Toward controllable Si-doping in oxide molecular beam epitaxy using a solid SiO source: Application to β-Ga₂O₃

Due to a high variety of functional properties, metal oxides are rising in popularity as material systems for innovative optoelectronic devices.¹ Among metal oxides, monoclinic β-Ga₂O₃ is one of the most interesting ones, and it has been particularly intensely investigated in the past decade.² In fact, due to a predicted breakdown field around 8 MV/cm as a consequence of its bandgap of about 4.8 eV, β-Ga₂O₃ is one of the most promising novel materials for power electronics.³ Moreover, it can be grown from the melt^4–7 in turn allowing for β-Ga₂O₃ homoepitaxy of high quality layers.³ 

To obtain a broad range of devices for power electronic application, a thorough control on the electrical properties is needed.⁸ Considering the lack of p-type doping for Ga₂O₃,⁹ the main focus is on the group-IV elements in order to tune n-type doping. So far, Ge, Si, and Sn have been already successfully employed as dopants in homoepitaxial layers grown with different technique, such as molecular beam epitaxy (MBE),^5,10–15 Metal Organic Chemical Vapor Deposition (MOCVD),^16–19 and Metal Organic Vapor Phase Epitaxy (MOVPE).^20,21

Lany has theoretically shown²² that Si can be considered as a better donor compared to Ge and Sn, since it is predicted to be the only truly shallow donor among them. From a survey of experimental data collected on semiconducting homoepitaxial β-Ga₂O₃ layers,⁸ the highest electron mobilities μ over a broad range of electron concentrations n are achieved with Si or Ge doping; the generally lower μ in Sn-doped films is likely related to a deep donor state identified for Sn.¹² Controlled Si doping in β-Ga₂O₃ has been already demonstrated in MOCVD but not in MBE. This is most likely linked to the two limitations of Si doping in MBE systems.

The first one is due to the unintentional incorporation of Si, probably related to the quartz cavity of the plasma source in oxygen plasma-assisted MBE (PAMBE)^23,24 and is limiting the low concentration side of the doping window (N_Si < 10¹⁸ cm⁻³).

The second one is due to instable Si-doping concentration in PAMBE-grown Ga₂O₃ layers that depend on the oxygen background pressure rather than the Si source temperature as pointed out by Kalarickal et al.¹³ As an underlying process, they identified the oxidation of the elemental Si source resulting in the source flux to consist of the SiO suboxide, which has a higher vapor pressure than Si. Further oxidation of the Si surface into solid SiO₂ was identified by Krishnamoorthy et al.¹⁵ to cause drastic flux reduction during layer growth due to the lower vapor pressure of SiO₂. Based on the underlying mechanisms, we conjecture ozone-MBE not to suffer from the first limitation but from the second one.

Indeed, the oxidation of the heated elemental source in an oxygen background into its volatile suboxide happens for many elements, including In, Ga, Ge, or Sn.²⁵ This suboxide formation at the source can determine the Ge- or Sn-doping of oxides (including in the Ga₂O₃ material system) or even the growth rates (GRs) for Ga₂O₃ during MBE deposition at relatively low Ga-source temperatures (e.g., <750 °C). Despite similar suboxide formation, the use of a Sn-metal source for Ga₂O₃ in PAMBE is more controllable with respect to a Si one¹² but can involve segregation problems.²⁶ For Ge-doping of Ga₂O₃ from a Ge-source in PAMBE, an additional strong dependence of doping concentration on the growth substrate temperature (T_g) has been shown.¹⁴ High concentrations (N_Ge ≈ 10²⁰ cm⁻³) required relatively low T_g (600 °C), potentially placing limits on the crystal quality of the deposited layers.

An efficient solution to control Si doping in oxide MBE while avoiding massive oxidation of the source could be the use of an oxide or suboxide source material in the cell,²⁷ similar to the use of SnO₂, SnO, or mixtures of Sn and SnO₂ to produce a SnO flux,^26,28 or mixtures of Ga and Ga₂O₃ to produce a Ga₂O flux.^28,29 Major advantages in the use of a suboxide (or mixed elemental + oxide) sources over an oxide one are the significantly lower cell temperatures required and the absence of parasitic oxygen formation from the decomposition of the oxide source material.²⁸ On the contrary, controllable Si doping would benefit from a SiO₂ source that cannot oxidize further as SiO could. However, based on the vapor pressure of SiO₂,²⁷ the geometry of our growth chamber, and the temperature limit of conventionally employed effusion cells (1200 °C), the Si concentration in layers deposited at a typical growth rate of 4.5 nm/min would be limited to N_Si ≤ 10¹⁹ cm⁻³ for a SiO₂ source. For example, a high-temperature effusion cell running at $TSiO2$ = 1400 °C would be required to obtain N_Si = 1 × 10²⁰ cm⁻³ [considering that a growth rate (GR) of 1 Å/s in our MBE system correlates with a partial pressure of the source material in the effusion cell on the order of 10⁻³ mbar (Ref. 28)].

In comparison, a SiO source could reach N_Si = 1.7 × 10²⁰ cm⁻³ at T_SiO = 900 °C, which prompted us to characterize a solid SiO source for PAMBE growth with a focus on doping β-Ga₂O₃ layers. In particular, we demonstrate the possibility to obtain Si-doping concentrations on a wide range—from 4 × 10¹⁷ cm⁻³ (limited by the background Si concentration in the PAMBE deposited layers) up to 1.7 × 10²⁰ cm⁻³—in both homoepitaxial and heteroepitaxial β-Ga₂O₃ layers, with negligible dependence on the growth orientation and/or the growth temperature. For our study, an Al₂O₃ crucible loaded with 10 g of 3–6 mm SiO lumps (4 N purity, Alfa Aesar) was placed in a conventional single-filament effusion cell.

At first, we characterized the direct flux from this SiO source using a quadrupole mass spectrometer (QMS) mounted line in sight to the cell inside a custom-built system, which is schematically shown in the inset of Fig. 1 and described in Ref. 28. The composition of the flux from the SiO source at a base pressure in the low 10⁻⁸ mbar regime is reported in Fig. 1(a) for a cell temperature of T_SiO = 1200 °C chosen to maximize the signal-to-noise ratio for the identification of the different desorbing species. Due to the natural abundance of stable isotopes of Si at 28 amu (92.23%), 29 amu (4.67%), and 30 amu (3.1%), the major signals shown in Fig. 1(a) can be clearly identified as SiO. A weaker Si signal is recorded and related to fragmentation inside the QMS.²⁸ To remove interference with residual N₂ (having the same mass per charge as ²⁸Si), the measurements with closed cell shutter were subtracted from those with opened shutter. An Ar signal due to the background pressure is also visible. The same qualitative SiO spectra could be recorded down to T_SiO = 880 °C where the ⁴⁴SiO signal reaches the noise level.

To calculate the activation energy E_a for SiO sublimation, the ⁴⁴SiO signal was recorded at T_SiO ranging from 1200 to 800 °C in vacuum. The corresponding Arrhenius plot yields E_a = 3.29 eV [red line in Fig. 1(b)] in good agreement with the E_a = 3.41 eV [black line in Fig. 1(b)] extracted from the thermodynamic calculation of Adkison et al.²⁷ 

To investigate potential source oxidation in molecular oxygen, the source was exposed to a controlled O₂ background of p = 1 × 10⁻⁵ mbar (typical for PAMBE growths) for periods of 30–180 min at various T_SiO. A potential surface oxidation to SiO₂ during this exposure is expected to reduce the SiO flux (⁠$ΦSiO$⁠) with respect to the untreated SiO source material. Figure 2 shows the comparison of the measured SiO partial pressure during the ramp up (performed in vacuum) from T_SiO = 700 to 1200 °C before and after exposure of the source to an O₂ background pressure of 1 × 10⁻⁵ mbar for 3 h at T_SiO = 700 °C. The matching partial pressure recorded in both experiments indicates that the SiO source did not get oxidized. The initial (up to 15 min) higher values detected for the SiO partial pressure after the oxidation process (red dashed lines in Fig. 2) are due to the higher background pressure caused by residual oxygen in the chamber after the treatment and a limited mass filtering of the QMS.

Next, the crucible with the SiO source material was mounted in our PAMBE growth chamber for doping experiments. In order to predict the SiO-flux and consequential Si doping concentration in MBE deposited β-Ga₂O₃ layers as a function of the T_SiO, we extrapolated the corresponding $ΦSiO$ for T_SiO = 1000 °C (⁠$ΦSiO1000 °C =4.8×1013 cm−2 s−1$⁠) toward lower T_SiO by

with Boltzmann's constant k, activation energy E_a from the QMS experiment [red line in Fig. 1(b)], and $ΦSiO1000 °C$ extracted from the growth rate of an amorphous SiO₂ layer as described in the supplementary material. The extrapolation described in Eq. (1) is shown as the solid line in Fig. 3. Knowing the β-Ga₂O₃ growth rate—in our case, a typical value is GR_Ga2O3 = 4.5 nm/min—it is possible to derive the expected Si doping concentration, e.g., Ν_Si = 6.4 × 10²¹ cm⁻³ for T_SiO = 1000 °C using

The predicted values obtained from Eqs. (1) and (2) were used as our guideline to investigate different doping concentrations in β-Ga₂O₃ layers on both Al₂O₃(0001) and β-Ga₂O₃(010) substrates grown at T_g of 550 and 750 °C, respectively (see the supplementary material). Depth profiles of the Si dopant were obtained by time-of-flight secondary ion mass spectrometry (ToF-SIMS IV, iontof GmbH, Germany). For quantification, the relative sensitivity factor for silicon in a gallium oxide matrix was obtained by measuring an implantation standard of Si into a nominally undoped β-Ga₂O₃ single crystal with a 10¹⁴ cm⁻² fluence and an implantation energy of 80 keV.

In Fig. 3, symbols represent the different ϕ_SiO at the substrate as function of the corresponding T_SiO, calculated as the product of N_Si (measured by SIMS) and $GRGa2O3$ (obtained from SIMS profile) following Eq. (2). For reference, the corresponding volumetric Si concentrations are shown assuming a fixed growth rate of 4.5 nm/min (average GR of the deposited samples) on the right y-scale of Fig. 3. The obtained broad range of Si doping concentrations from 3–4 × 10¹⁷ cm⁻³ (T_SiO = 700 °C) up to 1.7 × 10²⁰ cm⁻³ (T_SiO = 900 °C) demonstrates the possibility to use a SiO source charge for continuous doping in β-Ga₂O₃ thin films controlled by the source temperature in PAMBE. Nonetheless, it was not possible to demonstrate the possibility of achieving doping concentrations below 3 × 10¹⁷ cm⁻³ due to an unintentional Si incorporation in the nominally undoped β-Ga₂O₃ layers of around N_Si = 2 × 10¹⁷ cm⁻³ detected by SIMS. We tentatively relate this unintentional Si incorporation to the plasma source as recently pointed out by Asel et al.²⁴ 

A close inspection of the Si doping profiles of all the deposited β-Ga₂O₃ films reveals a systematically decreasing Si concentration toward the surface, as exemplarily shown in Fig. 4(a). The respective highest and lowest Si concentrations from the begin and end of the doped layers are reflected by the corresponding error bars in Fig. 3. Before the growth of the doped layers, the SiO cell was kept at the corresponding temperature for 15–60 min, in order to exclude the thermalization of the source as the possible origin of the slope. Consequently, we attribute the decreasing Si concentration in the doping profiles to progressive oxidation of the surface of the source material into SiO₂ during PAMBE growth. This finding is just apparently in contrast to the absence of source oxidation in molecular oxygen (see Fig. 2), since it confirms the findings of Kalarickal et al.¹³ who suggested active oxygen to play a major role for the oxidation of the Si source into SiO₂ in PAMBE. To further understand the impact of source oxidation, two different data sets are provided in Fig. 3. The empty symbols mark samples grown with a partially oxidized source, while the filled ones show data for samples where a high temperature cycle (T_SiO = 1100 °C, t = 30–60 min) was carried out before the layer growth to degas and restore the SiO surface. At T_SiO = 800 °C, the comparison between the two sets of data leads to a difference around 1.5 orders of magnitude for the $ΦSiO$ (cf. Fig. 3). Notwithstanding, the Si concentrations from the begin of the layers grown with a freshly degassed cell (upper error bar of filled symbols in Fig. 3) follow the vapor pressure behavior of SiO, confirming the principal control of Si-doping by the source temperature rather than the background pressure. Doping values from the literature¹³ concerning Si doping using an elemental Si source inside a PAMBE system are also reported in Fig. 3 (filled orange hexagons); the comparison with the experimental data collected in this work permits to highlight the significantly increased control of a SiO-source compared to a Si one. In addition, the matching incorporated SiO-flux concentration at the same T_SiO both on (0001) Al₂O₃ (T_g = 550 °C) and β-Ga₂O₃ (T_g = 750 °C) suggests (i) a negligible dependence of Si-incorporation on the T_g as was instead observed for Ge¹⁴ and (ii) a negligible dependence on the β-Ga₂O₃ growth orientation [i.e., (−201) and (010), respectively].

Further inspection of Fig. 4(a) suggests the slope of the decreasing Si-concentration to depend on the SiO cell temperature, being steeper for a T_SiO = 700 °C compared to the one at 800 °C. In a simple oxidation model [pictorially explained in Fig. 4(c)], the unoxidized area of the source material (that can provide a SiO flux) decreases with a decay constant λ. Considering a fixed probability per unit time that a certain percentage of the SiO source surface will further oxidize into SiO₂, as a function of T_SiO and the oxygen background pressure in the MBE chamber, we expect an exponential decay of the accessible SiO surface, and hereby of the SiO flux. Consequently, an exponentially decreasing $ΦSiO$ (which is proportional to this area) is expected during source oxidation,

where Φ_SiO(0) corresponds to the flux at t = 0. Using Eq. (3), Eq. (2), and the relation between layer thickness d and corresponding growth time t (d =$GRGa2O3$t), we extracted λ from the slopes of the SIMS profiles d(lnN_Si)/d(d) as

Figure 4(b) shows the extracted λ for layers doped at different T_SiO and suggests two different regimes: (i) for T_SiO > 730 °C, almost flat doping profiles signify a low decay constant, (ii) for lower T_SiO, a high λ indicates non-stable doping throughout the layer thickness (e.g., decrease in the doping concentration from 6.8 × 10¹⁷ cm⁻³ down to 2 × 10¹⁷ cm⁻³ in a deposition time t = 15 min, i.e., over a 90 nm layer thickness). These data suggest lower T_SiO (within the investigated range) to promote oxidation of the source, similar to the observations of Kim et al. for the Sr source oxidation,³⁰ and in very good agreement with Kalarickal et al.,¹³ that determined passive oxidation of an elemental Si source into SiO₂ at T_Si = 750 °C and active oxidation into SiO at T_Si ≥ 800 °C during PAMBE growth of Si-doped Ga₂O₃. Hence, the low temperature and, consequentially, low doping regime requires further measures to reduce the oxidation of the source in order to achieve more uniform doping profiles.

In order to understand how the active oxygen in the chamber affects the oxidation of the source, a preliminary study of the decay constant, for a fixed T_SiO = 800 °C, as a function of both the oxygen flux and the plasma power [inset Fig. 4(b)] is provided. More data will be needed in order to completely understand and model this behavior but, a reduction of the oxygen flux, from 1 sccm down to 0.33 sccm, clearly shows a significant reduction of the decay constant (around two times less at 400 W at the same T_SiO). For the plasma power the data show some inconsistency. In fact, while at the lower flux O_flux = 0.33 sccm and low plasma power (150 W), a lower decay constant is found compared to the sample with the same oxygen flux, at higher plasma power (400 W, hence, a larger amount of active oxygen), for the higher supplied flux O_flux = 1 sccm, the trend is inverted. This unexpected behavior is still not clearly understood, and further experiment is needed in order to address this issue.

Finally, room temperature van der Pauw–Hall measurements (details in the supplementary material) were performed on a homoepitaxially grown sample with a 124 nm-thick Si-doped layer (N_Si = 3 × 10¹⁹ cm⁻³). The extracted Hall electron concentration of n = 3 × 10¹⁹ cm⁻³ with an electron mobility μ of 25 cm²/V s and a sheet resistance R_s of 645 Ω/sq confirms effective Si-doping by our approach in line with the provided $ΦSiO$⁠.

In conclusion, we have demonstrated the potential of a solid SiO source to provide a wide range of SiO fluxes controlled by the source temperature of a conventional effusion cell. Using this source, SiO fluxes at the substrate ranging from 5.5 × 10¹³ (T_SiO = 1000 °C) to 2.9 × 10⁹ (T_SiO = 700 °C) cm⁻² s⁻¹ were used to grow a SiO₂ layer as well as continuously Si doping β-Ga₂O₃ layers with concentrations ranging from 1.7 × 10²⁰ (T_SiO = 900 °C) cm⁻³ to 3 × 10¹⁷ (T_SiO = 700 °C) cm⁻³ inside an oxide PAMBE. Hall measurements of a homoepitaxial Si-doped β-Ga₂O₃ layer deposited with a T_SiO corresponding to an expected N_Si = 3 × 10¹⁹ cm⁻³ (800 °C) revealed the same charge carrier density (n = 3 × 10¹⁹ cm⁻³) indicating effective doping. The Si-incorporation was essentially the same for Ga₂O₃(010) homoepitaxially grown at 750 °C and Ga₂O₃(−201) heteroepitaxially grown at 550 °C.

An oxidation of the SiO source, leading to a decreasing SiO flux, has been observed in active oxygen (plasma) but not in molecular oxygen at similar background pressures. The decreasing flux has been parametrized by a decay constant λ extracted from the measured Si-doping profiles. Our initial data indicate a strong oxidation regime (λ ≥ 0.14 min⁻¹) for relatively low T_SiO (≤730 °C) and a milder one (λ < 0.015 min⁻¹) at higher T_SiO (≥800 °C) at 250 W. The partial oxidation of the source can be reproducibly reverted by degassing at T_SiO = 1100 °C. Reducing the supplied oxygen flux has been shown to reduce the oxidation of the source (lowest recorded λ = 0.003 min⁻¹ at 0.33 sccm and 150 W), while the effect on the plasma power on the oxidation process is still unclear and further experiments will be needed in order to provide a definitive answer.

We believe that our approach can be also applied to O₃-MBE²⁶ as well as for doping of other oxides, e.g., In₂O₃. Suggested measures to reduce the source oxidation during growth by oxygen PAMBE include (i) an increased T_SiO or (ii) a decreased activated oxygen p_O2 at the SiO source. The (i) can be realized by a modified source geometry, e.g., using an aperture on the crucible³¹ or an increased source-to-substrate distance,³⁰ to necessitate a higher SiO vapor pressure (and thus higher T_SiO) inside the crucible to obtain the same SiO flux at the substrate. The (ii) can be realized by the same aperture as in (i), a differentially pumped SiO source,³² or by using growth conditions that require less oxygen,³³ e.g., metal-exchange catalyzed MBE (MEXCAT-MBE).^34–37 

See the supplementary material for the growth of the amorphous SiO₂ layer that was used in order to calibrate our flux predictions (Fig. 3). Furthermore, details on the growth of the β-Ga₂O₃ layers and additional information on the transport measurements are also provided.

We would like to thank Duc Van Dinh for critically reading the manuscript, as well as Hans-Peter Schönherr, Claudia Herrmann, Carsten Stemmler, and Steffen Behnke for their technical support on the MBE and test chamber. This work was performed in the framework of GraFOx, a Leibniz-ScienceCampus, and was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project No. 446185170.