# Modeling and Extraction of the Specific Contact Resistance of GaN p-i-n Diodes up to 40 GHz

Kevin Nadaud, Zihao Lyu, Daniel Alquier, Quentin Paoli, Julien Ladroue, Arnaud Yvon, Eric Frayssinet, Yvon Cordier, Jérôme Billoué

► To cite this version:

Kevin Nadaud, Zihao Lyu, Daniel Alquier, Quentin Paoli, Julien Ladroue, et al. Modeling and Extraction of the Specific Contact Resistance of GaN p-i-n Diodes up to 40 GHz. IEEE Transactions on Electron Devices, 2025, 72 (4), pp.1657-1662. 10.1109/TED.2025.3539644. hal-04949503

HAL Id: hal-04949503

https://hal.science/hal-04949503v1

Submitted on 15 Feb 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

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

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Modeling and Extraction of the Specific Contact Resistance of GaN p-i-n Diodes up to 40 GHz

Kevin Nadaud<sup>1,2</sup>, Zihao Lyu<sup>1,2</sup>, Daniel Alquier<sup>1,2</sup>, Quentin Paoli<sup>1,2</sup>, Julien Ladroue, Arnaud Yvon, Eric Frayssinet, Yvon Cordier<sup>1,2</sup>, Member, IEEE, and Jérôme Billoué<sup>1,2</sup>

**Abstract**— In this article, we propose a high-frequency model taking into account the series resistance of pseudo-vertical gallium nitride (GaN)-based p-i-n diodes. This model relies on the specific contact resistance on p-type GaN and the sheet resistance of the bottom n-type GaN. Those two quantities are obtained while fitting the RF experimental data and are slightly different from the dc values. The interest of this model is that the effective values, at the working frequency instead of “only” the dc values, are extracted using only a few devices. The novelty of the work resides in the consideration of the geometrical dimensions of the diode (anode radius and distance between anode and cathode) in the model. Furthermore, the model allows the determination of the most limiting geometrical parameters and can predict the series resistance of other topologies. In the present case, we show the most limiting factor is the radius of the anode due to the difficulties of achieving low specific contact resistance on p-type GaN. The parasitic capacitance is also extracted using the measured devices, allowing the modeling of the effective capacitance as a function of the frequency.

**Index Terms**— Cutoff frequency, gallium nitride (GaN), p-i-n diodes.

## I. INTRODUCTION

SWITCHES operating in the microwave band are key components for RF front-end since they can be used to select the path between transmitter and receiver, select a path for phase-shifter, etc. III-V semiconductors are widely used for applications with higher RF power thanks to their

Received 2 December 2024; revised 13 January 2025; accepted 3 February 2025. This work was supported in part by the ARD+ CERTeM 5.0 Program through the Regional Council Centre-Val de Loire and Tours Val de Loire Metropolis (France). The work of Kevin Nadaud, Daniel Alquier, and Yvon Cordier were supported by ECSEL-JU GaN4AP Project under Grant 101007310. The work of Daniel Alquier, Eric Frayssinet, and Yvon Cordier were supported in part by French National Research Agency (ANR) through the Investissements d'Avenir Program GaNeX under Grant ANR-11-LABX-0014 and in part by French Technology Facility Network RENATECH. The review of this article was arranged by Editor M. Hua. (Corresponding author: Kevin Nadaud.)

Kevin Nadaud, Zihao Lyu, Daniel Alquier, Quentin Paoli, and Jérôme Billoué are with GREMAN UMR 7347, CNRS, INSA-CVL, Université de Tours, 37071 Tours, France (e-mail: kevin.nadaud@univ-tours.fr).

Julien Ladroue and Arnaud Yvon are with STMicroelectronics, 37100 Tours, France.

Eric Frayssinet and Yvon Cordier are with CNRS, CRHEA, Université Côte d'Azur, 06560 Valbonne, France.

Digital Object Identifier 10.1109/TED.2025.3539644

excellent physical properties, particularly in terms of electron transport (high electron saturation velocity, high mobility in high-density electron gases). It is thus possible to manufacture high electron mobility transistors (HEMTs) operating at high frequency which can be used for amplification but also for switching [1], [2], [3]. Compared to devices based on other semiconductors such as silicon or gallium arsenide, gallium nitride (GaN)-based ones can sustain higher operation temperatures, can be used in harsh environments, and can present a high breakdown voltage [4]. With GaN, it is also possible to realize p-i-n diodes that have high linearity compared to their FET counterpart [5], [6], [7]. Their low level of distortion is due to the low modulation of the ON-resistance when the diode is forward biased and to the small variation of the capacitance when reversed biased [8].

The common criterion to evaluate the switching capability of a component is the cutoff frequency

$$f_c = \frac{1}{2\pi C_{\text{off}} R_{\text{on}}} \quad (1)$$

with $C_{\text{off}}$ the equivalent OFF-state capacitance and $R_{\text{on}}$ the equivalent ON-state resistance. This cutoff frequency, which should be as high as possible, represents the trade-off between high isolation (low capacitance) and low insertion losses (low series resistance).

To be used in a circuit, equivalent electric models of p-i-n diodes have been developed, which include different levels of details depending on the frequency of operation [8], [9]. The elementary model of a p-i-n diode usually consists of a variable resistance $R_i$ whose value is inversely proportional to the dc current flowing through the component. When the diode is in OFF-state, the equivalent impedance of the p-i-n diode at high frequency corresponds to a capacitance $C_j$ whose value depends on the geometry of the diode and the depleted depth in the i-layer [10]. This capacitance may depend on the reverse bias voltage (like for p-n junction) but can be constant below a given reverse voltage for punchthrough diodes (when the i-type layer doping is sufficiently low, it is fully depleted) [8]. When the p-i-n diode is used in a microwave device, additional parasitic elements should be included, such as parasitic capacitance $C_p$ and parasitic inductance $L_s$ (see Fig. 1). An additional resistance $R_C$ can be introduced to include the impact of contact resistance on semiconductors, and represents
<figure><img src="image_3.png" /><figcaption>Fig. 1. Equivalent circuit of a p-i-n diode at high frequency. $C_j$ corresponds to the junction capacitance, $R_j$ to resistance of the i-type layer, $R_C$ is the contact resistance, and $C_p$ and $L_s$ are the parasitic capacitance and inductance.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 2. (a) Cross section and (b) top views of the measured GaN p-i-n diode. r is the anode radius, d is the distance between the anode and the cathode D = 225 µm is the external radius.</figcaption></figure>

the lower limit value for the series resistance [11]. Most of the time, the model does not include the effect of the geometrical dimensions of the p-i-n diode. The effect of the dimension of the diode, area of contacts on n- and p-type GaN influences both in an opposite way the OFF-state capacitance and on-state series resistance and a compromise needs to be found to obtain a high cutoff frequency [6]. This is especially true for GaN-based p-i-n diodes in which a low specific contact resistance on p-type is difficult to achieve [12].

In this article, we propose a model that considers the geometrical dimensions of the GaN p-i-n diode for calculating the series resistance. This model relies on the specific contact resistance on p-type GaN and the sheet resistance of the bottom n-type GaN which are obtained while fitting the RF experimental data. The goal is to have a model that can be used to identify the limiting parameter to get low ON-state resistance. This model is intended to be derived using a limited number of measured devices on a small area of GaN and to be used for the monitoring process.

## II. EXPERIMENTS

The sample used in this study was grown using metal-organic chemical vapor deposition (MOCVD) onto a c-face 2-in sapphire substrate. Fig. 2(a) shows the stack-up of the measured GaN p-i-n diode. From bottom to top, a 1.5 µm buffer layer of GaN is grown to mitigate lattice mismatch and promote the growth of high-quality epitaxial films. Then a 1 µm-thick $n^+$ GaN ([Si] $5 \times 10^{18}$ cm$^{-3}$), and a 4 µm-thick layer of $n^-$ GaN ([Si] $1.2 \times 10^{16}$ cm$^{-3}$) are grown. Finally, the epitaxial stack is achieved with a 0.5 µm-thick p GaN layer ([Mg] $1 \times 10^{19}$ cm$^{-3}$). To realize the mesa structure, 7 µm thick undoped silicon glass (USG) has been deposited to form the hard mask. Opening of the USG has been achieved using wet buffer oxide etch and the GaN etching is done using ion beam etching (IBE). Contact on n-type GaN is made of PVD deposited Ni/Al (70/200 nm) annealed at 650 °C for 3 min with rapid thermal annealing (RTA) in Ar atmosphere [13].

Contact on p-type GaN is made of physical vapor deposited (PVD) Ni/Au (20/20 nm) annealed at 500 °C for 5 min with RTA in N$_2$/O$_2$ mixture [12]. Parylene-C was deposited onto the sample surface as passivation, and then it was patterned by O$_2$ plasma [14]. In addition, a refill layer was sputtered and patterned to reduce the contact resistance. DC measurements of the specific contact resistance and the sheet resistance have been performed using the circular transmission line method (C-TLM).

The measured GaN p-i-n diode structure is presented Fig. 2(b). $r \in [20, 40, 60]$ µm is the anode radius, $d \in [10, 20, 50]$ µm is the distance between the anode and the cathode and $D = 225$ µm is the external radius. The high-frequency characteristics of the fabricated GaN p-i-n diodes were measured from 0.1 to 40 GHz using Vector Network Analyzer (Agilent N8361) and ACP probes GSG 200 µm (Form factor). Open-short-load calibration is performed to remove the effect of cable and probe and the reference plane is at the probe's tip. The dc bias is applied using an internal tee and the current compliance has been fixed to 200 mA.

The impedance of the diode is measured using the reflection coefficient

$$Z = Z_0 \frac{1 + S_{11}}{1 - S_{11}}. \qquad (2)$$

In the first section, the $C_s - R_s$ representation is used and the elements are extracted using

$$C_s = - \frac{1}{\omega \operatorname{Im}[Z]} \quad \text{and} \quad R_s = \operatorname{Re}[Z]. \qquad (3)$$

In the second section, a model with more elements is used to include the frequency dependence of the effective capacitance, such as the one presented in Fig. 1. As no interconnection is used, inductance is not necessary [6], [15].

## III. RESULTS AND DISCUSSION

The results are decomposed into three parts. The first part presents the equivalent $C_s - R_s$ parameters extracted at 40 GHz and the influence of the bias voltage. This allows us to justify the chosen voltage for the subsequent parts. Then, the influence of the dimension on the ON state equivalent series resistance is presented, with the associated model. In the third part, the modeling of the OFF-state capacitance is made as a function of the frequency.

### A. Influence of the Bias Voltage

Fig. 3 shows the dc $I(V)$ characteristic for various radii of the anode and for $d = 10$ µm. The turn-on voltage is 3.5 V for all the diodes. When the radius of the anode increases, the current increases. Nevertheless, the current rise is not proportional to the one of the anode area, indicating that the current is not only limited by the junction but also by series resistance.

Fig. 4(a) shows the extracted capacitance, at $f = 40$ GHz (the effect of the frequency is described later on) as a function of the bias voltage, for various radii of the anode and $d = 10$ µm. When the bias voltage varies from 0 to -10 V, the extracted capacitance decreases due to an increase of the
<figure><img src="image_5.png" /><figcaption>Fig. 3. Current-voltage characteristics for various radii of the anode and for $d = 10$ µm.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. (a) Extracted capacitance and (b) series resistance, at $f = 40$ GHz as a function of the bias voltage, for various radii of the anode and for $d = 10$ µm.</figcaption></figure>

depletion depth in the $n^-$ layer. A more accurate depth is given in Section III-C. Above 0 V, the extracted capacitance increases which corresponds to the depletion depth going to zero and above 5 V, the p-i-n diode is in the ON-state and the equivalent model mainly consists in a resistance.

Fig. 4(b) shows the extracted series resistance as a function of the bias voltage. The equivalent series resistance remains almost constant between 6 and 8 V, even if the current increases. For example, for $r = 20$ µm and $d = 10$ µm, the current increases from 38 to 120 mA when the bias voltage

<figure><img src="image_7.png" /><figcaption>Fig. 5. Extracted series resistance at $V_{dc} = 6$ V as (a) function of the surface and (b) for various annular length. Dashed lines correspond to (6).</figcaption></figure>

varies from 6 to 8 V. This points out the contribution to the total resistance from $n^-$ layer which depends on the current, namely $R_i$ in Fig. 1, is very small and the total measured resistance mainly corresponds to the contribution from contacts $R_C$ [11]. Since the series resistance is almost constant in the [6;8 V] range, results are presented for $V_{dc} = 6$ V in the rest of the article.

For the diode with dimensions $r = 20$ µm and $d = 10$ µm, we extract $C_{off} = 68$ fF and $R_{on} = 14$ Ω, at 40 GHz. This gives performances higher than the state of the art concerning GaN p-i-n diodes, $f_c = 167$ GHz [6], [7]. One can note that the capacitance extracted here (and thus the computed cutoff frequency) includes the parasitic capacitance of the structure and not only the junction capacitance, contrary to the approximation made in [6].

## B. On State Series Resistance Modeling

To better decorrelate the effect of the radius and the distance between the electrodes, Fig. 5 shows the series resistance ($V_{dc} = 6$ V) as a function of the area and the distance at the fixed frequency of $f = 40$ GHz. The presented data correspond to the average of measurements on four diodes of each condition ($r, d$), with the associated standard deviation.
<figure><img src="image_8.png" /><figcaption>Fig. 6. Representation of the different contributions of the series resistance. $R_{cp}$ and $R_{cn}$ are the contact series resistance on the p-type and n-type GaN, respectively. $R_i$ is the resistance of the undoped i layer and $R_{sn}$ is the resistance of annular region of n+-type GaN. Only half of the structure is represented.</figcaption></figure>

As seen on Fig. 5(a), the increase of the area largely reduces the series resistance. Nevertheless, the area is not the only factor since the series resistance decreases from 14.6 to 3.75 Ω (by a factor of about 4) for $d = 10$ µm while the area increased from $10^3$ µm$^2$ to $12.5 \times 3$ µm$^2$ (multiplied by 12.5). If the anode was the only limiting factor, the reduction factor should be in the same order of magnitude.

Reducing the parameter $d$, as shown in the Fig. 5(b), allows reducing significantly the series resistance since for $r = 60$ µm, the series resistance decreases from 8.4 to 3.75 Ω when $d$ is reduced from 50 to 10 µm. An explanation is that the spread resistance in the annular region made of n+ layer is not negligible.

The series resistance in the ON-state of the diode has multiple contributions (see Fig 6)

$$R_s^{on} = R_{cp} + R_i + R_{sn} + R_{cn} + R_{pt}. \quad (4)$$

$R_{cp}$ and $R_{cn}$ are the contact series resistance on the p-type and n-type GaN, respectively. In our case, given the larger surface on n-type GaN and a one decade smallest specific contact resistance ($\rho_n = 1 \times 10^{-5}$ Ωcm$^2$ [13]), the predominant resistance is the contact resistance on p-type GaN. By considering the larger values of $r$ and $d$, for which the annular area of the contact on n-type GaN is the smaller, $R_{cn} \le 0.1$ Ω. $R_i$ is the resistance of the undoped i layer, which is modulated by the bias current. In the present case, we assume this resistance is very small since increasing the bias voltage does not change the total resistance but cannot be considered negligible compared to the others. $R_{sn}$ is the resistance of annular region of n+-type GaN, and can be expressed [16]

$$R_{sn} = \frac{R_{sh}}{2\pi} \ln\left(1 + \frac{d}{r}\right). \quad (5)$$

$R_{sh}$ is the sheet resistance of the n+ GaN layer. Finally, the total series resistance is expressed

$$R_s^{on} = \frac{\rho_p}{\pi r^2} + \frac{R_{sh}}{2\pi} \ln\left(1 + \frac{d}{r}\right) + R_0 = R_C. \quad (6)$$

$R_0$ includes $R_i + R_{cn}$, even small, and an eventual contact resistance from the probe tip $R_{pt}$.

Using measurements with various dimensions ($r, d$) of the diodes, we can extract $\rho_p$, $R_{sh}$, and $R_0$ by fitting the experimental data (using [17]). The extracted parameters ($\rho_p$, $R_{sh}$, and $R_0$) and (6) can thus be used to predict the performances

<table><caption>TABLE I
$\rho_p$, $R_{sh}$ AND $R_0$ EXTRACTED FOR DIFFERENT BIAS VOLTAGES</caption><thead><tr><th rowspan="2"></th><th colspan="3">V<sub>DC</sub></th></tr><tr><th>6 V</th><th>7 V</th><th>8 V</th></tr></thead><tbody><tr><td>ρ<sub>p</sub> (Ω cm<sup>2</sup>)</td><td>1.05 ± 0.02 × 10<sup>-8</sup></td><td>1.07 ± 0.03 × 10<sup>-8</sup></td><td>1.26 ± 0.06 × 10<sup>-8</sup></td></tr><tr><td>R<sub>sh</sub> (Ω)</td><td>68 ± 1</td><td>67 ± 2</td><td>67 ± 4</td></tr><tr><td>R<sub>0</sub> (Ω)</td><td>1.2 ± 0.1</td><td>1.7 ± 0.2</td><td>1.8 ± 0.4</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Extracted series resistance ($V_{DC} = 6$ V) as a function of the frequency, for various radii of the anode and $d = 10$ µm. Solid lines are the fits from (6).</figcaption></figure>

in terms of series resistance of diode with given dimensions, and to determine the most limiting parameter. More, this gives effective specific contact resistance and sheet resistance at the frequency of operation (instead of using only the dc value).

By fitting our RF measurements, the parameters have been obtained from 6 to 8 V and are reported Table I. The uncertainties are given during the fitting process and correspond to the confidence interval. Values are very close to each other for this bias range. This shows that the bias voltage (and thus the bias current) does not influence the extracted resistance values, confirming the resistance of the intrinsic region $R_i$ (which is current dependent) is small. The series resistance expression with these parameters is plotted with a dashed line in Fig. 5(a) and (b). The dc value of the specific contact resistance is $\rho_p^{dc} = 5 \times 10^{-4}$ Ωcm$^2$ which is in the same order of magnitude as the one obtained using fitting the RF data, even slightly higher. The slightly higher value for dc may be explained by some impurities as the interface between the metal contact and the p-GaN which degrades the resistance for low frequencies but not for high frequencies due to capacitive coupling. The dc value of the sheet resistance of the annular region between the electrodes is $R_{sh}^{dc} = 83.5$ Ω, which is close to what is obtained by fitting the RF data.

The contribution of the specific contact resistance on p-type GaN represents 64 % of the total resistance for the fabricated diode with the highest cutoff frequency ($r = 20$ µm and $d = 10$ µm) and the spread resistance in the annular region made of n+ layer represents 28 %. Thus, this model confirms that the specific contact resistance is the key point to optimize to reduce the ON state resistance.

Fig. 7 shows the measured series resistances in the ON-state as a function of the frequency with the proposed model (6).
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. Extracted capacitance as (a) function of the surface and (b) for various annular length.</figcaption></figure>

From 10 to 40 GHz, the series resistance is constant showing the model is adapted in this frequency range.

### C. Off State Capacitance Modeling

The capacitance, presented Fig. 8(a), is strongly affected by the anode area, indicating that the capacitance of the device is mainly determined by the depletion of the n⁻ GaN region. The fact the capacitance is not proportional to the area is due to the presence of the parasitic capacitance $C_p$. The distance between the electrodes seems to have no effects on the capacitance [see Fig. 8(b)].

To simulate the OFF-state, the model given in Fig. 1 is used (without the inductance), which gives for the equivalent series capacitance

$$C_s^{\text{off}} = C_p + \text{Re} \left[ \frac{C_j}{j \omega C_j (R_C + R_i) + 1} \right]. \quad (7)$$

$R_C$ is equivalent to the ON-state series resistance determined in the previous part and it can be computed using (6). $C_j$ is the junction capacitance

$$C_j = \varepsilon_0 \varepsilon_r \frac{\pi r^2}{t_d} \quad (8)$$

with $\varepsilon_r = 9.5$ [18] the dielectric permittivity of the GaN, $\pi r^2$ the area of the anode and $t_d$ the depleted depth, that later needs

<figure><img src="image_12.png" /><figcaption>Fig. 9. Extracted capacitance ($V_{dc} = -10$ V) as a function of the frequency, for various radii of the anode and for $d = 10$ µm. Solid lines are the fits from (7).</figcaption></figure>

to be determined. $C_p$ is the parasitic capacitance, which has to be extracted too; we assume its value is independent of the radius $r$. Contrary to the ON-state, $R_i$ cannot be considered small and its value may be difficult to obtain theoretically (depending on carrier mobility and density). Nevertheless, we can assume this resistance is inversely proportional to the area, which gives $R_i = (\rho_i / \pi r^2)$, with $\rho_i$ a parameter which needs to be determined.

By fitting the equivalent OFF-state capacitance as a function of the frequency, it is possible to extract $t_d = 1.21 \pm 0.01$ µm, $C_p = 13.2 \pm 0.3$ fF and $\rho_i = 2.08 \pm 0.01 \times 10^{-14}$ Ωcm². The other parameters used to compute $R_C$ have been determined previously. One can note the depletion depth is $t_d = 1.21 \pm 0.01$ µm, which indicates the 4 µm-thick n⁻ layer is not fully depleted. This is attributed to the doping level ($1.2 \times 10^{16}$) which does not allow to have a punchthrough diode in the bias range [8].

Fig. 9 shows the extracted capacitance ($V_{dc} = -10$ V) as a function of the frequency, for various radii of the anode and $d = 10$ µm. The effective capacitance decreases as the frequency increases, and the equivalent circuit matches the measurements results well from 4 to 40 GHz.

## IV. CONCLUSION

In this study, we propose a simple expression to compute the series resistances of GaN-based p-i-n diodes, with concentric electrodes. This model is based on the geometrical parameters of the diode, the radius of the anode, and the distance between the anode and the cathode, and relies on the specific contact resistance on p-type doped GaN and the sheet resistance of the bottom n-type doped GaN. The parameters are extracted by fitting the experimental data which allows the extraction of specific contact resistance and sheet resistance. The extracted values, in the RF range, are slightly lower than the ones obtained from dc measurements. The model allows us to show that the distance between the two concentric electrodes seriously degrades the quality factor and must be reduced as much as possible while matching with the process resolution. In addition to the modeling of the
ON-state resistance, OFF-state equivalent capacitance modeling has been made, as a function of the frequency using the same geometrical approach.

## REFERENCES

[1] M. Marso, J. Bernat, A. Wolter, P. Javorka, A. Fox, and P. Kordos, "MSM diodes based on an AlGaN/GaN HEMT layer structure for varactor and photodiode application," in *Proc. 4th Int. Conf. Adv. Semiconductor Devices Microsyst.*, Oct. 2002, pp. 295-298.

[2] M. Marso, A. Fox, G. Berliner, P. Kordos, and H. Luth, "Comparison of AlGaN/GaN MSM varactor diodes based on HFET and MOSHFET layer structures," in *Proc. Int. Conf. Adv. Semiconductor Devices Microsys- tems*, Oct. 2006, pp. 229-232.

[3] M. Marso, M. Horstmann, H. Hardtdegen, P. Kordoš, and H. Lüth, "Electrical behaviour of the InP/InGaAs based MSM-2deg diode," *Solid- State Electron.*, vol. 41, no. 1, pp. 25-31, 1997.

[4] U. K. Mishra, S. Likun, T. E. Kazior, and Y.-F. Wu, "GaN-based RF power devices and amplifiers," *Proc. IEEE*, vol. 96, no. 2, pp. 287-305, Feb. 2008.

[5] A. K. Sattu, J. Yang, R. Gaska, Md. B. Khan, M. Shur, and G. Simin, "Small- and large-signal performance of III-nitride RF switches with hybrid fast/slow gate design," *IEEE Microw. Wireless Compon. Lett.*, vol. 21, no. 6, pp. 305-307, Jun. 2011.

[6] J. G. Yang and K. Yang, "GaN-based pin diodes for microwave switching IC applications," *Electron. Lett.*, vol. 48, no. 11, pp. 650-652, May 2012.

[7] J. G. Yang and K. Yang, "High-linearity K-band absorptive-type MMIC switch using GaN PIN-diodes," *IEEE Microw. Wireless Compon. Lett.*, vol. 23, no. 1, pp. 37-39, Jan. 2013.

[8] S. C. Bera, *P-I-N Diode*, vol. 533. Singapore: Springer, 2019, pp. 13-31.

[9] R. H. Caverly and G. Hiller, "The frequency-dependent impedance of p-i-n diodes," *IEEE Trans. Microw. Theory Techn.*, vol. 37, no. 4, pp. 787-790, Apr. 1989.

[10] R. H. Caverly and G. Hiller, "The small signal a.C. impedance of gallium arsenide and silicon p-i-n diodes," *Solid-State Electron.*, vol. 33, no. 10, pp. 1255-1263, Oct. 1990.

[11] R. H. Caverly, "Modeling PIN diodes for high power RF and microwave applications," in *IEEE MTT-S Int. Microw. Symp. Dig.*, Jun. 2009, pp. 897-900.

[12] C. Mauduit et al., "Importance of layer distribution in Ni and Au based ohmic contacts to p-type GaN," *Microelectronic Eng.*, vol. 277, May 2023, Art. no. 112020.

[13] D. Alquier, F. Cayrel, O. Menard, A.-E. Bazin, A. Yvon, and E. Collard, "Recent progresses in GaN power rectifier," *Jpn. J. Appl. Phys.*, vol. 51, no. 1S, Jan. 2012, Art. no. 01AG08.

[14] Z. Lyu et al., "Pseudo-vertical GaN-on-Sapphire PiN diode: Process optimizations and electrical properties," in *Proc. 19th Eur. Microw. Integr. Circuits Conf. (EuMIC)*, Sep. 2024, pp. 383-386.

[15] K. Kobayashi, A. K. Oki, D. K. Umemoto, S. Claxton, and D. C. Streit, "GaAs HBT PIN diode attenuators and switches," in *Proc. IEEE Microw. Millim.-Wave Monolithic Circuits Symp. Dig. Papers*, Jun. 1993, pp. 151-154.

[16] Z. Ma et al., "RF measurement technique for characterizing thin dielec- tric films," *IEEE Trans. Electron Devices*, vol. 45, no. 8, pp. 1811-1816, Aug. 1998.

[17] M. Newville, T. Stensitzki, D. B. Allen, and A. Ingargiola. (2014). *LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python*. [Online]. Available: https://zenodo.org/record/11813

[18] J. Krupka, M. Zając, R. Kucharski, and D. Gryglewski, "Dielectric properties of highly resistive GaN crystals grown by ammonothermal method at microwave frequencies," *AIP Adv.*, vol. 6, no. 3, Mar. 2016, Art. no. 035313.