In this study, we experimentally determined the impact ionization coefficients of GaN using homoepitaxially grown p-n diodes with avalanche capability. The extracted hole impact ionization coefficient is obtained as β(E) = 4.39 × 106 exp (−1.8 × 107/E) cm−1, and the electron impact ionization coefficient is obtained as α(E) = 2.11 × 109 exp (−3.689 × 107/E) cm−1. This study also presents the temperature dependence of impact ionization coefficients in GaN. The results presented in this experimental study are an important contribution to the database on the material properties of GaN, which will enable more accurate prediction of the avalanche in GaN devices.

While Si is showing only incremental improvement,1 wide bandgap materials with superior properties, such as the high breakdown electric field, high mobility, and high temperature stability, are looking more practical in various power converters due to their higher converter efficiency, faster speed, and higher operating temperature.2,3 Owing to their potential of rendering a power density of 100× compared to Si, silicon carbide (SiC) and gallium nitride (GaN) are being explored as power switches.4–6 The material properties of SiC have been studied in depth compared to GaN revealing important results, including determining impact ionization coefficients. The availability of high-quality SiC wafers has helped such successful studies.

Prior to the availability of high-quality freestanding GaN substrates, studies done on impact ionization did not yield repeatable results. However, recent progress in the material growth and substrate technology has demonstrated avalanche capability in GaN vertical devices.7–9 Kunihiro et al.10 reported impact ionization in AlGaN/GaN HEMT structures, and Ozbek11 reported impact ionization in GaN using Schottky diodes. More recently, Cao et al.12 reported the impact ionization behavior of GaN based on p-n junctions using In0.07Ga0.93N as the hole injection layer. In this study, impact ionization coefficients of electrons and holes in GaN were determined using a different approach that utilized activated buried p-GaN layers, where both n-p diodes (NPDs) and p-n diodes (PNDs) were used for the measurement and analysis.

Figure 1(a) shows the schematic of the NPD. The epitaxial structure included a 1-μm-thick heavily doped p+ GaN layer (Mg: 5 × 1019 cm−3) grown on a single crystalline GaN substrate. This was followed by a 1.2-μm-thick GaN layer and then by a 200-nm-thick n+ GaN. The doping concentrations obtained by SIMS and C-V measurements are shown in Figs. 1(b) and 1(c). Based on the SIMS analysis, the drift region contained Si at a doping density between 1 × 1016 cm−3 and 2 × 1016 cm−3 along with both Mg and H ions around 2 × 1017 cm−3. The buried p+ GaN was activated by diffusing out hydrogen through sidewalls, reported in Refs. 13 and 14, and demonstrated in this study as well. The measured sheet resistance was 7 × 104 Ω/sq (7 Ω cm), which is in the range for p-type GaN. The Ti/Au and Ni/Au stacks were deposited by E-beam evaporation to form the cathode and anode electrodes, respectively.

FIG. 1.

Schematic illustration of the designed devices: (a) schematic of the NPD with a buried p-GaN layer; (b) the doping concentration of the NPD structure obtained by SIMS; (c) the carrier concentration (n) obtained by C-V analysis; (d) the schematic of the PND with a top p-GaN layer; (e) the doping concentration of the PND structure obtained by SIMS; and (d) the carrier concentration (n) obtained by C-V analysis. In the NPD structure, all the Mg ions in the drift region were compensated by H ions, and therefore, they do not contribute to the charge distribution in the drift region.

FIG. 1.

Schematic illustration of the designed devices: (a) schematic of the NPD with a buried p-GaN layer; (b) the doping concentration of the NPD structure obtained by SIMS; (c) the carrier concentration (n) obtained by C-V analysis; (d) the schematic of the PND with a top p-GaN layer; (e) the doping concentration of the PND structure obtained by SIMS; and (d) the carrier concentration (n) obtained by C-V analysis. In the NPD structure, all the Mg ions in the drift region were compensated by H ions, and therefore, they do not contribute to the charge distribution in the drift region.

Close modal

Figure 1(d) shows the schematic of the PND. The epitaxial growth began with an n+ contact layer doped at 5 × 1018 cm−3 grown on a single-crystalline GaN substrate, followed by a 1.2 μm thick n-GaN (Si: 2.2 × 1017 cm−3), capped by a 200-nm-thick heavily doped p+ GaN layer. Figures 1(e) and 1(f) show the doping concentration of the drift region obtained by SIMS and C-V measurements. The activation of p-GaN was achieved by rapid thermal annealing at a temperature of 750 °C. The cathode and anode electrodes were again formed by Ti/Au and Ni/Au metal stacks.

The impact ionization coefficients of both the hole and the electron were measured using the ultraviolet light (UVL) assisted method.15,16 According to Monte Carlo simulation,17 the hole has a much higher impact ionization coefficient than the electron when the electric field is less than 2.5 MV/cm. In this field range, the electron-initiated multiplication can be considered negligible.

To measure the hole-initiated impact ionization multiplication, a UV laser with a wavelength of 350 nm was used to generate electron-hole pairs in the top n+ GaN layer in the NPD. For the UVL with a wavelength of 350 nm, the absorption coefficient in GaN is about 8 × 104 cm−1.18 The thicknesses of top n+ GaN and p+ GaN layers in NPD and PND are 200 nm, ensuring that the UVL is absorbed in the top layers. When the NPD was reverse biased, only UVL generated holes were swept into the space charge region, while the UVL generated electrons were collected by the cathode.19 The UVL generated holes passed through the high electric field region and gained enough kinetic energy to knock a bound electron out of the valence band to the conduction band, creating an electron-hole pair by the impact ionization process. By measuring the current at high reverse bias voltage close to the breakdown voltage, the multiplication of the hole was observed, and the hole's impact ionization coefficient was calculated.

The PND was used to measure the electron-initiated impact ionization multiplication and coefficient. Under the UV illumination, UVL generated holes were collected by the anode, and the UVL generated electrons were swept into the space charge region to initiate the impact ionization process.19 The electron's impact ionization coefficient was obtained by measuring the reverse current due to the avalanche.

Figure 2(a) shows the temperature-dependent reverse breakdown characteristics of the NPD, which shows the positive temperature coefficient as expected for avalanche breakdown. These reverse I-V characteristics were recoverable and repeatable. Figure 2(b) shows the reverse I-V characteristics of NPDs with different device areas, which indicates the revere current scaling well with the device area. Figure 2(c) shows the temperature dependent reverse characteristics of the PND, from which a positive temperature coefficient was observed. The reverse current of the PND scaled well with the device area, as shown in Fig. 2(d).

FIG. 2.

(a) Measured reverse current of the NPD at different temperatures; the device has a circular layout with a diameter of 100 μm; (b) reverse I-V characteristics of NPDs with different device areas; (c) measured reverse current of the PND at different temperatures; the device has a circular layout with a diameter of 200 μm; and (d) reverse I-V characteristics of PNDs with different device areas. The reverse blocking voltage at which the current shows a significant increase due to multiplication shows a positive temperature coefficient, indicating avalanche.

FIG. 2.

(a) Measured reverse current of the NPD at different temperatures; the device has a circular layout with a diameter of 100 μm; (b) reverse I-V characteristics of NPDs with different device areas; (c) measured reverse current of the PND at different temperatures; the device has a circular layout with a diameter of 200 μm; and (d) reverse I-V characteristics of PNDs with different device areas. The reverse blocking voltage at which the current shows a significant increase due to multiplication shows a positive temperature coefficient, indicating avalanche.

Close modal

Figure 3(a) shows the reverse characteristics of the NPD under the dark condition and UV illumination, respectively. Under a high electric field, the hole-initiated multiplication (Mp) can be obtained by (IUVIdark)/(IUV,Init), where IUV,Init is the initial photocurrent. The hole-initiated multiplication as a function of the electric field is shown in Fig. 3(b); when the electric field is over 1.5 MV/cm, carrier multiplication occurs, which is close to the recently reported value.12 

FIG. 3.

Measured multiplication by the UVL assisted method: (a) I-V characteristics of the NPD measured under UV illumination and dark; (b) the measured hole-initiated multiplication as a function of the electric field; (c) I-V characteristics of the PND measured under UV illumination and dark conditions, respectively; (d) the measured electron-initiated multiplication as a function of the electric field.

FIG. 3.

Measured multiplication by the UVL assisted method: (a) I-V characteristics of the NPD measured under UV illumination and dark; (b) the measured hole-initiated multiplication as a function of the electric field; (c) I-V characteristics of the PND measured under UV illumination and dark conditions, respectively; (d) the measured electron-initiated multiplication as a function of the electric field.

Close modal

The reverse characteristics of the fabricated PND under the dark condition and UV illumination are shown in Fig. 3(c). The initial current was determined by the linear extrapolation method to consider the increasing depletion layer under reverse bias.15 The electron-initiated multiplication is shown in Fig. 3(d).

In the NPD, the Mg ions (∼2 × 1017 cm−3) in the drift region were compensated by H (∼2 × 1017 cm−3) completely [as shown in Fig. 1(b)], giving the net charge density of about 1016 cm−3, as measured by the C-V measurement. Therefore, the electric field was uniformly set in the drift region within an error of less than 10%. No significant effect on hole-initiated impact ionization by the neutral Mg-H complexes was assumed in this study. The hole impact ionization coefficient can be written as a function of multiplication Mp and the space charge region length W,

β=lnMpW.
(1)

The calculated hole impact ionization coefficient as a function of the reverse electric field is shown in Fig. 4(a). The exponential fit to the hole impact ionization coefficient using Chynoweth's law yields

βE=4.39×106e1.8×1071Ecm1,
(2)

where the electric field E has a unit of volts per centimeter.

FIG. 4.

Experimentally determined impact ionization coefficients in GaN: (a) hole impact ionization coefficient in GaN; (b) electron impact ionization coefficient. The symbols represent the experimentally determined data, and the solid curves represent the fitted data using Chynoweth's law.

FIG. 4.

Experimentally determined impact ionization coefficients in GaN: (a) hole impact ionization coefficient in GaN; (b) electron impact ionization coefficient. The symbols represent the experimentally determined data, and the solid curves represent the fitted data using Chynoweth's law.

Close modal

In the PND, since the doping density in the drift region was 2.2 × 1017 cm−3, it created a triangular electric field distribution over the drift region, the electron impact ionization coefficient can be therefore written as

α=qNDε0εs1MndMndEmMn1βEm.
(3)

By using Eq. (3), the electron impact ionization coefficient was calculated. The electron impact ionization coefficient can be written as a function of the electric field

αE=2.11×109e3.689×1071Ecm1.
(4)

The measured electron impact ionization coefficient is shown in Fig. 4(b).

Following the technique used in the extraction of α and β in SiC,15 in this study, β was experimentally obtained in a limited electric field range and then projected to the entire electric field range using Chynoweth's law. Based on the projected β, α can be extracted using Eq. (3). The key feature of this method was to separate the hole- and electron-initiated impact ionization using the electric field in the drift region.

To validate our analysis, the multiplication factor and photocurrent in the NPD and PND structures were calculated by solving the following two equations numerically, where α and β appear inside the integral:

11Mp=0Wβe0xβαdxdx,
(5)

and

11Mn=0WαexWαβdxdx,
(6)

where α and β were the extrapolated values from the experimental set of data, stretching over the entire range of the electric field. Mn and Mp obtained from the solution were then used to calculate the photocurrent, as shown in Figs. 5(a) and 5(b).

FIG. 5.

(a) Comparison of the measured photocurrent in the NPD structure with the calculated photocurrent using obtained impact ionization coefficients; (b) comparison of the measured photocurrent in the PND structure with the calculated photocurrent using the obtained impact ionization coefficients. The symbols represent the experimentally determined data, and the solid curves represent the calculated data by using α and β values given by Eqs. (2) and (4).

FIG. 5.

(a) Comparison of the measured photocurrent in the NPD structure with the calculated photocurrent using obtained impact ionization coefficients; (b) comparison of the measured photocurrent in the PND structure with the calculated photocurrent using the obtained impact ionization coefficients. The symbols represent the experimentally determined data, and the solid curves represent the calculated data by using α and β values given by Eqs. (2) and (4).

Close modal

The measured and calculated photocurrents in both NPD and PND have been overlaid for comparison. The close agreement between the calculated and measured photocurrent in the two device structures proves the accuracy of the present study. It is important to note that using the most general form of the multiplication equations [Eqs. (5) and (6)], we can accurately reproduce the photocurrent. The validation process in essence proves the correctness of the initial assumption of β > α under a low electric field.

In conclusion, this paper presents a systematic experimental study on impact ionization coefficients in GaN using homoepitaxially grown p-n diodes on GaN substrates. By using NPD and PND structures, both hole and electron impact ionization coefficients of GaN were experimentally determined. The hole impact ionization coefficient obtained in this study can be written as β(E) = 4.39 × 106 exp (−1.8 × 107/E) cm−1, and the electron impact ionization coefficient can be written as α(E) = 2.11 × 109 exp (−3.689 × 107/E) cm−1. Furthermore, the temperature dependent impact ionization coefficients in GaN were analyzed. Using the impact ionization coefficients derived from this study, photocurrent in the two devices as a function of reverse bias was reproduced, which indicates the accuracy of this study. The impact ionization coefficients that we obtained are close to the values reported by the Monte Carlo method.17 This study is therefore a valuable contribution to establishing reliable material properties of GaN.

This work was funded by the ARPA-E SWITCHES program. We are thankful to Dr. Isik Kizilyalli, Professor J. Plummer, and Professor U. K. Mishra for very productive discussions on impact ionization studies done on various semiconductor systems.

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