Ultrahigh-yield growth of GaN via halogen-free vapor-phase epitaxy

The material yield of Ga during GaN growth via halogen-free vapor-phase epitaxy (HF-VPE) was systematically investigated and found to be much higher than that obtained using conventional hydride VPE. This is attributed to the much lower process pressure and shorter seed-to-source distance, owing to the inherent chemical reactions and corresponding reactor design used for HF-VPE growth. Ultrahigh-yield GaN growth was demonstrated on a 4-in.-diameter sapphire seed substrate.

Wafer cost generally consists of processing cost (the sum of crystal growth, slicing, and polishing costs as well as depreciation costs of production facilities) and raw materials cost. For GaN wafer production, the cost of Ga, which is much higher than that of Si or C, accounts for much of the total wafer cost. The high cost of Ga is due to its low abundance (18-19 ppm 27,28) ) in Earth's crust, as well as the absence of mineral ore primarily containing Ga (Ga is typically produced as a by-product of Al extraction from bauxite 29) ). The global supply of Ga is thus quite limited (300-400 tons=year 30) ) compared with that of major metals. Therefore, the efficient incorporation of Ga into GaN crystals in the growth process (i.e., a high material yield of Ga) is critically important for reducing the total cost of GaN wafers as it would minimize Ga consumption in the production of GaN wafers (see the online supplementary data at http:// stacks.iop.org/APEX/11/065502/mmedia for details).
The material yield of Ga obtained using conventional hydride vapor-phase epitaxy (HVPE), 31,32) the most commonly used growth technique for producing GaN wafers, is very low (less than 10%). This has resulted in a very high cost of GaN wafers and may lead to a shortage of Ga in the future (see Fig. S1 in the online supplementary data at http:// stacks.iop.org/APEX/11/065502/mmedia). This low yield is probably due to several factors, including a reverse reaction (etching) and the presence of a thick stagnant boundary layer on the seed surface (since the process is carried out under atmospheric pressure). Halogen-free vapor-phase epitaxy (HF-VPE) is a good alternative for the bulk growth of GaN at a high rate. [33][34][35] In our previous studies, we demonstrated the HF-VPE GaN growth of high-quality thick GaN layers at the relatively high growth rate of ∼100 µm=h. Moreover, HF-VPE with an additional component, a Ga evaporator, enabled us to significantly enhance Ga vapor supply and potentially achieve an ultrahigh growth rate of ∼500 µm=h. HF-VPE employs a simple reaction scheme [Ga(g) + NH 3 → GaN(s) + 3=2H 2 ], leading to an efficient reaction, a low reverse reaction rate, or both. Furthermore, the much lower pressure at which GaN is grown using HF-VPE than that using HVPE leads to a more efficient transport of Ga vapor to the seed surface through the stagnant layer. These factors contribute to the high-yield growth of GaN with HF-VPE, which promises to lower the cost of GaN wafers. In the present study, the critical growth parameters and mechanisms that govern the material yield of Ga in HF-VPE GaN growth are investigated, and ultrahigh-yield HF-VPE GaN growth is demonstrated.
The setup employed here for HF-VPE GaN growth, utilizing a vertical radio-frequency heating reactor, was almost the same as that described in previous reports (see Fig. S2 in the online supplementary data at http://stacks.iop. org/APEX/11/065502/mmedia). 33,34) The reactor was equipped with three process-gas channels, one each for the carrier N 2 , the sheath N 2 , and NH 3 (diluted with N 2 ); the corresponding flow rates are denoted as Q carrier , Q sheath , Q NH3 , and Q dilution , respectively. To significantly enhance the Ga vapor supply rate and thus the GaN growth rate, a Ga evaporator made of porosity-controlled TaC ceramic was installed in the Ga source crucible. 34) A total of 27 growth experiments (4-20 min each) under identical conditions were carried out using a 2-in. (5.08 cm)-diameter sapphire substrate as a seed. The growth parameters are listed in Table SI in the online supplementary data at http://stacks.iop.org/APEX/11/ 065502/mmedia. The growth parameters of concern were the seed substrate holder temperature (i.e., growth temperature), the Ga crucible temperature, the background pressure (process pressure) p, the gas flow rate, and the seed-to-crucibleoutlet distance d; their effects on the material yield of Ga, Y Ga , during HF-VPE GaN growth were investigated. Y Ga was calculated as where Δm substrate and Δm crucible are the weight gains for the seed substrate and Ga crucible, experimentally measured after each growth process, and M Ga (= 69.723 g=mol) and M N (= 14.0067 g=mol) are the molar weights of Ga and N atoms, respectively. A linear multivariate analysis was conducted to find the critical growth parameters that govern Y Ga . The relationships between these parameters and Y Ga were then verified. Furthermore, a demonstration of ultrahigh-yield growth was carried out using 3-in.  Table SI in the online supplementary data at http://stacks.iop.org/APEX/11/065502/ mmedia. The Y Ga values are in the range of 14-23%, which is considerably higher than those for conventional HVPE GaN growth (5-10%). The details of the linear multivariate analysis are given in the online supplementary data at http:// stacks.iop.org/APEX/11/065502/mmedia.
The relationship between Y cal Ga calculated using Eq. (2) and the experimentally obtained Y Ga is plotted in Fig. 1. The coefficient of determination, R 2 , is ∼0.96, indicating that the prediction power of Eq. (2) for Y Ga is quite high. In other words, Eq. (2) can be used to determine appropriate growth conditions for obtaining high Y Ga values in practice. According to Eq. (2), higher Y Ga values can be achieved with a shorter d, a lower p, and a lower gas-flow-rate ratio φ [defined as a combined critical parameter of (Q NH3 · Q carrier )= (Q sheath · Q dilution ) based on their regression coefficients]. In the following sections, the dependence of Y Ga on the individual critical growth parameters is discussed to clarify the mechanisms underlying the high material yield during HF-VPE GaN growth.
The R 2 values (= 0.87-0.997) for the regression equations indicate that the explanatory power is quite high. Furthermore, the exponential decay function with a y offset does not diverge (Y cal Ga never exceeds 100%) when the growth parameters are extrapolated to zero; i.e., this function is valid for all considered growth conditions. Thus, the exponential decay function with a y offset is the most appropriate.
As described in our previous study, 33) the rate-controlling factor for HF-VPE GaN growth is not surface kinetics but mass transport, which suggests that Y Ga for HF-VPE GaN growth is also governed by mass transport. There was no apparent correlation between Y Ga and the growth and crucible temperatures (see Fig. S3 in the online supplementary data at  http://stacks.iop.org/APEX/11/065502/mmedia); hence, Y Ga should be primarily governed by mass transport. If mass transport governs both the growth rate and Y Ga during HF-VPE GaN growth, the increase in Y Ga with decreasing p [ Fig. 2(b)] suggests a decrease in stagnant layer thickness 36) on the seed surface with increasing gas-stream velocity (∝ p −1 ). However, the extrapolation of the fitting curve in Fig. 2(b) to near-zero pressure (i.e., zero stagnant layer thickness) does not yield a steep increase in Y Ga ; therefore, the dependence of Y Ga on p does not necessarily support the hypothesis that mass transport is limited by the stagnant layer on the seed surface.
The dependence of Y Ga on d [ Fig. 2(a)] suggests that the gas-stream pathways for Ga vapor nearer the seed substrate surface are a dominant factor in achieving a higher Y Ga , as shown in Fig. 3. With a low p and a small d [Fig. 3(a)], most of the gas-stream pathways for Ga vapor (denoted by blue arrows) almost reach the seed surface owing to their high gasstream velocity and the short seed-to-source distance. However, when a larger d [ Fig. 3(b)] is employed, some of the gas-stream pathways for Ga vapor escape to the exhaust system without reaching the seed surface, which hinders the effective mass transport of Ga and thus results in a lower Y Ga . This reasoning also explains the dependence of Y Ga on p. When a higher p [ Fig. 3(c)] is employed, the reduced gasstream velocity diminishes the straightness of the gas-stream pathways for Ga vapor so that some of them escape to the exhaust system without reaching the seed surface, which hinders the effective mass transport of Ga and thus results in a lower Y Ga . Mass transport, which is mainly determined by the gas-stream pathways for Ga vapor, thus governs the material yield during HF-VPE GaN growth.
The gas-flow rate has a relatively minor effect on Y Ga . As defined above, φ is a combined critical parameter for gas flow rates, roughly corresponding to the degree of supersaturation in the gas phase. Figure 2(c) shows that a higher φ (i.e., higher degree of supersaturation) tends to decrease Y Ga . Under such higher-supersaturation-degree growth conditions, a larger number of GaN polycrystals tend to form on or near the crucible outlet; this parasitic GaN polycrystal formation consumes some of the Ga vapor, decreasing Y Ga .
As mentioned in the above discussion, a lower p and a smaller d are favorable for increasing Y Ga . From Figs. 2(a) and 2(b), decreasing d is expected to further increase Y Ga , whereas decreasing p is expected to yield a limited increase. Therefore, we investigated the possibility of further increasing Y Ga by reducing d through estimation using the regression equations derived above. Figure 4 shows the dependence of Y cal Ga on d extrapolated using Eqs. (2) and (3) (black and blue solid curves, respectively) at a process pressure of 1.26 kPa. From both curves, an ultrahigh Y cal Ga of ∼50% is predicted for a very small d range (0.3-0.5 cm). However, this range is not practically applicable as it would not allow the sufficient mixing of Ga vapor with NH 3 source gas to ensure GaN formation without undesirable Ga droplet formation. 37) Instead, considering the above discussion on the gas-stream pathways of Ga vapor, we employed larger-diameter seed substrates (3-and 4-in.-diameter sapphire substrates) to demonstrate the suppression of Ga vapor escape and the resultant higher Y Ga . Figure 5 shows the summarized results for Y Ga , the appearance of as-grown GaN layers, and surface morphologies on 2-, 3-, and 4-in.-diameter sapphire substrates (see the online supplementary data at http://stacks.iop.org/APEX/ 11/065502/mmedia for the data on growth rate, polarity, and impurity concentrations). Y Ga increases almost linearly with increasing seed substrate diameter, with an ultrahigh Y Ga of ∼47% obtained for the 4-in.-diameter substrate. With this ultrahigh material yield, we believe that HF-VPE can be used to produce a sufficient number of GaN wafers for high-power vertical GaN devices at moderate prices without depleting the global Ga supply.
Finally, we discuss the origins of the high material yield in HF-VPE GaN growth by comparing the growth conditions and material yield with those obtained for conventional HVPE GaN growth. The dependence of Y cal Ga on d at a process pressure of 100 kPa (identical to that used for conventional HVPE GaN growth) was calculated using Eq. (2) (see the black broken line in Fig. 4). At a d of ∼10 cm (similar to that used for conventional HVPE GaN growth), Y cal Ga is in the range of 7-8%, which is almost the same as that for HVPE GaN growth. In other words, the material yield obtained with HF-VPE is almost identical to that obtained with HVPE for a given set of critical growth parameter values. Fortunately, HF-VPE GaN growth can utilize a lower p owing to the absence of chlorine chemistry in its reactions; thus, a lower p is favorable for increasing the material yield as well as the supply rate of Ga vapor (resulting in a high growth rate 33) ). In addition, the supply rate of Ga vapor in HF-VPE must be (c) Fig. 3. Schematic drawings of gas-stream pathways for Ga vapor from crucible outlet to seed substrate in cases of (a) low pressure and small seedto-crucible-outlet distance, (b) larger seed-to-crucible-outlet distance, and (c) higher pressure (lower gas-stream velocity). Arrow length corresponds to gas-stream velocity for Ga vapor emitted from the crucible outlet. Fig. 4. Material yields of Ga predicted using Eqs. (2) and (3) with respect to seed-to-crucible-outlet distance.
enhanced by heating the Ga source crucible to a temperature of over 1200°C to achieve a high growth rate. 33) This is done using radio-frequency heating to locally heat the Ga source crucible without overheating the other reactor components, which enables the creation of a steep temperature gradient in the growth zone and allows growth to be carried out with a small d (conventional HVPE GaN growth setups use resistive heating and thus cannot use d values smaller than 10 cm). The higher material yield obtained with HF-VPE GaN growth than that obtained with HVPE GaN growth is thus attributed to the lower process pressure and shorter seed-tosource distance due to the inherent chemical reactions and corresponding reactor design for HF-VPE GaN growth.
In conclusion, we investigated the critical growth parameters that govern the material yield of Ga during HF-VPE GaN growth and discussed the mechanisms and origins of the observed high material yield. The major critical growth parameters were identified as process pressure and seed-tocrucible-outlet distance. A regression equation that can predict the material yield of Ga was derived. The dependence of the material yield on individual critical growth parameters indicates that mass transport, which is mainly determined by the gas-stream pathways for Ga vapor, governs the material yield during HF-VPE GaN growth. Furthermore, an ultrahigh material yield of ∼47% was achieved using a 4-in.-diameter substrate. With this ultrahigh material yield, HF-VPE can potentially be used to produce a sufficient number of GaN wafers for high-power vertical GaN devices at moderate prices without depleting the global Ga supply.  5. Dependence of material yield of Ga during HF-VPE GaN growth on seed substrate diameter. Insets show images of respective as-grown samples and their surface morphologies. Hexagonal hillock structures on the surface are due to direct growth on sapphire without a buffer layer, and the blackish appearance of grown layers is due to the optical confinement effect caused by hexagonal hillock structures.