Influence of metal choice on (010) β-Ga₂O₃ Schottky diode properties

Gallium oxide in its monoclinic beta-phase (β-Ga₂O₃) is promising for next generation power electronic devices due to its wide bandgap of ∼4.8 eV, large theoretical breakdown field of ∼8 MV/cm, projected Baliga figure of merit greatly exceeding those of GaN and SiC counterparts, and the availability of free-standing native substrates synthesized by low-cost melt methods.^1–10 With the recent reports on β-Ga₂O₃ field-effect transistors raising tremendous interest for this future wide bandgap technology that is based on homoepitaxial rather than lattice-mismatched structures,^1–3 there is now a great need to understand the key material and interface properties of β-Ga₂O₃, the knowledge of which are currently lacking due to the early stages of device development. For instance, in order to realize high quality devices, investigation of metal/β-Ga₂O₃ contacts is extremely important as ohmic contacts with low contact resistance and Schottky contacts with controllable barrier height are among the major requirements for superior device performance.^10–12 However, only sparse information is available regarding Schottky barrier properties of β-Ga₂O₃ compared with contemporary wide-bandgap semiconductors such as SiC and GaN. For example, there have been reports of Schottky diode characteristics on float zone and edge-defined film-fed growth (EFG) (010) substrates using Pt⁴ and Ni,⁹ on Czochralski-grown (100) using Ni,⁵ Au,⁸ and EFG-grown (100) using Pt,¹³ on EFG-grown (−201) using Ni,^6,14 Pt,^15,16 TiN¹⁶ and on halide vapor phase-grown (001) using Pt.¹⁷ To date, a systematic study of Schottky barrier height (SBH) using different metals on any particular orientation of β-Ga₂O₃ is still lacking. A detailed understanding is not only fundamentally compelling, but it is also essential since a leading interest for β-Ga₂O₃ is related to high power electronics and identifying a stable Schottky barrier with large SBH and low leakage current to sustain large breakdown voltages is required.^18,19

Therefore, we have investigated Schottky diode characteristics on β-Ga₂O₃ (010)-oriented substrates by quantitatively comparing several different metals Ni, Pt, Pd, and Au with respect to Schottky barrier properties. The non-cleavage (010)-oriented substrate is of particular interest due to its supporting high growth rate of β-Ga₂O₃ using molecular beam epitaxy (MBE).⁷ Capacitance-voltage (C-V), current-voltage (I-V) and internal photoemission (IPE) measurements are utilized to characterize the Schottky barrier. The relationships between the measured metal work function and SBH values are also discussed to provide an idea of barrier height engineering with metal choices for β-Ga₂O₃ (010).

To perform the investigations, all samples were fabricated using commercially available (Tamura) unintentionally doped (UID) β-Ga₂O₃ (010) substrates grown by the EFG method.²⁰ The structures were processed into 300 μm × 300 μm diodes using Ni, Pt, Pd, and Au, each with 8 nm of thickness deposited by e-beam evaporation, to form semitransparent Schottky contacts needed to allow optical penetration for IPE measurements. For ohmic contact formation, an ∼430 nm Ti/Al/Ni/Au metal stack was deposited in an RIE-etched 200 nm-deep trench on the substrate. This standard Schottky structure has been reported in Ref. 9.

After fabrication, I-V and C-V measurements were performed to characterize the fundamental diode properties. C-V characteristics were measured at room temperature using a standard 1 MHz measurement frequency. For SBH determination by IPE, all measurements were performed at 0 V bias at 300 K using a 600 W quartz-halogen (Q_TH)-lamp and a 1000 W Xe-lamp whose outputs are dispersed through a high-resolution monochromator that can provide optical excitation from 0.50 eV to 2.00 eV (Q_TH-lamp) and 1.20 eV to 5.00 eV (Xe-lamp) in 0.02 eV steps. All samples revealed 1 MHz C-V extracted doping of ∼1.1  $×$ 10¹⁷ cm⁻³ uniformly appearing across the reverse bias sweep from −4 V to 0 V. For each metal, multiple diodes were measured by every method, and the error magnitudes for all reported SBH values are determined from the statistical standard deviation of the dataset per method case.

The 300 K I-V characteristics of representative Schottky diodes for all metals are shown in Fig. 1. Excellent rectifying behavior with low leakage current is observed for all diodes with 300 K ideality factors ranging from 1.03 to 1.09, an early suggestion that thermionic emission (TE) might be the dominant transport mechanism for all cases. Furthermore, the diode turn-on voltages are seen to vary for different metals, suggesting an influence on SBH due to choice of the metal. The measured forward bias I-V characteristics were first analyzed using the ideal TE model²¹ 

where

Here, $Is$ is reverse saturation current, $A$ is diode area, $A *$ is Richardson constant, $V$ is applied bias, $n$ is ideality factor, $T$ is temperature, $k$ is Boltzmann constant, and $ϕ B$ is the SBH. Using $A *$= 41 A/cm² K² for β-Ga₂O₃,⁴ the room temperature barrier heights for Pd, Ni and Pt are obtained as $ϕ P d$=1.29  $±$  $0.03$V, $ϕ N i$=1.50  $±$  $0.03$V and $ϕ P t$=1.53 $±$  $0.01$V. The Au Schottky barrier sample yielded the highest ideality factor (1.09), and though the extracted SBH (1.62  $±$  $0.05$ V) appears reasonable, the I-V-T results and analysis discussed later will show the Au does not follow the ideal TE transport model.

To more precisely determine the accuracy of the TE model, Eq. (2) is commonly rearranged to create a Richardson plot according to²¹ 

from which the SBH (slope) and Richardson constant (y-intercept) can be extracted from a linear fit to a plot of $ln(Is/A T 2 )$ versus $1/kT$ from the I-V-T data taken over a range of temperatures. However, this analysis assumes that the ideality factor is independent of temperature. Various factors can influence the temperature dependence of $n$ such as presence of interface states, image forces and surface or interface charging in general.^22,23 To account for this within the TE transport, a modified Richardson relation of $ln(Is/A T 2 )$ versus $1/n T kT$ has been proposed, which considers such temperature dependence of $n$ within the Richardson formulation, enabling more accurate extraction of the Richardson constant.^23–26 

Implementing the modified Richardson relation as shown in Fig. 2, the SBH values for Ni and Pt were determined to be 1.52 V and 1.57 V, whereas the Richardson constants were extracted as 42.27 A/cm² K² and 48.85 A/cm² K², respectively. The close match of extracted $A *$ with the theoretical value of 41 A/cm² K² for β-Ga₂O₃,⁴ the agreement of the SBH values with the simply derived ones from Eqs. (1) and (2), the near unity ideality factor over a wide temperature range and the excellent linearity of $ln(Is/A T 2 )$ versus $1/n T kT$ plots, all confirm that thermionic emission is indeed the dominant transport mechanism for both Ni/β-Ga₂O₃ and Pt/β-Ga₂O₃ Schottky diodes. In contrast, the extracted SBH for the Au/β-Ga₂O₃ diodes was 1.21 V, which is unreasonably low given the I-V results shown in Fig. 1. In addition, the value of the extracted $A *$ using this model was 3.2  $×$ 10⁻⁶A/cm² K², orders of magnitude smaller than the theoretical value, which indicates that transport is not due to simple TE. The complexities of the Au SBH and associated current transport are discussed later in detail.

While I-V-T analysis provides information regarding both transport mechanism and SBH values, those are dependent on the particular transport model. To obtain a more direct determination of SBH, IPE measurements were carried out on the same devices. Here, SBH values are determined from the photocurrent generated by monochromatic light incident on the semi-transparent Schottky contact as a function of photon energy. As the photon energy becomes larger than the SBH, a measurable photocurrent is obtained. From Fowler’s theory,²⁷ the photoyield $(Y)$⁠, defined as the ratio of collected electrons to incident photons per second is proportional to the number of electrons per unit volume of a metal excited with photon energy (⁠ $hv)$⁠, whose kinetic energy normal to the surface is sufficient to overcome the SBH. Thus, $Y$ relates to the SBH via the density of electrons $(N E )$ of a metal meeting Fowler’s condition expressed as²⁷ 

for $hv> q ϕ B$⁠, where $m$ is electron mass and $μ$ is the highest occupied electron energy level in the metal at T = 0 K. Assuming photoemission occurs from a sufficiently wide-occupied energy band, when $hv=q ϕ B$ (approximately), then $μ+ q ϕ B −hv≈constant$ and $Y$ is expressed as^27,28

for $hv> q ϕ B +3kT$⁠, where $C$ is a constant. The linear fitting of $Y$ versus $hv$ thus yields the SBH from the horizontal axis intercept.

The 300 K IPE results for each metal/β-Ga₂O₃ Schottky diode is shown in Fig. 3. The corresponding onsets from the photoyield reveal barrier heights of $ϕ P d$=1.27  $±$  $0.01$ V, $ϕ N i$=1.54  $±$  $0.01$ V, $ϕ P t$=1.58  $±$  $0.01$ V and $ϕ A u$=1.71 $±$  $0.01$ V. Not only do the trends monotonically follow the shift in turn-on voltages apparent in Fig. 1, but the quantitative values are also in close agreement with those extracted from I-V measurements that were fitted to simple TE model at room temperature for each metal (noting the exception for the Au Schottky barrier discussed above). The SBH values for Ni and Pt from IPE are also very similar to what was obtained from the full I-V-T data analysis using the modified Richardson plot, further establishing self-consistency between in assignment of SBH values and current transport modes.

To gain even further confidence in the extracted SBH values, the Schottky contacts were characterized by the well-known C-V method (Fig. 4). Here, the C-V relationship for a Schottky diode is expressed as²¹ 

where $N D$ is doping concentration, $E C$ is the conduction band minimum, $E F$ is Fermi level, $ε 0$ is vacuum dielectric constant and relative permittivity $ε s$ = 10 for β-Ga₂O₃.²⁹ For ideal cases, the horizontal axis intercept of a 1/C²-V plot provides the built-in voltage $V b i = ϕ B −( E C − E F )/q$⁠. Using the C-V extracted $N D$ and an electron effective mass of $0.34 m$⁠,³⁰  $E C − E F$ was estimated to be ∼0.09 eV for the quasi-neutral region of the substrates. With this, the SBH of each metal was obtained as $ϕ P d$=1.28  $±$  $0.02$ V, $ϕ N i$=1.54  $±$  $0.02$ V, $ϕ P t$=1.59  $±$  $0.02$ V and $ϕ A u$=1.97  $±$  $0.02$ V. The trends between each metal SBH match the trends observed for the I-V, I-V-T and IPE methods with the actual SBH values being closely consistent for all metals, except the Au Schottky diode, with C-V yielding 1.97 V, well above the values from IPE and TE transport modeling.

The results from I-V, IPE and C-V analysis obtained so far reveal that SBHs for Pd, Ni and Pt are very similar from all measurement methods. This indicates that these metals form ideal Schottky contacts on (010) β-Ga₂O₃ with ideal TE transport being dominant, and the range of SBH values implies that neither Fermi level pinning nor interfacial oxide layers fully dominate the metal-semiconductor interfaces. Therefore, high quality Schottky diodes appear to be possible with a range of SBHs on (010) β-Ga₂O₃. However, the exception is the Au Schottky diode, which has proven to be more complex. To recap, unlike the other metals tested, first it was shown that simple TE transport theory cannot explain the observed carrier transport behavior despite the good ideality factor (1.09). Second, IPE and C-V analyses, which are independent from the I-V/I-V-T TE model issues, both show that the Au Schottky diodes yielded the highest SBH of the four metals tested, consistent with the trend in the measured I-V data but not consistent with the simple TE model. Since greater depth is needed to improve the understanding of the dominant current transport mechanism, several mechanisms were considered to explain the Au Schottky barrier transport behavior. These included thermionic field emission (TFE), image force lowering, interfacial layer or barrier inhomogeneity.^12,31–35 TFE transport and image force lowering are ruled out due to the low doping of the semiconductor side of the Schottky diode, since these should be negligible. The presence of interfacial layers is also unlikely since all samples for all metals were processed together, and this issue is not apparent for any of the other metal choices. This leaves the possibility of a spatially non-uniform barrier for the Au Schottky diode, and indeed this has been commonly reported for Au Schottky diodes fabricated on a wide range of semiconductor materials.^31,32 We are, therefore, currently investigating the Au Schottky contact transport properties in more detail, as the C-V and IPE results suggest Au could be an ideal Schottky metal for β-Ga₂O₃.

Finally, we analyzed the SBH for different metals as a function of metal work-function. For the ideal Schottky-Mott rule,²¹ which is rarely observed, the SBH would reflect the difference between the metal work function $( ϕ m )$ and the semiconductor electron affinity (⁠ $χ S )$⁠. However, in III-V semiconductors (e.g., GaAs, GaSb, InP, GaN), SBHs are usually independent of $ϕ m$ due to strong surface Fermi level pinning related to surface donor or acceptor defects.^21,36,37 Hence, we explored here the relationship of the SBH with $ϕ m$ for each metal/(010) β-Ga₂O₃ Schottky diodes, to ascertain the degree of surface pinning that might be present. Considering the large spread of the work function values available in the literature for any particular metal,^38,39 we performed contact potential difference (⁠ $V C P D$⁠) measurements on each Schottky metal via scanning Kelvin probe microscopy using a Pt-coated Si cantilever to provide a well-controlled measure of $ϕ m$ relative to Pt expressed as $V C P D = ϕ m − ϕ t i p$⁠, where $ϕ t i p$ is tip metal (Pt) work function.^40,41 Using the widely accepted Pt work function of 5.65 V as reference, the $V C P D$ values for other metals were utilized to calculate their work functions as 5.20, 5.25, and 5.30 V for Pd, Ni and Au, respectively, which are in line within the range of literature values (Pd∼5.12–5.60 V, Ni∼5.04–5.35 V, Au∼5.10–5.47 V).^38,39 A compilation of the SBH results versus metal work function is shown in Table I. The Pt and Ni Schottky diodes showed nearly similar barrier heights of ∼1.58 V and 1.54 V, respectively, although there exists a noticeable difference in their measured work function. However, the Pd/β-Ga₂O₃ SBH (∼1.27 V) was the lowest of all metals investigated, even though the Pd work function is close to that of Ni. Thus, the relation between the SBH and $ϕ m$ does not appear to follow a consistent trend for (010) β-Ga₂O₃ in this small sample set. However, the wide range of SBH values observed (1.27–1.71 V) does suggest that classic, $E F$ pinning might not dominate for (010) β-Ga₂O₃ Schottky diodes.

In summary, four Schottky metals (Ni, Pd, Pt and Au) were characterized to assess and compare SBHs and current transport mechanisms on (010) β-Ga₂O₃. Excellent diode properties were observed with classic thermionic emission transport for Ni, Pd and Pt Schottky barriers, and non-ideal thermionic transport for the Au Schottky barrier that is likely due to the presence of a spread of barrier heights due to an inhomogeneous interface. Close agreement was observed between measured SBH values using three independent methods (I-V, IPE, and C-V) for Ni, Pt and Pd contacts with the Au SBH value requiring further modeling to include the effects of SBH inhomogeneity. The spread of SBH values across the choices of metal suggests that Fermi level pinning does not fully dominate the SBH formation for (010) β-Ga₂O₃, implying that gate metal engineering of the SBH is possible for future device applications.

This work was supported by the Air Force Office of Scientific Research under Grant No. FA9550-14-1-0012 managed by Ali Sayir. The authors are grateful to Dr. Gregg Jessen (AFRL/RYDD) for the technical discussions and sample procurement from Darren Thomson (AFRL/RYDH).