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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Phys.</journal-id>
<journal-title>Frontiers in Physics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Phys.</abbrev-journal-title>
<issn pub-type="epub">2296-424X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1084214</article-id>
<article-id pub-id-type="doi">10.3389/fphy.2022.1084214</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Physics</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Analysis of electrical properties in lateral Schottky barrier diode based on n-GaN and AlGaN/GaN heterostructure</article-title>
<alt-title alt-title-type="left-running-head">Liu et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphy.2022.1084214">10.3389/fphy.2022.1084214</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Liu</surname>
<given-names>Honghui</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/2066785/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Liang</surname>
<given-names>Zhiwen</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Fengge</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Xu</surname>
<given-names>Yanyan</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yang</surname>
<given-names>Xien</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1430526/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Liang</surname>
<given-names>Yisheng</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Xin</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/2080724/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Lin</surname>
<given-names>Lizhang</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wu</surname>
<given-names>Zhisheng</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Liu</surname>
<given-names>Yang</given-names>
</name>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Zhang</surname>
<given-names>Baijun</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
</contrib>
</contrib-group>
<aff>
<institution>State Key Laboratory of Optoelectronic Materials and Technologies</institution>, <institution>School of Electronics and Information Technology</institution>, <institution>Sun Yat-sen University</institution>, <addr-line>Guangzhou</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1625613/overview">Ye Yuan</ext-link>, Songshan Lake Material Laboratory, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2078609/overview">Liuan Li</ext-link>, Jilin University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2080419/overview">Liang He</ext-link>, No.5 Electronics Research Institute of the Ministry of Industry and Information Technology, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Baijun Zhang, <email>zhbaij@mail.sysu.edu.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Interdisciplinary Physics, a section of the journal Frontiers in Physics</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>21</day>
<month>11</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>1084214</elocation-id>
<history>
<date date-type="received">
<day>30</day>
<month>10</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>11</day>
<month>11</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Liu, Liang, Wang, Xu, Yang, Liang, Li, Lin, Wu, Liu and Zhang.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Liu, Liang, Wang, Xu, Yang, Liang, Li, Lin, Wu, Liu and Zhang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>In this paper, the lateral Schottky barrier diodes (SBDs) with small capacitance and low turn-on voltage (<italic>V</italic>
<sub>
<italic>on</italic>
</sub>) were fabricated on n-GaN and AlGaN/GaN heterostructure. The capacitances of lateral n-GaN SBD and lateral AlGaN/GaN SBD are 1.35&#xa0;pF/mm and 0.70&#xa0;pF/mm, respectively. Compared with the planar SBDs, the capacitances of lateral SBDs are reduced by about two orders of magnitude without sacrificing the performance of on-resistance (<italic>R</italic>
<sub>
<italic>on</italic>
</sub>) and reverse leakage current. For the planar and lateral n-GaN SBDs, the value of the <italic>V</italic>
<sub>
<italic>on</italic>
</sub> is similar. However, compared with the planar AlGaN/GaN SBD, the <italic>V</italic>
<sub>
<italic>on</italic>
</sub> of lateral AlGaN/GaN SBD is reduced from 1.64 V to 0.87&#xa0;V owing to the anode metal directly contacting the two-dimensional electron gas. According to temperature-dependent <italic>I-V</italic> results, the barrier inhomogeneity of the lateral SBD is more intensive than the planar SBD, which is attributed to etching damage. The withstand voltage of SBD is a very important parameter for power electronic applications. Compared with the breakdown voltage of 73&#xa0;V in the lateral n-GaN SBD, the lateral AlGaN/GaN SBDs exhibit a breakdown voltage of 2322&#xa0;V. In addition, we found that Schottky contact introduces anode resistance (<italic>R</italic>
<sub>
<italic>A</italic>
</sub>) by analysing the <italic>R</italic>
<sub>
<italic>on</italic>
</sub> distribution of lateral SBDs. The experimental results also show that the <italic>R</italic>
<sub>
<italic>A</italic>
</sub> of lateral n-GaN SBD and lateral AlGaN/GaN SBD are 10.5&#xa0;&#x3a9;&#xa0;mm and 9.2&#xa0;&#x3a9;&#xa0;mm respectively, which are much larger than the ohmic contact resistance due to worsening anode contact by metal-induced gap states.</p>
</abstract>
<kwd-group>
<kwd>GaN</kwd>
<kwd>AlGaN/GaN</kwd>
<kwd>Schottky barrier diodes</kwd>
<kwd>metal-induced gap states</kwd>
<kwd>inhomogeneous SBHs</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>GaN-based Schottky barrier diodes (SBDs) exhibit outstanding power handling capabilities in power electronic applications [<xref ref-type="bibr" rid="B1">1</xref>, <xref ref-type="bibr" rid="B2">2</xref>] and multipliers [<xref ref-type="bibr" rid="B3">3</xref>] due to the physical properties of wide bandgap and high breakdown electric field [<xref ref-type="bibr" rid="B4">4</xref>&#x2013;<xref ref-type="bibr" rid="B6">6</xref>]. In particular, AlGaN/GaN SBDs exhibit excellent characteristics of high electron mobility and high electron density due to the 2D electron gas (2DEG) [<xref ref-type="bibr" rid="B7">7</xref>, <xref ref-type="bibr" rid="B8">8</xref>], offering wide applications for high-frequency and high-power devices [<xref ref-type="bibr" rid="B9">9</xref>, <xref ref-type="bibr" rid="B10">10</xref>]. SBD is one of the most essential components in microwave power transmission systems [<xref ref-type="bibr" rid="B3">3</xref>, <xref ref-type="bibr" rid="B10">10</xref>&#x2013;<xref ref-type="bibr" rid="B12">12</xref>]. However, the high-frequency performance of SBD requires low turn-on voltage (<italic>V</italic>
<sub>
<italic>on</italic>
</sub>) to reduce conduction loss, and high cut-off frequency to improve operating frequency. In addition, the cut-off frequency of SBD is limited by the product of capacitance and the on-resistance (<italic>R</italic>
<sub>
<italic>on</italic>
</sub>), hence reducing the anode size cannot effectively improve the cut-off frequency. Conventional planar AlGaN/GaN SBDs have undesirable high <italic>V</italic>
<sub>
<italic>on</italic>
</sub> and large capacitance. The metals (TiN, Mo, and W) of the low Schottky barrier can reduce <italic>V</italic>
<sub>
<italic>on</italic>
</sub>, which are accompanied by a higher reverse leakage current (<italic>J</italic>
<sub>
<italic>r</italic>
</sub>) [<xref ref-type="bibr" rid="B13">13</xref>&#x2013;<xref ref-type="bibr" rid="B15">15</xref>]. The recessed anode structure is an effective solution to avoid these two shortages because the 2DEG directly contacts the anode metal [<xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B17">17</xref>]. Even so, this design still has a large capacitance due to the parallel plate capacitor caused by the anode field plate (FP) and 2DEG [<xref ref-type="bibr" rid="B18">18</xref>, <xref ref-type="bibr" rid="B19">19</xref>]. Compared with the SBD of the recessed anode structure, the capacitance of the lateral SBD can be further reduced. Moreover, the lateral GaN-based SBDs also have low <italic>V</italic>
<sub>
<italic>on</italic>
</sub> because the carriers directly contact the anode metal. Many researchers have reported studies about the transport mechanism [<xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B20">20</xref>, <xref ref-type="bibr" rid="B21">21</xref>], Schottky barrier heights (SBHs) [<xref ref-type="bibr" rid="B22">22</xref>, <xref ref-type="bibr" rid="B23">23</xref>], metal-induced gap states (MIGS) [<xref ref-type="bibr" rid="B24">24</xref>&#x2013;<xref ref-type="bibr" rid="B26">26</xref>], and barrier inhomogeneity [<xref ref-type="bibr" rid="B27">27</xref>&#x2013;<xref ref-type="bibr" rid="B30">30</xref>] on planar n-GaN SBDs or AlGaN/GaN recessed-SBDs. Nevertheless, the electrical properties in lateral GaN-based SBDs are rarely reported.</p>
<p>In this paper, the strategy of lateral GaN-based SBDs was used to eliminate the FP capacitance and reduce <italic>V</italic>
<sub>
<italic>on</italic>
</sub> without sacrificing the performance of <italic>R</italic>
<sub>
<italic>on</italic>
</sub> and reverse leakage. The simulated results show the characteristics of the energy band and carrier distribution. The analysis of electrical properties in lateral GaN-based SBDs was described by current-voltage (<italic>I-V</italic>) and capacitance-voltage (<italic>C-V</italic>) characteristics. According to the results of temperature-dependent <italic>I-V</italic> measurements, the barrier inhomogeneity of the lateral SBDs is more intensive than that of planar SBDs, which is attributed to etching damage. In addition, anode resistance (<italic>R</italic>
<sub>
<italic>A</italic>
</sub>) was present, which is possibly due to the worsening anode contacts by MIGS.</p>
</sec>
<sec id="s2">
<title>Experimental details</title>
<p>The lateral GaN-based SBDs in this study were fabricated on n-GaN and AlGaN/GaN heterostructure and were shown in <xref ref-type="fig" rid="F1">Figure 1A</xref>. The wafers were grown by metal-organic chemical vapor deposition (MOCVD) on 2-inch c-sapphire substrates. The epitaxial layers consist of a &#x223c;40&#xa0;nm-thick AlN, a 4&#xa0;&#x3bc;m-thick high resistive (HR) GaN buffer layer, and a 300&#xa0;nm-thick i-GaN. Based on this template, the n-GaN and AlGaN/GaN heterostructure continued to grow 500&#xa0;nm-thick n-GaN and 24/0.7&#xa0;nm-thick Al<sub>0.25</sub>Ga<sub>0.75</sub>N/AlN, respectively. The electron mobility, electron density, and channel thickness of n-GaN and AlGaN/GaN are summarized in <xref ref-type="table" rid="T1">Table 1</xref>. The ring cathode metals (Ti/Al/Ni/Au &#x3d; 20/150/50/80&#xa0;nm) were deposited on the wafer surface by E-beam evaporation and annealed at 850&#xb0;C for 30&#xa0;s in N<sub>2</sub> ambient. Using the transfer length method (TLM), the ohmic contact resistances (<italic>R</italic>
<sub>
<italic>C</italic>
</sub>) of n-GaN and AlGaN/GaN are 0.65&#xa0;&#x3a9;&#xa0;mm and 1.13&#xa0;&#x3a9;&#xa0;mm, respectively. The anode metals (Ni/Au &#x3d; 50/80&#xa0;nm) were deposited on the wafer surface. <xref ref-type="fig" rid="F1">Figure 1B</xref> shows the cross-sectional schematic of the fabricated planar SBD. For lateral SBD, the anode region was etched to the HR GaN buffer layer by inductively coupled plasma (ICP), followed by direct deposition of anode metal to the sidewall, as shown in <xref ref-type="fig" rid="F1">Figure 1C</xref>. The diameter of the circular anode metal was 200&#xa0;&#xb5;m. The distance between the anode metal and the ring cathode metal was 40&#xa0;&#xb5;m. The <italic>I-V</italic> and <italic>C-V</italic> characteristics were measured by the Agilent B1500A at room temperature.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>
<bold>(A)</bold> Schematic illustrations of n-GaN and AlGaN/GaN SBDs with epitaxial information. The schematic cross-section of <bold>(B)</bold> planar and <bold>(C)</bold> lateral SBDs.</p>
</caption>
<graphic xlink:href="fphy-10-1084214-g001.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>The key material parameters of n-GaN and AlGaN/GaN.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left"/>
<th align="left">Electron density (cm<sup>&#x2212;3</sup>)</th>
<th align="left">Electron mobility (cm<sup>2</sup>/Vs.)</th>
<th align="left">Channel thickness (nm)</th>
<th align="left">
<italic>R</italic>
<sub>
<italic>sh</italic>
</sub> (&#x3a9;/&#x25a1;)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">n-GaN</td>
<td align="char" char="&#xd7;">3.4&#xd7;10<sup>17</sup>
</td>
<td align="left">448</td>
<td align="left">500</td>
<td align="left">786</td>
</tr>
<tr>
<td align="left">AlGaN/GaN</td>
<td align="char" char="&#xd7;">3.4&#xd7;10<sup>19</sup>
</td>
<td align="left">1969</td>
<td align="left">&#x223c;2.8</td>
<td align="left">306</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec sec-type="results|discussion" id="s3">
<title>Results and discussion</title>
<p>According to the n-GaN and AlGaN/GaN SBDs structures, the characteristics of the energy band and carrier distribution are simulated by Synopsys&#x2019; Sentaurus technology computer-aided design (TCAD), and the results are shown in <xref ref-type="fig" rid="F2">Figure 2</xref>. The depletion directions of the planar and lateral SBDs are perpendicular and parallel to the (0,001) plane, respectively. The energy band and carrier distribution are very similar between planar and lateral n-GaN SBDs because both are Ni/n-GaN contacts. The simulation results show that the sample with SBH of about 1.18&#xa0;eV has a depletion width of about 44.5&#xa0;nm for n-GaN with doping concentration of 3.4&#xd7;10<sup>17</sup>&#xa0;cm<sup>&#x2212;3</sup>, as shown in <xref ref-type="fig" rid="F2">Figures 2A,B</xref>. However, the energy band structures of the planar and lateral AlGaN/GaN SBDs are very different, as shown in <xref ref-type="fig" rid="F2">Figures 2C,D</xref>. The energy band structure of the planar AlGaN/GaN SBD displays that anode metal cannot deplete the 2DEG channel at 0&#xa0;V, and its SBH is 1.60&#xa0;eV. The 2DEG is distributed in the i-GaN layer of the AlGaN/GaN heterostructure, which is only a &#x223c;2.8&#xa0;nm-thick sheet channel. The simulation results of the energy band and carrier distribution of the lateral AlGaN/GaN SBD are shown in <xref ref-type="fig" rid="F2">Figure 2D</xref>. For lateral AlGaN/GaN SBD, the lateral contact of Ni-2DEG can be treated as SBD of a heavily doped n<sup>&#x2b;</sup>-GaN sheet channel. The Ni-2DEG forms a SBH of 1.08 eV, which only depletes 4.5&#xa0;nm 2DEG.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The energy band and carrier distribution of <bold>(A)</bold> planar n-GaN SBD, <bold>(B)</bold> lateral n-GaN SBD, <bold>(C)</bold> planar AlGaN/GaN SBD, and <bold>(D)</bold> lateral AlGaN/GaN SBD at 0&#xa0;V.</p>
</caption>
<graphic xlink:href="fphy-10-1084214-g002.tif"/>
</fig>
<p>As shown in <xref ref-type="fig" rid="F3">Figures 3A&#x2013;H</xref>, we measured the <italic>I-V</italic> and <italic>C-V</italic> characteristics of each SBD at different temperatures from 298 to 504&#xa0;K. The <italic>I-V</italic> and <italic>C-V</italic> curves conform to traditional SBD depletion characteristics for planar n-GaN SBD, lateral n-GaN SBD, and lateral AlGaN/GaN SBD. However, the <italic>I-V</italic> and <italic>C-V</italic> curves of the planar AlGaN/GaN SBD are different from the characteristics of traditional SBD depletion. Because anode metal and 2DEG channel are separated by AlGaN barrier layer. The <italic>V</italic>
<sub>
<italic>on</italic>
</sub> of the planar AlGaN/GaN SBD is as high as 1.64&#xa0;V since the device conduction requires electrons to pass through the AlGaN barrier layer, while the other three devices show very low <italic>V</italic>
<sub>
<italic>on</italic>
</sub> because electrons only need to overcome the barriers to flow to the anode. The <italic>J</italic>
<sub>
<italic>r</italic>
</sub> of the planar AlGaN/GaN SBD reaches saturation at pinch-off voltage (-4.2&#xa0;V) due to 2DEG depletion, as shown in <xref ref-type="fig" rid="F3">Figure 3C</xref>. The capacitance characteristic of planar AlGaN/GaN SBD is fitted to the parallel plate capacitor model of the anode metal and 2DEG [<xref ref-type="bibr" rid="B18">18</xref>]. At lower reverse bias voltage, the planar AlGaN/GaN SBD maintains a stable capacitance value due to the characteristics of parallel plate capacitors. With increasing reverse bias voltage, the 2DEG is gradually depleted, which causes the capacitance to drop rapidly due to the disappearance of the plate capacitor. At higher reverse bias voltage, the capacitance tends to zero, the 2DEG is completely depleted, as shown in <xref ref-type="fig" rid="F3">Figure 3G</xref>. The capacitance approaching zero also shows the HR characteristics of the buffer layer. The n-GaN and AlGaN/GaN SBDs of different FP widths are measured, the values of zero bias capacitance are linear with the area of the FP, so the lateral SBD without FP can effectively eliminate the FP capacitance. Compared with the planar SBDs, the capacitances of the lateral SBDs are reduced by two orders of magnitude without sacrificing the performance of the <italic>R</italic>
<sub>
<italic>on</italic>
</sub> and <italic>J</italic>
<sub>
<italic>r</italic>
</sub>. This is attributed to two characteristics of lateral SBDs: the small anode area and the elimination of spreading resistance under the anode metal. The capacitances of lateral n-GaN SBD and lateral AlGaN/GaN SBD are 1.35&#xa0;pF/mm and 0.70&#xa0;pF/mm, respectively.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>The <italic>I-V</italic> <bold>(A&#x2013;D)</bold> and <italic>C-V</italic> <bold>(E&#x2013;H)</bold> characteristics of planar n-GaN SBD, lateral n-GaN SBD, planar AlGaN/GaN SBD, and lateral AlGaN/GaN SBD at temperatures of 504&#xa0;K, 474&#xa0;K, 429&#xa0;K, 399&#xa0;K, 364&#xa0;K, 324&#xa0;K and 298&#xa0;K.</p>
</caption>
<graphic xlink:href="fphy-10-1084214-g003.tif"/>
</fig>
<p>In order to extract the SBH <italic>&#x3a6;</italic>
<sub>
<italic>B</italic>
</sub>, the ideality factor <italic>n</italic>, and the <italic>R</italic>
<sub>
<italic>on</italic>
</sub> from the <italic>I-V</italic> curve, the thermionic emission (TE) can be described as the major forward current contribution [<xref ref-type="bibr" rid="B28">28</xref>, <xref ref-type="bibr" rid="B31">31</xref>],<disp-formula id="e1">
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<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">n</mml:mi>
<mml:mi mathvariant="bold-italic">k</mml:mi>
<mml:mi mathvariant="bold-italic">T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <italic>A</italic> is the area of the anode metal, <italic>A</italic>
<sup>
<italic>&#x2a;</italic>
</sup> is the effective Richardson constant (226.4&#xa0;Acm<sup>&#x2212;2</sup>K<sup>&#x2212;2</sup>), <italic>k</italic> is the Boltzmann constant, and <italic>T</italic> is the temperature. From the <italic>I-V</italic> and <italic>C-V</italic> curves at room temperature, the device parameters of each SBD are summarized in <xref ref-type="table" rid="T2">Table 2</xref>. The SBHs extracted by the <italic>I-V</italic> characteristics are lower than the simulation results, which may be due to electron tunneling and inhomogeneity SBHs [<xref ref-type="bibr" rid="B27">27</xref>&#x2013;<xref ref-type="bibr" rid="B29">29</xref>]. The ideality factors of each SBD are larger than 1, which indicates that in addition to TE, other transport mechanisms include thermionic field emission (TFE) and field emission (FE) [<xref ref-type="bibr" rid="B32">32</xref>, <xref ref-type="bibr" rid="B33">33</xref>]. For planar AlGaN/GaN SBD, the ideality factor of &#x223c;2 illustrates the existence of various transport types other than TE, such as trap-assisted tunneling (TAT) and recombination [<xref ref-type="bibr" rid="B34">34</xref>].</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>The electrical characteristics of n-GaN SBDs and AlGaN/GaN SBDs at room temperature.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left"/>
<th colspan="2" align="left">n-GaN</th>
<th colspan="2" align="left">AlGaN/GaN</th>
</tr>
<tr>
<th align="left">Planar SBD</th>
<th align="left">Lateral SBD</th>
<th align="left">Planar SBD</th>
<th align="left">Lateral SBD</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">
<italic>V</italic>
<sub>
<italic>on</italic>
</sub> (V)</td>
<td align="left">0.72</td>
<td align="left">0.83</td>
<td align="left">1.64</td>
<td align="left">0.87</td>
</tr>
<tr>
<td align="left">Capacitance at 0&#xa0;V (pF)</td>
<td align="left">65.89</td>
<td align="left">0.85</td>
<td align="left">104.24</td>
<td align="left">0.44</td>
</tr>
<tr>
<td align="left">Leakage current at -15&#xa0;V (A)</td>
<td align="left">4.79 &#xd7; 10<sup>&#x2212;5</sup>
</td>
<td align="left">8.54 &#xd7; 10<sup>&#x2212;7</sup>
</td>
<td align="left">2.88 &#xd7; 10<sup>&#x2212;8</sup>
</td>
<td align="left">2.27 &#xd7; 10<sup>&#x2212;7</sup>
</td>
</tr>
<tr>
<td align="left">SBH<sub>(<italic>I-V</italic>)</sub> (eV)</td>
<td align="left">0.83</td>
<td align="left">0.91</td>
<td align="left">1.15</td>
<td align="left">0.84</td>
</tr>
<tr>
<td align="left">SBH<sub>(<italic>simulated</italic>)</sub> (eV)</td>
<td align="left">1.19</td>
<td align="left">1.16</td>
<td align="left">1.60</td>
<td align="left">1.08</td>
</tr>
<tr>
<td align="left">Ideality factor</td>
<td align="left">1.21</td>
<td align="left">1.34</td>
<td align="left">1.99</td>
<td align="left">1.58</td>
</tr>
<tr>
<td align="left">
<italic>R</italic>
<sub>
<italic>on</italic>
</sub> (&#x3a9;)</td>
<td align="left">55.1</td>
<td align="left">32.9</td>
<td align="left">62.4</td>
<td align="left">59.5</td>
</tr>
<tr>
<td align="left">
<italic>R</italic>
<sub>
<italic>A</italic>
</sub> (&#x3a9;&#xb7;mm)</td>
<td align="left">12.3</td>
<td align="left">10.5</td>
<td align="left">23.1</td>
<td align="left">9.16</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The ideality factors of each SBD are extracted from the <italic>I-V</italic> curve at different temperatures and shown in <xref ref-type="fig" rid="F4">Figure 4A</xref>, which are larger than 1. Hence, the transport mechanism includes other mechanisms other than TE. What&#x2019;s more, TE is more sensitive to temperature, and the ideality factors are positively related to 1,000/T due to the domination of the TE mechanism at high temperatures.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>
<bold>(A)</bold> Ideality factor, <bold>(B)</bold> barrier height, and <bold>(C)</bold> <italic>J</italic>
<sub>
<italic>r</italic>
</sub> as a dependence of 1,000/T for each SBD device.</p>
</caption>
<graphic xlink:href="fphy-10-1084214-g004.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F4">Figure 4B</xref> shows SBHs for each SBD at temperatures ranging from 298 to 504&#xa0;K. The SBHs of each SBD were extracted from the forward <italic>I-V</italic> curves by <xref ref-type="disp-formula" rid="e1">Eq. 1</xref>. The SBHs decrease with increasing 1,000/T due to the inhomogeneous nature of the barrier. The electrons only overcome lower barriers at lower temperatures. With increasing temperature, the energy of the electrons increases to overcome the higher barriers at the Ni/GaN interface, where the higher SBHs were exhibited. The inhomogeneous SBHs can be expressed as a Gaussian distribution with a mean barrier height <inline-formula id="inf1">
<mml:math id="m2">
<mml:mrow>
<mml:mover accent="true">
<mml:msub>
<mml:mi>&#x3a6;</mml:mi>
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula> and a standard deviation &#x3c3;, as shown in <xref ref-type="disp-formula" rid="e2">Eq. 2</xref> [<xref ref-type="bibr" rid="B30">30</xref>].<disp-formula id="e2">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3a6;</mml:mi>
<mml:mi mathvariant="bold-italic">B</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold-italic">T</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mover accent="true">
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">B</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:msup>
<mml:mi mathvariant="bold-italic">&#x3c3;</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mi mathvariant="bold-italic">k</mml:mi>
<mml:mi mathvariant="bold-italic">T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<p>In GaN-based SBDs, inhomogeneous SBHs are attributed to multiple factors such as material defects, interface dipole layers, morphological features, and surface Fermi level pinning [<xref ref-type="bibr" rid="B27">27</xref>&#x2013;<xref ref-type="bibr" rid="B30">30</xref>, <xref ref-type="bibr" rid="B35">35</xref>]. According to the linear fits of the SBHs vs 1,000/T curve, the values of <inline-formula id="inf2">
<mml:math id="m4">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> were estimated to be 145, 199, 200 and 239&#xa0;meV for planar n-GaN SBD, lateral n-GaN SBD, planar AlGaN/GaN SBD and lateral AlGaN/GaN SBD, respectively. Compared to the planar SBDs, the lateral SBDs exhibit larger &#x3c3; may be due to the etching damage caused by ICP. The lateral AlGaN/GaN SBD has the largest &#x3c3; value, which is attributed to the higher trap concentration at the contact of anode metal and 2DEG. Thermal annealing is an effective step to reduce the damages induced by ICP etching, and wet treatment methods are used to further treat etching damage, such as hydroxide (KOH) and (NH<sub>4</sub>)<sub>2</sub>S [<xref ref-type="bibr" rid="B36">36</xref>, <xref ref-type="bibr" rid="B37">37</xref>].</p>
<p>At the voltage of -15 V, the <italic>J</italic>
<sub>
<italic>r</italic>
</sub> vs 1,000/T (<italic>J</italic>
<sub>
<italic>r</italic>
</sub>
<italic>-T</italic>) characteristics are shown in <xref ref-type="fig" rid="F4">Figure 4C</xref>, which appears linear on the Arrhenius plot. This suggests that the thermal activation mechanism has a dependence on the <inline-formula id="inf3">
<mml:math id="m5">
<mml:mrow>
<mml:mi mathvariant="italic">exp</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mo>&#x2061;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mi>k</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> function, where <italic>E</italic>
<sub>
<italic>A</italic>
</sub> is the activation energy. Therefore, a possible reverse leakage mechanism is defined as TAT, which is associated with thermally activated current [<xref ref-type="bibr" rid="B38">38</xref>]. The values of <italic>E</italic>
<sub>
<italic>A</italic>
</sub> were estimated to be 215, 214, 387 and 156&#xa0;meV for planar n-GaN SBD, lateral n-GaN SBD, planar AlGaN/GaN SBD, and lateral AlGaN/GaN SBD, respectively, according to linear fitting <italic>J</italic>
<sub>
<italic>r</italic>
</sub>
<italic>-T</italic> data. In addition, the <italic>J</italic>
<sub>
<italic>r</italic>
</sub> is related to the trap concentration on the interface of anode metal and semiconductor.</p>
<p>The withstand voltage of SBD is a very important parameter for power electronic applications. The reverse breakdown voltages of these SBDs are shown in <xref ref-type="fig" rid="F5">Figure 5</xref>. The planar n-GaN SBD has no breakdown phenomenon at -28.5&#xa0;V. The lateral n-GaN SBD shows a relatively low leakage current, which is breakdown at -73&#xa0;V. Compared with n-GaN SBD, the AlGaN/GaN SBDs exhibit a breakdown voltage of more than 2300&#xa0;V, which is mainly attributed to the undoped AlGaN/GaN materials.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Reverse <italic>I-V</italic> characteristics of <bold>(A)</bold> n-GaN SBDs and <bold>(B)</bold> AlGaN/GaN SBDs.</p>
</caption>
<graphic xlink:href="fphy-10-1084214-g005.tif"/>
</fig>
<p>For planar and lateral SBDs, the <italic>R</italic>
<sub>
<italic>on</italic>
</sub> consists of the <italic>R</italic>
<sub>
<italic>C</italic>
</sub>, channel resistance (<italic>R</italic>
<sub>
<italic>channel</italic>
</sub>) and anode resistance (<italic>R</italic>
<sub>
<italic>A</italic>
</sub>). Using the TLM, we calculated the <italic>R</italic>
<sub>
<italic>C</italic>
</sub> and <italic>R</italic>
<sub>
<italic>channel</italic>
</sub> for each SBD. Unitized <italic>R</italic>
<sub>
<italic>on</italic>
</sub> distributions of each SBD are summarized in <xref ref-type="fig" rid="F6">Figure 6A</xref>. The experimental results show that the <italic>R</italic>
<sub>
<italic>A</italic>
</sub> of lateral n-GaN SBD and lateral AlGaN/GaN SBD are 10.5&#xa0;&#x3a9;&#xa0;mm and 9.2&#xa0;&#x3a9;&#xa0;mm, respectively. The <italic>R</italic>
<sub>
<italic>A</italic>
</sub> are much larger than the <italic>R</italic>
<sub>
<italic>C</italic>
</sub> in each SBD, which is probably due to the worsening anode contacts by MIGS. The energy diagram of n-GaN SBD with MIGS is displayed in <xref ref-type="fig" rid="F6">Figure 6B</xref>. The planar AlGaN/GaN SBD exhibits larger <italic>R</italic>
<sub>
<italic>A</italic>
</sub> due to the electrons passing through the AlGaN barrier layer under the anode metal [<xref ref-type="bibr" rid="B39">39</xref>].</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>
<bold>(A)</bold> Unitized <italic>R</italic>
<sub>
<italic>on</italic>
</sub> distributions in planar and lateral SBDs. <bold>(B)</bold> Energy diagram of n-GaN SBD with MIGS and inhomogeneous SBHs.</p>
</caption>
<graphic xlink:href="fphy-10-1084214-g006.tif"/>
</fig>
</sec>
<sec sec-type="conclusion" id="s4">
<title>Conclusion</title>
<p>In summary, the lateral SBDs based on n-GaN and AlGaN/GaN heterostructure were fabricated, and the temperature-dependent <italic>I-V</italic> and <italic>C-V</italic> characteristics were used to evaluate the electrical properties, such as transport mechanisms of the forward and reverse current, SBHs, <italic>R</italic>
<sub>
<italic>on</italic>
</sub> distribution, MIGS, inhomogeneous SBHs, etc. For the planar and lateral n-GaN SBDs, the values of the <italic>V</italic>
<sub>
<italic>on</italic>
</sub> are similar. However, compared with conventional planar AlGaN/GaN SBD, the <italic>V</italic>
<sub>
<italic>on</italic>
</sub> of lateral AlGaN/GaN SBD is reduced from 1.64 V to 0.87&#xa0;V. The capacitances of lateral n-GaN SBD and lateral AlGaN/GaN SBD are 1.35&#xa0;pF/mm and 0.70&#xa0;pF/mm, respectively, which are much smaller than the capacitance of planar SBDs. According to the analysis of inhomogeneous SBHs, etching damage degrades the uniformity of SBHs. Compared with the breakdown voltage of 73&#xa0;V in the lateral n-GaN SBD, the lateral AlGaN/GaN SBDs exhibit a breakdown voltage of 2322&#xa0;V. In addition, the <italic>R</italic>
<sub>
<italic>A</italic>
</sub> is much greater than the <italic>R</italic>
<sub>
<italic>C</italic>
</sub> due to worsening anode contact by MIGS from the analysis of the <italic>R</italic>
<sub>
<italic>on</italic>
</sub> distributions of each SBD.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>Conceptualization: HL and BZ. Investigation: HL, ZL, FW, YX, XY, and YiL. Methodology: HL and BZ. Project administration: XL, LL, YaL, and ZW. Software: HL and BZ. Validation: HL, ZL, and BZ. Writing&#x2014;original draft: HL, ZL, and BZ.</p>
</sec>
<sec id="s7">
<title>Funding</title>
<p>This work was supported by Science and Technology Plan of Guangdong Province, China (Grant Nos. 2019B010132003 and 2019B010132001), the joint funding of the Nature Science Foundation of China (NSFC) and the Macao Science and Technology Development Fund (FDCT) of China (Grant No. 62061160368), the National Key Research and Development Program (Grant Nos. 2016YFB0400105 and 2017YFB0403001), and the Zhuhai Key Technology Laboratory of Wide Bandgap Semiconductor Power Electronics, Sun Yat-sen University, China (Grant No. 20167612042080001).</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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