Epitaxial stabilization of rutile germanium oxide thin film by molecular beam epitaxy

Ultra-wide-bandgap (UWBG) semiconductors possess a bandgap significantly wider (>3.4 eV)¹ than traditional semiconductors (1–2.3 eV). UWBG semiconductors have tantalizing advantages for power devices as the wider bandgap allows for larger breakdown strength, which can lead to increased power density and reduced energy loss.² AlN/AlGaN, $β$-Ga₂O₃, c-BN, and diamond currently lead UWBG electronics research;² however, each material has serious drawbacks that restrict the development of high-performance UWBG electronics. For example, AlN/AlGaN and diamond suffer from high cost and limited availability of native substrates, which impedes their adoption for device applications.^3–5 While $β$-Ga₂O₃ has generated excitement due to its high Baliga Figure of Merit (BFOM),⁶ it suffers from inefficient heat removal owing to its poor thermal conductivity⁷ as well as from doping asymmetry,⁸ which limits its application to unipolar transistors. Therefore, alternative UWBG materials must be examined to realize suitable power devices.

Recently, theoretical predictions have identified rutile germanium oxide (r-GeO₂) as a promising UWBG material having a bandgap of 4.68 eV, ambipolar dopability, and large BFOM.^9,10 Among different polymorphs of GeO₂, the rutile phase is thermodynamically the most stable at ambient conditions and insoluble in water.^11,12 The electron mobility (⁠$μe$⁠) and breakdown electric field (⁠$EC$⁠) are theoretically predicted, and the predicted Baliga Figure of Merit (BFOM) is higher than that of $β$-Ga₂O₃.¹⁰ Another advantage of r-GeO₂ is its high thermal conductivity (37 W m⁻¹ K⁻¹ $⊥ c→$ and 58 W m⁻¹ K⁻¹ $∥c→$ from theory and 51 W m⁻¹ K⁻¹ from experiment measured for polycrystalline samples, >2 times higher than the highest value of $β$-Ga₂O₃),¹³ which allows efficient thermal management of devices.¹⁴ In addition, while most of the current UWBG semiconductors suffer from doping asymmetry, r-GeO₂ is theoretically predicted to display ambipolar doping through the shallow ionization energies (<0.04 eV) for Sb, As, and F donors and the 0.45 eV ionization energy for Al acceptors.¹⁵ 

Despite the superior properties predicted by theory, there is a lack of experimental investigation of r-GeO₂ for its potential application in power electronics. This is mainly due to the technical challenges associated with material synthesis as a crystalline thin film. A major challenge for the synthesis of r-GeO₂ lies in the existence of different polymorphs. Although rutile-GeO₂ is the lowest free energy phase at the ambient condition, both amorphous-GeO₂ and quartz-GeO₂ are deeply metastable polymorphs (Fig. 1). Particularly, the commercially available source of GeO₂ is the quartz (hexagonal) phase and, due to the large negative volume change of ∼50% (⁠$ρ$_quartz= 4.29 g/cm³, $ρ$_rutile = 6.23 g/cm³), phase conversion from quartz to rutile relies on high pressure (>100 MPa), which cannot be achieved in a typical vacuum deposition system.^13,16 On the other hand, the glass phase is kinetically the easiest to form, readily forming from thermal oxidation of elemental Ge metal species (crystallization of the quartz-GeO₂ phase occurs at T_s $≥$600 °C).¹⁷ This is the result of the high valence state (+4) of germanium that bonds to oxygens forming the interconnected backbone of the glass network that is close in energy to the rutile phase. Thus, along with SiO₂ and BO₃, GeO₂ is a strong glass former.¹⁸ 

For molecular beam epitaxy (MBE) of oxide films, it is typical to co-supply elemental metal and reactive oxygen species (i.e., ozone or oxygen plasma) and, thus, films are synthesized from the oxidation of metal species. In the case of group-III and IV oxides (e.g., Ga₂O₃, In₂O₃, SnO₂, or GeO₂), where the elemental metal can oxidize into suboxides (e.g., Ga₂O, In₂O, SnO, or GeO), challenges emerge regarding achieving the proper stoichiometry and reasonable growth rates due to the formation and desorption of the suboxides on the film surface as intermediate reaction products. This can place strict limits on the growth window using substrate temperature, oxygen reactivity, and metal to oxygen flux ratio.¹⁹ The use of a preoxidized metal source, however, can have advantages in achieving a better growth rate and film quality by using simpler reaction kinetics.²⁰ For instance, Raghavan et al.²¹ have reported that using a SnO₂ source promotes the two-dimensional growth of BaSnO₃ films and leads to enhanced mobility, contrary to a Sn metal source that promotes island growth and degraded mobility. Due to the competing reaction between oxide and suboxide formation when using a Sn source, SnO (g) consumes active oxygen leaving behind Sn droplets that are not yet oxidized, which results in a defective interface layer.²¹ On the other hand, a preoxidized Sn source that creates a molecular beam in the form of SnO_x prevents excess Sn incorporation by avoiding the two-step reactions.²¹ Similar opportunities and challenges are expected for the GeO₂ film growth as the intermediate, GeO (g), is more volatile compared to those for SnO₂ or Ga₂O₃ (Fig. S1 and Ref. 22).

Here, we report the synthesis of (101)-oriented single-crystalline r-GeO₂ thin films on R-plane sapphire substrates. The r-GeO₂ thin films are synthesized by ozone-assisted molecular beam epitaxy (MBE) using a preoxidized source (quartz-GeO₂ powder) to establish a molecular flux of GeO. Despite the competition from a kinetically stabilized glass phase, we find that an adsorption-controlled growth from a molecular precursor that balances epitaxial strain, adsorption/desorption rate, and surface adatom kinetics is able to stabilize the crystalline phase. Utilizing a buffer layer of (Sn,Ge)O₂ on R-plane sapphire substrates, varied by the relative ratio of the Sn/Ge composition, the degree of lattice mismatch for epitaxial stabilization of the r-GeO₂ thin film was investigated; the experimentally calculated lattice mismatch value of 4.4% (⁠$∥$a) and 5.3% (⁠$∥$c) for the r-GeO₂ on (Sn,Ge)O₂ buffer enabled crystalline r-GeO₂ growth, while the calculated lattice mismatch value greater than 4.8% (⁠$∥$a) and 6.3% (⁠$∥$c) leads to amorphous GeO₂ films. The adsorption/desorption behavior of the GeO molecular-beam flux, and their influence/competition on rutile and glass phase formation, was investigated as a function of growth parameter (i.e., substrate temperature and ozone pressure). Therefore, our results allow for r-GeO₂ films to be explored as an alternative UWBG material and provides insights to overcome the synthesis of crystalline materials prone to glass formation.

Prior to growth, a 200 nm thick Pt back side coating was deposited on the R-plane sapphire substrate to enhance the efficiency of radiation heating from the substrate heater. GeO₂ powder (Alfa Aesar, 99.9999%) and SnO₂ powder (Alfa Aesar, 99.996%) were used as the source materials to generate preoxidized mono-oxide beam fluxes.^20,23 The flux from the source materials was calibrated using a quartz crystal microbalance (QCM) before each deposition. The flux of GeO₂ was varied from 5.5 × 10¹² to 1.4 × 10¹⁴ molecules/cm² s and the flux of SnO₂ was varied from 8.5 × 10¹² to 5.3 × 10¹³ molecules/cm² s to study GeO₂ thin film crystallinity depending on the (Sn,Ge)O₂ buffer layer composition. The flux of GeO₂ and SnO₂ as a function of inverse cell temperature is plotted in Fig. S1. Owing to the generation of the parasitic oxygen molecule while heating GeO₂ and SnO₂ sources [i.e., GeO₂ (s) $→$GeO (g) + ½ O₂ (g) and SnO₂ (s) $→$SnO (g) + ½ O₂ (g)], the base pressure of the growth chamber was on the order of 10⁻⁷Torr. At the flux of GeO₂ = 6.9 × 10¹³ and SnO₂ = 2.8 × 10¹³ molecules/cm² s, we first deposited a rutile SnO₂ seed layer on a R-plane sapphire substrate at 600 °C for 15 min and then opened both GeO₂ and SnO₂ shutters to deposit the (Sn,Ge)O₂ buffer layer for 1 h. During the SnO₂ and (Sn,Ge)O₂ buffer-layer growth, an ozone (∼15% O₃ + 85% O₂) background pressure of 7 $×$ 10⁻⁶Torr was provided. After the buffer layer deposition, the substrate was cooled down to 450 °C, the ozone background pressure was decreased to 1 $×$ 10⁻⁶Torr, and GeO₂ thin film was deposited for 4 h.

The crystal structure and epitaxial registry of our samples were determined by x-ray diffraction using an Empyrean diffractometer with a 1.5406 Å Cu K $α1$ source with a hybrid monochromator. Figure 2(a) shows the x-ray diffraction 2 $θ$-$ω$ scan of a r-GeO₂ thin film grown on a (Sn,Ge)O₂ (flux ratio of Ge:Sn = 2.5:1)/SnO₂-buffered R-plane sapphire substrate. Strong diffraction peaks are observed for the films, which correspond to the (⁠$101$⁠)-orientation of rutile SnO₂, (Sn,Ge)O₂, and GeO₂, respectively. A wide-range x-ray diffraction scan also shows that only the (⁠$101$⁠)-oriented film peaks [with the (⁠$11¯02$⁠)-substrate peak] are present, revealing a single-phase rutile GeO₂ film. The out-of-plane planar spacing, d₍₁₀₁₎, is determined to be 2.629 Å for SnO₂, 2.533 Å for (Sn,Ge)O₂, and 2.401 Å for GeO₂. The values for SnO₂ and GeO₂ are close to the bulk values (2.639 Å for SnO₂ and 2.400 Å for GeO₂), which suggests relaxed films.

In order to determine the lattice constants and misfit strain of the films, a reciprocal space map around the asymmetric $112$ reflections of the rutile films was measured as shown in Fig. 2(b). Making the assumption that the a and b axes of the rutile films are equivalent, we estimate the misfit strain of the films. The $a$ and $c$ lattice constants of the SnO₂ film grown on the R-plane sapphire substrate are 4.612 Å and 3.199 Å, indicating strains of −2.50% and 0.61% along the $a$ and $c$ directions, respectively. The $a$ and $c$ lattice constants of the r-GeO₂ film are determined to be 4.390 Å and 2.865 Å (which are close to the bulk lattice constants, $a$ = 4.394 Å and $c$ = 2.866 Å). The $a$ and $c$ lattice constants of (Sn,Ge)O₂ are 4.598 Å and 3.026 Å and, assuming linear Vegard's law for the $a$ and $c$ lattice parameters, the estimated composition of Ge in the alloy is 0.39–0.49.

Prior work has reported (⁠$101$⁠)-oriented SnO₂ film growth on R-plane sapphire substrates and determined that the in-plane epitaxial relationship is [$010$] SnO₂ $∥$ [$112¯0$] Al₂O₃ and [$1¯01$] SnO₂ $∥$ [$1¯101$] Al₂O₃.^24–27 The epitaxial relationship of our samples was determined from the asymmetric rutile 002 Bragg peaks observed using a 2 $θ$-$ω$ x-ray diffraction scan in skew geometry at $χ$ = 33° [Fig. 2(c)]. The [001] directions of the rutile layers are found to be parallel to the [$11¯00$] direction of the Al₂O₃ substrate. Projection of these directions onto the (⁠$101$⁠) and (⁠$11¯02$⁠) planes of GeO₂ and Al₂O₃, respectively, leads to an in-plane registry of [010] GeO₂ ǁ [$112¯0$] Al₂O₃ and [$1¯01$] GeO₂ ǁ [$1¯101$] Al₂O₃ in agreement with prior reports.²⁴ Figures 2(d)–2(f) illustrate the epitaxial relationship.

Next, the effect of lattice mismatch on the epitaxial stabilization of r-GeO₂ thin films was investigated using a compositionally tuned (Sn,Ge)O₂ epitaxial buffer layer. The supplied flux ratio between GeO₂ and SnO₂ and the ozone pressure were tuned to adjust the ratio of Sn and Ge in the (Sn,Ge)O₂ buffer layer and the lattice constant accordingly. When the supplied flux ratio between SnO₂ and GeO₂ is 1:0.1 at the background ozone pressure of 1 × 10⁻⁶Torr, the 101 peak position of the (Sn,Ge)O₂ layer from x-ray diffraction does not noticeably shift from the SnO₂ peak position [Fig. 3(a)], indicating a highly Sn rich film. The corresponding calculated misfit strains to r-GeO₂ on this buffer layer are then 9.0% and 7.1% along the [$1¯01$] and [010] axis of bulk r-GeO₂, respectively. Though we observe a distinct (Sn,Ge)O₂ (101) Bragg's peak when the supplied flux ratio between SnO₂ and GeO₂ is 1:0.4 [Fig. 3(b)], still, the (101) Bragg's peak position of the (Sn,Ge)O₂ layer is much closer to SnO₂. In these two cases, GeO₂ films deposited on top of the Sn-rich (Sn,Ge)O₂ buffer layer immediately turned into the amorphous phase as observed by in situ RHEED patterns. When the supplied flux ratio between SnO₂ and GeO₂ is 1:2.5, the (Sn,Ge)O₂ film peak moved toward the GeO₂ film peak position and the corresponding lattice constants are $a$ = 4.618 Å and $c$ = 3.059 Å [Fig. 3(c)], leading to calculated misfit strains of 5.8% and 4.8% along the [$1¯01$] and [010] axes for bulk GeO₂, respectively. The lattice constant value of (Sn,Ge)O₂ is still closer to the that of SnO₂ (⁠$a$ = 4.73 Å and $c$ = 3.18 Å) than that of GeO₂ (⁠$a$ = 4.395 Å, $c$ = 2.866 Å) yet GeO₂ deposited on this buffer layer started growth in the crystalline phase but transitioned into the amorphous phase after ∼30 min of deposition. To incorporate more Ge into the (Sn,Ge)O₂ buffer layer and further reduce the misfit-strain on the GeO₂ film, the ozone pressure under the fixed flux of SnO₂ and GeO₂ (1:2.5 ratio) was increased up to 7 $×$ 10⁻⁶Torr to reduce desorption of volatile GeO (g) [Fig. 3(d)]. The lattice constants for this (Sn,Ge)O₂ buffer layer are $a$ = 4.598 Å and $c$ = 3.026 Å, which are approximately the average value of SnO₂ and GeO₂. The corresponding calculated misfit strains are 5.0% and 4.4% along the [$1¯01$] and [010] axis for bulk GeO₂, respectively. Using this buffer layer, we were able to stabilize rutile GeO₂ throughout the 4-h deposition (∼40 nm thick film). The compositional dependence of the (Sn,Ge)O₂ buffer layer on the stabilization of the r-GeO₂ film illustrates that the degree of lattice mismatch is of critical importance to stabilize the rutile phase.

To further reduce GeO desorption and induce adsorption as GeO₂ (s), we studied the growth of GeO₂ films at a range of substrate temperatures (T_s from 375 °C to 750 °C) and background pressures (P—mid 10⁻⁷Torr to 10⁻⁵Torr). Here, P indicates the total background pressure measured by the ion gauge, including molecular oxygen flux from the source and ozone pressure. An empirical phase diagram is shown in Fig. 4(a). GeO (g) desorption dominates when T_s $≥$ 600 °C at P = 10⁻⁶Torr or T_s $≥$ 750 °C at P = 10⁻⁵Torr, as determined by monitoring RHEED patterns during GeO₂ deposition. For all T_s studied at P = 10⁻⁵Torr and T_s = 475 °C at P = 10⁻⁶Torr, the resultant films are in the glass phase [Figs. 4(b) and 4(c) RHEED patterns]. We believe that a proper ratio between GeO_x (g) and O₂ (g) reactants is required at the film surface for the crystallization of r-GeO₂. If the flux of oxygen species is too high at P = 10⁻⁵Torr, the imbalance between the amount of GeO_x (g) and O₂ (g) reactants can lead to a high condensation rate that exceeds the necessary adatom mobility for crystallization and promote the formation of amorphous phase. Or if the sublimation of GeO is too high at T_s $≥$ 475 °C and P = 10⁻⁶Torr, the higher oxygen chemical potential can lead to the formation of defects such as metal vacancies and oxygen interstitials, which avoids crystallization.²⁸ 

At T_s $≤$ 420 °C, the film growth is amorphous, suggesting that this temperature range does not provide sufficient adatom mobility to crystallize. The range of T_s from 420 °C to 450 °C at P = 10⁻⁶Torr is found to stabilize r-GeO₂ throughout the deposition, indicating a balance between these factors. The RHEED pattern after 2 h of deposition is shown in Figs. 4(d) and 4(e). The RHEED pattern is spotty throughout the growth, indicating a three-dimensional growth mode, but a single crystalline film. Thus, Fig. 4(a) illustrates that stabilization of r-GeO₂ requires a thermodynamic growth condition that balances GeO (g) adsorption/desorption.

In summary, we report the synthesis of epitaxial r-GeO₂ thin films. This has been achieved by using a preoxidized GeO₂ powder precursor source in the manner of adsorption-controlled MBE growth. The heteroepitaxial films are (⁠$1$0$1$⁠)-oriented on a r-(Sn,Ge)O₂/SnO₂ buffered (⁠$11¯02$⁠) sapphire substrate with an in-plane registry of [010] GeO₂ ǁ [$112¯0$] Al₂O₃ and [$1¯01$] GeO₂ ǁ [$1¯101$] Al₂O₃. Despite the presence of a kinetically stabilized glass phase of GeO₂, epitaxial stabilization of r-GeO₂ thin films was enabled by a buffer layer with a low lattice misfit, optimal substrate temperature, and an ozone pressure that leads to an appropriate ratio between GeO_x (g) and O₃ (g) reactants. Our finding allows r-GeO₂ to be experimentally assessed as a candidate UWBG material for power electronics.

See the supplementary material for the flux of SnO₂ and GeO₂ molecular species as a function of source temperature.

We gratefully acknowledge Christopher Parzyck for SEM and EDXS measurements. Experimental work was supported by the National Science Foundation [Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM)] under Cooperative Agreement No. DMR-1539918. N.V. and J.H. acknowledge support from the Semiconductor Research Corporation (SRC) as the NEWLIMITS Center and NIST through the Award No. 70NANB17H041. H.P. acknowledges support from the National Science Foundation [Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM)] under Cooperative Agreement No. DMR-1539918. Substrate preparation was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the NSF (Grant No. NNCI-1542081).