The Barrier Inhomogeneity and the Electrical Characteristics of W/Au β-Ga₂O₃ Schottky Barrier Diodes

Abstract

In this work, the electrical properties of the Ga₂O₃ Schottky barrier diodes (SBDs) using W/Au as the Schottky metal were investigated. Due to the 450 °C post-anode annealing (PAA), the reduced oxygen vacancy defects on the β-Ga₂O₃ surface resulted in the improvement in the forward characteristics of the W/Au Ga₂O₃ Schottky diode, and the breakdown voltage was significantly enhanced, increasing by 56.25% from 400 V to 625 V after PAA treatment. Additionally, the temperature dependence of barrier heights and ideality factors was analyzed using the thermionic emission (TE) model combined with a Gaussian distribution of barrier heights. Post-annealing reduced the apparent barrier height standard deviation from 112 meV to 92 meV, indicating a decrease in barrier height fluctuations. And the modified Richardson constants calculated for the as-deposited and annealed samples were in close agreement with the theoretical value, demonstrating that the barrier inhomogeneity of the W/Au Ga₂O₃ SBDs can be accurately explained using the TE model with a Gaussian distribution of barrier heights.

1. Introduction

With the development of technology, there is a growing demand for higher operating voltages, ambient temperatures, and more efficient energy conversion. Materials such as BN, AlN, Ga₂O₃, and diamond, known for their wide bandgap, ultra-high breakdown voltage, and exceptional chemical and mechanical stability, have increasingly gained attention [1,2,3,4]. Among them, β-Ga₂O₃ is the only material that can be grown through the melt growth method [5], and high-quality β-Ga₂O₃ native bulk crystal substrates are available through single crystal growth. Currently, 4-inch β-Ga₂O₃ single crystal substrates have been commercially mass-produced [6]. In addition, β-Ga₂O₃ also boasts an extremely high critical breakdown field [7], a much smaller power loss [8] compared to silicon and gallium nitride [9], and higher electron saturation velocity [10], making it promising for use in the next generation of commercial power conversion and radio frequency electronic devices [11,12].

Various structures of β-Ga₂O₃ SBDs have been extensively investigated [13]. One of the primary design considerations for Schottky diodes is achieving homogeneous Schottky contacts to predict the diode’s electrical performance under varying temperatures and voltages [14]. However, Schottky contact inhomogeneity is commonly observed in β-Ga₂O₃. Similar to that in other semiconductors such as GaN and SiC [15,16,17], the Schottky contact inhomogeneity can lead to the strong temperature dependence of the Schottky barrier height (Ф_b) and the ideality factor, and the experimental Richardson constant is significantly lower than the theoretical value (A** = 41.1 A/cm²K²) [18]. The barrier height and ideality factor vary widely with temperature being sometimes attributed to large-density of surfaces states, resulting in Fermi-level pinning effect at metal/β-Ga₂O₃ interface [19]. The origin of large-density surface states is likely to be associated with surface contaminants and surface defects like grain boundaries, multiple phases, facets, vacancies, and different threading dislocations [20]. The large density states on the surface serve as the patch of low barrier height regions, resulting in bad device characteristics and barrier inhomogeneity in Schottky diodes [21]. In the past several decades, the barrier inhomogeneity has been extensively investigated, and many types of barrier height distribution functions have been proposed to describe the barrier inhomogeneity. So far, the barrier inhomogeneity of metals with high work function (such as Ni, Pt, Pd) on β-Ga₂O₃ SBDs has been explained on basis of thermionic emission theory [22,23,24]. However, the barrier inhomogeneity of metals with lower work function on β-Ga₂O₃ SBDs, like tungsten, has not yet been explored.

In this work, we report a detailed analysis on electrical characteristics and barrier inhomogeneity of vertical β-Ga₂O₃ SBDs using W/Au as the Schottky metal. The capacitance–voltage (C-V) characteristics, the forward current density–voltage (J-V) characteristics, and the reverse breakdown voltage (BV) were investigated. An improvement in the diode characteristics is observed in the W/Au Ga₂O₃ SBDs following PAA treatment. Furthermore, the barrier inhomogeneity was observed from the current–voltage (I-V) characteristics of the Schottky diodes at varied temperatures ranging from 300 K to 450 K. Based on the thermionic emission model combined with Gaussian distribution of barrier heights, the temperature dependence of barrier heights and ideality factors was explained, and the barrier height fluctuation was reduced after anode metal annealing. Meanwhile, the modified Richardson constants are close to the theoretical value, demonstrating that the barrier height distribution of the W/AuGa₂O₃ Schottky contacts is followed by Gaussian distribution.

2. Device Structure and Process

The schematic cross section structure of the fabricated Ga₂O₃ SBDs and the fabrication process are shown in Figure 1a and b, respectively. The substrate material was Sn-doped (n = 1 × 10¹⁸ cm⁻³) β-Ga₂O₃ single crystal substrates grown by the edge-defined film-fed growth method, then a 10-μm Si-doped (n = 1 × 10¹⁶ cm⁻³) epitaxial layer is grown by halide vapor phase epitaxy on top of β-Ga₂O₃ substrates. Prior to device fabrication, the wafer was cleaned with piranha solution and then soaked in dilute buffered oxide etch for 10 min to remove the surface residual contaminants. The full-area back cathode metal Ti/Au (40/100 nm) was deposited by electron-beam evaporation, followed by rapid annealing process at 470 °C in N₂ for 60 s to form ohmic contacts. Then, the Schottky contacts were formed by the deposition of W/Au (30/60 nm), and 450 °C post-anode annealing for 2 min was performed in N₂. Lastly, the mesa isolation was formed by inductively coupled plasma (ICP) dry etching with 1 μm depth. The C-V characteristics, the I-V measurement at varied temperatures ranging from 300 K to 450 K, and the reverse BV characteristics of the W/Au-Ga₂O₃ SBDs were taken with the Keysight B1505A semiconductor parameter analyzer, and the four-point probe testing method was used to reduce probe resistance.

3. Results and Discussion

Figure 2a shows the forward J-V characteristics of the W/Au Ga₂O₃ SBDs for the as-deposited sample and the sample with PAA. The barrier heights and ideality factors were extracted by fitting the linear regime of I-V curves using the thermionic emission model. After post-anode annealing, the barrier height increases from 0.85 eV to 0.88 eV and the ideality factor decreases from 1.21 to 1.14, respectively. In addition, as shown in Figure 2b, the breakdown voltage at the current density of 1 mA/cm² increases by 56.25%, rising from 400 V to 625 V after the PAA treatment. On the surface of the Ga₂O₃ material, surface defects such as oxygen vacancies can lead to a large number of surface states, which can seriously affect the device characteristics [25]. The improvement of W/Au Ga₂O₃ diode characteristics after PAA treatment can be attributed to the reduction of surface defects, with further analysis shown below.

To investigate the improvement of W/Au Ga₂O₃ diode characteristics following PAA treatment, X-ray photoelectron spectroscopy (XPS) measurements were performed on the β-Ga₂O₃ samples. As shown in Figure 3a, a 5 nm thick W metal layer was deposited on the surface of the β-Ga₂O₃ sample. Prior to the XPS measurement, the W-deposited sample was etched with Ar⁺ plasma to enhance the accuracy of the results. Figure 3b presents the XPS valence band plots for the β-Ga₂O₃ sample, the as-deposited sample with the 5 nm W metal film, and the sample-deposited 5 nm W and with 450 °C annealing. According to Figure 3c, the barrier height (ϕ_b) of the metal contact with β-Ga₂O₃ can be expressed as ϕ_b = ϕ_m – χ_s – eV_i, where the surface potential (V_i) is induced by the surface states located within the bandgap [26]. As illustrated in Figure 3b, the valence band maximum of the sample treated at 450 °C increases from −0.71 eV to −0.66 eV compared to the as-deposited sample. This difference indicates that the surface potential is reduced by about 0.05 eV after the 450 °C annealing, which is consistent with the increased barrier height extracted from the I-V characteristics. In addition, Figure 3d shows the O 1s core level spectra, which can be fitted into two peaks. The peaks around 531 eV (O_I) and 533 eV (O_II) are attributed to O²⁻ ions and oxygen vacancies, respectively [27], and the proportion of O_II represents the relative concentration of oxygen vacancies on the β-Ga₂O₃ surface. As shown in Figure 3d, the proportion of O_II decreases from 35.2% to 23.1% after the 450 °C annealing treatment, indicating that the oxygen vacancies on the β-Ga₂O₃ surface are reduced. These oxygen vacancy defects act as surface states, whose reduction can lead to a decrease in the surface potential and an increase in the barrier height. At the same time, the oxygen vacancy defects and gallium–oxygen vacancy pairs are the origin of the donor-type defects and acceptor-type defects in the Ga₂O₃ material bandgap, respectively [28], where the reduction of oxygen vacancy defects on the β-Ga₂O₃ surface can also reduce the paths of electron assisted tunnelling through these defects [29], resulting in a decreased leakage current under reverse bias and an increased breakdown voltage.

The reduction of oxygen vacancies on the β-Ga₂O₃ surface can be attributed to two aspects. On the one hand, the W metal has a low chemical affinity (i.e., lower oxide stability and no intermetallic compounds) with Ga₂O₃, so that WO_x oxides are easily reduced to the W native metal during annealing [30]. Figure 4a and b show the W 4f spectra for the sample-deposited 5 nm W and the sample-deposited 5 nm W with 450 °C annealing. As shown in Figure 4a and Figure 4b, the peaks around 36.1 eV and 31.6 eV are attributed to WO₃ and W metal, respectively. The W 4f core level spectra were deconvoluted using a doublet of two Gaussian peaks of equal width corresponding to the W 4f_7/2 and W 4f_5/2 spin-orbit components [31]. After annealing, the ratio of WO₃ to W metal decreases from 2.76 to 1.25, indicating that WO₃ oxides are partially reduced to the W native metal during annealing. Meanwhile, the excess oxygen atoms diffuse into the Ga₂O₃ material surface in the presence of pure nitrogen, thus reducing the surface oxygen vacancies. On the other hand, during the annealing process in nitrogen atmosphere, the oxygen atoms previously present in the Ga₂O₃ material interstitial positions have the probability to migrate to the correct position, which can also result in the reduction of oxygen vacancy and the improvement of Ga₂O₃ material crystal quality [32]. Figure 4c shows the PL spectra for the untreated Ga₂O₃ epitaxial material and the Ga₂O₃ epitaxial material with 450 °C annealing. As shown in Figure 4c, a significant emission peak at about 387 nm and a broad blue-green emission band are observed. In various Ga₂O₃ materials, the broad 350–620 nm emission band is common, and the origin can be ascribed to the emission recombination of electron and hole pairs between donor-type oxygen vacancy defects and acceptor-type gallium–oxygen vacancy pairs [28]. The PL emission intensity of the Ga₂O₃ epitaxial material decreases after annealing, demonstrating that the oxygen vacancies in the Ga₂O₃ material are reduced after annealing. Additionally, Figure 4d shows the XRD images for the untreated Ga₂O₃ epitaxial material and the Ga₂O₃ epitaxial material with 450 °C annealing in nitrogen atmosphere. The XRD results show that the intensity of the (002) diffraction peak (about 31.5°) is enhanced in the Ga₂O₃ epitaxial material with annealing. This indicates that the crystal quality of Ga₂O₃ epitaxial material is improved after annealing at 450 °C in N₂ atmosphere, and the stress release leads to the location of the (002) peak shift [33]. These results are consistent with the previous conjectures.

Figure 5a shows the C-V characteristics of the W/Au SBDs as a frequency of 1 MHz for the as-deposited sample and the sample with PAA, and it conforms to the typical behavior of vertical Schottky barrier diodes. As the anode voltage increases, majority carrier electrons accumulate gradually, leading to an increase of the capacitance [34]. Meanwhile, the capacitance 1/C² versus applied voltage plots is shown in Figure 5b, and the relationship of the 1/C²-V is given by the following Equation [35]:

$${\displaystyle \frac{1}{C^2}}={\displaystyle \frac{2}{A^{2}q{\epsilon }_s{N}_D}}({\Phi }_b-V_n-V{\displaystyle \frac{k_{B}T}{q}})$$

(1)

where C is the capacitance, A is the Schottky electrode area, ε_s is the dielectric constant of β-Ga₂O₃, N_D is the effective carrier concentration, Ф_b is the effective barrier height, and V_n is the voltage corresponding to the difference between the conduction band edge (E_c) and the Fermi level (E_f) in the flat-band condition, which can be expressed as:

$$V_n=E_c-E_f={\displaystyle \frac{k_{B}T}{q}}\mathit{ln}{\displaystyle \frac{N_c}{N_D}}$$

(2)

where N_c is the effective state density of the conduction band edge, which is given by:

$$N_c=2{\left({\displaystyle \frac{2\pi m^{*}{k}_{B}T}{h^2}}\right)}^{3/2}$$

(3)

where m* is the effective mass of electron, and h is the Planck constant. By combining Equations (1) and (2), the effective carrier concentration and barrier height can be calculated from the 1/C²-V plots as follows:

$$N_D={\displaystyle \frac{2}{A^{2}q{\epsilon }_s}}{\displaystyle \frac{1}{K_c}}$$

(4)

$${\Phi }_{b,0}=V_{\mathit{bi}}+V_n+{\displaystyle \frac{k_{B}T}{q}}$$

(5)

where K_c and V_bi are the slope of the 1/C²-V plots and the x-axis intercept of the 1/C²-V plots, respectively. As shown in Figure 5b, the calculated effective carrier concentrations are approximately 1.2 × 10¹⁵ cm⁻³, and the Ф_b,0 values obtained from C-V measurements are 0.72 eV for the as-deposited sample and 0.76 eV for the sample with PAA, where the calculated barrier heights are consistent with the results reported in the literature [36].

In order to investigate the barrier inhomogeneity of the W/Au Ga₂O₃ SBDs, the I-V characteristics of the Schottky diodes at varied temperatures ranging from 300 K to 450 K, as shown in Figure 6, were analyzed. A zero-crossing voltage V_zero was observed at 0.85 V in the as-deposited sample and the sample with PAA, which may be due to two different conduction mechanisms in the temperature dependence of the I-V characteristics [37]. When the forward voltage is below 0.85 V, electron thermionic emission is dominated between the W/Au metal and Ga₂O₃ contacts, with more electrons acquiring sufficient energy to overcome the Schottky barrier as the temperature rises, leading to an increase in current. Conversely, when the voltage exceeds 0.85 V, electron transport occurs within the drift layer, whereas the current is governed by the mobility of electrons in the drift layer. In this region, as the temperature rises, electron mobility decreases, resulting in a reduction in current.

Based on the TE theory, the I-V characteristics are expressed by the following relationships [22,38]:

$$I=A{A}^{**}{T}^2\mathit{exp}(-{\displaystyle \frac{q{\Phi }_b}{\mathit{kT}}})[\mathit{exp}({\displaystyle \frac{\mathit{qV}}{\mathit{kT}}}-1)]$$

(6)

and

$$I_s=A{A}^{**}{T}^2\mathit{ex}p\left(-{\displaystyle \frac{q{\Phi }_{b,0}}{\mathit{kT}}}\right)$$

(7)

where A is the area of the Schottky contact, A** is the Richardson constant, with a theoretical value of 41.1 A/cm²K² for β-Ga₂O₃, (calculated using m* = 0.34m₀ from first-principles calculations), while k, q, T, and I_s are the Boltzmann constant, electron charge, absolute temperature, and saturation current density, respectively. The Schottky barrier height qФ_b is the V-dependent Schottky barrier height and can be expressed as Ф_b = Ф_b,0 + βV, where β is the positive constant. Substituting this into Equation (6), the current can be rewritten as:

$$\begin{gathered} I=A{A}^{**}{T}^2\mathit{ex}p\left(-{\displaystyle \frac{q{\Phi }_{b,0}+\beta V}{\mathit{kT}}}\right)[\mathit{exp}({\displaystyle \frac{\mathit{qV}}{\mathit{kT}}}-1\left)\right] \\ =I_s\mathit{ex}p\left({\displaystyle \frac{\mathit{qV}}{\eta \mathit{kT}}}\right)[1-\mathit{exp}(-{\displaystyle \frac{\mathit{qV}}{\mathit{kT}}}\left)\right] \end{gathered}$$

(8)

where η = 1/1 – β, and η is the ideality factor. When V > 3kq/T, Equation (8) simplifies to:

$$I=I_s\mathit{exp}\left({\displaystyle \frac{\mathit{qV}}{\eta \mathit{kT}}}\right)$$

(9)

According to Equation (9), the saturation current density I_s and the ideality factor η can be extracted from the slope and y-intercept y-intercept and slope of the ln(I)-V plots, respectively. In addition, the barrier height Ф_b was calculated from Equation (7). As shown in the inset of Figure 6, the barrier height was extracted by selecting a segment of the semi-logarithmic plot (approximately 0.1–0.5 V) within the linear region for linear fitting, from which the slope of the fitted Equation was determined. The obtained average goodness-of-fit metric R² is very close to 1. Figure 7a shows the barrier height and ideality factor for the as-deposited sample and the sample with PAA as they were extracted at temperatures ranging from 300 K to 450 K. As the temperature increases, the barrier height increases and the ideality decreases, which is attributed to barrier inhomogeneities at the W/Au and Ga₂O₃ interface. The barrier inhomogeneities exhibited a strong temperature dependence process. At room temperature, carriers primarily cross regions with low barrier heights, often associated with defects at the W/Ga₂O₃ contact surface, resulting in a large ideality factor. However, as the temperature increased, the carriers gained sufficient energy to cross the higher barrier heights, leading to a smaller ideality factor. Furthermore, conventional Richardson’s plots ln(I_s/T²) as a function of 1/kT were plotted for temperatures 300–450 K in Figure 7b. The barrier height qФ_b,0 and the Richardson constant A** were extracted from the slope and intercept of the linear fit, respectively. For the as-deposited sample, the calculated qФ_b,0 and A** are 0.69 eV and 0.082 A/cm²K² respectively, while for the PAA-treated sample, these values are 0.76 eV and 0.481 A/cm²K². The obtained Richardson constants are several orders of magnitude lower than the theoretical value of A** for β-Ga₂O₃. This discrepancy arises because the conventional Richardson plot assumes that the barrier height and ideality factor are temperature-independent, which is not valid in the presence of barrier inhomogeneities [25].

Thus, to explain the previously observed temperature dependence of barrier heights and ideality factors and the abnormal Richardson constants, barrier inhomogeneity was incorporated into the TE model in combination with a Gaussian distribution function for the barrier height, as expressed by the following Equation [39,40,41]:

$${\Phi }_{\mathit{ap}}={\stackrel{-}{\Phi }}_{b0}-{\displaystyle \frac{{q\sigma }_0^2}{2\mathit{kT}}}$$

(10)

where Ф_ap is the apparent barrier height, Ф_b0 and σ₀ are the mean barrier height and standard deviation, respectively. Figure 8a shows the Ф_ap versus q/2kT plot, and the σ₀ was determined with the slope of the fit line. The obtained σ₀ values are 112 meV for the as-deposited sample and 92 meV for the sample with PAA. This reduction in σ₀ after post-anode annealing is attributed to the reduction of oxygen vacancies, which serve as low-barrier height patches on the W/Ga₂O₃ contact surface, thereby decreasing fluctuations in the barrier height. Furthermore, a modified Richardson plot was derived using the following Equation:

$$\mathit{ln}\left({\displaystyle \frac{I_s}{T^2}}\right)-{\displaystyle \frac{q^2{\sigma }_0^2}{{2k}^2{T}^2}}=\mathit{lnA}{A}^{**}-{\displaystyle \frac{q{\Phi }_{b0}}{\mathit{kT}}}$$

(11)

According to Equation (11), the modified Richardson plots are shown in Figure 8b. The modified Richardson constants were determined from the y-axis intercepts of the linear fits to the plots, yielding values of 42.59 A/cm²K² for the as-deposited sample and 42.83 A/cm²K² for the sample with PAA treatment. These values are close to the theoretical Richardson constant of 41.1 A/cm²K². This result indicates that the barrier height of the W/Au-Ga₂O₃ Schottky contacts follows Gaussian distribution for both the as-deposited sample and the sample with PAA.

4. Conclusions

In conclusion, the electrical characteristics of β-Ga₂O₃ Schottky barrier diodes using W/Au as the Schottky metal were studied. Due to 450 °C post-anode annealing, the oxygen vacancy defects on the β-Ga₂O₃ surface were reduced, resulting in a decrease in the surface potential. The increase in barrier height and the reduction in leakage paths improved the characteristics of the W/Au-Ga₂O₃ SBDs, whereas the breakdown voltage increased by 56.25%, rising from 400 V to 625 V after PAA treatment. Additionally, the temperature dependence of barrier heights and ideality factors was observed over a temperature range of 300 K to 450 K, attributed to barrier inhomogeneity. The thermionic emission model combined with a Gaussian distribution of barrier heights was used to explain this temperature dependence. Post-annealing was found to reduce barrier height fluctuations from 112 meV to 92 meV. As evidenced by the modified Richardson constants of 42.59 A/cm²K² for the as-deposited sample and 42.83 A/cm²K² for the PAA-treated sample, both of which are very close to the theoretical Richardson constant for β-Ga₂O₃. These results demonstrate that the barrier inhomogeneity of W/Au-Ga₂O₃ SBDs can be effectively described using the TE model with a Gaussian distribution of barrier heights.