorrect interpretations of the n-carrier density changes (Wieser et al., 1997). To our knowledge, this issue has not been widely
<figure><img src="image_8.png" /><figcaption>Fig. 5. 2D maps of E₂H Raman shift peak values (a), (c) and A₁(LO) Raman shift peak values (b), (d). On the top a 154 µm diameter mesa and on the bottom a 308 µm diameter mesa. Mesas structures are taken from sample 1.</figcaption></figure>

addressed. In the following paragraphs, we present our attempt to resolve this issue and apply our methodology to our samples.

For undoped biaxial stressed GaN layers, the biaxial stress-induced shift of the E₂H Raman shift peak (Δω<sub>E₂H</sub><sup>B</sup>) can be expressed by equation (1) (Raja et al., 2022), (Kozawa et al., 1995), (Demangeot et al., 1996):

$$\Delta\omega_{E_2^H}^B = \omega_{E_2^H}^B - \omega_{E_2^H}^0 = K_{E_2^H}^B \sigma_B, \quad (1)$$

where ω<sub>E₂H</sub><sup>B</sup> is the E₂H peak value for the biaxial stressed layer and ω<sub>E₂H</sub><sup>0</sup> (in cm⁻¹) is the E₂H peak value for an unstressed layer, K<sub>E₂H</sub><sup>B</sup> (in cm⁻¹/GPa) is the biaxial stress coefficient associated to the E₂H peak and σ<sub>B</sub> (GPa) is the biaxial stress. For a compressive biaxial stress, σ<sub>B</sub> > 0 so is Δω<sub>E₂H</sub><sup>B</sup>, and for tensile stress σ<sub>B</sub> < 0, so is Δω<sub>E₂H</sub><sup>B</sup>. The biaxial stress-induced shift for A₁(LO) Raman shift peak (Δω<sub>A₁(LO)</sub><sup>B</sup>) is analog to Δω<sub>E₂H</sub><sup>B</sup> (Demangeot et al., 1996), where:

$$\Delta\omega_{A_1(LO)}^B = \omega_{A_1(LO)}^B - \omega_{A_1(LO)}^0 = K_{A_1(LO)}^B \sigma_B, \quad (2)$$

with ω<sub>A₁(LO)</sub><sup>B</sup> being the A₁(LO) peak value of the biaxial stressed layer, ω<sub>A₁(LO)</sub><sup>0</sup> the A₁(LO) peak value for an unstressed layer and K<sub>E₂H</sub><sup>B</sup> (in cm⁻¹/GPa) the biaxial stress coefficient associated with the A₁(LO) peak.

The interdependency of ω<sub>A₁(LO)</sub> and ω<sub>E₂H</sub><sup>B</sup> to the biaxial stress as expressed in equations (1) and (2) can be observed in Fig. 5, where we present typical 2D maps of E₂H and A₁(LO) Raman peaks values for 154 and 308 µm diameter mesas. We can notice that ω<sub>A₁(LO)</sub> is mainly varying from 734.1 to 735.4 cm⁻¹

and ω<sub>E₂H</sub><sup>B</sup> is mainly varying from 568.7 to 570.1 cm⁻¹. In contrast, it was reported that ω<sub>A₁(LO)</sub> and ω<sub>E₂H</sub><sup>B</sup> values for lightly Si-doped (n 8×10¹⁵ cm⁻³) GaN-on-GaN layers free of biaxial stress are respectively 733.4 cm⁻¹ and 567.1 cm⁻¹ (N’Dohi et al., 2022). Therefore, compared to these GaN-on-GaN layers, the present GaN-on-sapphire layers are effectively compressed. We can notice a decrease of both ω<sub>A₁(LO)</sub> and ω<sub>E₂H</sub><sup>B</sup> as we approach the edge of the mesa, indicating a reduction in the biaxial stress. Indeed, the crystal lattice at edge tends to relax more than in the center due to the presence of a free surface (Wieser et al., 1997), (Hossain et al., 2013). This relaxation effect is observed for all characterized mesa structures, as we will discuss later.

For lightly Si-doped (n < 10¹⁷ cm⁻³) biaxial stressed or unstressed GaN layers, the variation of the E₂H Raman shift peak (Δω<sub>E₂H</sub><sup>B</sup>) was proven to be negligibly influenced by the n-carrier density such that Δω<sub>E₂H</sub><sup>B</sup> ≈ Δω<sub>E₂H</sub><sup>B</sup> (N’Dohi et al., 2022), (Kisielowski et al., 1996). In contrast, it was found that for unstressed, lightly Si-doped GaN layers, the A₁(LO) Raman shift peak (Δω<sub>A₁(LO)</sub><sup>B</sup>) is linearly dependent on the n-carrier density such that Δω<sub>A₁(LO)</sub> = Δω<sub>A₁(LO)</sub><sup>n</sup> = 1.4 × 10⁻¹⁷ · n (N’Dohi et al., 2022), with Δω<sub>A₁(LO)</sub><sup>n</sup> being the n-carrier concentration induced shift. Hence, we propose that for biaxial stressed lightly Si-doped GaN layers, in the first linear approximation, Δω<sub>A₁(LO)</sub> can be described as a linear combination of the biaxial stress-induced shift (Δω<sub>A₁(LO)</sub><sup>B</sup>) and the n-carrier concentration induced shift (Δω<sub>A₁(LO)</sub><sup>n</sup>) where:

$$\Delta\omega_{A_1(LO)} = \omega_{A_1(LO)} - \omega_{A_1(LO)}^0 = \Delta\omega_{A_1(LO)}^B + \Delta\omega_{A_1(LO)}^n. \quad (3)$$

Replacing Δω<sub>A₁(LO)</sub><sup>B</sup> by K<sub>A₁(LO)</sub><sup>B</sup>σ<sub>B</sub> and using equation (1) to replace σ<sub>B</sub>, equation (3) becomes:
$$ \omega_{A_1(LO)} = \frac{K_{A_1(LO)}^B}{K_{E_2^H}^B} \omega_{E_2^H} + \omega_{A_1}^0 - \frac{K_{A_1(LO)}^B}{K_{E_2^H}^B} \omega_{E_2^H}^0 + \Delta\omega_{A_1(LO)}^n, \quad (4) $$

where the A₁(LO) peak value, $\omega_{A_1(LO)}$, is linearly correlated to the E₂H peak value, $\omega_{E_2^H}$, due to the interdependency of these two peaks with the biaxial stress. However, the slope of equation (4) ($\alpha = \frac{K_{A_1(LO)}^B}{K_{E_2^H}^B}$) is a dimensionless parameter that is independent of the biaxial stress and the n-carrier density. The y-intercept can be written as a function of n-carrier density ($f(n)$), since only $\Delta\omega_{A_1(LO)}^n$ can vary: $f(n) = \Delta\omega_{A_1(LO)}^n + \omega_{A_1}^0 - \frac{K_{A_1(LO)}^B}{K_{E_2^H}^B} \omega_{E_2^H}^0$. Doing so, equation (4) can be simplified as:

$$ \omega_{A_1(LO)} = \alpha\omega_{E_2^H} + f(n). \quad (5) $$

Thanks to equation (5), we obtain that the A₁(LO) Raman peak value is linearly correlated to the E₂H Raman peak value with a coefficient that is independent of the biaxial stress and the doping concentration. In addition, one can assess the n-carrier density variation by analyzing the variation of the y-intercept, such that an increase of the y-intercept value corresponds to an increase of the n-carrier concentration and vice-versa. However, determining the absolute value of the n-carrier density would require additional calibration.

In order to verify the validity of this hypothesis, we calculate the mean value of $\omega_{E_2^H}$ ($\overline{\omega_{E_2^H}}$) and $\omega_{A_1(LO)}$ ($\overline{\omega_{A_1(LO)}}$) for each 2D peak map of the 36 mesa structures studied. We plot $\overline{\omega_{A_1(LO)}}$ vs $\overline{\omega_{E_2^H}}$ and present results in Fig. 6. We can observe that $\overline{\omega_{A_1(LO)}}$ and $\overline{\omega_{E_2^H}}$ increase with the diameter of the mesa, such that the 80 µm diameter mesa structures have the lowest values ($\overline{\omega_{A_1(LO)}}$, $\overline{\omega_{E_2^H}}$) and the 308 µm diameter mesa structures have the highest ones. This effect is due to the elastic relaxation at the free edges which affects more significantly the smaller structures, as shown in Fig. 5 and demonstrated by Hossain et al. (Hossain et al., 2013). We also observe that the dispersion

<figure><img src="image_9.png" /><figcaption>Fig. 6. Mean values of A₁(LO) Raman shift peak vs mean values of E₂H Raman shift peak for the three samples, with mesa structure diameter ranging from 80 µm to 308 µm. The solid line represents the relationship connecting all data points, except for mesas A and B. The dashed lines indicate the range of acceptable variation.</figcaption></figure>

of the $\overline{\omega_{E_2^H}}$ decreases as the mesa diameter increases, indicating an increase in biaxial stress uniformity with the increase of the mesa diameter.

Using the minimum and the maximum slope method and assigning an uncertainty of 0.05 cm⁻¹ to each value, we determine a linear correlation between $\overline{\omega_{A_1(LO)}}$ and $\overline{\omega_{E_2^H}}$ (solid line) excluding data from mesas A and B, which will be discussed in Section 4. The obtained linear correlation has a slope $\alpha = (0.8 \pm 0.2)$ and an intercept $f(n) = (275 \pm 125)$ cm⁻¹. The dashed lines represent the acceptable range of variation for the data points that conform to the linear correlation. Fig. 6 shows that majority of mesa structures are following the main linear correlation and fall within the range of acceptable variation, except for mesas A and B. We will discuss about the implications of this results in Section 4.

## 3.2. Electrical characterization

### Forward characteristics

For the forward current density model, we use the thermionic emission model, such that the current density ($J_{TE}$) is expressed by equation (6) (Sang et al., 2017):

$$ J_{TE} = J_s \cdot \left( \exp\left(\frac{q(V-IR_s)}{nkT}\right) - 1 \right), \quad (6) $$

with $J_s = A^*T^2\exp(-\frac{q\Phi_B}{kT})$ (SZE & KWOK, 2007), q the elementary charge, V the applied voltage, I the induced current, $R_s$ the diode series resistance, k the Boltzmann constant, T is the temperature, the Richardson's constant (for n-type GaN, $A^* = 26.4$ A cm⁻² K⁻² (Kumar et al., 2013)), n the ideality factor and $\Phi_B$ the Schottky barrier height. n, $\Phi_B$, and $R_s$ are important parameters that are commonly used to evaluate SBDs electrical properties and conduction. For $V \ge 3\frac{kT}{q}$ (N'Dohi, 2023), equation (6) becomes:

$$ \ln J_{TE} = \frac{q}{kT} \left( -\Phi_B + \frac{V-IR_s}{n} \right) + \ln(A^*T^2). \quad (7) $$

Equation (7) describes a linear relation, in semi-log scale, between $J_{TE}$ and V for which the slope is $\frac{q}{nkT}$ and the intercept depends on $\Phi_B$. In this regime, the current is limited by the

<figure><img src="image_10.png" /><figcaption>Fig. 7. Direct current density vs applied voltage for 308 µm diameter SBDs in different regions.</figcaption></figure>
Schottky barrier height and the ideality factor and $J_{TE}$ evolves exponentially with $V$. A second regime is also commonly defined, since it helps in determining $R_S$ (also known as $R_{on}$): in this regime, $V$ is sufficiently high so that current is limited by the diode series resistance. $V$ is then the combination of the diode voltage $V_D$ plus the voltage drop across the diode series resistance, $V_R = J_{TE}R_{on,sp}$, with $R_{on,sp}$ being the specific on-resistance ($R_{on,sp} = R_{on} \cdot A$, with $A$ being the surface of the anode), such that (N’Dohi, 2023):

$$J_{TE} = \frac{V-V_D}{R_{on,sp}}. \qquad (8)$$

In this regime, $J_{TE}$ is linearly dependent on $V$ and the slope is $1/R_{on,sp}$. The threshold voltage or the turn-on voltage, $V_{th}$, is defined as the transition voltage between the two regimes and it is obtained when $J_{TE} = 0 \Rightarrow V = V_D = V_{th}$.

Typical direct J-V curves for the 308 µm diameter diodes are presented in Fig. 7. It is important to note that direct current density is calculated with respect to the anode surface. The current density varies from $10^{-8}$ A/cm² to $10^2$ A/cm² for samples 1 and 2, while it does not exceed $1$ A/cm² for sample 3.

Using equations (7) and (8), we extract $n$, $\Phi_B$, $R_{on,sp}$ and $V_{th}$ as functions of the diode diameter and present the results in Fig. 8. For $n$ and $\Phi_B$, samples 1 and 2 exhibit similar mean values and dispersion, at around 1.4 and 0.85 eV, respectively. However, for sample 3, $n$ and $\Phi_B$ show a larger dispersion, varying from approximately 1.1 to 1.8 and from 0.90 to 1.15 eV, respectively. Given the dispersions of $n$ and $\Phi_B$, no significant effect of the diode diameter is observed.

For $R_{on,sp}$, sample 1 has the lowest mean values, at around $10$ mΩ·cm² while sample 2 has mean values around 20

mΩ·cm² and the $R_{on,sp}$ mean values of sample 3 are around 1 Ω·cm². The three samples exhibit similar dispersion and we do not observe a strong dependency of $R_{on,sp}$ to the diode diameter. TLM measurements reveal that the contact specific resistance is similar for the three samples and is ~2 µΩ·cm², which is negligible compared to the specific on-resistances. The resistivity of n+ GaN layer is also similar for the three samples and is ~5 mΩ·cm. This value is also negligible compared to the specific on-resistances, considering that the maximum length where the current spreads is ~290 µm.

For $V_{th}$, sample 1 exhibits the lowest mean values (and dispersion) around 0.65 V, while samples 2 and 3 have similar mean values of around 1.10 V. We notice that sample 2 displays the largest dispersion among the three samples with $V_{th}$ ranging from 0.60 to 1.40 V. Given the observed dispersions, a correlation between $V_{th}$ and the diode diameter is again not established.

In conclusion, for most SBDs, varying the diode diameter from 154 to 308 µm has a negligible impact on the ideality factor, the Schottky barrier height, the threshold voltage and the series resistance. This means that most SBDs exhibit uniformly distributed currents. Samples 1 and 2 have similar results, while sample 3 demonstrates slightly higher mean values for $n$ and $\Phi_B$ and exhibits the greatest dispersion. Threshold voltage and series resistance dispersion and mean values are both sensitive to the sample characteristics, with sample 3 having the highest resistance (× 100 higher than samples 1 and 2). The nature of these observations will be discussed in Section 4.

### Reverse characteristics

Reverse current density or leakage current density ($J_R$) are presented in Fig. 9 for 308 µm diameter diodes in different

<figure><img src="image_11.png" /><figcaption>Fig. 8. Extracted direct J-V parameters as functions of the diode diameter. (a), (b) and (c) show ideality factors and Schottky barriers heights while (d), (e) and (f) show threshold voltages and specific on-resistances.</figcaption></figure>
regions of the three samples. We use the anode surface to calculate the reverse current density. We notice that for voltages between 0 and -100 V, the reverse current density ranges from $10^{-8}$ to few mA·cm$^{-2}$. Furthermore, at least two different regimes of $J_R$ can be observed: a first regime between approximately 0 and -40 V, with the current slowly increasing and the second one between -40 V and -100 V with a sharp increase of $J_R$. This implies the existence of at least two different leakage mechanisms, which are being currently investigated. Most of SBDs tested here exhibit similar reverse J-V curves. However, some SBDs abruptly reach the compliance of the SMU for voltages lower than -100 V as shown in Fig. 9, for samples 2 and 3, region 4. Some others display an abnormal shape as in regions 2 and 5 of sample 1.

<figure><img src="image_12.png" /><figcaption>Fig. 9. Reverse current density vs applied voltage for 308 µm diameter SBDs in different regions.</figcaption></figure>

In order to better evaluate the effect of the diode diameter and compare samples together, we present in Fig. 10, the maximum reverse current density of each diode whether it reached -100 V or not. It is worth mentioning that the 288 and 308 µm diameter diodes have the same anode area. Therefore, since the compliance was fixed at 1 µA, the maximum reachable $J_R$ is 1.8 mA/cm$^2$ for the 288 and 308 µm diameter

diodes and 7.1 mA/cm$^2$ for the 154 µm ones. Fig. 10 shows that the maximum $J_R$ ranges from 4 µA/cm$^2$ to 7 mA/cm$^2$. A correlation between the diode diameter and the maximum $J_R$ is not established and samples have similar reverse current.

Fig. 10 also shows that more than 75% of the diodes (48 out of 62) have a maximum $J_R$ lower than 0.5 mA/cm$^2$. The 14 remaining diodes have a maximum $J_R$ higher than 1 mA/cm$^2$. From these diodes, only two reached -100 V while their leakage current almost reached compliance. Thus, diodes for which leakage current crosses 1 mA/cm$^2$ are more likely to reach compliance and thus, are more likely to have a breakdown voltage lower than or equal to 100 V. For these reasons, we define 1 mA/cm$^2$ as the leakage current density limit to evaluate the quality of the diode in reverse configuration. On this basis, sample 2 has the best reverse characteristics, while samples 1 and 3 are similar in this regard. We will discuss more in details the origin of these observations in Section 4.

## 4. DISCUSSION

### Raman: Study of n-doping concentration

From Fig. 7, the slope of the equation (5) is 0.8 ± 0.2 which corresponds to the ratio $\frac{K_{A_1(LO)}^B}{K_{E_2^H}^B}$. This agrees well with the reported values, between 0.60 and 0.80 (Wagner & Bechstedt, 2002), (Lu et al., 2011), (Wagner & Bechstedt, 2000), (Kolomys et al., 2017), (Demangeot et al., 2004; Lu et al., 2011), (Lu et al., 2010). Considering the reported values for $\frac{K_{A_1(LO)}^B}{K_{E_2^H}^B}$ and the values of $\omega_{E_2^H}^0$ and $\omega_{A_1(LO)}^0$ given in [6], one can expect the y-intercept to vary between 279 and 393 cm$^{-1}$. Therefore, our y-intercept being 275 ± 125 cm$^{-1}$ is in good agreements with the literature. Our y-intercept error is such that all $(\omega_{A_1(LO)}^0, \omega_{E_2^H}^0)$ values are within the acceptable variation zone of the main line, except for mesas A and B, as shown in Fig. 7. However, the fact that most $(\omega_{A_1(LO)}^0, \omega_{E_2^H}^0)$ values follow the main regression line, despite the different mesa's diameters and locations in the wafer, seems to indicate a high homogeneity of the doping concentration across the samples for n-doping concentrations around $10^{15}$ cm$^{-3}$.

### Study of peculiar defects in mesas A and B

In the case of mesas A and B from sample 1, that are outside the regression zone, we notice two major surface defects. SEM images reveal a large defect (15 µm in diameter), deeply rooted at the edge of mesa A, see Fig. 12a, and a small defect of almost 1 µm diameter on the surface of mesa B, see Fig. 12b. These defects slightly affect the mean value of the $E_2^H$ Raman shift peak for mesas A and B. Indeed, the peak value slightly increases close to the large defect, see Fig. 12c, and slightly decreases around the small defect, see Fig. 12e. This implies that the large defect slightly increases the compressive stress in the mesa A, while the small defect slightly reduces locally the compressive stress in mesa B.

In contrast, the mean values of the $A_1(LO)$ Raman shift peak for mesas A and B are strongly impacted by those defects, with two opposing effects being observed. Firstly, for both mesas, the $A_1(LO)$ Raman shift peak increases significantly around the defect, see Fig. 12d and Fig. 12f. Secondly, for both mesas, the

<figure><img src="image_13.png" /><figcaption>Fig. 10. Maximum leakage current density for all SBDs. Semi-filled, crossed and filled symbols stand respectively for 154, 288 and 308 µm diameter diodes. The empty square is the mean value of each sample.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. 11. (a) and (b) are SEM images of the mesas A and B, respectively. Mesa A is a 154 µm diameter structure with a large defect (diameter ~15 µm) while mesa B is a 308 µm diameter structure with a small defect (diameter ~1 µm). (c) and (d) are the 2D maps of A₁(LO) and E₂<sup>H</sup> Raman peaks for mesa A. (e) and (f) are the 2D maps of A₁(LO) and E₂<sup>H</sup> Raman peaks for mesa B. In (c) and (d), defect is excluded from the characterized zone.</figcaption></figure>

aforementioned peak decreases significantly across the entire mesa, resulting in means values lower than other diodes. Since these effects are not observed in E₂<sup>H</sup> Raman peak value maps of mesas A and B, they are then likely due to a spatial variation in n-carrier effective density. This implies that, for both mesas, a high density of electrons is located around the defect, while the rest of the mesa is almost depleted.

The diodes fabricated with these two peculiar defects (diode A, for mesa A and diode B, for mesa B) reach quickly the current compliance, at an approximate reverse voltage of -1 V. Therefore, defects of this nature are highly detrimental to the reverse current characteristics. Note that despite its size, the small defect in mesa B degrades the reverse current characteristics the same way as the large defect in mesa A.

The ideality factor, Schottky barrier height, specific on-resistance and threshold voltage are respectively 2.8, 0.60 eV, 53 mΩ·cm⁻² and 1.0 V for diode A and 1.9, 0.70 eV, 10 mΩ·cm⁻² and 0.7 V for diode B. It seems that direct current is not significantly reduced by the presence of surface defects that are highly detrimental to reverse current.

Given the size and the implantation of the large defect, it was likely created during the growth process. For the small defect, we do not know yet its origin and more investigations are needed to identify its chemical nature. In light of these observations, we can better understand the effect of peculiar physical defects on direct and reverse current characteristics.

## Study of the samples' electrical properties

It has been reported that, for a Ni/Au Schottky contact, the reduction in n-doping concentration should lift up Φ<sub>B</sub>, reduce the ideality factor and increase V<sub>th</sub> (Witte et al., 2012). Furthermore, it is well known that the decrease in n-doping concentration leads to a decrease in reverse current density (Raja et al., 2022), (N'Dohi et al., 2022), (Witte et al., 2012). Given the range of variation of the n-doping concentration (1.4

5.5 × 10¹⁵ cm⁻³), one can expect samples to have similar ideality factors, Φ<sub>B</sub>, V<sub>th</sub> and reverse current densities. Furthermore, the ideal R<sub>on,sp</sub> should slightly decrease going from sample 1 to 3.

Ideality factors, Φ<sub>B</sub> values and most of the reverse current densities of samples 1 and 2 overlap, while overall values of V<sub>th</sub> and R<sub>on,sp</sub> increase. The previous discussion on diodes A and B shows that V<sub>th</sub> and R<sub>on,sp</sub> are also sensible to some surface defects. It was also demonstrated in the literature that V<sub>th</sub> and R<sub>on,sp</sub> are affected by the diode diameter, especially in the case of quasi-vertical Schottky diodes (Zhang et al., 2017). Therefore, it is reasonable to associate the overall increase of V<sub>th</sub> and R<sub>on,sp</sub> values with an increase in the surface defects density. Indeed, sample 1 with its low surface defects density (~7 × 10³ cm⁻²) has the lowest mean values of V<sub>th</sub> (0.7 V) and R<sub>on,sp</sub> (9 mΩ·cm⁻²) while sample 2 with its higher defects density (~9 × 10⁴ cm⁻²) has a higher mean value of V<sub>th</sub>(1.1 V) and of R<sub>on,sp</sub> (20 mΩ·cm⁻²).

Sample 3 exhibits the highest dispersion and values for ideality factors, Schottky barrier heights and specific on-resistances while having similar reverse current densities as samples 1 and 2. If the increase of Φ<sub>B</sub> were due to a reduction in n-doping density, the ideality factor would have accordingly decreased in comparison to samples 1 and 2, which is not strictly observed in Fig. 8a, b and c. Furthermore, sample 3 would have the lowest reverse current densities. In addition, samples 3 and 1 have a similar portion of diodes reaching the compliance before -100 V, while sample 2 has the lowest one. Major surface defects are likely to cause some of diodes to reach the compliance before -100 V as it is the case for diodes A and B. Therefore, no effective reduction in leakage current density is observed for sample 3 in comparison with samples 1 and 2. Hence, the observed increase in values and dispersion of
$\Phi_B$ and ideality factors for sample 3 are unlikely due to doping concentration variation.

The observed $R_{on,sp}$ values of sample 3 (~100 times higher than samples 1 and 2) cannot be justified by its surface defects density value, while its threshold voltages can. Furthermore, the physical characterizations do not indicate significant structural differences in comparison to samples 1 and 2. Therefore, we suppose sample 3 may have encountered issues during the diodes fabrication process that damaged electrical performance compared to the other two samples.

Considering only samples 1 and 2, one can notice that the mean values of ideality factor (1.4 – 1.5), Schottky barrier height (0.80 – 0.85 eV) and specific on-resistance (10 – 20 mΩ·cm⁻²) diverge from their theoretically values being respectively 1, 1.0 eV (Gu et al., 2019) and 1 – 2 mΩ·cm⁻² (mobilities are taken from (T. Mnatsakanov et al., 2002)). For MOCVD GaN-on-sapphire layers grown at 1050 °C, it has been reported that increasing the growth pressure from 100 to 600 Torr decreases the carbon concentration, specific on-resistance, ideality factor, and turn-on voltage, while increasing the Schottky barrier height (Tompkins et al., 2011). Given the similarity between our growth parameters and those reported in (Tompkins et al., 2011), the deviation of the forward characteristics from the theoretical values can, in part, be attributed to the presence of carbon impurities. Additional measurements such as Secondary Ion Mass Spectroscopy (SIMS) will be needed to elucidate this issue. However, it is also plausible that the presence of interface states is affecting the ideality factor and the Schottky barrier height, as reported in (Ahaitouf et al., 2012). I-V-T measurement in direct current configuration will be needed to evaluate this hypothesis.

Nevertheless, diodes with a breakdown voltage of 1650 V [11] and 1200 V [13] exhibit a $R_{on,sp}$ close to the one of sample 1. Our samples display low turn-on voltages, as expected for an SBD, and similar to what has been reported for the best GaN-on-GaN SBDs (between 0.5 and 1.7 V) [8 – 13]. We report Schottky barrier height values that agree well with the ones reported in (Raja et al., 2022), (Witte et al., 2012) and (Tompkins et al., 2011) for an Ni/Au contact (0.80 – 0.94 eV).

SBDs that did not reach the compliance for samples 1 (67 %) and 2 (95 %) have a similar mean reverse current density at -100 V that is ~2 × 10⁻⁴ A/cm². Our mean reverse current density at -100 V is similar to the one reported in [12] ($V_{BD}$ = 995 V) and better to the one reported in [11] at -100 V, while both authors used edge-termination techniques on low dislocation density GaN-on-GaN SBDs (~10⁶ cm⁻²). This seems to indicate that in our diodes, the high dislocation density has a limited impact on the reverse current density. We may attribute these observations to the low density of pure screw-type dislocations as observed in AFM images. Indeed, it has been reported that the main leakage current pathways in vertical GaN-on-GaN SBDs are through pure screw-type dislocations (Sang et al., 2017).

In conclusion, despite the surface defects and the deviation of the forward and the reverse characteristics from theoretical values, most of GaN-on-sapphire SBDs of samples 1 and 2 exhibit electrical properties comparable to, and in some cases exceeding, some of the best GaN-on-GaN SBDs. Given the similitude between our SBDs and the ones reported in (Witte et

al., 2012), and given the fact that our samples exhibit lower reverse current densities, we expect breakdown voltages higher than 460 V.

## 5. CONCLUSION

In this article, we report the fabrication of low n-doped MOCVD GaN-on-sapphire layers (1.4 – 5.5 × 10¹⁵ cm⁻³). Results from XRD, AFM, C-V measurements and Raman spectroscopy suggest that samples have similar crystalline quality and homogenous n-doping concentration. SEM results suggest surface defects, some of which are identified with Raman spectroscopy as major causes of the n-carrier density variation. The quasi-vertical SBDs fabricated from those layers exhibit similar forward and reverse characteristics for most of the samples. Peculiar defects, pre-identified through SEM and Raman spectroscopy, are proven to severely damage reverse current characteristics. Turn-on voltage and specific on-resistance are found to be influenced by the surface defects density. Nevertheless, most of the fabricated SBDs display electrical properties comparable to and in some cases better than some of the best GaN-on-GaN SBDs. We attribute these observations to a uniformly low n-doping concentration and the low density of pure screw-type dislocations.

## AUTHOR CONTRIBUTIONS

Ndembi Ignoumba-Ignoumba: Data curation; Formal analysis; Investigation; Methodology; Software; Roles/Writing - original draft; Writing - review & editing. Camille Sonneville: Methodology; Supervision; Validation; Review & editing. Adrien Bidaud: Resources; Investigation. Pierre Brosselard: Methodology. Eric Frayssinet: Resources; Investigation; Formal analysis. Florian Bartoli: Resources; Investigation; Formal analysis. Yvon Cordier: Methodology; Supervision; Validation; Review & editing. Farid Medjdoub: Supervision; Review. Dominique Planson: Methodology; Supervision; Validation; Review & editing. Cyril Buttay: Review & editing; Project administration, Funding acquisition.

## DECLARATION OF INTERESTS

The authors declare no conflicts of interest.

## FUNDING SOURCES

This work is a part of the VERTIGO PEPR project and was founded by the french ANR, Grant No. ANR-22-PEEL-0004.

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(4 – 5) µm n-GaN

(1.4 – 5.5) x 10¹⁵ cm⁻³

2.1 µm n++/n+ GaN

(1 – 2) µm nid GaN

Sapphire substrate
80 - 308 µm

(4 - 5) µm n-GaN

(1.4 - 5.5) x 10¹⁵ cm⁻³

2.1 µm n++/n+ GaN

(1 - 2) µm nid GaN

Sapphire substrate