Impact Ionization Avalanche Transit Time Research Articles

Direct observation of radio-frequency negative differential resistance in GaN-based single drift region IMPATT diodes

We report the direct observation of radio-frequency negative differential resistance, via on-wafer S-parameter measurements, in GaN-based impact ionization avalanche transit time (IMPATT) diodes. Clear signatures of reflection gain are observed from 18.7 to 30.6 GHz. These observations have been made possible by suppressing the reverse leakage current (and thereby parasitic shunt conductance) by optimization of the fabrication process, in conjunction with the use of pulsed measurements to suppress device self-heating. Consistent with avalanche-dominated behavior, the measured DC reverse bias current–voltage measurements show a positive temperature coefficient of breakdown. For the high-frequency on-wafer characterization, pulsed-bias S-parameter measurements with low (0.0067%) duty cycle were used to mitigate thermal effects. The measured avalanche frequency aligns closely with theoretical predictions based on Gilden and Hines' small signal model [Gilden and Hines, IEEE Trans. Electron Devices ED-13(1), 169–175 (1966)], measured impact ionization coefficients [Cao et al., Appl. Phys. Lett. 112(26), 262103 (2018)], and experimental saturation velocity measurements [Bajaj et al., Appl. Phys. Lett. 107(15), 153504 (2015)]; this excellent agreement confirms IMPATT operation and provides insights needed to further optimize device performance.

The latest developments of microwave diagnostics for high temperature plasma in ELVA-1 company

For nearly 30 years, we have been designing and supplying instruments for microwave diagnostics of high temperature plasma. This report provides a description of the mm-wave components we utilize to make diagnostics within the frequency range of 26–330 GHz. While most of these components are standard and readily available on the market, we have also developed a few specific devices that simplify the architecture of our instruments. The article includes descriptions of these devices: Backward Wave Oscillators (BWO), Impact Ionization Avalanche Transit-Time diode (IMPATT) sources, IMPATT Active Frequency Multipliers (AFM), Noise Sources, and Electronically Controlled Attenuators. Furthermore, we offer an overview of the microwave plasma diagnostics we have supplied, including ECE radiometers operating at 50–220 GHz, as well as heterodyne interferometers operating at fixed frequency 94 GHz, 140 GHz, or 300 GHz. We also discuss methods employed to ensure measurement stability and present the achieved results. The advent of the new era of modern Monolithic Microwave Integrated Circuit (MMIC) based devices has brought forth exciting possibilities. As an example, we discuss the upgrade of the low noise receiver for the Collective Thomson Scattering (CTS) diagnostic at Wendelstein 7-X, which enables ion temperature measurements in the plasma core [1]. Lastly, we provide a list of MMIC-based devices that are currently available and have garnered the attention of the plasma diagnostics community.

Junction Diameter Dependence of Oscillation Frequency of GaN IMPATT Diode Up to 21 GHz

An experimental study on the effects of junction capacitance and current density on the oscillation characteristics of GaN single-drift-region (SDR) impact ionization avalanche transit-time (IMPATT) diodes were carried out using GaN p+-n abrupt junction diodes of various diameters, 200, 150, and 100 μm, with a depletion layer width of 2 μm. The fabricated diodes showed a clear avalanche breakdown at 315 V and a pulsed microwave oscillation with a peak output power exceeding 30 dBm. The oscillation frequency depended on junction diameter and current density. It was widely modulated from 8.56 to 21.1 GHz with decreasing junction diameter and increasing current density. The highest oscillation frequency was obtained with a current density of 13.8 kA/cm2 and a junction diameter of 100 μm. A numerical calculation based on Read-type small-signal theory was carried out and found to well explain the experimental results.

Simulation on different orientation hexagonal SiC-based hetero-polytype IMPATT terahertz diodes

SiC hetero-polytypes that could be fabricated by chemical vapor deposition etc. methods can be employed to design the power devices. Herein, the 〈0 0 0 1〉(〈1 1 2¯ 0〉)4H(6H)-SiC-based hetero-polytypes are adopted to construct the n+/n/i/p/p+-type impact ionization avalanche transit time diodes (IMPATTDs) and mixed tunneling avalanche transit time diodes (MITATTDs). The DC, large-signal and noise performance of the proposed diodes operating at 0.85 THz are numerically simulated based on the fundamental equations for semiconductor devices. The results indicate that, the diodes with 〈0 0 0 1〉4H(6H)-SiC in each of the i-type, n-type and p-type regions can render higher break-down voltage and conversion efficiency while lower quality factor comparing to those with 〈1 1 2¯ 0〉4H(6H)-SiC in the three regions, the latter devices involve lower noise. The diodes contained 3C-SiC show lower break-down voltage and quality factor while higher noise than those without 3C-SiC. Little difference of DC, large-signal and noise properties between IMPATTDs and MITATTDs is implied due to very weak tunneling through thick intrinsic-region. The present diodes show higher conversion efficiency comparing to the n+/n/p/p+-type devices. In addition, the fabricating feasibility of the proposed devices is discussed. This paper can guide to design the reasonable structures by using suitable anisotropic semiconductors to achieve high-performance devices.

Nonlinear Carrier Dynamics in a Single Photon Avalanche Diode: Stability, Bifurcation, and Quenching Condition

Nonlinear carrier dynamics during quenching of a single photon avalanche diode (SPAD) are investigated. A Lienard type differential equation is derived from carrier continuity equations and it is solved analytically and numerically. Universal characteristics of the quenching carrier dynamics, i.e., stability, bifurcation, and quenching conditions, are analyzed on a trace-determinant plane of the Jacobian matrix and on a phase plane as functions of the quenching resistance (QR). With a finite QR or a resistive quenching (RQ), the breakdown voltage is found to be an attractor leading to a nonquenched final state. In order to produce a successful quenching, i.e., a status identified as an unstable fixed point (FP) with a zero-carrier state, two conditions are found to be necessary: 1) bias voltage dropping below breakdown voltage to ensure carrier decrease and 2) carrier extinction (CE) in this carrier decreasing period. The two conditions together lead to a threshold of QR. On the other hand, a capacitive quenching (CQ) appearing as a special case of RQ with an infinite resistance is found to show a completely different bifurcation character. CQ is derived to be equivalent to a logistic equation giving a transcritical bifurcation at the breakdown voltage and a final state identified as a stable FP with natural CE. Finally, two time constants both governed by an excess voltage are derived. In particular, one of them, a lifetime of impact ionizations, is found to be equivalent to the ``avalanche frequency'' of an impact ionization avalanche transit-time diode (IMPATT).

Study of In x Ga1-x N/GaN Homotype Heterojunction IMPATT Diodes

In this work, a novel n-In <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-<i>x</i></sub> N/N-gallium nitride (GaN) homotype heterostructure is proposed instead of P-GaN/N-GaN homostructure to produce impact-ionization-avalanche-transit-time (IMPATT) diode. Conventional GaN IMPATT device will lose its working ability due to the immature p-type GaN, so this work predicts that the n-In <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-<i>x</i></sub> N/N-GaN IMPATT diode can be an alternative to the GaN p-n IMPATT diode; thus, the difficulty of the p-type doping process is avoided. The dc and RF large-signal output characteristics with different compositions are investigated in detail. The simulation results show that the power and efficiency of the novel structure device increase when the In composition increases. When the In composition is greater than 0.4, the performance of the homotype heterojunction IMPATT is better than that of p-n IMPATT. Moreover, homotype heterojunction IMPATT is better in frequency bandwidth, and it can hold greater bias current density than p-n IMPATT. Meanwhile, the performance of homotype heterojunction IMPATT does not depend on the thickness of the InGaN layer, but it decreases as the thickness of the p-type region in p-n IMPATT increases. As it has greater potential in the application, this work brings a reference for the design and manufacture of IMPATT devices based on wide bandgap semiconductor materials, especially GaN materials.

Study on Electric Field Modulation and Avalanche Enhancement of SiC/GaN IMPATT Diode

This paper proposes a 6H-materials silicon carbide (SiC)/gallium nitride (GaN) heterogeneous p-n structure to replace the GaN homogenous p-n junction to manufacture an impact-ionization-avalanche-transit-time (IMPATT) diode, and the performance of this 6H-SiC/GaN heterojunction single-drift-region (SDR) IMPATT diode is simulated at frequencies above 100 GHz. The performance parameters of the studied device were simulated and compared with the conventional GaN p-n IMPATT diode. The results show that the p-SiC/n-GaN IMPATT performance is significantly improved, and this is reflected in the enhanced characteristics in terms of operating frequency, rf power, and dc-rf conversion efficiency by the two mechanisms. One such characteristic that the new structure has an excessive avalanche injection of electrons in the p-type SiC region owing to the ionization characteristics of the SiC material, while another is a lower electric field distribution in the drift region, which can induce a higher electron velocity and larger current in the structure. The work provides a reference to obtain a deeper understanding of the mechanism and design of IMPATT devices based on wide-bandgap semiconductor materials.

Investigation of Dielectric Resonator Oscillator Using High-Electron Mobility Transistor at 26GHz for Space Applications

An oscillator is a vital component as the energy source in microwave telecommunication system. Microwave oscillators designed using Gunn diode have poor DC to RF efficiency. IMPact Ionization Avalanche Transit-Time diode (IMPATT) oscillators have the drawback of poor noise performance. The transistorized oscillators have a limitation to the maximum oscillation frequency which means that they cannot be used for oscillators designed for high frequencies. To design negative series feedback Dielectric Resonator Oscillator (DRO), the resonant unit uses a dielectric resonator (DR) since it is small in size, light in weight, has high-Quality ([Formula: see text]) factor, better stability and also it is inexpensive. It has the benefits of low-phase noise, low cost, miniaturization, high stability, applicable for devices designed at high frequencies and had already been widely applied, so the research on microwave dielectric oscillator has also been one of the focus of today’s microwave integrated circuits. DRO is widely used in electronic warfare, missile, radar and communication systems. The DRO incorporates High-Electron Mobility Transistor (HEMT) as an active device since it offers higher power-added efficiency combined with excellent low-noise figures and performance. The entire circuit of DRO using HEMT at 26[Formula: see text]GHz is designed using Agilent Advanced Design System (ADS) software. In this, DRO different measurements of parameters are done such as output power which is typically [Formula: see text][Formula: see text]dBm for 26[Formula: see text]GHz DRO, phase noise at 10[Formula: see text]kHz offset for 26[Formula: see text]GHz DRO it is 80[Formula: see text]dBc/Hz. The frequency pushing and frequency pulling for 26[Formula: see text]GHz DRO its typical values are 30[Formula: see text]kHz/V and 1[Formula: see text]MHz, respectively.

Study of p-SiC/n-GaN Hetero-Structural Double-Drift Region IMPATT Diode.

Nowadays, the immature p-GaN processes cannot meet the manufacturing requirements of GaN impact ionization avalanche transit time (IMPATT) diodes. Against this backdrop, the performance of wide-bandgap p-SiC/n-GaN heterojunction double-drift region (DDR) IMPATT diode is investigated in this paper for the first time. The direct-current (DC) steady-state, small-signal and large-signal characteristics are numerically simulated. The results show that compared with the conventional GaN single-drift region (SDR) IMPATT diode, the performance of the p-SiC/n-GaN DDR IMPATT proposed in this design, such as breakdown voltage, negative conductance, voltage modulation factor, radio frequency (RF) power and DC-RF conversion efficiency have been significantly improved. At the same time, the structure proposed in this design has a larger frequency bandwidth. Due to its greater potential in the RF power density, which is 1.97 MW/cm2 in this study, indicates that the p-SiC/n-GaN heterojunction provides new possibilities for the design and manufacture of IMPATT diode.

반도체 전자소자 기반 테라헤르츠 신호원

Terahertz (THz) signal sources are important elements that are used in THz systems and have been gaining interest in recent times. THz signal sources can be realized using either optical devices or electronic devices. The latter approach can be divided into signal sources based on vacuum devices and solid-state devices. This paper provides an overview of THz sources that use semiconductor electronic devices, which are a typical kind of the solid-state devices. First, the operational principles and recent performance trends of diode-based THz signal sources, such as Gunn diodes, impact ionization avalanche transit-time (IMPATT) diodes, and resonant tunneling diodes (RTDs), are provided. Next, three types of transistor circuit-based THz signal sources, namely, LC cross-coupled oscillators, Colpitts oscillators, and ring oscillators, are described according to their topologies and performance. Finally, various types of 300 GHz and 600 GHz oscillators are introduced as representative examples of transistor circuit-based signal sources.

Influence of SiC hetero-polytype barriers on the performance of IMPATT terahertz diodes

The SiC hetero-polytypes with perfect interfaces and no diffusion pollution are adopted to innovatively design the impact ionization avalanche transit-time (IMPATT) diodes. The performance of DC, large-signal and noise of the proposed diodes operating at the atmospheric low-loss window frequency 0.85 THz are estimated via numerically solving the fundamental device equations with and without quantum correction incorporated the tunnel and density-gradient of carriers. The influence from SiC hetero-polytype barriers and material properties on the performance of IMPATT diodes is analyzed. The advantages in power, efficiency and noise generating in the diodes of 4H/6H–SiC hetero-polytypes can be due to high critical breakdown electric field strength and weak ionizing in 4H–SiC and 6H–SiC. However, small power and heavy noise emerging from the devices of 3C/4H–SiC and 3C/6H–SiC hetero-polytypes can be owing to low critical breakdown electric field strength and strong ionizing in 3C–SiC. The noise electric field peaks arising from the strong ionizing layers while deviating from the interfaces in hetero-polytypes are illustrated. The evident quantum effect on the diodes without 3C–SiC while the slight effect on the devices included 3C–SiC are attributed to low-barriers embedded in the former diodes while high-barriers involved in the latter devices, respectively. • The SiC hetero-polytypes are employed to design the impact ionization avalanche transit-time diodes (IMPATTDs). • The 4H/6H-SiC hetero-polytype IMPATTDs imply advantages in power, efficiency and noise due to weak ionizing in materials. • The noise electric field peaks arise from the strong ionizing layers while deviate from the in hetero-interfaces. • The IMPATTDs with 3C/4H-SiC and 3C/6H-SiC hetero-polytype high-barriers encounter weak quantum effect.

Синхронизация генераторов на ЛПД импульсного и непрерывного действия в мм-диапазоне длин волн. Часть 2. Стабилизация СВЧ-параметров синхронизированных генераторов

This is the second part of the two-part article, which summarizes the state-of-the-art results in the development of synchronized oscillators based on IMPATT (IMPact ionization Avalanche Transit-Time) diodes. The first part of the paper presented the electrodynamic design of oscillators, which contain a resonant oscillatory system with silicon IMPATT diodes and are synchronized by an external source of microwave oscillations. The second part of the paper considers the methods for stabilizing the parameters of IMPATT oscillators, which make it possible to create coherent power sources in the millimeter wavelength range. The specifics of pulse generators lies in the change in frequency within the microwave pulse relative to the change in temperature, which leads to a change in the impedance of the diode and thus to a phase change with respect to the synchronizing signal. Phase modulation is reduced or completely eliminated (which is necessary to ensure the coherence of the microwave transmitter) by using current compensation, i.e., by using the control current pulse with a special shape. The study demonstrates the expediency of introducing additional heating of the semiconductor structure of the IMPATT diode, which allows the initial temperature of the IMPATT diode in the region of the leading edge of each pulse to remain virtually constant and independent of the ambient temperature. Using these methods on silicon double-drift IMPATT diodes allowed creating synchronized oscillators with high frequency stability and an output power level from 20 to 150 W, which have a high degree of coherence in the synchronization mode with an external signal. The paper also presents the designs and parameters of coherent microwave power sources in the short-wave part of the millimeter wavelength range using the nonlinear properties of the IMPATT diodes in the radio-pulse conversion mode. This mode makes it possible to provide the output power level of the signal at the n-th harmonic Pout ≈1/n, which significantly exceeds the achieved characteristics of the frequency multipliers with charge accumulation, where Pout ≈ 1/n2. The output power of such devices is achieved at the level of 50–20 mW in the 75–180 GHz frequency range with a frequency multiplication factor of 1–15.

Синхронизация генераторов на ЛПД импульсного и непрерывного действия в мм-диапазоне длин волн. Часть 1. Конструкции генераторов и обобщенная модель их синхронизации внешним сигналом

Advances in the development of ultrahigh-frequency semiconductor electronics open wide opportunities for developing optimal schemes and designs of microwave power sources in the millimeter wavelength range providing high stability of the frequency and electromagnetic oscillation phase. Synchronized diode generators used in transmit/receive module for active phased array antennas, coherent low-power radar stations, etc. show great promise. The mode of external synchronization of semiconductor generators allows effectively implementing the task of creating output stages of the transmitters with high gain factor, low frequency noise and an output power level corresponding to the maximum power mode. This article presents the first of two parts of the study, which summarizes the results achieved so far in the development of synchronized oscillators based on impact ionization avalanche transit-time (IMPATT) diodes. The first part presents the electrodynamic designs of the oscillators, which are synchronized with an external source of microwave oscillations and contain a resonant oscillating system with a silicon IMPATT diode. The silicon two-drift IMPATT diode was chosen as an active element due to the fact that its use allows reaching significant levels of pulsed microwave power – an order of magnitude higher than those of the most well-known HEMT and pHEMT transistors in the millimeter wavelength range. It is shown that to reduce losses, the oscillating system should be made in the form of a radial resonator with a diode casing, which has distributed parameters. This eliminates the use of additional reactive inhomogeneities in the initial cross-section of the waveguide section of the generator. Due to the low quality factor of the resonant casing of the diode, the generalized quality factor of the microwave circuit takes the minimum value required to implement a stable generator synchronization process in the millimeter wavelength range. The second part of the work will be devoted to synchronized pulse generators with an output power of 20–150 W.

Theoretical investigation of incomplete ionization of dopants effect on p+nn-n+ 4H-SiC IMPATT diode

The effect of incomplete ionization of dopants on p+nn-n+ 4H silicon carbide (4H-SiC) impact-ionization-avalanche-transit-time (IMPATT) diodes has been investigated. Breakdown voltage, avalanche region width, DC to RF conversion efficiency and RF output power of the 4H-SiC IMPATT device with incomplete and complete ionization are given at different temperatures. Theoretical analysis reveals that the influence of the incomplete ionization of dopants on the performance of the p+nn-n+ 4H-SiC IMPATT devices cannot be ignored.

A novel model of avalanche current generation in the GaN HEMT equivalent circuit

We consider the large-signal equivalent circuit of a field-effect transistor (FET) with characteristics and parameters calculated using a two-dimensional (2D) quasi-hydrodynamic model while taking into account the electron velocity overshoot. In accordance with this equivalent circuit when applied to an AlGaN/GaN high-electron-mobility transistor (HEMT), the avalanche current (in the feedback branch) is zero at all operating points. However, this contradicts the significant difference seen between the results of time-domain simulations of a radiofrequency (RF) amplifier in which the transistor is simulated using a 2D model that does versus does not include the avalanche multiplication of the charge carriers. We propose a new model for the avalanche current generation, based on such simulations including the avalanche multiplication and on the theory of impact-ionization avalanche transit-time (IMPATT) diodes. This model allows the synthesis of amplifiers with high power-added efficiency (PAE).

Improved performance of Ni/GaN Schottky barrier impact ionization avalanche transit time diode with n-type GaN deep level defects

In this paper, the effects of n-type GaN deep level defects on the DC, small signal AC, and radio frequency (RF) characteristics of Ni/GaN Schottky barrier impact ionization avalanche transit time (IMPATT) diode are investigated. A double avalanche termination region (DATR) structural IMPATT diode is proposed to mitigate the influences caused by these deep level defects. Simulation results show that the internal electric field, carrier generation rate and carrier velocity of IMPATT diode are affected by these deep level defects. With the increase of deep level defects density, the maximum RF output power, DC-to-RF conversion efficiency and optimum frequency of the diode all show a tendency to degenerate correspondingly. Through adjusting the electric field property properly of the diode, the DATR structural IMPATT diode improves the performances of IMPATT diode. The negative peak conductance of the improved diode is 11.4 × 103 S cm−2 at 248 GHz, showing the lowest quality factor of 1.42, the improved maximum RF output power of 1.35 MW cm−2 and DC-to-RF conversion efficiency of 15.7% at 220 GHz under the same deep level defects density, these characteristics of the improved DATR structural IMPATT diode reach the level which the low deep level defects density original diode shows.

Noise characteristics of Ni/GaN Schottky barrier IMPATT diode based on polar- and nonpolar-oriented wurtzite GaN for terahertz application

Abstract This paper reports a study investigating the noise performance of Ni/GaN Schottky barrier impact-ionization-avalanche-transit-time (IMPATT) diodes based on the polar- and nonpolar-oriented wurtzite GaN by a numerical simulation. Results show that the nonpolar IMPATT diode exhibits a significant wider and higher frequency-band corresponding to the low noise measure (NM). The upper limit of the low-noise frequency-band of the IMPATT diode shifts from 159.2 GHz to 184.3 GHz, from 183.4 GHz to 245.7 GHz and from 212.2 GHz to 285.6 GHz when J0 = 1 kA/cm2, 10 kA/cm2 and 100 kA/cm2, respectively, comparing the polar with the nonpolar IMPATT diodes. Our analysis proves that the mechanism comes from excellent properties of the Negative Differential Mobility (NDM) characteristic in the nonpolar orientation wurtzite GaN. In particular, the nonpolar diode still demonstrates better unity between the noise and RF power performances and can significantly improve the stability of IMPATT diodes at terahertz frequency.

GaN/AlxGa1−xN/GaN heterostructure IMPATT diode for D-band applications

In this paper, a novel structural impact ionization avalanche transit time (IMPATT) diode configured by GaN/AlxGa1−xN/GaN heterostructure is investigated at the operation frequency of D-Band. Simulation results show that, with Al composition x varies from 0.2 to 0.6, a more localized avalanche region width is obtained, the device breakdown voltage increases gradually, while the RF output power and the DC-to-RF conversion efficiency have also shown significant improvement as compared with the GaN homostructure IMPATT diode. The highest values of the RF output power density and the DC-to-RF conversion efficiency of GaN/Al0.4Ga0.6N/GaN heterostructure are obtained as 1.56 MW/cm2 and 21.99%, larger than that of 1.02 MW/cm2 and 16.37% for GaN homostructure IMPATT diode. Meanwhile, the lowest Q factor can be achieved, which implies that heterostructure IMPATT diodes exhibit better stability and higher growth rate of microwave oscillation compared with conventional IMPATT diodes.

An 82-GHz 14.6-mW Output Power Silicon Impact Ionization Avalanche Transit Time Transmitter With Monolithically Integrated Coplanar Waveguide Patch Antenna

The design, fabrication, and characterization of a 4.08 mm2 monolithic 82-GHz silicon impact ionization avalanche transit time (IMPATT) transmitter are presented. The vertical IMPATT diode was grown by molecular beam epitaxy and followed by the typical circuit fabrication process. The oscillator design is experimentally well verified both by the Kurokawa condition from impedance matching and by Barkhausen’s criteria from the reflection coefficient aspect, respectively. An 82.5-GHz coplanar waveguide (CPW) patch antenna with 50- $\Omega $ input impedance is monolithically integrated to an IMPATT oscillator with similar working frequency. Under the biasing condition of 25 mA (13.41 V), the $H$ -plane radiation pattern of the monolithic IMPATT transmitter was characterized at 82.17 GHz in an E-band anechoic chamber. From link budget calculation, the equivalent isotropically radiated power of the transmitter chip achieved 18.43 dBm (69.66 mW). With the simulated directive gain (7.35 dBi) of CPW patch antenna and measured CPW interconnect loss (0.57 dB), the output power of transmitter achieved 11.65 dBm (14.62 mW) with dc-to-radio frequency efficiency of 4.36%.

Anisotropy effects on the performance of wurtzite GaN impact-ionization-avalanche-transit-time diodes

We demonstrate that a GaN impact-ionization-avalanche-transit-time (IMPATT) diode exhibits a higher frequency and a wider bandwidth in the basal plane (Γ–M direction) than along the c-axis (Γ–A direction). Because of the better efficiency, RF power, and negative resistance performance at a high frequency, the use of the diode in the Γ–M direction is more appropriate for high-frequency operation. In addition, the diodes are cut off when the specific contact resistances are ∼10−6 and ∼10−5 Ω·cm2. Thus, the very high specific contact resistance of p-type GaN of about ∼10−4 Ω·cm2 provides an important limitation to the fabrication of pn junction GaN IMPATT diodes.