Electrical properties of high permittivity epitaxial SrCaTiO₃ grown on AlGaN/GaN heterostructures

Advances in epitaxial growth techniques in recent years have enabled the monolithic integration of multifunctional perovskite oxides on a wide variety of conventional semiconductors including Si, Ge, GaAs, and GaN.^1–8 The GaN platform is especially attractive due to its wide bandgap, thermal and chemical stability, high saturation electron velocity, and large breakdown electric field.⁹ Notably, the development of AlGaN/GaN high-electron-mobility transistors (HEMTs)¹⁰ brought forth significant improvements in solid-state power-switching and high-power, high-frequency electronics.¹¹ GaN-based HEMTs have demonstrated RF power densities of >40 W/mm,¹² but as operation extends to millimeter-wave (mm-wave) frequencies, breakdown voltage reduces, lowering output power density. Field plate technology, while effective at managing electric fields for microwave HEMTs,¹³ suffers from parasitic capacitance at higher frequencies. High charge density barrier materials such as ScAlN have been studied to increase the current density and improve the power density.^14,15 However, increased channel density can cause premature breakdown due to high peak electric fields in the gate–drain region. Recently, a transistor design with “extreme-κ” (>100) dielectric layers has been proposed for improved electric field management, which reduces peak electric fields and enhances the breakdown voltage of the device.^16,17

Perovskite oxides such as SrTiO₃ (STO) and CaTiO₃ (CTO) could be considered “extreme-κ” dielectric materials in this sense, as they have bulk room temperature dielectric constants of 300¹⁸ and 180,¹⁹ respectively. The alloy Sr_1−xCa_xTiO₃ (SCTO) has a rich phase diagram in which the Ca alloy fraction can both tune the dielectric constant and induce ferroelectric and antiferroelectric phase transitions.²⁰ Integrating these oxides with GaN can both provide further reductions in gate leakage in HEMTs due to their high dielectric constants and provide better field management.²¹ Epitaxial oxides also have benefits for GaN-integration over amorphous oxides due to degradation of dielectric constants in amorphous films,²² as well as multiferroic⁵ and ferroelectric behavior.²³ 

The growth of epitaxial (111)-oriented STO thin films on (0002) GaN has been pursued by several research groups, via thin rutile TiO₂^5,24,25 or TiN²⁶ buffer layers, which help reduce the substantial 13.3% lattice mismatch between cubic STO and wurtzite GaN. Our previous work demonstrated the epitaxial integration of STO and SCTO films on GaN with a 1-nm-thick TiO₂ buffer layer and showed improved crystallinity from the introduction of the buffer layer.²⁷ In this work, we demonstrate the epitaxial growth of (111)-oriented SCTO thin films on AlGaN/GaN templates using RF-plasma-assisted molecular beam epitaxy (MBE). Structural characterizations are presented to investigate the lattice constant as both the Ca alloy fraction and SCTO layer thickness are independently varied. Current–voltage (I–V) measurements provide insight into the leakage current behavior, and capacitance–voltage (C–V) measurements are used to observe shifts in the threshold voltage, V_T, and extract κ in the dielectric oxide layer. RF characterizations are presented to compare values of κ at microwave frequencies.

The AlGaN/GaN high-electron-mobility transistor structure was grown using a ScientaOmicron PRO-100 MBE system, using N₂ gas and a Veeco Unibulb RF plasma to create the active nitrogen flux and dual filament gallium and aluminum effusion cells to provide the group-III flux. A 65-nm AlN nucleation layer was first grown on a 3-in. 4H-SiC substrate, followed by a 200-nm GaN layer grown in the intermediate regime to reduce the threading dislocation density, a 400-nm Ga-rich GaN buffer/channel layer, and a 24-nm Al_0.38Ga_0.62N barrier layer. The majority of the GaN buffer layer was grown at 2.15 Å/s, with the final 100 nm of the GaN and the AlGaN layers grown at 0.72 Å/s. The GaN layer thicknesses are nominal and estimated based on separately grown calibration samples. The Al composition and AlGaN barrier layer thickness were confirmed from x-ray diffraction (XRD) measurements using a monochromated Rigaku SmartLab diffractometer with a rotating copper anode. The oxide samples used for RF characterization were grown on 1-μm-thick unintentionally doped (uid) GaN/6H-SiC substrates with a 50-nm AlN nucleation layer, with growth conditions similar to that of previous work.²⁷ 

The AlGaN/GaN template wafers were cut with a diamond saw into 10 × 10 mm² squares and cleaned in a 5:1 H₂SO₄:H₂O₂ solution for 10 min at 80 °C²⁸ before loading into a Vacuum Generators V80H MBE deposition chamber for the growth of the SCTO film. The wafer and stainless steel holder were degassed at 600 °C for 30 min before oxide growth. More details of the V80H growth chamber can be found in Ref. 27. Prior to SCTO film growth, a nominally 1-nm-thick TiO₂ buffer layer was first deposited at 500 °C. The TiO₂ layer was grown by first depositing a half monolayer of Ti metal on the AlGaN surface before a 30 s oxidation step in molecular oxygen at a flow of 0.2 sccm. TiO₂ was subsequently deposited with an active oxygen flux provided by an RF plasma at a forward power of 250 W. Typical growth rates were 1–1.2 nm/min. The vacuum chamber pressure during growth was ∼2 × 10⁻⁶ Torr. Following the TiO₂ buffer layer, SCTO films were deposited at a higher temperature of 650 °C. A thickness series at a fixed composition of x = 0.22 was grown with film thicknesses between 7 and 126 nm. A composition series was grown with Ca fractions of x = 0 (i.e., STO), 0.22, 0.33, and 0.53 with film thicknesses of ∼90 nm. Thicknesses were calibrated using a quartz crystal microbalance and x-ray reflectivity (XRR) measurements and confirmed with cross-sectional scanning electron microscopy (SEM) imaging (supplementary material). Material structural characterization was performed in situ with a Staib reflection high-energy electron diffraction (RHEED) at 13.5 keV and ex situ with XRD and atomic force microscopy (AFM, Bruker Dimension FastScan). Stoichiometry was calibrated using a Thermo Scientific K-Alpha x-ray photoemission spectroscopy (XPS) system, cross-referenced with Rutherford backscattering spectrometry (RBS) analysis (Eurofins EAG Laboratories), leading to an estimated composition accuracy of 1–2 at. % (see the supplementary material).

Contactless sheet resistance measurements were performed on the 10 × 10 mm² AlGaN/GaN/SiC samples prior to oxide deposition and compared to measurements afterward. Hall effect measurements were performed on the samples before and after the SCTO deposition to observe any change to the AlGaN/GaN 2DEG properties (measurements of sheet resistance R_s, carrier density n_s, and electron mobility μ). A diamond scribe was used to mark the corners of the samples before In contacts were soldered in a van der Pauw geometry for measurement to establish a good electrical contact to the 2DEG.

Test capacitor structures were then fabricated using Ni/Au (20/100 nm) metallization on SCTO/AlGaN/GaN samples with 50-µm diameter circular small-area capacitors separated by a 25-µm gap from a large-area top contact for I–V and C–V measurements with the structure shown in Fig. 1. Voltage is applied to the small circular electrode, while the large-area contact is grounded. The Ni/Au metal electrodes directly contact the SCTO film, and the area ratio between the large-area contacts and the circular contact is ∼2300:1. Vertical C–V measurements were performed at 2 MHz with an Agilent E4980A LCR meter and a small-signal level of 100 mV rms. Interdigitated capacitors (IDCs) were fabricated via a Cr/Au (10/300 nm) metallization on SCTO/uid GaN samples with finger width and spacing ranging from 4 to 7 μm. The IDCs were characterized at RF frequencies using S-parameters with a power level of −15 dBm (32 μW), and the capacitance was extracted using a small-signal equivalent circuit model using a parallel RC circuit after de-embedding contribution from the probe pad. S-parameters were also measured as a function of DC bias to determine the effect of electric field on capacitance. A conformal mapping technique²⁹ was then used to extract the dielectric constant of the SCTO films at microwave frequencies.

The epitaxial growth of SCTO on AlGaN is qualitatively similar to that of previous work for STO on GaN,²⁷ whereby the SCTO film has a (111) orientation and roughens as the film thickness increases. Figure 2 shows RHEED and AFM characterization of the SCTO samples with x = 0.22 at various thicknesses. The RHEED patterns show the epitaxial relationship between SCTO and AlGaN as (111)[1$1̄$0] SCTO || (0001)[11$2̄$0] AlGaN. Prior transmission electron microscopy analysis has established the epitaxial relationship between SCTO and GaN as (111)[11$2̄$] SCTO || (0001)[10$1̄$0] GaN or, equivalently, (111)[1$1̄$0] SCTO || (0001)[11$2̄$0] GaN. Because the AlGaN layers are grown pseudomorphic to the GaN layers in this work, the in-plane epitaxial relationship is preserved. As the SCTO thickness increases, the RHEED patterns transition from streaky to spotty, indicating island formation and film roughening. This is also seen in the AFM images, where the surface roughness correspondingly increases. Thick (∼90 nm) samples grown at x = 0, 0.33, and 0.53 exhibited similar RHEED patterns and roughness values. The SCTO film coverage across all samples is generally smooth, with root-mean-square roughness values of approximately 1–2 nm, and often reproduces the spiral hillock morphology of the underlying AlGaN surface.

XRD measurements for the SCTO samples are shown in Fig. 3. A cubic structure should have threefold symmetry about the (111) axis, but we observe a sixfold symmetry from off-axis (110) phi scans of the SCTO films [Fig. 3(a)], matching the sixfold symmetry of the (10$1̄$1) phi scans of the underlying GaN [Fig. 3(b)]. This suggests that the SCTO film is twinned in the growth plane, with two domains separated by a modulo 60° in-plane rotation, a feature reported from previous studies of STO growth on GaN.^5,26,30 The twin domains can also be observed in the RHEED patterns (Fig. 2), in which the extra spots of the SCTO film can be attributed to the different domain orientations.²⁶ The similar intensity of each peak in the phi scans indicates that there is no preferred orientation for the domains, and is expected given that each of the 111-oriented threefold symmetric grains should populate one of two equally likely orientations on the sixfold symmetric AlGaN surface.³¹ 

Figure 3(c) shows the diffraction intensity of the SCTO film increasing as the film thickness increases, with the (111) Bragg peak seen at ∼40°. No other diffraction peaks besides the (111) family were observed [Fig. 3(f)], which indicate a single orientation for the epitaxial SCTO film. The full width at half maximum (FWHM) of the SCTO (111) rocking curves decreases with increasing film thickness, with the ∼90 nm-thick films having FWHM values generally <1° [Fig. 3(e)]. The c-lattice parameters for the SCTO samples, calculated using Bragg’s law, are shown in Table I. Assuming Vegard’s law dependence of lattice constant between bulk STO (a = 3.905 Å) and CTO (pseudocubic a = 3.82 ų²), the nominal c-lattice parameter for an unstrained x = 0.22 sample would be 3.886 Å. Table I indicates that the samples all have slightly larger lattice parameters than expected, with the largest difference observed for the thinner samples. This suggests that despite the large lattice mismatch between the SCTO and AlGaN, there may be residual coherency strain in the thinner samples. Alternatively, defects in the SCTO film could result in larger lattice parameters.³³ Oxygen vacancies are also known to change the lattice parameter and induce conductivity in STO³⁴ but are ruled out as being dominant from a separate study where homoepitaxial STO films grown in identical oxygen environments as for this study were measured to be electrically insulating (not shown). We note that there may still be a small amount of oxygen vacancies remaining in the film due to the low oxygen pressures used during deposition. However, more investigation is necessary to determine if these vacancies may change the dielectric properties of the film.

The composition series were purposefully grown thicker to obtain higher XRD intensity and to provide a larger contribution to the total capacitance of the heterostructures. Figure 3(d) shows 2θ−ω line scans that indicate a transition to a smaller c-lattice parameter with increasing Ca composition. A comparison of the measured lattice parameters to the nominal lattice parameter by Vegard’s law is shown in Fig. 3(g). There is good agreement, which suggests that at a thickness of 90 nm, the films are likely relaxed to their bulk values. No other diffraction peaks besides the (111) family are seen, indicating single orientation for the samples in the composition study. XRD spectra for the SCTO film grown on uid GaN looked similar to data presented in earlier work (see Ref. 27).

Sheet resistance measurements for the AlGaN/GaN samples averaged 343 Ω/□ before oxide growth and 372 Ω/□ afterward, representing a <10% change. Values for μ ranged from 750 to 1000 cm²/V-s and n_s ranged from 1.5 to 1.9 × 10¹³ cm⁻² and confirmed that the presence of the SCTO layers did not substantially change the transport characteristics of the 2DEG in the AlGaN/GaN layers. More details are included in the supplementary material. The I–V characteristics of the vertical capacitor structures on the AlGaN/GaN samples are shown in Fig. 4 for both the thickness and composition series and compared to a control Ni/Au Schottky contact made directly to the AlGaN layer. The leakage current reduction trends with the thickness of the SCTO film for both forward and reverse current. The high leakage seen in the thinner samples may be due to a small Schottky barrier between the oxide and the AlGaN layers [Fig. 6(b)]. Small conduction band offsets at STO/semiconductor heterojunctions have been shown to result in high gate leakage currents.³⁵ There is no obvious trend in leakage current with composition, aside from a somewhat lower leakage seen for the STO sample (x = 0). This could be explained by the fact that the bandgaps of SrTiO₃ (E_g = 3.25 eV³⁶) and CaTiO₃ (E_g ∼ 3.4–3.8 eV^37–39) are not substantially different. Although this work does not investigate the bandgaps and offsets between SCTO and AlGaN, the conduction band offsets between the different compositions are likely only a few tenths of an eV apart, and not significant enough to change the vertical transport across the heterojunction. The samples are compared to a Schottky diode control AlGaN/GaN sample with no oxide deposited, which exhibits more than 5 orders of magnitude higher leakage than the thicker samples at −10 V (18 A/cm² for the Schottky sample compared to 5 × 10⁻⁵ A/cm² for the thick STO sample). The high permittivity of the SCTO film likely accounts for the drastic reduction in the leakage current due to a lower electric field across the SCTO layers and, hence, lower current.

C–V characteristics of the SCTO/AlGaN/GaN heterostructures are shown in Figs. 5(a) and 5(c) for the thickness and composition studies, respectively. The voltage is swept at 0.12 V/s and a frequency of 2 MHz. Samples showed typical hysteresis of less than 200 mV [Fig. 5(a), inset]. For clarity, only the down sweeps are plotted in Fig. 5. At lower frequencies, we observe that the depletion region of the C–V curve stretches, with the threshold voltage shifting to more negative values [Fig. 5(a), inset]. The shifts can be attributed to trap states at the SCTO/AlGaN interface. Similar threshold voltage shifts have been observed in other dielectrics on III-N semiconductors.⁴⁰ V_T and its dependence on dielectric thickness can be used to determine the charge at the dielectric–semiconductor interface.^41,42 V_T is determined by finding the regression-determined intersection of the accumulation and depletion regions in the C–V curves. The total capacitance in the accumulation region decreases as the SCTO thickness increases, but we note only by small amounts. This is expected for capacitors in series in which one layer has a very high permittivity. By plotting inverse capacitance at a n_s of 1.5 × 10¹³ cm⁻² to account for the GaN quantum capacitance against total dielectric thickness—defined as the SCTO layer thickness plus the 1 nm TiO₂ buffer layer [Fig. 5(b)], a linear relationship is seen. We use a simple series capacitor model considering the capacitance of the SCTO and AlGaN layers as well as the GaN quantum capacitance, in which the slope is proportional to κ_SCTO (dielectric constant of the SCTO), and calculate a value for κ_SCTO of 244 ± 15, with error bars representing the standard deviation of six measurements for each sample. The y-intercept is 2.72 cm²/μF, corresponding to a capacitance density of 0.367 μF/cm², which represents the sum of the AlGaN and GaN quantum capacitances, and is consistent with the zero-bias capacitance of the measured Schottky sample (0.357 μF/cm²). A similar analysis is performed for the composition series in Fig. 5(c) and plotted in Fig. 5(d), where it is assumed that the AlGaN and GaN quantum capacitance is 0.367 μF/cm² from the linear fit in Fig. 5(b) and κ_SCTO is again extracted from a series capacitance approach for each individual film composition. The dielectric constants range from 170 to 290, with the x = 0.33 sample having the highest value. These values are notably close to the bulk dielectric constants of STO and CTO and highlight an advantage of high crystallinity epitaxial oxide films over amorphous or polycrystalline oxides, which have lower dielectric constants.⁴³ 

Following the analysis of Downey et al.,⁴² the change in V_T with dielectric thickness, t_SCTO, has the relationship

where κ_SCTO is the dielectric constant of the SCTO, ɛ₀ is the permittivity of free space, Q_π,GaN is the polarization-induced charge of GaN (+1.8 × 10¹³ cm⁻²⁴⁴), N_int is the fixed interfacial charge at the SCTO/AlGaN interface, and N_bulk is the bulk charge in the SCTO layers. The threshold voltage is linear [Fig. 6(a)] and negative with thickness, indicating that N_bulk is small, and hence, the final term in Eq. (1) can be neglected. The negative slope is consistent with a positive interface charge, and from the slope in Fig. 6(a) (0.0043 V/nm), N_int is calculated to be +2.38 × 10¹³ cm⁻² based on κ_SCTO extracted from Fig. 5(b), a value comparable to the polarization-induced interfacial charge in Al_0.38Ga_0.62N (3.97 × 10¹³ cm⁻²⁴⁴). We note that the extremely shallow slope is more than 100 times smaller than what was observed in standard high-κ dielectrics such as SiN_x,⁴² as a result of the significantly higher κ of SCTO.

The effects of the high permittivity SCTO layers and N_int on n_s are modeled with 1D Poisson–Schrödinger simulations using the nextnano solver⁴⁵ and band diagrams are shown in Fig. 6(b) for three thicknesses of SCTO where the SCTO/AlGaN interface is set to 0 nm on the plot for visual clarity. A bandgap of 3.3 eV is assumed for the SCTO, a bandgap of 4.17 eV is assumed for Al_0.38Ga_0.62N, and a bandgap of 3.44 eV is assumed for GaN.⁴⁶ A conduction band offset of 0.5 eV is assumed between SCTO and Al_0.38Ga_0.62N based on calculated band offsets between STO and GaN from Ref. 46. The barrier height at the SCTO surface (metal/SCTO interface) is set to 1 eV based on the calculated charge neutrality level from Ref. 46. The effect of a thicker SCTO layer is seen to decrease the 2DEG sheet density by less than 13% up to 126 nm of SCTO, as depicted in Fig. 6(c). This small change in the sheet density for the given thickness of SCTO is attributed to the extremely high permittivity in the SCTO, which results in only a comparatively small voltage drop across the layer while maintaining a high effective barrier capacitance. The trend in the simulations is in good agreement with the experimentally measured carrier densities, which are extracted from the C–V measurements at zero bias by integrating the C–V curves.

The expected change to the 2DEG mobility due to remote charge scattering (RCS) from fixed charge at the SCTO/AlGaN interface is negligible, given the relatively thick AlGaN barrier layer used in this study. The effect of RCS on mobility arises from Coulombic scattering of the interface charge with the carriers in the 2DEG. For our barrier thickness of 24 nm and a fixed interface charge density of 2.38 × 10¹³ cm⁻², a 2DEG density of >10¹³ cm⁻² would yield a RCS mobility contribution of >10⁶ cm²/V-s.^42,47 Matthiessen’s rule would thus suggest a change in the 2DEG mobility of <0.1% from the addition of the interface charge. For scaled barrier structures though, RCS scattering should be taken into account, as the effect has a strong dependence on the barrier thickness and could lead to mobility degradation.

The extracted capacitance and subsequently calculated dielectric constants of the nominally 90-nm SCTO films grown on uid GaN are shown in Fig. 7 for an IDC structure with 6 μm finger width and spacing at 2 GHz. Note that similar trends are observed for each IDC geometry. The trends in dielectric constant measured under lateral fields at 2 GHz are consistent with those measured at 2 MHz under the vertical field for the SCTO/AlGaN/GaN heterostructures (Fig. 5) with the x = 0.22 SCTO film having a higher κ compared to the STO and x = 0.53 samples. Additionally, the extracted κ value for the x = 0.22 SCTO film is 260 for the 2 MHz vertical measurement, while κ at 2 GHz is 220 at 0 V DC bias. A similar reduction in κ is shown for the x = 0.53 SCTO film with a slightly smaller reduction for the STO film. Only a small apparent change in κ is observed for the samples under the DC bias with a less than 10% reduction when biased from 0 to ±40 V with κ appearing to saturate thereafter. The quality factor Q (reciprocal of the dielectric loss tangent) is also plotted in Fig. 7(a), with values that are comparable to MBE-grown STO on lattice-matched oxide substrates.⁴⁸ Measurements of a control IDC sample fabricated directly on GaN (i.e., without an SCTO layer) had a zero-bias Q of 22 at 2 GHz, a similar value to the IDCs shown in Fig. 7. This suggests that Q of the IDCs on the SCTO heterostructures are limited by the GaN/SiC. Further RF characterization is required to fully understand the limitations of these films through millimeter-wave frequencies and greater electric fields; however, the RF measurements demonstrate that the SCTO film κ remains high at microwave frequencies and κ does not appear to be strongly dependent on the electric field.

In summary, the epitaxial growth of (111)-oriented Sr_1−xCa_xTiO₃ on AlGaN/GaN heterostructures is demonstrated using a thin TiO₂ buffer layer, and electrical measurements are performed on vertical capacitor structures to probe the I–V and C–V characteristics and lateral IDC structures to investigate microwave frequency response. The “extreme-κ” of the SCTO layer minimizes the reduction in barrier capacitance for a given dielectric thickness, which can result in maintaining frequency performance and device scaling, while improving the electric field management and therefore breakdown. For the AlGaN/GaN heterostructure presented here, barrier capacitance is only reduced by 13% for a 90 nm Sr_1−xCa_xTiO₃ film with x = 0.22. No significant change in channel transport or V_T is seen, even for very thick films. An up to five order of magnitude reduction in vertical leakage is seen in the SCTO heterostructures, as a consequence of the high κ oxide layers. A positive interface charge is observed from the negative threshold voltage shift for increasing SCTO thickness, while 1D Poisson–Schrödinger simulations indicate that the experimentally measured sheet charge density closely follows the predicted values with dielectric thickness. High dielectric constants of up to 290 are extracted from the SCTO film, and RF characterization demonstrates that the “extreme-κ” is maintained into microwave frequencies, with a weak dependence of κ on the electric field. These characterizations demonstrate an epitaxial oxide integration with AlGaN that can prove useful for future high-κ-based GaN HEMT designs.

See the supplementary material for RHEED and AFM characterization of samples in the stoichiometry study, XPS measurements to determine SCTO composition, cross-sectional SEM images to analyze film thickness, and a table with extracted electrical properties.

This work was supported by the Office of Naval Research. E.N.J. and V.J.G. were supported by the National Research Council Postdoctoral Fellowships. The authors would like to acknowledge valuable technical discussions with Andrew Lang.

The authors have no conflicts to disclose.

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