In the low doping range below 1 × 1017 cm−3, carbon was identified as the main defect attributing to the sudden reduction of the electron mobility, the electron mobility collapse, in n-type GaN grown by low pressure metalorganic chemical vapor deposition. Secondary ion mass spectroscopy has been performed in conjunction with C concentration and the thermodynamic Ga supersaturation model. By controlling the ammonia flow rate, the input partial pressure of Ga precursor, and the diluent gas within the Ga supersaturation model, the C concentration in Si-doped GaN was controllable from 6 × 1019 cm−3 to values as low as 2 × 1015 cm−3. It was found that the electron mobility collapsed as a function of free carrier concentration, once the Si concentration closely approached the C concentration. Lowering the C concentration to the order of 1015 cm−3 by optimizing Ga supersaturation achieved controllable free carrier concentrations down to 5 × 1015 cm−3 with a peak electron mobility of 820 cm2/V s without observing the mobility collapse. The highest electron mobility of 1170 cm2/V s was obtained even in metalorganic vapor deposition-grown GaN on sapphire substrates by optimizing growth parameters in terms of Ga supersaturation to reduce the C concentration.
I. INTRODUCTION
Wide bandgap semiconductors play an important role for power electronic devices, which are needed for efficient electrical conversion and transmission.1 In particular, GaN-based Schottky barrier diodes2 are promising for the fabrication of compact inverters for high power densities due to their high breakdown voltage and high operating frequency.3 In order to obtain efficient GaN Schottky diodes, it is important to create a drift layer with controllable low free carrier concentration and high charge carrier mobility to provide for low specific on-resistances. However, as first observed by Bougrioua et al., the electron mobility can sharply decrease below a certain free electron concentration.4 The origin of this phenomenon, called mobility collapse, is not clear although it has been related to either threading dislocations or some other point defects within the layer. Generally, the density of threading dislocations (TDD) in the crystal limits the electron mobility in the drift layer.5 In addition, it is also understood that the density of point defects has a significant impact on the electrical and optical properties of GaN.6 Specifically, the range of possible free carrier concentrations in the doped GaN films is limited by the incorporation of compensating defects.
Carbon is one of the most common point defects in GaN grown by metalorganic vapor deposition (MOCVD),7,8 originating mostly from the large quantity of C delivered by the dissociation of organometallic molecules such as trimethylgallium (TMG) or triethylgallium (TEG). It has been suggested that C acts as a deep acceptor in n-type GaN, compensating donors such as Si, O, or Ge, thus limiting the achievable free electron concentrations of the n-type GaN films grown by MOCVD.9 Following this donor compensation, C in GaN may also reduce the electron mobility, since it has been reported that n-type GaN with electron mobility above 1000 cm2/V s was more likely to be achieved in carbon-free growth processes, such as hydride vapor-phase epitaxy and molecular beam epitaxy (MBE), rather than in MOCVD.10,11 However, the direct effect of C on free carrier concentration and mobility in n-type GaN grown by MOCVD has not been clarified due to the lack of controllability of C incorporation in the MOCVD process.
The relationship between the C incorporation and MOCVD growth parameters (V/III ratio, growth temperature, growth rate, growth pressure, and diluent process gas) has been widely discussed.12–15 However, the variety of seemingly different growth parameters makes it difficult to make a logical connection between the C incorporation and this multi-dimensional parameter space. We have previously demonstrated that the C incorporation is inversely proportional to the Ga supersaturation, which was developed by following the simplified GaN chemical reaction, Ga + NH3 = GaN + 3/2H2.16 The concept of the Ga supersaturation helps to quantify the driving force for the growth process from an all-inclusive parameter perspective and reduces a multi-dimensional problem to a simple, one-dimensional parameter space. Thus, the Ga supersaturation concept empowers the grower to easily understand the interdependence between the reaction driving force and C incorporation and lets him navigate through the available input parameters with relative ease.
In this work, we investigated the relationship between the C impurity concentration and electron mobility collapse within the low doping regime for n-type GaN. Different C concentrations were achieved by controlling the Ga supersaturation. It was found that the electron mobility as a function of free carrier concentration collapsed once the C concentration approached the Si concentration. By managing the Ga supersaturation, carbon incorporation was lowered to values well below the standard Secondary ion mass spectroscopy (SIMS) detection limit, which enabled us to achieve controllable free carrier concentrations down to 5 × 1015 cm−3 with peak electron mobility of 820 cm2/V s and without the mobility collapse for samples grown on sapphire substrates. The highest electron mobility of 1170 cm2/V s was achieved in GaN grown with a dislocation density of 1 × 109 cm−2 by MOCVD by reducing C concentration via high supersaturation conditions.
II. EXPERIMENTAL DETAILS
All GaN samples studied were grown on 2-in. (0001) sapphire substrates in a vertical, cold-walled, RF-heated, low pressure MOCVD reactor. The growth pressure was 20 Torr at a constant total mass flow of 7.5 slm. Triethylgallium (TEG) and ammonia (NH3) were used as Ga and N precursors, respectively. Silane (SiH4) was used as the n-type dopant source gas. The GaN samples were grown on the low temperature AlN nucleation layers (LT-AlN) or high-temperature AlN templates (HT-AlN). Room temperature Hall effect measurements were used to determine the free carrier concentration and electron mobility. Secondary ion mass spectroscopy (SIMS) was used to determine silicon and carbon concentrations. Double crystal x-ray diffraction (DCXRD) measurements were performed to obtain the full width at half maximum (FWHM) of ω-scan rocking curves for the estimation of the threading dislocation density (TDD).17
Following the Ga supersaturation model, several equivalent experimental growth processes for GaN growth were designed to demonstrate the control of C incorporation into the Si-doped GaN layers. Our base growth conditions, if not otherwise mentioned, consisted of a TEGa flow rate of 134 μmol/min and a growth temperature of 1040 °C. Both H2 and N2 were used as diluent gases. The V/III ratio was varied from 100 to 2000 by changing the NH3 flow rate from 13.4 to 268 mmol/min while keeping the TEG and total flow rates constant; the resulting GaN growth rate was 2.6 μm/h. To achieve even higher V/III ratios (4000, 8000, and 16 000), the TEG flow rate was reduced while keeping all other parameters constant; this resulted in GaN growth rates of 1.3 μm/h, 0.65 μm/h, and 0.33 μm/h, respectively. Three ladder structures with varying doping levels were prepared for SIMS studies: one grown with N2 diluent and two with H2 diluent.
III. RESULTS AND DISCUSSION
Vapor supersaturation or just simply supersaturation measures the driving force for growth given by the deviation from the equilibrium; it is expressed as
where Pi is the input partial pressure of the process limiting reactant (in this case Ga) and Peq is the equilibrium partial pressure of the same reactant as obtained from the governing chemical reaction. The driving force for the reaction toward equilibrium is directly given by the free energy change, which can be expressed in terms of supersaturation as
At equilibrium, supersaturation is 0; thus, there is no energy available for the process. In our particular case, a reaction between the gas precursors led to the deposition of the solid film; thus, the energy or driving force for the reaction was provided by continuously injecting reactants to replace those that were consumed.
Here, this force also implies the driving force for the surface kinetic processes that lead to the crystal growth. Thus, from the MOCVD process point of view, supersaturation is the single parameter that determines every aspect of growth, including the growth mode, incorporation of point defects, and surface morphology. From this perspective, supersaturation is the absolute metric by which we can compare different, seemingly unrelated process conditions. Although a complete knowledge of the chemical reaction energetics is needed to determine supersaturation accurately, selecting a main reaction that determines the overall behavior of the system is a practical way of analysis as it gives the grower the direction of change. Koukitu and Kumagai16 and Mita et al.18 recognized that for the case of GaN deposition by MOCVD, consider only a simple reaction
In our set of experiments, we considered the influence of the Ga supersaturation on the incorporation of C. This was evaluated by determining the C concentration as a function of different growth conditions, which were reduced to a Ga supersaturation value. An efficient way of accessing this parameter space is by growing alternating layers, different growth conditions and doping levels, and using the depth profiling capabilities of SIMS to measure the incorporation of C at an each particular change of growth conditions. An example of a doping ladder structure grown in the H2 diluent gas is shown in Figure 1. Four 500 nm thick Si-doped layers were grown at progressively higher supersaturation values achieved by increasing the V/III ratio (100, 500, 1200, and 2000). The first half of each layer was undoped while the second half was doped at a constant SiH4 flow rate of 22 nmol/min. The corresponding SIMS depth profiles for C and Si concentrations are shown in Figure 1(b). An increase in the Ga supersaturation lowered the C concentration, while the Si incorporation was not affected or it influenced the C incorporation. At the lowest Ga supersaturation (V/III ratio of 100), the C level was as high as 7 × 1019 cm−3, whereas the highest supersaturation in this growth sequence (V/III ratio of 2000) led to a C level of 2 × 1017 cm−3. As a comparison, the experiment was repeated for a three-layer Si-doped GaN sample, again with a stepwise increasing supersaturation (V/III ratio 100, 500, and 2000), but for the N2 diluent process. The observed dependence of the carbon concentration as a function of the V/III ratio under both N2 and H2 diluent gases is summarized in Figure 1(c). It can be seen that the C concentration was consistently lower for the N2 diluent gas process. One important generalization that arises from the main chemical reaction (3) is that H2 is one of the reaction products; thus, its use as a diluent gas shifts the reaction to the left and decreases supersaturation via Equation (1). Figure 1(d) illustrates the Ga supersaturation calculated following the procedure described in Ref. 18 as a function of the V/III ratio for different diluent gases. Even if H2 is not directly used as the diluent gas, it is always present to some degree due to the irreversible decomposition of ammonia, which is not a part of the growth reaction. This presence of hydrogen significantly reduces the Ga supersaturation below what one would expect for pure nitrogen. In practice, the process using N2 diluent is better described by assuming a certain fraction of H2 in the diluent gas (e.g., F = 0.2 in Figure 1(d) assumes 20% of H2). The exact effective ratio is estimated to be somewhere between F = 0.1 and 0.3 under practical growth conditions. However, the important trend of the supersaturation is always the same for low percentages of H2 and increases with V/III ratio. The Ga supersaturation in the H2 diluent gas process increases by about two orders of magnitude with the increase in the V/III ratio by 20 times, as shown in Fig. 1. In contrast, the Ga supersaturation exhibited a more moderate change in the N2 diluent gas process.18
The total C concentration was inversely proportional to the increase in Ga supersaturation. A thermodynamic analysis of the point defect incorporation process suggested that the ratio of the point defect concentrations under two different process conditions was inversely proportional to the ratio of the Ga supersaturation if their chemical potentials were related to the process functionality of the Ga supersaturation.
This is expected for an N-substitutional impurity such as CN. Lyons et al. described the formation energy of both CN and CAl in GaN as a function of the Fermi level and C and N chemical potentials relative to the respective reference phases.19 The Ga and N chemical potentials are related through , where is the free energy of the formation of GaN. In their description, consistent with thermodynamic expectations, they obtain an increase in the formation energy for a decrease in the Ga chemical potential when the process conditions go from Ga-rich to N-rich. The increase in the formation energy corresponds to a reduction in the concentration of the two species and . The Ga chemical potential is related to supersaturation through the equilibrium Ga partial pressure near the growth surface. As supersaturation increases, without changing the input Ga partial pressure, a lower equilibrium Ga partial pressure is expected with a corresponding reduction in the Ga chemical potential. This generalization between supersaturation and chemical potential helps to visualize the role of process conditions and impurity incorporation. Even though it could naively be expected that the reduction in C is due to the resulting N richer environment obtained by increasing the V/III ratio, this is not consistent with the role that the diluent gas was demonstrated to play in the process. This last part can only be made consistent by considering that the increase in supersaturation brings a further reduction in the equilibrium Ga partial pressure. Although these two pictures are equivalent, clearly the concept of supersaturation brings a unifying and simpler way of describing the actual process conditions. The following discussion will use Ga supersaturation as the control parameter to investigate the limits for C incorporation into Si-doped layers within technologically useful ranges. Ga supersaturation control will be achieved through variations in V/III ratio, input Ga partial pressure, and choice of diluent gas.
In order to investigate the effect of C on Si-doped GaN, several Si-doped 0.7 μm thick GaN layers with different C concentrations, achieved by the scheme discussed above, were grown on nominally undoped 1.3 μm GaN templates deposited on LT-AlN. Si-doped layers were grown using different V/III ratios, diluent gases, and different SiH4 flow rates. GaN templates were grown using a V/III ratio of 100 in N2 diluent gas resulting in all Si-doped layers to possess approximately the same TDD of 1 × 1010 cm−2. It was found that GaN became semi-insulating when the C concentration exceeded that of Si or any other background donor. Carrier concentrations obtained from the Hall effect measurements indicated partial compensation when the C concentration was approaching that of Si. The compensation levels were in good agreement with the concentrations of Si and C as determined by SIMS, thus suggesting that C acted as an acceptor-type trap as expected for CN. All GaN templates used in this study were semi-insulating.
As a compensator, C should have an impact on the electron mobility of Si-doped GaN. To study its impact, four sets of samples, with a structure as described in the previous paragraph, were grown under different supersaturation conditions. The resulting electron mobilities as a function of carrier concentration for all different conditions are shown in Figure 2. Each data point corresponds to one particular GaN sample grown at that particular growth condition and doping level. The results from three V/III ratios using the N2 diluent gas process are shown: 100, 500, and 2000. All samples grown using a V/III ratio of 2000 had a C concentration of 2 × 1017 cm−3; those grown using a V/III ratio of 500 and 100 had a C concentration of 3 × 1017 cm−3 and 1 × 1018 cm−3, respectively. One set of samples grown with a V/III ratio of 2000 in H2 diluent gas process with a C concentration of 2 × 1017 cm−3 was also included for comparison. The electron mobility seemed to converge to a value of slightly less than 200 cm2/V s for all samples with carrier concentrations around 1 × 1019 cm−3, regardless of different carbon concentrations. In this doping regime, the electron mobility was limited by the ionized impurity scattering due to the Si donor itself. However, when the doping level was decreased, the impact of the growth conditions on electron mobility became significant. For samples grown using a V/III ratio of 100, the mobility was nearly constant until a free carrier concentration of 1 × 1018 cm−3, followed by a sharp drop for lower doping concentrations. The electron mobility for samples grown with a V/III ratio of 500 had a maximum mobility of 300 cm2/V s at a carrier concentration of 2 × 1018 cm−3. This effect is more evident for the V/III ratio of 2000 in both gas processes. A mobility maximum of 350 cm2/V s was observed at the carrier concentration of around 2 × 1017 cm−3 and decreased rapidly for lower concentrations. In all cases, the electron mobility collapsed once the carrier concentration approached carbon concentration for the particular process, as shown by the three dashed vertical lines indicating three different C levels for each growth process.
It is clear from previous results that the control of C incorporation is necessary to achieve high electron mobility in the low doping regime below 1 × 1017 cm−3. In previous studies, it has been observed that the amount of C decreased with the decrease of TEGa flow rate, as the main source of C in MOCVD-grown GaN were metalorganic precursors such as TEGa or TMGa.20 In the simplest concept of supersaturation, reducing the TEGa flow rate decreases the Ga supersaturation, and based on the discussion above, an increase in the C incorporation is expected. Nevertheless, since the C source is also expected to decrease in the gas phase by the reduction of the TEGa, C incorporation into GaN should also strongly depend on other process parameters. That is, it should depend on how the TEGa is reduced relative to other precursors and thermodynamic variables. Figure 3 shows the dependence of mobility on carrier concentration for GaN films grown under different V/III ratios and diluent gases. The V/III ratios exceeding 2000 were achieved by reducing the TEGa flow during the Si-doped GaN growth, whereas the ammonia flow remained constant. The growth temperature was changed to accommodate for the decrease in the Ga supersaturation brought by the decrease in the TEGa flow rate. Based on the particular conditions in which the V/III ratio was increased and the TEGa decreased, it is expected that even though the supersaturation could have decreased, the equilibrium Ga partial pressure remained stable at a particular value away from the Ga-rich conditions as previously described. This kept the Ga chemical potential constant; thus, a further reduction in C incorporation was only possible if the remaining C in the gas phase was further reduced by another reaction or process. In terms of the formation energy, this would correspond to a reduction in the C chemical potential while leaving the Ga chemical potential more or less constant.19 For samples grown using H2 diluent gas, an increase in V/III ratio led to a lower carrier concentration value for the mobility collapse, which is indicated by the red lines inserted in Figure 3 as guide for the eye. As previously mentioned, this lower critical value for the mobility collapse indicated that the C concentration was decreased in the films. In contrast, an increase in the V/III ratio while using an N2 diluent gas process had no influence over the trend of mobility as observed in samples grown under an H2 diluent gas process. Since there was no significant difference in the Ga supersaturation for the two diluent gas processes at the higher V/III ratios, an independent decrease of the remaining C in the gas phase must have occurred. As discussed, this indicates the existence of an additional process that reduces C under the presence of H2. One possible reaction is through an increase in the probability of removal of ethyl or methyl groups produced from the decomposition of either TEGa or TMGa. An example of this could be an adsorbed state such as CH3 (ad) + H (ad) = CH4 (g) for the case of TMGa, the lack of ethyl radicals in TEGa or through another gas phase mechanism.21,22 This reduction in the carbon concentration is typically assigned to hydrogen when used as a diluent gas in the MOCVD processes, especially in the growth of III-As compounds.23
It was demonstrated that C acted as a compensator and, as such, prevented the achievement of high electron mobility in the low doping regime. However, with a further reduction in the C concentration, other electron scattering processes, e.g., due to dislocations, limit the electron mobility. As shown in Figure 3, the maximum electron mobility was limited to values around 400 cm2/V s at a carrier concentration of 2 × 1017 cm−2, in samples grown at higher V/III ratios. This mobility value is in good agreement with theoretically calculated mobility by considering GaN with a dislocation density of 1 × 1010 cm−2.24 In order to achieve higher electron mobilities in the low doping regime, the Si-doped GaN films need to have low C concentrations and low dislocation densities.
Following this hypothesis, a set of Si-doped samples was grown on 1.3 μm GaN templates and on HT-AlN templates. The TDD in these samples was 1 × 109 cm−2, as measured by the rocking curve values for the 00.2 and 30.2 reflections with FWHM of about 450 arc sec and 450 arc sec, respectively, for all samples. The Si-doped samples were grown at a V/III ratio of 4000 in H2 diluent gas and a temperature of 1000 °C in order to increase Ga supersaturation further. The room temperature electron mobility as a function of free carrier concentration for this series of GaN samples is shown in Figure 4(a). The electron mobility exceeds values of 700 cm2/V s over the whole carrier concentration range between 1016 cm−3 and 1017 cm−3. The maximum electron mobility was 820 cm2/V s at a free carrier concentration of 5 × 1016 cm−3. The mobility collapse in this sample series occurred at free carrier concentrations below 1 × 1016 cm−3. To further support the statement that compensation through C induces the mobility collapse, the Matthiessen's rule was used to model the mobility24 with a threading dislocation density of 1 × 109 cm−2 and a concentration of compensating defects of 9 × 1015 cm−3 (see below); the result of the calculation is given by the red curve in Figure 4(a). The calculated behavior assuming the expected C concentration as the degree of compensation closely followed the experimental data.
By controlling C incorporation via Ga supersaturation, a precise control of the free carrier concentration below 1016 cm−3 is possible. This control is demonstrated in Figure 4(b), which shows the dependence of free carrier concentration on SiH4 flow rates. The carrier concentration follows a linear relation with Si input into the 1015 cm−3 range, suggesting that the C concentration was suppressed below these values.
These observations suggest the possibility for verifying certain assumptions about the role of dislocations and the importance of C as an acceptor/compensator within the GaN system. To check any possible limitations in the C incorporation in the MOCVD-grown GaN, Si-doped GaN samples were grown at a V/III ratio of 16 000 by decreasing the TEGa flow rate during the growth of the Si-doped layer even further. This procedure was similar to the one described previously. The room temperature mobility was increased to a maximum value of 1170 cm2/V s at a carrier concentration of 5 × 1016 cm−3, which agrees with the carrier concentration of the mobility maximum of the previous series. In addition, it agrees with the observations of the highest mobility GaN sample from Kyle et al. grown by MBE on native substrates.11 Figure 5 shows the temperature-dependent electron mobility curves of the two GaN samples grown at V/III ratios of 4000 and 16 000.
To confirm previous observations of the reduction in C incorporation, SIMS analysis was realized in alternating doped layers grown under different conditions on the same template. The process conditions used were those used to achieve the high electron mobility. This measurement was possible by the low C measurement protocol SIMS conducted at Evans Analytical Group that allowed for C detection below the typical background values of ∼1 × 1016 cm−3. The growth conditions for all layers were identical, and the V/III-ratio was increased to values as high as 16 000 by only reducing the flow of TEGa into the reactor. The resulting SIMS measurement is shown in Figure 6. The average atomic carbon concentration in the layers with V/III ratios of 4000, 8000, and 16 000 was measured as 9 × 1015 cm−3, 3 × 1015 cm−3, and 2 × 1015 cm−3, respectively. These measurements, especially the one for a V/III ratio of 4000, are in good agreement with the onset of mobility collapse in Figure 4 and the respective atomic carbon concentration. Based on these results, it is necessary to reduce the C incorporation to the levels in the low 1015 cm−3 range to achieve controllable carrier concentrations at or below 1 × 1016 cm−3 with high electron mobility. Such a degree of growth control has not been systematically demonstrated, and only recently modern MOCVD process designs are taking this into consideration. Previous results suggesting the importance in the reduction of C for achieving devices close to their ideal limits were not directly able to measure the predicted influence on the electron mobility.7 This was a consequence of the growth of the test samples on conducting templates, making Hall measurements impossible. Nevertheless, it is clear that C reduction is necessary if properly designed drift layers for high voltage applications are needed. Currently, it is not clear if the C incorporation levels in MOCVD can be reduced even further, or other techniques to further reduce the compensating point defects may be necessary.25–27
IV. CONCLUSION
In summary, we related residual carbon impurities to the mobility collapse of the n-type GaN films grown by MOCVD. The results indicate that the electron mobility of GaN films is strongly influenced by carbon impurities as they act as compensators within the Si-doped GaN. By increasing Ga supersaturation during growth, C incorporation is significantly reduced, which enables high mobility GaN films with low free carrier concentrations as necessary for drift layers in power devices.
The maximum mobility of with a V/III ratio of 4000 was 820 cm2/V s at a free carrier concentration of 5× 1016 cm−3. Controllable doping with Hall mobility consistently greater than 700 cm2/V s was possible down to carrier concentrations below 1 × 1016cm−3 with very low fluctuations in electrical, optical, and structural properties. By implementing all the growth principles discussed in this work, a maximum mobility of 1170 cm2/V s at a carrier concentration of 5 × 1016 cm−3 was achieved in MOCVD, where it was thought that this was possible only by using MBE.
ACKNOWLEDGMENTS
We thank Fred Stevie from the Analytical Instrumentation Facility (AIF) at NCSU and Jeffrey Serfass from Evans Analytics Group (EAG) for the SIMS measurements of our samples using special techniques for high accuracy. Partial financial support from NSF (DMR-1108071, DMR-1312582, ECCS-1508854, DMR-1508191) and ARO (W911NF-15-2-0068, W911NF-14-C-0008) is greatly appreciated. One of the co-authors, A. Franke, held an NRC Research Associateship.