Effect of metal contacts on (100) β-Ga₂O₃ Schottky barriers

Beta-gallium oxide (β-Ga₂O₃) is a semiconductor that has garnered interest over the past decade due to its ultrawide bandgap (∼4.6–4.9 eV),¹ wide range of n-type doping^2–5 (Si, Ge, and Sn), and its ability to be produced as large-area, melt-grown substrates that serve as a platform for device-quality epitaxial layers.^6–8 For these reasons, Ga₂O₃ is being pursued for high power devices⁹ and UV photodetectors.¹⁰ Other wide bandgap semiconductors such as GaN and SiC suffer from higher costs to produce substrates from vapor phase growth methods. In addition, Ga₂O₃ has a higher theoretical breakdown field (∼8 MV/cm) and Baliga figure of merit (∼3400) than GaN and SiC.¹¹ 

Studies of Schottky contacts to β-Ga₂O₃ play a fundamental role in designing metal-semiconductor field-effect transistors¹² and Schottky diodes.¹³ As such, it is important to develop contacts with high Schottky barrier heights and low leakage currents. Metals with a wide range of work functions have been explored as Schottky contacts to Ga₂O₃, including W,¹⁴ Cu,¹⁵ Ni,¹⁶ Au,¹⁷ Pt,¹⁸ TiN,¹⁹ Pd,²⁰ Ir,²¹ Ag,²⁰ and Mo.²² Similarly, Schottky contacts to (100), (010), (001), and $(2¯01)$ orientations of β-Ga₂O₃ substrates grown via edge-defined film fed growth,^23,24 Czochralski,^16,25 and floating zone²⁶ and to β-Ga₂O₃ epitaxial layers grown via metalorganic chemical vapor deposition,^27–30 halide vapor phase epitaxy,^6,28 and pulsed laser deposition³¹ have been reported. Yao et al. investigated five different Schottky metals to $(2¯01)$ β-Ga₂O₃ substrates and found that the metal work function was not a strong indicator of the Schottky barrier height.¹⁸ In a subsequent study, authors examined oxidized and pure (unoxidized) metal contacts to $(2¯01)$ β-Ga₂O₃ and also concluded that the work function was not a strong indicator of Schottky barrier height,²⁰ whereas Farzana et al. established evidence that the Fermi level is not completely pinned for Ni, Pd, and Pt Schottky contacts to the (010) β-Ga₂O₃ surface,³² and other data suggest that the metal work function is not a strong indicator of Schottky barrier height on the (010) β-Ga₂O₃ surface.²¹ There is limited published work on Schottky contacts on the (100)^{16,17,33–35} and (001)^36,37 orientations of β-Ga₂O₃. In this work, we measured the electrical behavior, at both room temperature and as a function of elevated temperature, of Ti, Mo, Co, Ni, Pd, and Au Schottky contacts to (100) β-Ga₂O₃ and calculated the Schottky barrier heights and ideality factors from these measurements. Observed trends are discussed and compared with previously published results for other Ga₂O₃ surfaces.

N-type, unintentionally doped (100) β-Ga₂O₃ single crystal wafers were grown by the Czochralski method at the Leibniz-Institut für Kristallzüchtung (IKZ) in Berlin, Germany. The as-received samples were 1 cm² and had resistivity, mobility, and free-carrier concentration of 0.2 Ω cm, 60 cm²/V s, and 5 × 10¹⁷ cm⁻³, respectively, as determined from Hall effect measurements. The doping concentration calculated from the C-V measurements of Schottky diodes was 2.5–4.5 × 10¹⁷ cm⁻³.

All metals were deposited onto unheated substrates by electron-beam evaporation (base pressure of ∼10⁻⁸ Torr). Ohmic contacts were formed using Ti/Au (20/100 nm) annealed at 450 °C, either for 1 min in N₂ in a rapid thermal annealing furnace (for backside ohmic contacts, referred to below as vertical structures) or for 5 min at 400 °C in Ar in a resistively heated quartz tube furnace (for frontside ohmic contacts, referred to as the lateral structures). Prior to deposition of all Schottky contacts, each substrate was soaked in 10% hydrochloric acid (HCl) for 5 min, rinsed in de-ionized (DI) water, and immersed for 5 min in boiling H₂O₂ at 85 °C. All samples were blown dry in nitrogen after each DI water rinse. The Schottky metals were subsequently deposited through a Mo shadow mask to form circular Schottky contacts with diameters of 125, 250, and 500 μm. Ti, Co, and Pd Schottky contacts were fabricated as vertical device structures with backside ohmic contacts, whereas Mo, Ni, and Au were fabricated as lateral structures with frontside ohmic contacts. The thickness of all deposited Schottky contacts is 30 nm. The Ti Schottky contacts were coated with 50 nm of Au to serve as a passivation layer.

Hall measurements were acquired using an MMR Technologies Hall Measurement System at room temperature. For these measurements, Ti/Au (20/50 nm) contacts were deposited in a van der Pauw pattern onto a (100) β-Ga₂O₃ substrate and annealed at 400 °C for 5 min in Ar. J-V and J-V-T measurements were obtained using an Agilent 4155C Semiconductor Parameter Analyzer and a Signatone S-1160A-4N probe station. C-V measurements were performed at 1 MHz using an HP 4284 LCR meter and a Signatone S-1160A-4N probe station.

For Schottky contacts that follow the thermionic emission model, the current density (J) vs voltage (V) behavior is described in the following equation:

where q is the electronic charge, I is the current, R_S is the series resistance, n is the ideality factor, and k is the Boltzmann constant. J_s is the saturation current density defined as follows:

where A** is Richardson's constant for the semiconductor and $ϕBJV$ is the J-V determined Schottky barrier height. The Richardson constant for β-Ga₂O₃ has been calculated to be 33.65 A/cm²K².³⁸ 

Figure 1(a) shows representative log-J versus V characteristics for each Schottky metal under forward bias conditions. Most metals display linearity over several decades of current before reaching series resistance limitations. An exception is Au, which displays multiple linear regions, suggestive of an inhomogeneous Schottky barrier, as established by other authors on other β-Ga₂O₃ surfaces.^18,39

Ideality factors and Schottky barrier heights were calculated from J-V characteristics using the Cheung and Cheung method.⁴⁰ This method uses a plot of

where A = diode area to extract n from the y-intercept of a $dVdln⁡J$ versus J plot; and a function

from which $ϕBJV$ is determined from the y-intercept of a $H(J)$ versus J plot. Table I lists the $ϕBJV$ values for Ti, Mo, Co, and Ni Schottky metal contacts, along with the ideality factors and the leakage current density values at −5 V for all Schottky contacts. Because of the higher ideality factors for Pd and Au contacts, the calculated Φ_B^JV values (1.42 ± 0.07 and 1.37 ± 0.09 eV, respectively) for these contacts do not follow thermionic emission and are not included in the analysis. The higher ideality factors for the Au and Pd contacts are associated with spatial inhomogeneity of the Schottky barriers for Au/Ga₂O₃ and Pd/Ga₂O₃ interfaces. Spatially inhomogeneous Schottky barriers are believed to result from Au-Ga and Pd-Ga alloy formation at the metal semiconductor interface. Pd-Ga and Au-Ga elemental formations have been reported on other Ga-based semiconductors including GaAs^41,42 and GaN.^43,44 The larger ideality factors observed for the Pd and Au contacts would be compatible with this phenomenon. Others have also reported evidence for an inhomogeneous Schottky barrier in Au Schottky contacts to (010) β-Ga₂O₃.³² Furthermore, our analysis of J-V-T measurements of Pd contacts, described below and in the supplementary material,⁵¹ indicates the presence of significant barrier inhomogeneity, as quantified by the standard deviation of the gaussian distribution, $σ0$⁠. The $σ0$ value of the barrier shows a higher value for Pd than both Co and Ti, implying more variance in the measurements of the Schottky barrier height for Pd.

Schottky barrier heights were also calculated from C-V measurements. As derived from depletion approximation,⁴⁵ 

where $ϕBCV$⁠, $εs$⁠, and $Nd$ are the C-V determined Schottky barrier height, semiconductor permittivity, and doping concentration, respectively. $Nc$⁠, the conduction band density of states, is expressed as follows:

where $m∗=0.28m0$ is the electron effective mass in β-Ga₂O₃ and m₀ is the free electron mass. For β-Ga₂O₃ at room temperature, the conduction band density of states is calculated to be $Nc=2.67x1018cm−3$⁠. Therefore, by plotting A²/C² versus V [as shown in Fig. 1(b)], $Nd$ can be calculated from the slope and the barrier height can be calculated from the x-intercept.

The C-V determined Schottky barrier heights are listed in Table I, column 6. Note that differences in C-V and J-V determined barrier heights are commonly reported. For example, barrier heights from C-V measurements are typically higher than those calculated from J-V measurements. Tung⁴⁶ attributes this effect to slight nonidealities (or spatially inhomogeneous Schottky barriers) in the diodes. For Mo, Co, and Ni, the agreement between the C-V and J-V determined barrier heights are within 3%–9%, whereas the agreement between these values for Ti is ∼20%–30%.

A homogeneous Schottky barrier height, $ϕBHom$⁠, can be defined by plotting $ϕBJV$ versus n and extrapolating to n = 1, as shown in Fig. 2. This method⁴⁷ works well for diodes with low ideality factors. For example, the $ϕBHom$ values (Table I, column 5) for Ti, Mo, Co, and Ni are in relatively close agreement with $ϕBJV$ and $ϕBCV$ values. For Pd, there is also a reasonably close agreement between $ϕBHom$and Φ_B^CV, but for Au, these values differ by ∼0.5 eV.

We accounted for spatial distribution of Schottky barriers in our analysis of J-V-T measurements of the vertical (Ti, Co, and Pd) device structures. As such, J-V-T measurements provided a potential third method to determine Schottky barrier heights for these diodes. However, as evidenced by the high ideality factors of the Pd diodes (∼1.3), the current transport is not dominated by thermionic emission. Although minimum ideality factors of 1.10–1.15 are obtained in the 150–200 °C range was observed, corresponding to a calculated barrier height of ∼1.7 eV at that temperature, the generally high ideality factors precluded a determination of a reliable Φ_B^JVT for the Pd contacts.

The J-V-T data for the vertical devices were fit using a model developed by Werner and Güttler,⁴⁸ which assumes the measured Schottky barriers yield a normalized Gaussian spatial distribution, P$(ϕB)$⁠, with average barrier height, $ϕB¯$⁠, and standard deviation, σ,

By applying this model as detailed in the supplementary materials,⁵¹ we obtain the following J-V-T relationship:

where $σ0$ is the standard deviation at zero bias and serves as a metric that determines the degree of spatial inhomogeneity of the Schottky barrier and also represents how strongly the Schottky barrier changes with temperature. $σ0$ was determined to be 92, 72, and 197 meV for the Ti, Co, and Pd contacts, respectively. Figure 3 plots the left-hand side of Eq. (8) versus 1 /kT, which provides a graphical method to calculate both Richardson's constant of β-Ga₂O₃ (see Fig. 3 inset table) and the $ϕBJVT$values (listed in the last column of Table I). The Richardson's constant values calculated from this experimental data are in reasonable agreement with the theoretical value of β-Ga₂O₃ of 33.65 A/cm²K².³⁸ The near linear behavior of the curves in Fig. 3 indicates that this model fits our data well.

The Schottky barrier heights calculated from the J-V, C-V, and J-V-T measurements discussed above are plotted versus the metal work functions in Fig. 4. The black dashed line in the lower part of the plot represents the Schottky–Mott theory for an ideal metal-semiconductor contact,

where Φ_M is the work function of the metal and χ_S is the electron affinity of the semiconductor; in this case, χ_S for β-Ga₂O₃ was assumed to be 4.05 eV.³⁸ 

According to the seminal study by Kurtin et al.,⁴⁹ Ga₂O₃ is expected to closely follow this predicted Schottky–Mott behavior due to its high degree of ionicity; that is, the slope of the plot, $S=dϕBdϕM$⁠, termed the index of interface behavior, should be close to 1.00. However, much research since that time has shown other factors can play a dominant role: for example, large variations in S values for different surface planes of the same semiconductor, e.g., SiC and Ga₂O₃, or for different forms of the same semiconductor, e.g., SnS and diamond/NCD.⁵⁰ A least squares fit to each set of data produced the following lines:

The corresponding S values are S_JV = 0.70 and S_CV = 0.97. Furthermore, for the two data points from J-V-T measurements, S_JVT = 0.82.

As discussed earlier, differences between Schottky barrier heights (and therefore, S values) calculated from different measurement methods can be attributed to the presence of Schottky barrier inhomogeneities, particularly for the contacts (Pd and Au) with higher ideality factors. Overall, however, the results from this study on (100) β-Ga₂O₃ reveal a strong positive correlation between the calculated Schottky barrier heights and the work function of the metal contacts. In contrast, previous studies of metal contacts to $(2¯01)$ β-Ga₂O₃ did not demonstrate a discernable correlation between Schottky barrier height and metal work function,^18,20 whereas results on (010) β-Ga₂O₃ have been mixed.^21,32 Hou et al.²⁰ attribute the strong Fermi level pinning on the $(2¯01)$ Ga₂O₃ surface to its higher oxygen dangling bond density and oxygen vacancies. Our conclusion from the present study in comparison with previous studies discussed above is that the surface plane/orientation of β-Ga₂O₃ has a significant effect on the electrical properties (e.g., Schottky barrier height) of metal contacts to this ultrawide bandgap semiconductor.

In summary, Ti, Mo, Co, Ni, Pd, and Au Schottky contacts to (100) Czochralski-grown β-Ga₂O₃ were electrically characterized via J-V, C-V, and/or J-V-T measurements. Analysis of the measurements revealed a strong correlation between the calculated Schottky barrier heights and the metal work functions. The electrical behavior of the Au and Pd contacts are associated with the presence of spatially inhomogeneous Schottky barriers, which require further investigation.

This material is based upon work supported by the Air Force Office of Scientific Research (Program Manager, Ali Sayer) under Award No. FA9550-18-1-0387. This work was partially performed in the framework of GraFOx a Leibniz-Science Campus partially funded by the Leibniz Association.

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