β-Ga2O3 has been considered as a promising semiconductor candidate for high power and radio frequency (RF) electronics because of its ultrawide energy bandgap (4.8 eV) and predicted high critical field strength (8 MV/cm) [1][2][3]. Yet, the material is n-type dopable with shallow donors and a wide range of doping concentration from 10 16 cm -3 to 10 20 cm -3 [4][5][6][7][8]. The availability of high crystalline quality Ga2O3 substrates [9] with different orientations ((010), (100), (001), (-201)) enables high quality epitaxy of β-Ga2O3 [5][6][7][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]and β-AlGaO [28][29][30][31][32][33][34]. Several growth methods have been used to develop β-Ga2O3 thin films including molecular beam epitaxy (MBE) [6,11,35,36], pulsed laser deposition (PLD) [37][38][39], halide vapor phase epitaxy (HVPE) [5,[40][41][42], low pressure chemical vapor deposition (LPCVD) [8,14,[43][44][45] and metalorganic chemical vapor deposition (MOCVD) [4,7,16,17,23,25,[46][47][48]. Among them, MOCVD has been demonstrated to produce high crystalline quality materials with record room temperature and low temperature mobilities that approach the theoretical values [7,20,23,49]. The typical growth rate for MOCVD β-Ga2O3 using triethylgallium (TEGa) as the Ga precursor ranges between 0.2-1.0 µm/h [17,23,48,49]. For devices require thick epi-layers such as vertical power devices, epifilms with fast growth rate and high crystalline quality are required. Current device demonstrations on vertical β-Ga2O3 Schottky diodes or vertical pn diodes with thick drift layers are mainly based on HVPE grown materials [13,[50][51][52][53][54][55][56]. However, due to rough and non-uniform surface morphologies of HVPE grown β-Ga2O3 [41], chemical-mechanical polishing process is required for device processing, which can cause impurities incorporation and prevent in-situ epitaxy of heterojunctions.

On the other hand, MOCVD growth of β-Ga2O3 using trimethylgallium (TMGa) as the Ga precursor on (010) Ga2O3 substrates has been demonstrated with relatively fast growth rate up to ~3 μm/h [25]. Room temperature mobility as high as 190 cm 2 /Vs with carrier concentration of 1.8 x10 16 cm -3 and compensation level of ~ 1.5×10 15 cm -3 was achieved [25]. Previously, MOCVD growth of (010) β-Ga2O3 using TMGa with growth rate of 1.5 μm/h reported room temperature mobility of 125 cm 2 /Vs with carrier concentration of 1.5 x10 16 cm -3 , and low temperature peak mobility of 23000 cm 2 /Vs at 32 K [20]. These results indicate a great potential to develop high quality thick β-Ga2O3 films via MOCVD using TMGa as the Ga precursor. As compared to TEGa (3 torr at 20℃), TMGa has a higher vapor pressure (65 torr at 0℃) [57] and a shorter reaction pathway (in contrast to TEGa, which undergoes a three-step decomposition process, TMGa pyrolyzes via a two-step unimolecular reaction, generating monomethylgallium and a methyl group as by-products) [20,58,59], which enables faster growth rates of β-Ga2O3. Carbon (C) is considered as one of the most common impurities in MOCVD grown materials as it originates from the metalorganic (MO) precursors. Particularly, C incorporation is higher using TMGa as compared to that of the TEGa. TEGa decomposes via β-elimination and has a lower decomposition temperature, thus lowering carbon incorporation into the surface during MOCVD growth [60]. It was well understood that C is one of the main sources of charge compensation in the MOCVD grown n-type GaN [61,62]. However, the role of C in MOCVD growth of β-Ga2O3 is still not well understood.

In this work, C incorporation in MOCVD grown β-Ga2O3 on (010) Ga2O3 substrates using TMGa as the Ga precursor is systematically studied as a function of the growth rate and growth temperature. TMGa and pure O2 were used as the precursors of Ga and O, respectively. Argon was used as the carrier gas. Si doping was introduced by using the diluted silane source (diluted with N2, 25ppm) in the Si-doped samples. The growth pressure was set at 60 Torr and the O2 flow rate was set at 800 standard cubic centimeter per minute (sccm). The TMGa molar flow rate was varied between 39 μmol/min and 116 μmol/min. The growth temperature was controlled between 700℃ and 950℃. All samples were grown on Fe-doped semi-insulating (010) β-Ga2O3 substrates, which were ex-situ cleaned with acetone, IPA, and DI-water prior loading to the growth chamber.

Quantitative secondary ion mass spectroscopy (SIMS) was used to probe the impurity profiles of C, hydrogen (H), and silicon (Si). C and H represent the common impurities in MOCVD-grown materials, as they originate from the metalorganic (MO) precursors. Background Si is also a common impurity in MOCVD grown Ga2O3, which is from the growth chamber. From our previous studies, the background Si incorporation is highly dependent on the growth pressure [24].

Room temperature carrier transport characteristics were measured via van der Pauw Hall measurement (Ecopia HMS 3000, magnetic field=0.975 T). Ti/Au (30/100 nm) contacts were deposited on the four corners of the sample and annealed at 470 ℃ under N2 for 1 min to obtain Ohmic contacts.

The impurity concentrations of C, Si and H, as a function of the TMGa molar flow rate was studied by quantitative SIMS on a multi-layer stack sample (stack I) as shown in Fig. 1(a). The growth temperature was kept at 950 ℃. The silane flow rate was set at 0.416 nmol/min in the Sidoped sub-layers, which were sandwiched between the un-intentionally doped (UID) layers. The TMGa molar flow rate was varied from 39 to 116 μmol/min. The SIMS profiles of C, H, and Si remain constant in each sub-layer, suggesting that the diffusion process for C, H, and Si is negligible. Fig. 1(b) shows the SIMS depth profiles of the impurity elements C, H and Si. The detection limit for C, H and Si is 3 x 10 16 cm -3 , 5 x 10 16 cm -3 , and 5 x 10 15 cm -3 , respectively. The To study the compensation effect from C, a series of samples grown at different growth rates with different silane flow rates were designed for Hall measurements. As shown in Fig. 3, the carrier concentration and electron mobility of three sets of samples with different growth rates (2.8 μm/h, 5.3 μm/h and 6.7 μm/h) were characterized as a function of the silane flow rate. With the tuning of silane flow rate in a wide range, the measurable range of free carrier concentration differs drastically for the three sets of samples. For the samples grown at relatively low TMGa flow rate (58 μmol/min) or low growth rate (2.8 μm/h), a wide range of carrier concentration from 1.6 x 10 16 to 3.8 x 10 19 cm -3 was measurable. However, as the growth rate increases, the measurable range of carrier concentration becomes narrower. In the case of fast growth rate condition at 6. Prior theoretical studies based on the density-function theory (DFT) predicted that C on Ga site (CGa) acts as a shallow donor in Ga2O3 and C on oxygen site (CO) acts as a compensating acceptor [63]. However, experimental results do not show good agreement with either of these two cases. In our previous studies [25], the temperature dependent Hall measurement of the β-Ga2O3 epi-film grown with the TMGa flow rate of 58 μmol/min (growth rate of 2.95 μm/h) revealed an extracted charge compensation level of 1.45×10 15 cm -3 , while the corresponding SIMS data showed [C] and [H] were at ~ mid-10 16 cm -3 . This shows a strong indication of the passivation effect of H on the C compensation. Recent DFT calculations also show the neutralization of C-H complexes in β-Ga2O3 [63]. The strength of C-H bond, which is related to the small atomic size of C, makes the C-H combination behave as a unit, similar to a nitrogen atom, and lowers the overall formation energy. Therefore, for the MOCVD growth of β-Ga2O3, the incorporation of both C and

). Thus, the controllable net carrier concentration strongly depends on the growth rate.

The electron mobility as a function of carrier concentration for samples grown with different TMGa flow rates/growth rates is shown in Fig. 3(b). With the same TMGa flow rate/growth rate, the general trend shows that the electron mobility decreases as the carrier concentration increases.

For the case with fast growth rate at 6.7 μm/h and strong compensation, the electron mobility does not show obvious dependence on the carrier concentration within the measurable range. With the same carrier concentration, the electron mobility decreases as the growth rate increases. This is likely due to the increased scattering mechanism from the high compensation concentration.

In addition to the growth rate, the growth temperature is expected to affect C incorporation in MOCVD β-Ga2O3. In this work, the impurities incorporation as a function of growth temperature were studied with another designed growth stack (stack II), as shown in Fig. 4 (a).

The TMGa molar flow rate and chamber pressure were set at 58 μmol/min and 60 torr, respectively. The silane flow rate was set at 0.416 nmol/min in the Si-doped sub-layers. The growth temperature was varied from 950 ℃ to 700 ℃. The SIMS depth profiles of impurity elements C, H and Si were shown in Fig. 4(b). The detection limit for C, H and Si is 1 x 10 17 cm -3 , 5 x 10 16 cm - 3, and 5 x 10 15 cm -3 , respectively. The growth rate of β-Ga2O3 under different growth temperature was estimated from the SIMS depth profiles and was listed in Fig. 4(a). As shown in Fig. 4(b), the C incorporation has a strong dependence on the growth temperature. The [C] increases from ~7 x 10 16 cm -3 to 3.5 x 10 21 cm -3 as the growth temperature decreases from 950 ℃ to 700 ℃. Within the same growth temperature range, the [H] increases from 7.0 x 10 16 cm -3 to 1.0 x 10 19 cm -3 . In contrast, [Si] does not show a strong dependence on the growth temperature. The extracted C, H and Si concentrations as a function of the growth temperature was plotted in Fig. 5. Both [C] and [H] increase as growth temperature decreases, but [C] increases faster as compared to [H]. The faster decrease in carbon impurity incorporation at higher temperatures as compared to that of hydrogen can be attributed to the enhanced H diffusion at higher temperatures. At relatively high growth temperature, the net compensation ([C]-[H]) can be maintained at relatively low level. The slight decrease of [Si] from 950℃ to 800℃ is mainly due to the slight increase of the corresponding growth rate from 2.7 μm/h to 3.1 μm/h. The lower Si concentration at 700℃ is mainly attributed to the lower Si incorporation efficiency at low temperatures.

In conclusion, the role of C on the compensation effect in the MOCVD β-Ga2O3 epitaxy using TMGa as the Ga precursor was systematically investigated. The results revealed that both high TMGa flow rate/growth rate and low growth temperature can lead to higher C incorporation. can be widely controlled from below C detection limit (~5x10 16 cm -3 ) to as high as mid-10 21 cm -3 , indicating a potential effective approach to control the conductivity of the film; and (iii) intentional incorporation of H in MOCVD β-Ga2O3 can potentially suppress the compensation level via the passivation of C. These results will provide valuable guidance and flexibility for future device design and development.