This paper is dedicated to discussing the physics and applications of avalanche on III-Nitrides, primarily using Gallium Nitride as the example. Understanding the breakdown phenomenon in wide bandgap materials is of great interest to the device and circuit community as it directly impacts design and applications with these emerging semiconductors. In this paper, first, we go over the various approaches that have been reported on estimating the impact ionization coefficients in GaN, then discuss about the estimation of the critical electric field for punch-through and non-punch-through designs, and, finally, go over two avalanche-based devices that we have recently demonstrated.

A substantial amount of effort is currently committed to create high-power and high-frequency devices in Gallium Nitride and other III-Nitrides. The major material advantage for these applications is the high electric field strength of GaN, which only increases as we go toward Aluminum-rich Nitrides. The data related to avalanche breakdown in GaN are still very limited and missing for Al-rich GaN since it is still not a usual form of breakdown in GaN. Problems exist with material defects, which result in premature breakdown of junction devices. In addition, device edge termination is still an issue, and in many cases, avalanche breakdown is dominated by device periphery. Furthermore, very little conclusive information on high-field material properties can be obtained unless all three—material quality, device design, and processing—are optimized enough to ensure well-behaved uniform avalanche multiplication and breakdown. In this report, we analyze some of our recent work along with other reported work on avalanche and impact ionization in GaN and make our observations on fabrication of GaN p–n junction devices with uniform avalanche breakdown. We also discuss two devices that have been recently studied in our group and benefit from avalanche in GaN.

Avalanche breakdown was not reported in GaN p–n diodes until 2013.1 Since that first report on avalanche, there have been other reports discussing avalanche, including ours.2–12 Besides few early studies on impact ionization coefficients based on GaN grown on foreign substrates and GaN Schottky diodes,13–15 recently, at least three different studies reported impact ionization coefficient estimation using p–n junctions, which relies on avalanche multiplication.9–11 All three of these studies applied photomultiplication-based approaches to determine impact ionization coefficients of the carriers (with α and β representing the electrons and holes, respectively) in GaN. We adopted a photomultiplication method by illuminating the p–i–n and n–i–p structures to trigger electron-initiated and hole-initiated impact ionization process, respectively. The impact ionization coefficients of electrons and holes can be calculated by characterizing the avalanche multiplication of each carrier.9 Cao et al. took the photomultiplication approach and implemented it on a p-i-n structure with an InGaN insert layer as the hole injection layer.10 The impact ionization coefficients were calculated by assuming a uniformly distributed electric field in the p–i–n structure. Maeda et al. adopted p-i-n structures in their study and relied on the Franz-Keldysh effect to realize hole injection in the buried junction interface.11 

The estimated ionization coefficients using photomultiplication-based approaches are listed in Table I and are plotted in Fig. 1.

TABLE I.

Estimated impact ionization coefficients in GaN.

α (cm−1)β (cm−1)
Ji et al.9  2.11 × 109exp(−3.689 × 107/E) 4.39 × 106exp(−1.8 × 107/E) 
Cao et al.10  4.48 × 108exp(−3.39 × 107/E) 7.13 × 106exp(−1.46 × 107/E) 
Maeda et al.11  2.69 × 107exp(−2.27 × 107/E) 4.32 × 106exp(−1.31 × 107/E) 
α (cm−1)β (cm−1)
Ji et al.9  2.11 × 109exp(−3.689 × 107/E) 4.39 × 106exp(−1.8 × 107/E) 
Cao et al.10  4.48 × 108exp(−3.39 × 107/E) 7.13 × 106exp(−1.46 × 107/E) 
Maeda et al.11  2.69 × 107exp(−2.27 × 107/E) 4.32 × 106exp(−1.31 × 107/E) 
FIG. 1.

Impact ionization coefficients of electrons (α) and holes (β) in GaN from studies using photomultiplication-based approaches.9–11 

FIG. 1.

Impact ionization coefficients of electrons (α) and holes (β) in GaN from studies using photomultiplication-based approaches.9–11 

Close modal

Based on the impact ionization coefficients from Ref. 9, one can calculate the breakdown electric field by solving the impact ionization integration equations in p–n junctions where the upper limit of the integral is set by the distance that the carriers can travel generating electron–hole pairs (EHPs) through multiplication,16 

0Wαexp[0xαβdx]dx=1
(1)
0Wβexp[xwβαdx]dx=1.
(2)
W=2BVEC,
(3)
Nd=εsEC22qBV,
(4)

where W = Depletion width, EC = critical electric field, Nd = donor density, BV = breakdown voltage, εs = permittivity of the semiconductor and q=electronic charge.

Equations (1) and (2) can be solved to determine avalanche condition for any device structure with arbitrary electric field profiles. Devices that are limited by avalanche (such as power diodes and transistors) or dependent on avalanche [such as Avalanche Photo Diodes (APDs) and impact ionization avalanche transit time (IMPATT) diodes] have completely different electric field profiles. One can classify them into two general categories: the non-punch-through (NPT) device design or the punch-through (PT) device design. The NPT design has a triangular electrical field in the high voltage region [Eqs. (3) and (4)], whereas the PT designs have trapezoidal fields to nearly rectangular (or nearly constant electric field). Vertical power devices, such as DMOS devices, are designed such that the lightly doped (voltage-bearing) region width is chosen to be close to but larger than the maximum depletion region width at reverse bias, an NPT design. In contrast, IMPATT and avalanche diodes operate in the PT mode with a nearly constant electric field. The accurate solutions of Eq. (1) and (2) reveal two very important but non-intuitive design guidelines. NPT designs in GaN avalanche at a voltage lower than the voltage at which the maximum critical field is reached, whereas PT designs avalanche at a voltage closer to the voltage that generates a maximum electric field. In Figs. 2(a) and 2(b), we present the maximum electric field as a function of doping, with the lightly doped region width, W, as a parameter. It is clear in Fig. 2(a) that the maximum electric field for avalanche in the thicker samples avalanches at a much lower electric field. For example, for a given doping density of 2.4 × 1015 cm−3, by solving Eq. (1), we found a fully depleted drift region thickness in an NPT design to be close to 50 μm. This corresponds to an avalanche electric field of 2.5 MV/cm. Keeping doping the same, if we reduce the drift region thickness to achieve the PT design, then for the 1-μm-thick drift region, a higher electric field value (∼3MV/cm) would be required to reach the avalanche condition.

FIG. 2.

(a) Electric field for avalanche and (b) avalanche breakdown voltage of GaN pn junctions with different drift region thicknesses (1 μm, 5 μm, 10 μm, 20 μm, and 50 μm) as a function of doping concentration. These figures are based on data from Ref. 9.

FIG. 2.

(a) Electric field for avalanche and (b) avalanche breakdown voltage of GaN pn junctions with different drift region thicknesses (1 μm, 5 μm, 10 μm, 20 μm, and 50 μm) as a function of doping concentration. These figures are based on data from Ref. 9.

Close modal

Obviously, it is critical that the correct value of α and β as a function of electric field is used to solve Eqs. (1) and (2) and produce the plots in Figs. 2(a) and 2(b) in conjunction with Eqs. (3) and(4). This work is important to get a realistic estimation of the benefits of GaN in and a design guide for vertical power electronic devices. This is more fundamental than optimizing device structures utilizing guard rings and field plates to suppress spurious high electric fields and minimizing dislocations, which can reduce the operating voltage even further and, hence, have to be independently pursued. We have previously estimated experimentally and reported our measurements of α and β using carefully designed n–i–p and p–i–n structures, where the intrinsic avalanche regions had a constant electric field. Electrons and holes were separately injected to trigger the avalanche in the (p–i–n) and (n–i–p) structures independently.

Next, we will go over defining an αeff in GaN avoiding any simplification often used in Si, where the simplification suggests α = β=αeff. For mathematical generality, Fulop's power law approximation can be used in this context to simplify the analysis of avalanche breakdown in GaN.17 Although it might not seem consequential from the physics point of view, this mathematical treatment is beneficial for performing analytical derivations for GaN device designs. By introducing an effective impact ionization coefficient, αeff, which represents the combined impact ionization effects of both electrons and holes, the impact ionization integration equations, as shown in Eqs. (1) and (2), can be simplified as

0Wαeffdx=1,
(5)

where

αeff=0.5×αexp[0xαβdx]+βexp[xwβαdx].
(6)

By plotting αeff as a function of electric field (E) on a log –log scale, a power law expression of αeff can be obtained by linearly fitting the curve, as shown in Fig. 3. The power law expression of αeff as a function of temperature can be written as

αeff=5×10551+0.001×T3005E9.
(7)
FIG. 3.

Effective impact ionization coefficients follow the power law extracted from Ref. 9. Solid curves indicate the data from Ref. 18, which assumes α = β.

FIG. 3.

Effective impact ionization coefficients follow the power law extracted from Ref. 9. Solid curves indicate the data from Ref. 18, which assumes α = β.

Close modal

Temperature-dependent αeff values, which were extracted from our previous study, are shown in Fig. 3.

In this section, we will discuss the importance of a uniform electroluminescence (EL) as a signature of multiplication, which can be extended to define robust avalanche. As a direct bandgap semiconductor, the EL is another notable phenomenon during avalanche, under which situation both hot electrons and holes are present. The EL in the semi-insulating GaN films grown on sapphire substrates under high bias was first observed in the early 1970s.19,20 EL without a positive temperature coefficient of breakdown voltage suggests multiplication over avalanche. For GaN devices grown on bulk GaN substrates, Mandal et al. reported the sign of bright EL in GaN p-n diodes during avalanche breakdown,21 which was validated by temperature-dependent measurements.

The EL observation, along with the positive temperature coefficient of the breakdown, served as a certain evidence of the avalanche condition in GaN. Since that observation, we have paid a lot of attention on studying the EL during the breakdown. Uniformity of avalanche breakdown can be verified through investigation of reverse-bias current–voltage (IV) curves and of images of breakdown EL, as shown in Fig. 4].8 Single or a couple of EL spots resulting from material defects in p-n diodes indicate local avalanching. Diodes with uniform avalanches showed a uniform rim of light, which we characterize as uniform avalanche. A very high power can be dissipated in reverse-biased devices without irreversible degradation if the avalanche in the bulk material is reached and sustained. Degradation at higher dissipated power can lead to the failure of the Ohmic contacts. A simple and reliable technique to verify the breakdown uniformity is observation of the images of breakdown luminescence along with the positive temperature coefficient of breakdown. The breakdown EL in wurtzite GaN originates from band-to-band recombination of hot electrons and holes, and its intensity is approximately proportional to the density of breakdown current. In the presence of Mg, which is a deep acceptor in GaN, the EL spectrum peaks with a wavelength of 410 nm. When GaN is grown on foreign substrates, no robust avalanche has been ever reported. From our studies, we conclude that the presence of low-defect density material and field management using the edge termination technique are necessary to support a uniform avalanche multiplication in these diodes.

FIG. 4.

Images of avalanche-induced electroluminescence in the GaN p–n diodes with (a) uniform electric field distribution and (b) non-uniform electric field distribution.

FIG. 4.

Images of avalanche-induced electroluminescence in the GaN p–n diodes with (a) uniform electric field distribution and (b) non-uniform electric field distribution.

Close modal

Besides power devices where avalanche rating is considered to be a benchmark and often a desired quality, there are at least two other well-known applications we will be discussing here: (1) avalanche photodiodes (APDs)8,22–26 and (2) impact ionization avalanche transit time (IMPATT) diodes.27–31 

The dominant device for UV light detection is still photomultiplier tube. Although photomultiplier tubes have high sensitivity for UV light detections, the short lifetime and high cost make them less attractive compared to semiconductor-based devices. Wide bandgap semiconductors, such as GaN, AlGaN, and SiC, are promising material candidates for UV light detectors. Depending on the bandgap energy, GaN and SiC are candidates for the UVA light (315 nm–400 nm) detections; AlxGa1−xN and AlN are candidates for UVB (280 nm–315 nm) and UVC (200 nm–280 nm) detections. AlxGa1-xN is particularly attractive due to the flexible bandgap engineering: the bandgap of the material can be adjusted from 3.4 eV to 6.0 eV, which correspond to the bandgap energies of GaN and AlN, respectively.

Unlike silicon and SiC, the avalanche in GaN was not reported until 20131 Although the concepts of GaN-based APDs were reported,22–26 the confirmation of “avalanche” by measuring the positive temperature coefficient of its breakdown was lacking. In a recent study reported by our group,8 we demonstrated a GaN-based APD with a robust avalanche capability. A positive temperature coefficient of the breakdown voltage (0.1 V/°C) and an avalanche induced EL were observed, both confirmed the avalanche capability of the device.

Figure 5(a) shows the schematic illustration of the GaN-based APD, which features with a free-standing GaN substrate. The temperature-dependent reverse I–V characteristics are shown in Fig. 5(b). Figure 5(c) shows the reverse I-V characteristics of the device measured in the dark environment and under UV light illumination. The photoresponsivity of the GaN APD peaks at a wavelength from 350 nm to 370 nm [as shown in Fig. 5(d)]. Under a reverse bias of 280 V, where avalanche occurs, the device showed a high responsivity of 60 A/W [Fig. 5(e)]. The gain of the APD as a function of reverse voltage is plotted in Fig. 5(f) following conventions used in Si APDs.32 

FIG. 5.

(a) Schematic of the fabricated APD; (b) the temperature-dependent reverse I–V characteristics; (c) the I–V characteristics under UV illumination; (d) the responsivity of the device; (e) the responsivity of the device under different reverse biases; (f) A plot of gain in the GaN APD as a function of reverse voltage. Part of the data are from our published work.8 

FIG. 5.

(a) Schematic of the fabricated APD; (b) the temperature-dependent reverse I–V characteristics; (c) the I–V characteristics under UV illumination; (d) the responsivity of the device; (e) the responsivity of the device under different reverse biases; (f) A plot of gain in the GaN APD as a function of reverse voltage. Part of the data are from our published work.8 

Close modal

Another feature of the GaN APDs is the high-temperature applications. As a wide bandgap semiconductor, GaN can sustain much higher temperature than Si and other narrower bandgap materials. Figure 6 compares the dark current of GaN, Si, and InGaAs-based APDs at different measurement temperatures. The temperature coefficients of the dark currents of the GaN APD is 1.006 times/°C, which is smaller than that of Si and InGaAs-based devices, the values of which are 1.1 and 1.07 times/°C, respectively.33,34

FIG. 6.

Comparison of dark current densities as a function of temperature of GaN, Si, and InGaAs APDs.33,34

FIG. 6.

Comparison of dark current densities as a function of temperature of GaN, Si, and InGaAs APDs.33,34

Close modal

The other application of the avalanche can be realized through IMPATT diodes. IMPATT diodes based on Si and GaAs have been used for RF generators at frequencies between 0.3 GHz and 300 GHz,27–31 which are widely used in radar and communication systems. According to Johnson's figure of merit,35 GaN shows potential for more powerful IMPATT diodes with power density 10× higher than Si. RF reflection gain in avalanche GaN diodes at frequencies > 350MHz was reported.36 Simulations showed GaN as an ideal candidate for W-band MPATT diodes.37 

Taking the advantage of the free-standing substrate, we have recently demonstrated a GaN IMPATT diode.38 A robust avalanche capability was confirmed by the positive temperature coefficient of breakdown voltage and the observation of avalanche-induced EL. The measured resonant frequency of the diode is 0.8 GHz. The resonator and the output power spectrum are shown in Fig. 7.

FIG. 7.

(a) A resonator based on the GaN IMPATT diode and (b) the output power spectrum of the diode. This figure is adopted from our published work.38 

FIG. 7.

(a) A resonator based on the GaN IMPATT diode and (b) the output power spectrum of the diode. This figure is adopted from our published work.38 

Close modal

The resonant frequency of an IMPATT diode can be found from the following equation:39 

ωa=2mI0ϵAτEC1/2,
(8)

where m is a parameter from the impact ionization coefficients, I0 is the average current, A is the device area, τ is the carrier's transport time in the high field region, and EC is the critical electric field. In our study, the device was unpackaged, and no heat sink was present; the avalanche current density was limited to the order of 1 A/cm2, which limited the resonant frequency. A resonant frequency on the order of 10 GHz could be expected with an avalanche current density of hundreds A/cm2.

In summary, we present a discussion on avalanche breakdown limits in epitaxial p-n diodes in wurtzite GaN grown using the MOCVD technique onto commercially available substrates. Using appropriate device termination, both breakdown stability and avalanche conditions were repeatedly observed in these devices. Uniformity of avalanche breakdown could be confirmed from EL observations along with positive temperature breakdown coefficients. This discussion underscores GaN's potential to offer high power devices with avalanche ruggedness. The drift region has been discussed under punch-through and non-punch-through design considerations using the experimentally measured impact ionization data.

The authors would like to acknowledge the support of Dr. Isik Kizilyalli (ARPA-E SWITCHES) and Mr. Lynn Petersen (ONR) for the high voltage diode work, and Dr. Paul Maki (ONR) for the study on high frequency applications. The authors would like to thank Siwei Li for the measurement shown in Fig. 4(b).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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