Bandgap engineering of indium gallium nitride layers grown by plasma-enhanced chemical vapor deposition Open Access

Thin films of indium gallium nitride compounds (In$x$Ga$1−x$N, simply referred to as InGaN in the following) are usually deposited by metal-organic chemical vapor deposition (MOCVD) or by molecular beam epitaxy (MBE), with the occasional assistance of a remote plasma to produce nitrogen radicals (“Plasma-Assisted MBE”—PAMBE). These are high temperature (high-T, 600 $°$C and higher)^1,42 deposition methods, which imply three major drawbacks: (1) favored InN and GaN phase segregation,² (2) high manufacturing costs,³ and (3) inability to use glass or other temperature-sensitive substrates.¹ Moreover, in the case of monolithically MOCVD-grown Si-InGaN tandem solar cells, electronically active defects in the bulk of the silicon wafer can be created by such high temperatures if no specific precautions are taken, which decreases the device’s efficiency.^4,5 Growing InGaN films at lower temperatures would alleviate all these issues, provided sufficient layer quality can be achieved. Plasma-based methods, such as plasma-assisted atomic layer deposition or plasma-enhanced chemical vapor deposition (PECVD), are often used to grow electronic-quality materials at low temperature (low-T)^6–9 and are, therefore, also attractive for InGaN compounds.

What makes InGaN interesting for (tandem) photovoltaic (PV) applications is the ability to tune its bandgap between the values of InN and GaN. At an In/(In + Ga) ratio of 45 at. %, defect-free InGaN has a bandgap of 1.8 eV, which is optimal for a top-cell coupled with a silicon bottom cell in a tandem configuration, giving a theoretical efficiency of 43%.¹⁰ Coincidentally, the same composition enables a perfect alignment between silicon’s valence band (VB) and InGaN’s conduction band (CB), facilitating an Ohmic junction (see Fig. 1).^11,12 Alternatively, using InGaN alloys as carrier-selective contacts in combination with a silicon PV absorber is another application with high potential interest. In that case, low In-content alloy (or even simply GaN) could be used, provided it can be highly n-doped.

PV applications require careful consideration of the energy level of defects, which can affect carrier concentrations and carrier lifetimes in the material. In III-V semiconductors, the position of the Fermi level stabilization energy $EFS$ with respect to their band edges determines the doping density that will be observed in highly defective films. The stabilization of the Fermi level energy $EF$ at $EFS$ corresponds to a minimum free energy of the defect system in quasiequilibrium with the free-carrier gas.¹³ In GaN layers, defects are expected to be created in the midgap region, countering the effect of extrinsic doping. On the contrary, $EFS$ penetrates the conduction band of InGaN compounds for In/(In + Ga) ratios of about 30 at. % or more (see Fig. 1).¹² This induces defects inside the conduction band and naturally leads to an n-type behavior in defective layers.

In general, if $EF$ is intrinsically lower than $EFS$⁠, donorlike defects will form preferentially during growth until $EF$ approaches $EFS$⁠. Similarly, if $EF$ is higher than $EFS$⁠, then acceptorlike states will grow preferentially. Generally, for InGaN, but particularly for InN, a high density of donor-type defects yields a strong free-carrier absorption (FCA) in the infrared (IR) and a high optical bandgap due to the Burstein–Moss effect. This led to erroneous reports of 1.7 eV for the bandgap of InN,¹⁴ whereas the more likely value stands at 0.7 eV.¹² 

Thus, low-T InGaN layers for PV applications have development potential. This study aims to demonstrate the ability of PECVD to deposit InGaN layers over a broad range of chemical compositions and to investigate the effects of deposition parameters on material properties important for PV applications.

InGaN films were deposited by PECVD in a parallel-plate reactor at 110 MHz and 30 W, at a pressure of 500 $μ$bar and over a temperature range of 180–250 $°$C. InGaN layers were codeposited on glass, polished (001) silicon wafers, and a TEM grid, without any pre- or post-treatment. The precursors used are nitrogen (N$2$⁠), hydrogen (H$2$⁠), ammonia (NH$3$⁠), trimethylgallium (TMG), and N$2$-bubbled trimethylindium (TMI). The lowest reachable TMG and N$2$-bubbled TMI flow rates are 0.05 and 0.3 sccm, respectively. Table I shows the details of the deposition parameters used, while Fig. 2 sketches the PECVD setup.  Appendix A describes the plasma composition and the growth mechanism in further detail.

Spectroscopic properties were characterized by means of a Horiba UVISEL ellipsometer, and with a Perkin Elmer-Lamda 950 spectrometer for optical transmission and absorption using an integrating sphere. The thickness was assessed both with an Ambios Technology XP-2 profilometer and with ellipsometry coupled-modeling, using a Drude model and a Tauc-Lorentz oscillator. The layer crystallinity and composition were determined by a multipurpose diffractometer PANalytical Xpert Multipurpose x-ray diffraction (XRD) system, by a MonoVista Confocal Raman System (MonoVista CRS+) setup, and by an FEI Co. Talos F200X 200 keV field emission (scanning) transmission electron microscope. The composition was also estimated by means of energy dispersive spectroscopy (EDS) with a ZEISS GeminiSEM 450 microscope.

The film quality metrics are the optical bandgap $E04$⁠, the Urbach energy $EU$⁠, and the crystallite size. $E04$ is the energy at which the absorption coefficient reaches a value of 10 000 cm$−1$⁠. The final absorption coefficient calculation is shown in Eq. (1c), where it is deduced from the thickness $d$ and the experimental total reflectance $TR$ and total transmittance $TT$ of the layer, measured with the integrating sphere of the spectrometer. This is a simplified model, where the interferences between the layer and the glass substrate are not taken into account,

The Urbach energy $EU$ was evaluated by fitting the tail region of the absorption coefficient below the bandgap to the exponential given by Eq. (2),¹⁵ where $α0$ and $E1$ are the two empirical fitting parameters. Finally, the crystallite size was extracted using the Scherrer equation,^16,17 displayed here in Eq. (3), where $τ$ is the mean size of the ordered (crystalline) domains, $K$ is a dimensionless shape factor, $λ$ is the x-ray wavelength, $β$ is the full width at half maximum (FWHM) after subtracting the instrumental FWHM, and $θ$ is the Bragg angle.

Crystallinity and chemical composition were measured using the layers deposited on silicon, whereas layers deposited on glass were used to extract growth rate and optical bandgap. Further details regarding substrates and extraction of these properties are given in  Appendix B.

An InN or GaN layer of high quality would have an optical bandgap $E04$ close to its electronic bandgap value (0.7 or 3.4 eV, respectively), large crystallite size, and a low Urbach energy (preferentially below 0.05 eV). InGaN layers were first deposited using N$2$ as the nitrogen source, the results of which are presented in Sec. III A. This first subsection shows that better layer qualities are achieved at a lower growth rate. To further reduce the growth rate, InN and GaN layers were then grown using ammonia as the nitrogen source and the results are presented in Sec. III B.

For InGaN layers, different indium contents (⁠$19at.%≤XIn≤72at.%$⁠) and growth rates (⁠$4.1≤g≤8.4$ nm/min) were investigated. InN and GaN experimental layer characteristics define the extremes of this variation.

XRD measurements of In/GaN layers deposited on untreated 001 silicon wafers show a 002 preferential growth, whereas the In$0.3$Ga$0.7$N layer also shows a $100$ peak (see Fig. 3). Based on similar works on the growth of ZnO,^18,19 it is proposed that this behavior is due to the initial layer being aligned along the c axis, which is consistent with the lowest surface free energy of the (0002) plane in wurtzite InGaN or ZnO. This also implies that our growth conditions are not in thermodynamic equilibrium, which leads to the apparition of nonminimum surface free energy grain in the initial layer, whose preferential orientation will grow faster perpendicularly to the substrate. Different deposition conditions could then alter the overall preferential orientation, where the main adjusting factors would be temperature and layer thickness.

InN layers display sharper peaks than GaN, which, in turn, are sharper than InGaN ones. This implies that InN layers contain the largest crystals (25 nm) of the three species. No InN or GaN phase segregation is observed in any InGaN layer probed by XRD. Phase separation relies on multiple factors. In any alloy, it requires long range diffusion, and, thus, a correlation between phase separation and growth rate is expected. The different interatomic distances between GaN and InN can also give rise to a phase miscibility gap that increases with indium content.²⁰ At high temperatures, this phenomenon is also exacerbated by the high vapor pressure of InN with respect to that of GaN, leading to low indium incorporation in the InGaN layer. It is assumed that the reason for an absence of phase separation in the layers presented here is their thinness (less than 150 nm) and the choice of the deposition parameters used for growing the films: the use of relatively low growth temperatures, high V/III flow ratio, low growth rate, and low growth pressure.¹ 

Compared to InN and GaN reference peaks, InGaN peaks are then used to assess the atomic indium content of the layers, which are compared to the values extracted from EDS measurements (see Figs. 11 and 12 in  Appendixes A– E). Both methods confirm one another within a $±$3% error margin and are, thus, reliable. The XRD result is chosen for its higher reliability compared to EDS.

Figure 4 shows the absorption coefficients of the same layers as discussed in Fig. 3. Their optical bandgap $E04$ is determined from the intersection with the horizontal blue line. Due to their ternary nature, InGaN layers are expected to obey Vegard’s law, with a bowing parameter $b$ [see Eq. (4a)].²¹ Figure 5 shows the optical bandgap $E04$ as a function of the indium content X$In$⁠. The points are widely spread out and a single bowing parameter cannot be extracted. We note that layers deposited at a higher growth rate yield a higher $b$ parameter than the ones deposited at low growth rates. Thus, the bowing parameter of Vegard’s law seems to depend on the growth rate $g$⁠.

To test this observation, a model based on Vegard’s law is developed by letting Vegard’s three parameters (the GaN bandgap $EgGaN$⁠, the InN bandgap $EgIn$⁠, and the bowing parameter $b$⁠) depend on the growth rate $g$⁠. The dependency is chosen to be linear for each of the three parameters as a first approximation, as detailed in the set of Eq. (4). Six empirical fit parameters are then chosen for the lowest sum of squares of residuals of the model over the experimental points: $a1InN$⁠, $a2InN$⁠, $a1GaN$⁠, $a2GaN$⁠, $a1b$⁠, and $a2b$⁠. Given Vegard’s law’s configuration, this means that on top of having a quadratic dependency on the indium content $XIn$⁠, and the bandgap of InGaN layers also has a linear dependency on the growth rate $g$⁠,

This model is fitted to the experimental points without constraints, where each point represents an InGaN layer with measured growth rate $g$⁠, indium content $XIn$⁠, and optical bandgap $E04$⁠. The resulting fit parameters and statistics are presented in Table II. The model is in excellent agreement with experiments, with a fit residual under 10%. According to this model, Vegard’s bowing parameter b increases with increasing growth rate, reaching 4.33 eV at a growth rate of 8 nm/min. The bowing parameter usually takes values between 1 and 3 eV for InGaN compounds.²¹ 

According to Walukiewicz et al.,¹² InN layers with an optical bandgap above 1 eV indicate a high electron concentration. Hall effect measurements on an InN layer (⁠$E04=1.7eV$⁠) confirmed an electron concentration of $n=1.9×1021cm−3$ and a mobility of $μ=33.4cm2/Vs$⁠. This is coherent with the ellipsometry (assuming an effective mass of $0.25me$ in the Drude model),²³ and indeed confirms the link between the bandgap and the electron concentration proposed by Walukiewicz et al., based on the Burstein–Moss effect. Such high electron concentrations imply that these layers can be considered unsuitable for PV absorbers as the high carrier concentration would likely entail a short lifetime due to Auger recombination. InGaN layers with lower indium content are also suspected to be degenerately doped.

Given the behavior of the bowing parameter in the model, we infer that for degenerately doped layers, a relatively better crystallinity and, in turn, a lower subband absorption is reached at a lower growth rate. This claim is supported by a general decrease in the Urbach energy of all the layers with decreasing growth rate, for any $XIn$⁠, as shown in Fig. 6. The lower growth rate gives enough time to the adsorbates to arrange themselves with fewer native defects or carbon impurities,²⁴ leading to a lower Burstein–Moss shift and a lower Urbach energy, along with better crystallinity. A reduction in the defect concentration decreases the sub-bandgap absorption and results in a sharper band edge and a higher optical bandgap for GaN, or a lower optical bandgap for InN. This also explains the smaller bowing parameter for lower growth rates. Moreover, since the Fermi level stabilization energy lies within the conduction band (respectively, bandgap) for InN (respectively, GaN), InN layers are more easily degenerately doped. Thus, it is also observed that the growth rate has a higher influence on the InN bandgap than on the GaN bandgap, which is manifested in the $a1GaN$ factor being smaller than the $a1InN$ one.²⁵ In terms of XRD measurements, the lowest growth rates yield a higher XRD intensity (see filled symbols in Figs. 5 and 7). Peaks almost systematically appear for a growth rate below 6 nm/min.

Unfortunately, growth rates lower than 4 nm/min, which should further improve the crystallinity, could not be reached due to the instrumental limits of our system. This limit is also visible in Fig. 7, where indium contents between 5–20 at. % and 60–95 at. % (at low growth rates) are not achieved due to low TMI or TMG flow rates, and this parameter space could not be explored. In order to reach a different metallic composition in the plasma, one solution would be to increase the density of atomic nitrogen or hydrogen. However, we opted for a change in the precursors and used NH$3$ instead of N$2$⁠, as NH$3$ yields more free nitrogen radicals than N$2$ in similar plasma conditions. This allows a higher dilution, and, hence, a lower growth rate, enabling a wider parameter space exploration. InN and GaN layers were deposited with ammonia and are presented in Sec. III B. InGaN layers with intermediate compositions will be presented in a future publication.

Ammonia was used as a nitrogen source to achieve lower growth rates for InN and GaN layers. Owing to its lower bonding energy compared to dinitrogen,⁴⁰ ammonia has a higher dissociation rate, which leads to higher atomic nitrogen density in the plasma.

Given the similar parameter space explored with ammonia for InN and GaN layers, the deposition parameters have the same expected influence as with dinitrogen. Hydrogen and plasma power are expected to increase the growth rate due to an increased dissociation of TMG (or TMI) molecules. However, this is not observed because, within the explored parameter space, the TMG (or TMI) is already fully dissociated, leading to the growth being limited by metallic precursor flow rates.²⁶ For more details, see Table III, which is extracted from a design of experiment (DOE) on InN layers whose details are presented in  Appendix D. Using NH$3$⁠, InN and GaN layers could be deposited with growth rates down to 1.5 nm/min.

Regarding their crystallinity features, Fig. 8 shows clear nanocrystals of up to 30 nm, observed with a TEM. XRD measurements reveal higher peak intensities for both InN and GaN layers than with the $N2$ source, but with a similar crystallite size (see Fig. 9). For a more precise estimation of the crystallite size using XRD, see Eq. (D1b), along with corresponding Table VI in  Appendix D. This implies that the crystallites do not span across the entire thickness of the layer.

In terms of optical properties, the GaN layer displays the same features as with dinitrogen, as shown in Fig. 10, with an Urbach energy of around 290 meV. On the contrary, the InN layer deposited with ammonia exhibits an Urbach energy of 187 meV, while the one deposited using dinitrogen has an Urbach energy of 463 meV. Assuming that the electron concentration remains in the same order of magnitude, the Burstein–Moss effect will lead to the same shift. However, since there are fewer sub-bandgap defects when growing the layer with ammonia, the band tail is reduced, and the optical bandgap is pushed to higher values. Thus, despite the persistent Burstein–Moss effect, deposition with ammonia improves the layer quality noticeably for InN, more than for GaN. The FCA feature nevertheless remains present for all the layers, implying that they still cannot be used effectively as an absorber for PV applications.

In conclusion, using ammonia to reduce the growth rate is effective in terms of improving crystallinity and reducing sub-bandgap absorption. However, the defect concentration responsible for the FCA and the Burstein–Moss effect is still persistent, too high for PV integration to be possible. Indeed, fewer defects are necessary for a possible extrinsic doping of the layer, with a much cleaner band edge. In terms of electron transport, since the layer is a conglomerate of crystallites, charge carriers have a high probability of recombining at the grain boundaries. However, by reducing the growth rate with ammonia, we are able to prove that the crystallite size increases, the Urbach energy is reduced, and the crystallinity is improved, which are steps in the right direction.

As an outlook, the unexplored parameter space for InGaN layers mentioned in Sec. III A can be probed using ammonia. InN and GaN layers can still be improved with growth rates lower than 1 nm/min, to reach an Urbach energy below 0.1 eV. Postdeposition annealing or higher deposition temperatures can also help extend the crystallite size even further.²⁷ 

InGaN layers with varying chemical compositions were deposited using PECVD. A 3D fit was performed which described the variation of their optical bandgap with the growth rate and the indium content. An excellent fit with experimental values was observed within the parameter space explored here (⁠$19at.%≤XIn≤72at.%$ and $4.1≤g≤8.4$ nm/min). XRD peaks in InGaN layers shifted according to their indium content, and no phase segregation was observed in any layer.

Optical measurements showed that most layers were electronically degenerate, and thus, not suitable for PV applications. This behavior is explained using the position of the Fermi level stabilization energy and the concentration of intrinsic defects created during deposition. In order to avoid this degeneracy, the defect concentration needs to be reduced.

Even though they are degenerate, no clear relation could be established between the electron concentration and the growth rate since the layers were too resistive for reliable Hall effect measurements. Thus, it would be interesting to vary the growth rate at a constant In/(In + Ga) ratio to observe the dependence of the electron concentration on the growth rate with less resistive samples. That would allow a comparison between our results and those of Walukiewicz et al. (see Fig. 14 of their paper¹²).

Ammonia is helpful in that regard since it gives rise to a higher density of nitrogen radicals. This allows for higher metallic precursor flows without the detrimental growth of metal-rich films. Larger crystallites and lower Urbach energy were achieved, but the InN or GaN layers developed with ammonia still showed high extents of degeneracy, manifested by a persistent FCA and the Burstein–Moss shift. By improving these characteristics, maybe with the help of annealing or at higher deposition temperatures, extrinsic doping and integration as a carrier contact in a silicon heterojunction configuration can be achieved. The unexplored parameter space mentioned in Sec. III A can also be probed thanks to the use of ammonia.

The authors would like to acknowledge A. Schafflützel and C. Bucher for their outstanding maintenance of the PV-lab equipment, the Interdisciplinary Center for Electron Microscopy (CIME) EPFL for letting us access their Thalos TEM, and all group members in PV-lab EPFL. Funding from the Swiss National Science Foundation under Grant No. 200021_182171 is also acknowledged.

The authors have no conflicts to disclose.

Jonathan Emanuel Thomet: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Aman Kamlesh Singh: Conceptualization (lead); Formal analysis (supporting); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Mélanie Nelly Rouèche: Investigation (equal). Nils Toggwyler: Investigation (equal). Franz-Josef Haug: Project administration (supporting); Supervision (equal); Validation (equal); Writing – review & editing (supporting). Gabriel Christmann: Project administration (equal); Writing – review & editing (supporting). Sylvain Nicolay: Funding acquisition (supporting); Project administration (equal). Christophe Ballif: Funding acquisition (equal); Project administration (equal); Resources (lead); Writing – review & editing (supporting). Nicolas Wyrsch: Funding acquisition (lead); Project administration (equal); Supervision (supporting); Validation (supporting). Aïcha Hessler-Wyser:Funding acquisition (equal); Project administration (lead); Supervision (equal); Validation (equal); Writing – review & editing (lead). Mathieu Boccard: Conceptualization (equal); Methodology (supporting); Project administration (equal); Supervision (lead); Validation (lead); Writing – review & editing (equal).

The data that support the findings of this study are openly available in Zenodo at http://doi.org/10.5281/zenodo.6725480, Ref. 43.

Given the plasma conditions described in the experimental setup, all the precursors used will be dissociated to a certain degree, where N$2$ is the most difficult to break down and, thus, requires a high flow rate. An accurate description of the plasma dynamics with such a complex mix of precursors would include kinematics of processes such as dissociation, adsorption, nitridation, carbidization, and (re)synthesis, at different rates and equilibria. Since it is not the focus of this study, only a simplified version of the deposition process is presented here. When entering the plasma region, a TMI (or TMG) molecule will dissociate into its central indium (or gallium) radical atom and three unstable methyl radicals. N$2$ will also undergo dissociation to produce nitrogen radicals in the plasma, which in turn will bind with the indium (or gallium) radical to form InN (or GaN). This small molecule will eventually drift toward the substrate, where it will adsorb into a weakly bound precursor state and will finally either form a chemical bond or desorb from the substrate. The behavior of the InN (or GaN) species in the adsorbed precursor state will eventually determine crystallite quality and size.¹⁹ Both properties are governed by the parameters shown in Tables I and III, and agreement with reported works is observed.^28–32 During all these processes, hydrogen radicals are produced from H$2$ dissociation, from ammonia dissociation, or from the dissociation of the methyl groups of the dissociated TMI (or TMG). Their main role is to passivate surface defects and to help eliminate plasma by-products, particularly the organic ones.

Since the InGaN layers are simultaneously deposited on a glass and on a silicon substrate, the results presented here may differ depending on the substrate. Thus, specific substrates were used to extract some of the material parameters. The crystallite size (XRD) and the indium content (XRD and EDS) were extracted from the layer deposited on silicon wafers exclusively. The growth rate (ellipsometry and profilometer) and the optical bandgap (ellipsometry and spectroscopy) were extracted from the layer deposited on the glass wafer exclusively.

It is assumed that the indium content of the InGaN layer does not depend on the substrate.⁴¹ Indeed, once the first few atomic layers are deposited, the substrate does not have any influence anymore on the composition. However, we observed a loss of crystallinity in the InGaN layers deposited on glass. It is also assumed that, contrary to silicon, the InGaN bandgap does not depend on the crystal structure of the layer, be it crystalline or amorphous, whatever the indium content. Indeed, literature reports that the a-InN bandgap was observed at 1.7 eV instead of 0.7 eV,^33,34 but that makes it equivalent to a highly defective c-InN layer with intrinsic doping as discussed above (cf. also Ref. 12). Values between 3.1 and 3.4 eV were reported for a-GaN, similar to that of c-GaN.^35–38 The corollary of the previous assumption is that the substrate, inducing a different crystal structure as experimentally observed in the present work, will, in fact, not influence the spectroscopic and ellipsometric measurements.

Finally, the deposition rate was observed to be slightly lower on silicon (⁠$∼$10% thinner layers), most probably due to a more efficient arrangement in the crystal structure. The thicknesses reported in the present article are exclusively the ones measured on glass.

The indium content of the layers was determined using two methods that validated one another. On one side, for the layers that were crystalline enough, the XRD 110 peak position varies with the sinus of the interatomic distance (see Fig. 11). This allowed for a precise indium content determination when compared with pure InN and GaN layers. On the other hand, EDS measurements allowed for a straightforward measurement of the indium:gallium ratio, from which the indium content of the layers was deduced. The error between the two methods was less than 3% (see Fig. 12).

The design of experiments method and terminology can be learned from Hinkelmans et al.’s book.³⁹ For the DOEs on InN layers deposited using ammonia, the last six input parameters of Table III are explored. The chosen design is a fractional factorial design 2^6-2 with three central points, for a total of 19 layers characterized. The coefficients are not normalized here, to relate better to the physical input parameters, rather than explore their intercorrelation. For the growth rate $g$⁠, see Eq. (D1a) and corresponding Table IV. For the optical bandgap $E04$⁠, see Eq. (D1b) and corresponding Table V. For the crystallite size, see Eq. (D1c) and corresponding Table VI. See also the quality of the three models in Table VII 

In the ANOVA tables, the p-value for the different factors are displayed in green if they are below a value of 5%, and in red if they are above 5%. The 5% p-value threshold is the standard chosen p-value to reject the following null hypothesis: “this factor has no effect on the physical quantity observed,” where here the physical quantity is either $g$⁠, $E04$⁠, or the crystallite size. However, even though some factors express a dismissing coefficient, they are still retained because the overall model quality is optimal when including them. For the lack of fit, however, it is preferable to be unable to reject the null hypothesis following that “there is no lack of fit.” Hence, lack of fit p-values are displayed in red when they are below 5% and in green when above.

Since the optical bandgap was fitted as a function of two parameters (the growth rate and the indium content), the fitted model can be represented as a 3D surface, displayed in Fig. 13. Two of the three projections of this plot were used in this article. The back wall projection corresponds to Fig. 5 and the floor projection corresponds to Fig. 7. The sidewall projection was not used here.