Chasing Schottky–Mott: Metal-first non-alloyed contacts to β-Ga₂O₃ for interface quality and minimal surface modification

Beta-phase gallium-oxide (⁠ $β$-Ga $2$O $3$⁠) has been investigated in recent years as a promising material in power electronics thanks to its large estimated critical breakdown field (8 MV/cm), adequate electron mobility (200  $cm 2$/V s), and availability of large area substrates from melt.^1–3 Impressive devices demonstrations have been recorded with a record average breakdown electric field observed in both Schottky barrier diodes (SBDs) and field-effect transistors (FETs) at 5.7 MV/cm, with surface fields as high as 6 MV/cm enabled by oxidized metal Schottky contacts with barrier heights (⁠ $ϕ B$⁠) > 2 eV.^4–7 

Our previous work has demonstrated that conventional lift-off processing of metal contacts significantly modifies the surface of $β$- $Ga 2 O 3$ and impedes consistent and reliable ohmic contact formation, while a metal-first contact process improves both contact quality and consistency.¹³ Contact-first processes have also been demonstrated in prior studies, albeit not explicitly for the purpose of minimal surface modification, in ITO/AZO ohmic contacts that out-performed conventional lifted-off Ti/Au contacts reported by Carey et al., and in the ozone-MBE deposited oxidized Schottky contacts that attained 6 MV/cm reported by Cromer et al.^7,14,15 Given nearly all metal contacts to $Ga 2 O 3$ in the literature to date were formed by lift-off, it is reasonable to assume the same or similar processing inconsistencies observed in Ti/Au ohmic contacts (Ref. 13) may have led to the wildly varied values of $ϕ B$ and $S$ in the literature.

In this work, we demonstrate non-alloyed, metal-first ohmic and Schottky contacts fabricated with contact metals having a range of work functions to further explore the limitations of Fermi-level pinning in $β$- $Ga 2 O 3$⁠.We fabricated transfer length method (TLM) patterns for all six contact metals (Al, Ti, Cr, Ni, Pd, and Pt) and vertical SBDs for the high work-function metals (Ni, Pd, and Pt) and, by fitting the ohmic and Schottky IV behavior of these contacts to established emission mechanisms, are able to extract apparent specific contact resistances for metal contacts that exhibit ohmic IV characteristics and Schottky-barrier heights for both ohmic and Schottky characteristics.

The TLM patterns for all six contact metals were fabricated on two heavily n+ doped samples grown by metal–organic chemical vapor deposition (MOCVD), each diced into three pieces after growth to reduce inter-sample growth non-uniformity (samples A–F). The in situ doped samples were grown in an Agnitron Agilis 100 MOCVD system on Fe-doped (010) $β$-Ga $2$O $3$ substrates. Prior to growth, samples were ex situ etched with 48% HF for 30 min and immediately loaded.¹⁶ A 50 nm unintentionally doped buffer layer was grown first before growing the 220–250 nm highly doped layer. The samples were then diced and solvent cleaned. Further details of the MOCVD growth can be found in the supplementary material. Hall measurements on previously grown calibration samples gave a channel charge and mobility of $9× 10 19 cm − 3$ and 84  $cm 2$/V s for samples A, D, and F and $7× 10 19 cm − 3$ and 89  $cm 2$/V s for samples B–C and E. The metal stacks were then deposited by electron-beam evaporation. Circular TLM (CTLM) patterns were defined using contact lithography, and the metal stacks were then wet etched (see Table I for metal layer thicknesses and wet etch conditions). The detailed fabrication of metal-first ohmic contacts can be found in our prior report.¹³ 

The SBDs for the high work-function metals were fabricated on diced 1 $×$ 1 cm $2$ pieces (samples G–I) from a 2 in. (⁠ $2 ¯$01) Sn-doped $β$- $Ga 2 O 3$ substrate from Novel Crystal Technology, Inc. The fabrication process is diagrammed in Fig. S1 of the supplementary material, including a blanket backside ohmic contact, frontside blanket deposition of the Ni, Pd, or Pt followed by photolithographic and wet etch anode patterning, and a $BCl 3/ Cl 2$-based self-aligned mesa etch for isolation. During backside cathode deposition, the front side of the sample was protected by a blanket layer of photoresist. The protective layer was removed before cathode annealing by a long soak (>30 min) in heated (⁠ $∼$65  $°$C) 1165 Microposit Remover™. Coating and removal of a blanket photoresist layer by solvent strip has been demonstrated to still form uniform, low resistance metal-first Ti/Au ohmic contacts on n+ $β$- $Ga 2 O 3$⁠, sample B $′$⁠. The process information for sample B $′$ is included in Table I, with full process information detailed in the supplementary material. An additional solvent clean in acetone and isopropanol was performed prior to frontside anode deposition. Full process details are included in the supplementary material.

The CTLM patterns were measured using a Keithley 4200 Semiconductor Characterization System in a four-point probe configuration, with an inner radius of 50  $μ$m and TLM pad spacings from 3 to 12  $μ$m confirmed by scanning electron microscopy. Forward I–V, reverse I–V, and C–V were measured on the SBDs using the same system in a vertical two-point configuration on devices with an anode radius of 100  $μ$m. A Thermo-Nexsa G2 x-ray photoelectron spectrometer (XPS) with Al-K $α$ x-ray source with in situ ion mill and electron flood gun for charge compensation was used to measure the oxidation state of the metal contact at the metal–semiconductor interface.

Figure 1(a) shows the I–V curves from an example CTLM pattern with 5  $μ$m spacing for samples A–F. The low work-function contacts (samples A–C) are linear or nearly linear ohmic with the resistance apparently increasing with increasing $ϕ M$ of the contact metal from Al (⁠ $ϕ M$ = 4.2 eV) to Cr (⁠ $ϕ M$ = 4.5 eV). The high work-function metals (samples D–F) show varying degrees of Schottky behavior. From sampling at least four sets of TLM patterns per sample, we find that the Al contacts have an average non-alloyed $R c$ of $0.069±0.003$  $Ω$ mm, which leads to a specific contact resistance (⁠ $ρ c$⁠) of $1.1±0.1× 10 − 6$  $Ω$-cm $2$ [Figs. 1(b)–1(c)]. Notably, $R c$ is constant over the entire 100 mA measurement range [Fig. 1(b)]. This is among the lowest reported contact resistances on (010) $β$-Ga $2$O $3$⁠. These Al-based contacts, as well as the Ti and Cr contacts, are benchmarked in Fig. 2. Further improvements in contact resistance can be anticipated by increasing to doping densities beyond 1 $×$ $10 20 cm − 3$ and by refining surface cleanliness. Thermal stability of these metal-first interfaces also remains an open question beyond the scope of this work.

The Ti and Cr contacts on samples B and C have a higher average non-alloyed $R c$ of 0.48 $±$ 0.01  $Ω$-mm and 0.80 $±$ 0.01  $Ω$-mm, respectively, with a corresponding $ρ c$ of 2.9 $±$ 0.1 $×$ 10 $− 5$  $Ω$ cm $2$ and 1.1 $±$ 0.1 $×$ $10 − 4$  $Ω$  $cm 2$⁠. These results are summarized in Table II. The Ti/Au contacts on sample B $′$ are also linear and ohmic, with a non-alloyed $R c$ and corresponding $ρ c$ of 0.18 $±$ 0.01  $Ω$-mm and 6.5 $±$ 0.6 $×$ $10 − 6$  $Ω$- $cm 2$⁠, respectively. These contacts are also included in Table II and Fig. 2, with a full discussion of the contact behavior included in the supplementary material. The Ni, Pd, and Pt contacts do not show linear I–V behavior, and thus, a contact resistance is not extracted.

As for the second point, Zhang et al. further carried out hybrid DFT calculations and determined that the conduction band edge is minimally impacted by bandgap renormalization resulting from electron-impurity interactions (⁠ $Δ E ei$⁠) due to minimal hybridization between the Si 3s and Ga 4s state that forms the basis of the conduction band minimum.¹⁷ Therefore, all bandgap renormalization (⁠ $Δ E BGR$⁠) may be attributed to electron–electron interactions (⁠ $Δ E ee$⁠). As electron–electron interactions are largely absent in the depletion region near the metal–semiconductor contact interface, we anticipate no bandgap renormalization at the interface, and therefore, the location of $E c$ relative to $ϕ M$ (and, therefore, $ϕ B$⁠) is unaffected. In the bulk, bandgap renormalization is predominantly seen through lowering of the conduction band minimum due to the dispersive Ga 4s state from which the conduction band is derived compared to the flat valence band edge. Thus, $Δ E BGR=Δ E BGR, C$ for n+ Ga $2$O $3$ doped with Si and is sketched entirely in the conduction band in Fig. 3(b).¹⁷ 

Using the extracted specific contact resistance from TLM, $ϕ B$ can be solved for numerically. We attain barrier heights for Al, Ti, and Cr of $0.29±0.03$⁠, $0.57±0.01$⁠, and $0.69±0.01$ eV, respectively. These, and all extracted barrier heights, are listed in Table II. The values of $ϕ B$ monotonically increase with increasing $ϕ M$⁠. Similar analysis applied to Ti contacts on $3× 10 19$⁠, $7× 10 19$⁠, and $8× 10 19 cm − 3$ Si-doped $β$-Ga $2$O $3$ reported in our previous work yields similar barrier heights of 0.60, 0.54, and 0.56 eV, respectively, to the extracted $ϕ B$ for Ti of 0.57 eV reported here.¹³ 

Neglecting both BM and BGR (i.e., setting $E \,f$ at $E c$ in the bulk ignoring renormalization effects, as is commonly assumed for degenerate semiconductors), the extracted $ϕ B$ is $∼$40 meV higher than the values extracted here as, at doping densities $∼5-10× 10 19 cm − 3$⁠, the competing effects of BM and BGR on $V bi$ are approximately equal in magnitude and, therefore, nearly cancel out. Including BM but neglecting BGR, which is most commonly seen in the literature when applying the equation by Padovani and Stratton, leads to significantly larger barrier heights by $∼$0.5–0.6 eV due to the artificial increase in $V bi$⁠.

The extracted $N d$ and $ϕ B, CV$ were $5.58× 10 18 cm − 3$ and 1.31 $±$ 0.01 eV for Ni, $6.93× 10 18 cm − 3$ and 1.71 $±$ 0.25 eV for Pd, and $6.52× 10 18 cm − 3$ and 1.43 $±$ 0.11 eV for Pt.

The forward J–V characteristics of the diodes in the exponential region are fit with the TFE model according to Eqs. (8)–(10), with $N d$ set to the value extracted by C–V, $V F$ as the independent variable, and $ϕ B, FIV$ as the only fitting parameter. The agreement of forward J–V characteristics and the TFE model is shown in Fig. 4(b). The extracted values of $ϕ B, FIV$ for Ni, Pd, and Pt are 1.08 $±$ 0.12, 1.46 $±$ 0.02, and 1.32 $±$ 0.02 eV, respectively. Unlike for the heavily degenerately doped ohmic contacts, neglecting BM and/or BGR results in a minimal shift (⁠ $∼$20 meV) in the extracted $ϕ B$ as the doping density in these samples is similar to the conduction band density of states in $β$-Ga $2$O $3$⁠, meaning that the samples are barely degenerately doped and $E \,f= E c$ is a reasonable approximation.

The reverse J–V characteristics of the SBDs are fit using the numerical reverse leakage model developed by Li et al. (described in the supplementary material), which incorporates doping effects and image force lowering (IFL) into the models developed by Murphy and Good and expanded by Padovani and Stratton.^19,21,24 For fitting to the measured reverse J–V characteristics, $V R$ is related to $F surf$ according to $F surf= 2 q N d ( ϕ B, RIV − V R ) / ϵ s$⁠, with $N d$ again set to the value extracted from C–V. This leaves $V R$ as the independent variable and $ϕ B, RIV$ as the only fitting parameter. The agreement of reverse J–V characteristics and the numerical tunneling model is shown in Fig. 4(a). The extracted values of $ϕ B, RIV$ for Ni, Pd, and Pt are 1.10 $±$ 0.11, 1.44 $±$ 0.01, and 1.33 $±$ 0.02 eV, respectively.

Figure 5 plots the extracted barrier heights for Al, Ti, Cr, Ni, Pd, and Pt on $Ga 2 O 3$ vs their respective metal work function with prior published data. Prior studies imply that the measured barrier height on $Ga 2 O 3$ is heavily pinned and collectively demonstrate a minimal dependence on the work function of the contact metal. In this work, overall, we observe $ϕ Al< ϕ Ti< ϕ Cr< ϕ Ni$ $< ϕ {Pt}< ϕ Pd$⁠, which trends with increasing $ϕ M$ with the exception of Pd and Pt (5.4 vs 5.65 eV), which are reversed. Fitting these extracted barriers to the modified Schottky–Mott rule in Eq. (2) gives $S$ = 0.7 $±$ 0.2 with an $R 2$ of 0.85. For the barriers extracted by multiple methods, as is often observed, the barrier heights extracted by C–V are slightly higher than the barriers extracted from forward and reverse J–V.²⁵ The barrier heights, however, obey the same trend for all barrier height extraction methods.

Surface orientation and interface chemistry may both play a role in the observation of $S$-values less than 1. Previous work has indicated that Fermi-level pinning and Schottky barrier height can depend on the surface crystal orientation due to the low level of crystal symmetry in $Ga 2 O 3$⁠, which results in different surface energies and density of surface states.²⁶ On the (100) surface of $Ga 2 O 3$⁠, for example, Lyle et al. demonstrated a significantly lower amount of Fermi-level pinning with $S$ values ranging from 0.7 to 0.97, while Lingaparthi et al. obtained a similar value of $S$ $∼$ 0.66 on the (001) surface.^27,28 In contrast, Hou et al. observe near complete Fermi-level pinning (⁠ $S∼$ 0) on the (⁠ $2 ¯$01) and (010) surface, which was attributed to the large number of oxygen dangling bonds on this face.⁶ On the (010) surface, Farzana et al. do observe a spread of Schottky-barrier heights, though they do not trend as predicted by the Schottky–Mott rule (albeit within a fairly small data set), indicating that Fermi-level pinning may not dominate Schottky-barrier formation.²⁹ Our observation of a positive $S$ value of $∼$0.7 indicates that apparent Fermi-level pinning can at least be somewhat alleviated by processing techniques that preserve as-grown interface quality even on these historically pinned surface orientations. However, as this work does span two different crystal orientations, (010) and (⁠ $2 ¯$01), further work should investigate more closely Fermi-level pinning on different orientations with identical process conditions.

As stated previously, Fig. 5 is plotted using the metal work function, not necessarily the work function of the metal or metal oxide present at the metal–semiconductor interface that ultimately yields the electrical contact. As shown in the prior literature, oxidation does increase the work function of stoichiometric and non-stoichiometric metal oxides and may, at least partially, account for the non-unity values of $S$⁠.^30,31 Extracting the exact work function of these non-stoichiometric metal oxides is outside the scope of this study, except to note that their presence indicates an increase in the work function that may adjust $ϕ B$ of metals, such as Ti and Cr (Fig. 4), to be aligned with the Schottky–Mott model. To further investigate oxidation as a source of non-ideal $S$ values, we performed depth-resolved XPS measurements of the oxidation state of each contact metal at the contact- $Ga 2 O 3$ interface. The depth profiles are shown in Fig. 6. Despite all contacts not receiving a post-deposition anneal or thermal processing exceeding 200  $°$C for photoresist processing, the majority of the contact metals are at least partially oxidized. Due to the deposition occurring under ultrahigh vacuum pressures of $10 − 7$ Torr, it is unlikely that the deposited metal was oxidized by oxygen during the line-of-site e-beam evaporation; oxidation is more likely due to a redox reaction with the underlying $Ga 2 O 3$⁠.³² As expected, those metal oxides with the lowest free energy of formation at room temperature [i.e., $Al 2 O 3$⁠, $TiO 2$⁠, and $Cr 2 O 3$⁠, Figs. 6(a)–6(c)] show significantly more oxidation than the metal oxides with higher energy of formation [i.e., NiO, PdO, $PtO 2$⁠, Figs. 6(d)–6(f)].³³ 

As the metals with the lowest $ϕ M$ are also the metals that are most prone to oxidation and, therefore, most likely to experience an increase in the work function, the apparent Fermi-level pinning and low $S$ values observed in metal Schottky contacts to $Ga 2 O 3$ may be attributed to under-reporting the work function of these oxidized and partially oxidized layers, in addition to any adverse effect that conventional processing may have introduced to the interface—most of the reports in the literature to date with the exception of Carey et al. and Cromer et al. have used a liftoff process. This could also explain the discrepancy between $ϕ M$ and $ϕ B$ observed for Pd and Pt, as the Pd layer is partially oxidized and may, therefore, have a higher work function than reported. Precise measurement and understanding of the value of the work function for partially oxidized and oxidized metal contacts is beyond the scope of this work. Future studies of barrier height extraction ought to be mindful of the significant influence of minute changes in $E c$ relative to $ϕ M$ from bandgap renormalization for accurate barrier height determination.

In conclusion, we report non-alloyed metal-first ohmic and Schottky contacts on $β$- $Ga 2 O 3$ with a range of contact metal work functions. We attain an ultralow contact resistance of 0.069 $±$ 0.003  $Ω$ mm with Al contacts. Furthermore, we extract values for the Schottky-barrier height from the I–V characteristics of TLM patterns for the lower work-function metals and SBDs for the higher work-function metals. The extracted values of $ϕ B$ largely increase with increasing $ϕ M$ with an $S$ value of 0.7 $±$ 0.2, indicating that the Fermi-level may at least somewhat be un-pinned by metal-first processing that preserves the bare-substrate (⁠ $2 ¯$01) and as-grown (010) surfaces in contrast with historical reports showing complete Fermi-level pinning on the (⁠ $2 ¯$01) and (010) surfaces. Depth-resolved XPS investigation of the oxidation state of the contact metals indicates that the majority of contact metals are at least partially oxidized even without alloying, which may result in higher work functions than reported and partially explain the persistence of apparent Fermi-level pinning. Further understanding of the crystal orientation dependence coupled with the precise effect of the oxidation state on work function may assist in further un-pinning the Fermi-level in $β$- $Ga 2 O 3$ and improving quality and consistency of Schottky and ohmic metal contacts.

See the supplementary material for additional sample growth details and processing details, an expanded discussion of Burstein–Moss and bandgap renormalization, illustrations of the criteria distinguishing between the TE and TFE regimes, details of the numerical tunneling model used to fit the reverse IV of the SBDs, and tabulated historical Schottky-barrier height measurements.

This work was in part supported by ACCESS, an AFOSR Center of Excellence (No. FA9550-18-1-0529). C.A.G. acknowledges support from the National Defense Science and Engineering (NDSEG) Fellowship. This work was supported in part by SUPREME, one of seven centers in JUMP 2.0, a Semiconductor Research Corporation (SRC) program sponsored by DARPA. The device fabrication was performed in part at the Cornell Nanoscale Facility, a NNCI member supported by NSF grant (No. NNCI-2025233). This work used facilities and instrumentation supported by the NSF through the Cornell University Materials Research Science and Engineering Center (No. DMR-1719875).

The authors have no conflicts to disclose.

Kathleen T. Smith: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Cameron A. Gorsak: Investigation (supporting); Resources (equal); Writing – review & editing (equal). Joshua T. Buontempo: Investigation (supporting); Resources (equal). Bennett J. Cromer: Formal analysis (supporting); Visualization (supporting); Writing – review & editing (equal). Takumi Ikenoue: Funding acquisition (supporting); Supervision (supporting). Hemant Gulupalli: Investigation (supporting). Michael O. Thompson: Funding acquisition (equal); Supervision (equal). Debdeep Jena: Funding acquisition (equal); Supervision (equal). Hari P. Nair: Funding acquisition (equal); Supervision (equal). Huili Grace Xing: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Methodology (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

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