Optoelectronic properties of ultrathin ALD silicon nitride and its potential as a hole-selective nanolayer for high efficiency solar cells

Fully exploiting the power conversion efficiency limit of silicon solar cells requires the use of passivating contacts that minimize electrical losses at metal/silicon interfaces. An efficient hole-selective passivating contact remains one of the key challenges for this technology to be deployed industrially and to pave the way for adoption in tandem configurations. Here, we report the first account of silicon nitride (SiN x ) nanolayers with electronic properties suitable for effective hole-selective contacts. We use x-ray photoemission methods to investigate ultrathin SiN x grown via atomic layer deposition, and we find that the band alignment determined at the SiN x /Si interface favors hole transport. A band offset ratio, Δ E C / Δ E V , of 1.62 ± 0.24 is found at the SiN x /Si interface for the as-grown films. This equates to a 500-fold increase in tunneling selectivity for holes over electrons, for a film thickness of 3 nm. However, the thickness of such films increases by 2 Å–5 Å within 48 h in cleanroom conditions, which leads to a reduction in hole-selectivity. X-ray photoelectron spectroscopy depth profiling has shown this film growth to be linked to oxidation, and furthermore, it alters the Δ E C / Δ E V ratio to 1.22 ± 0.18. The SiN x /Si interface band alignment makes SiN x nanolayers a promising architecture to achieve widely sought hole-selective passivating contacts for high efficiency silicon solar cells.


I. INTRODUCTION
The need for renewable energy sources is ever increasing due to the immense pressure put on reserves of fossil fuels by our growing energy demands, as well as the environmental detriment from using these non-renewable counterparts. Among all renewable energy sources, photovoltaic (PV) technologies have shown great promise toward tackling such demands. This is primarily due to the abundance of solar energy and the rapid development and deployment of such technologies. 1,2 Currently, crystalline silicon comprises over 90% of the market share, and the PV community continues to strive toward reaching the power conversion efficiency (PCE) limit of this technology. 1 The bulk of this market is dominated by architectures that suffer from high electrical losses at the metal-Si interface, limiting these technologies to PCEs considerably lower than the theoretical limit of 29.4%. 3,4 This arises from the high density of electronically active states at the metal/Si interface, which increases the trap-assisted Shockley-Read-Hall recombination of photogenerated carriers. Attempts to mitigate this loss using highly doped regions at the contacts enhance the loss of carriers via Auger recombination, which further limits the overall performance. Currently, the silicon PV industry is striving toward the Shockley-Queisser PCE limit by adopting novel passivating and selective contact technologies. 5,6 Regardless of the cell architecture, the pathway to achieving higher performance silicon solar cells is to passivate the contacted regions of the device. [7][8][9] Passivating contacts incorporate a thin film between the silicon absorber and the metal contact. This architecture can simultaneously provide charge carrier selectivity and suppress recombination at this interface, resulting in a higher carrier ARTICLE scitation.org/journal/apm collection efficiency. 9,10 Ideally, a good passivating contact suppresses the electrical losses at the interface while maintaining a low resistivity. 9,11 Devices require passivation of both electron and hole contacts in order to reach PCEs exceeding 25%. 9 Commonly, silicon dioxide and phosphorous-doped hydrogenated amorphous silicon are used as electron-selective passivating contacts. The inherent silicon surface passivation ability and the favorable interfacial band alignments on crystalline silicon make these materials highly suitable. However, using SiO 2 for hole contacts has not reached the same high efficiencies. [12][13][14] Work into alternative structures for hole contacts is an important area of research. 15,16 Despite the advancements seen with electron-selective contacts, an efficient hole-selective passivating contact remains a key sought-after development to be accomplished in this industry. 9 To date, the most promising material candidates have been p-type amorphous silicon and silicon-rich silicon carbide, but compatibility with conventional high temperature Ag screen printing still remains an issue. 5,13 Silicon nitride (SiNx) is renowned for its superior silicon surface passivation ability. 17,18 The semi-continuum of forbidden energy states that arise at the surfaces in a solar cell are known to be well saturated by silicon nitride. The use of this material as an anti-reflection, surface passivating layer has led to studies on the interface between SiNx/Si. This material is known to be compatible with conventional Ag screen print metallization. The density of interface states at this interface is commonly reported in the 10 11 cm −2 to 10 12 cm −2 region, with the recombination velocity generally lower than 1 cm s −1 . 19,20 Incorporating an oxide or oxynitride layer can prove beneficial by offering a lower density of states that compliments the SiNx layers low surface recombination. 21 Furthermore, previous theoretical calculations for the band offsets at an Si 3 N 4 /Si interface show hole transport being favorable, with a 28% larger barrier to electron tunneling than that for holes, determined from a calculated ΔE C /ΔE V factor of 1.28. 22 Despite these promising attributes toward hole-selective contacts, previous reports have suggested that PECVD nitride is not a viable option for hole tunneling due to the fixed positive charges that would create an inversion layer. 23,24 To date, no report exists on whether these charges form during processing, their potential to cause inversion in a thin layer, or the empirical values of band alignment at the Si 3 N 4 /Si interface.
We report the first experimental study of the optoelectronic properties of silicon nitride nanolayers and their potential as holeselective contacts in silicon solar cells. We use bis(tertiary-butylamino)silane (BTBAS) to grow ultra-thin SiNx films via atomic layer deposition (ALD), following on from work by Knoops et al. 25 We then use x-ray photoelectron spectroscopy (XPS) to probe the electronic core levels (CLs) and states 26 at the SiNx/Si interface to experimentally determine the band alignments. This characterization has shown the potential for carrier selectivity of SiNx, thus corroborating theoretical predictions. Furthermore, we explore the effect of degradation over time on the band offsets at the SiNx/Si interface by probing and profiling the chemical states as a function of depth using XPS. In addition, we study the specific contact resistivity at various SiNx thicknesses using Au front and rear electrodes. Finally, we provide device simulations implementing a non-local tunneling method to calculate the improved tunneling of holes when SiNx nanolayers are used in silicon devices. Beyond the work reported here, full deployment as hole-selective passivating contacts still requires maintaining superior Si surface passivation with such ultra-thin films, relative to its non-passivating counterparts.

A. Specimen fabrication
The ALD process for each cycle of SiNx growth is comprised of two half-cycle reactions: (a) the precursor (BTBAS) half-cycle reaction and (b) nitrogen reactant half-cycle reaction. The first half-cycle consists of the chemisorption of precursor molecules onto the surface, followed by a purging step to remove excess molecules. The second half-cycle uses the nitrogen plasma to remove the unwanted surface ligands and form silicon-nitrogen bonds, followed by a purge to remove undesirable by-products. For this process, the chamber pressure was kept at 5 Pa, the plasma power at 400 W, and the bottom plate temperature at 350 ○ C. The film growth rate and the variation in the growth per cycle (GPC) were determined using different BTBAS dosing times (25 ms-225 ms) and different film thicknesses, grown on p-type Si (Cz, 1 Ω cm-10 Ω cm, ⟨100⟩, 300 μm) substrates and measured using spectroscopic ellipsometry. For optical bandgap determination, 10 nm and 25 nm of SiNx were grown on clear glass substrates that were ultrasonically cleaned in acetone and then rinsed in deionized water. For XPS measurements, 3 nm, 10 nm, and 25 nm thick SiNx films were grown on p-type Si (100) substrates that were immersed in buffered HF solution for native oxide removal prior to SiNx growth. A schematic representation of our process is shown in Fig. 1. The study of degradation from aging was carried out on several SiNx samples that were spin-coated with S1813 photoresist at 5000 rpm for 30 s and baked at 115 ○ C for 1 min. Photoresist was rinsed off using acetone and isopropanol immediately prior to each spectroscopic ellipsometry measurement during the degradation study. For specific contact resistivity measurements, we use photolithography to form circular patterns between 1 mm and 2 mm in diameter on p-Si substrates. SiNx layers with thicknesses between 1 nm and 4 nm are deposited in the openings, with another lithography step used to form the Au electrodes via E-beam evaporation.
SiNx films were grown in an Oxford Instruments Flex-AL Plasma Enhanced-ALD chamber. Spatial film thickness scans were taken using a M-2000 J.A. Woollam ellipsometer. For Au electrode formation, a Balzers BAK600 chamber is used. A Jasco V-750 UV-Visible (UV-Vis) spectrophotometer was used for transmission measurements to determine bandgap energy. A Thermo Scientific Theta Probe XPS system was used for the determination of core levels (CLs) and valence band maxima (VBM) of the grown films. This was done using a monochromatic A1 Kα x-ray (1.487 keV) source with the same geometry used for emission in all measurements. Since the incident x-ray energy is lower than 1.5 keV, the photoelectron kinetic energy is lower than 1.5 keV, which results in a shallow escape depth (between 3 nm and 5 nm) for photoelectrons. 27 Depth profiles are conducted by milling away the material using an Ar ion gun with a current density of 1 μA mm −2 and a raster area of 4 mm 2 .

B. Band offset determination
The x-ray photoemission-based method proposed by Kraut,28,29 and widely reported in the literature, [30][31][32][33] uses XPS spectra to determine the valence band offset (ΔE V ) and conduction band offset (ΔE C ) energies at a semiconductor interface. This method utilizes Poisson's equation to predict these offsets based on the deviations in charge distribution found at the interface relative to the semiconductor bulk. 28 In this approach, the binding-energy difference between the electronic core level energy (E CL ) and VBM are determined experimentally and used in Kraut's formulas to calculate ΔE V and ΔE C . A schematic band diagram at the SiNx/Si interface that illustrates ΔE V and ΔE C from these calculations is shown in Fig. 2.
The valence band offset at the SiNx/(p)-Si interface was calculated using Here, (E CL Si − E CL SiNx ) SiNx/Si is the energy difference between the CLs of the two materials at the interface, also known as ΔE CL . To probe the interface and determine ΔE CL , a 3 nm SiNx film on a Si substrate was studied, based on the XPS photoelectron escape depth being under 5 nm. The energy difference between the core level centroids and valence band edges for Si (E CL SiNx were obtained from XPS of the respective thick films. SiNx films with thicknesses of 25 nm and 10 nm were examined as independent bulk films in this study. The N 1s and Si 2p orbital peaks were used as E CL SiNx and E CL Si , respectively. Linear extrapolation of the leading edge to the baseline of the valence band spectra from the respective thick films was used to obtain E V Si and E V SiNx . 30 This method is widely reported as an accurate way of determining the VBM of semiconductors, assuming the use of high-precision (>0.1 eV) XPS. Following Kraut's method, ΔE C was also determined using where (ΔEg) Si−SiNx is the energy difference between the bandgap of Si and SiNx films, i.e., Eg Si − Eg SiNx . An energy gap of 1.12 ± 0.01 eV was used as Eg Si for these calculations. Eg SiNx was determined from

III. RESULTS AND DISCUSSION
A. Nanolayer growth dynamics The growth per cycle (GPC) as a function of precursor dosing time is presented in Fig. 3(a). This is conducted by growing SiNx films with different thicknesses (i.e., range of ALD cycles) at a fixed BTBAS dosing time. The relationship between GPC and dosing time can be interpreted as softly saturating, whereby GPC is seen to increase with BTBAS dosing time, but with some indication that the GPC is saturating at higher dosing times. The relationship between GPC and BTBAS dosing time matches well with the findings of Knoops et al., 25 despite some minor differences in the film growth recipe.
The relatively low growth rate is suggested to be due to the incomplete reaction of N 2 plasma with the tert-butyl groups of BTBAS. Furthermore, the non-uniform nucleation on the surface of the underlying substrate in the early cycles further reduces this growth rate. The schematic of the SiNx ALD cycle shown in Fig. 1 assumes uniform nucleation and surface reactions, which is unlikely to occur in the first few monolayers of growth. SiNx film growth at a fixed dosing time of 150 ms shows a linear increase in film thickness with the number of cycles [ Fig. 3(b)]. The growth rate can be determined using the gradient of the fitted line, indicating a rate of 0.12 Å/cycle. This relatively slow growth rate is useful for accurately growing ultra-thin films for use as selective contacts, where differences in film thickness at an Å scale can cause significant variations in device performance.

B. Optical and electronic properties
The transmission spectra for 10 nm and 25 nm thick SiNx films are presented in Fig. 4(a). The region of interest in the transmission spectra is the inflection point, corresponding to hν ≥ Eg. An abrupt absorption edge at ∼320 nm is seen, which can give some indication to Eg SiNx . Figure 4(b) shows the Tauc plots for the 10 nm and 25 nm thick SiNx films. The optical bandgap is determined by extrapolating the linear region of the absorption edge to the baseline. 32,36 Using this method, an optical bandgap of 3.98 ± 0.04 eV for this material is determined.  XPS spectra showing core level energy centroids and valence band edges for bulk Si, 25 nm SiNx and 10 nm SiN X , as well as the CLs at the (3 nm) SiNx/Si interface are shown in Fig. 5. The CL positions did not change with x-ray irradiation time, and all XPS spectra are calibrated to the C 1s peak at 284.8 eV. A Savitsky-Golay filter is used to fit all valence band edge spectra to a polynomial using the least squares method, 37 and all core level peaks are fitted using Shirley backgrounds and Voigt functions. 33 Fig. 5(h), two peaks are seen for the Si 2p core level at the interface. This is because the Si 2p core level at the interface has contributions from both the substrate and the ultra-thin SiNx layer. As the thickness of the 3 nm SiNx layer is less than the x-ray penetration depth and the photoelectron escape depth, Si 2p electrons from both the SiNx and Si bulk layers are detected, resulting in a convoluted core level peak. Based on the ALSCOF XPS peak fitting library, the Si 2p peaks found closest to 101.30 eV and 99.4 eV are known to be due to nitrides and elemental silicon, respectively. Therefore, by de-convoluting the Si 2p peak in Fig. 5(h), the core level energy at the interface of Si (E Si2p Si ) SiNx/Si is determined as 98.73 ± 0.01 eV. To complete the Kraut calculation for this study, the SiNx (E N1s SiNx ) SiNx/Si core level energy is determined as 397.24 ± 0.01 eV, resulting in an energy difference between these core levels at −298.51 ± 0.03 eV.
The valence band offset at the SiNx/Si interface is determined as −1.08 ± 0.08 eV and −1.09 ± 0.08 eV using the 25 nm and 10 nm thick SiNx films as bulk SiNx, respectively. A negative band offset value suggests that the valence band energy of SiNx is at a greater energy relative to the vacuum than the valence band energy of Si. From these ΔE V values and using the optical bandgap of the two bulk materials, the conduction band offset is determined as 1.78 ± 0.13 eV and 1.77 ± 0.13 eV. From these calculations, ΔE C /ΔE V ratios of 1.64 ± 0.24 and 1.62 ± 0.24 are established, suggesting favorability toward hole transport at this interface. The values calculated for both bulk SiNx films (10 nm and 25 nm thicknesses) are understandably in close agreement (and within the experimental uncertainty). Based on the ΔE C /ΔE V ratios, a lower tunneling potential barrier is defined for holes than for electrons. Despite showing favorability toward hole transport as-deposited, it is important to examine the stability of the films by studying how band offsets change over time.

C. Understanding nanolayer degradation
To understand the impact of aging on these films when stored under different conditions, 3 nm SiNx films grown on Si were stored in our cleanroom within a desiccator, both with and without photoresist, over a two-week period. During this time, film thickness was repeatedly measured by spectroscopic ellipsometry, the results from which are plotted in Fig. 6. The thickness of all SiNx films studied is shown to increase over time, with no significant difference observed between storing in a desiccator or cleanroom. Thickness alterations FIG. 6. SiNx thickness measured over two weeks when stored in a cleanroom and desiccator with and without the S1813 photoresist protection layer.
cease within the first 48 h. Films without photoresist protection are shown to increase in thickness by ∼0.2 nm, whereas the photoresist protected samples are shown to increase by ∼0.5 nm. This can be attributed to either remnants of photoresist after rinsing with acetone and isopropanol prior to each thickness measurement or due to alterations caused during the baking step after photoresist spinning.
Quantifying the impact of aging on the hole-selectivity of this film is crucial. Spectra and calculations presented for determining the band offsets in Sec. III B were all conducted immediately after film growth. Identical XPS measurements were conducted on these films after they were stored in the cleanroom for 1 week. The core levels and valence band edges for 25 nm and 10 nm thick SiNx and the core levels detected at the SiNx/Si interface after aging can be found in the supplementary material. The N1s core level energy and leading edge of the valence band spectra for the 25 nm thick films are detected at 397.47 ± 0.01 eV and 1.34 ± 0.02 eV, respectively. The N 1s core level energy and valence band spectra for the 10 nm thick film are detected at 397.51 ± 0.01 eV and 1.37 ± 0.02 eV, respectively. Therefore, this suggests an energy difference (E N1s − E V ) SiNx of 396.13 ± 0.03 eV and 396.14 ± 0.03 eV after degradation, using the 25 nm and 10 nm specimen as bulk SiNx. The core level energy peaks (E N1s SiNx and E Si2p Si ) at the interface are determined as 397.45 ± 0.01 eV and 98.79 ± 0.01 eV, respectively, resulting in ΔE CL as −298.66 ± 0.03 eV. Therefore, the valence band offset at the SiNx/Si interface is determined as −1.30 ± 0.08 eV and −1.29 ± 0.08 eV after degradation. The optical bandgap determined immediately after film growth did not show a considerable difference to the aged bandgap. The conduction band offset at the interface prior to film alteration can therefore be determined as 1.56 ± 0.13 eV and 1.57 ± 0.13 eV, suggesting ΔE C /ΔE V as 1.20 ± 0.17 and 1.22 ± 0.18. This implies that the hole-selectivity degrades.
Changes in the chemical composition of these films were investigated. The relative atomic concentrations of the elements in both freshly grown and aged 25 nm thick SiNx film were determined from CL peaks (Si 2p, N 1s, O 1s, and C 1s) taken from survey scans at multiple milling depths. These were fitted and corrected using their corresponding sensitivity factors, taking the mean free path of the photoelectrons and photoionization cross sections of these CLs into ARTICLE scitation.org/journal/apm account. 38,39 Survey identification and chemical state analysis techniques were used to investigate the chemical composition of this film. These are shown in Fig. 7. Based on the ion current density, sputter yield, and film density, the etch rate of this film using Ar ions was estimated to be ∼0.20 nm/s. When the thickness of the film is accurately known, etching beyond the interface using the Ar gun to identify the point at which there is a sudden drop of N concentration (in the substrate) further validates this etch rate. The relatively high concentration of carbon and oxygen at the surface is likely due to organic contaminants and hydroxyl groups, respectively. The carbon concentration is considered to be negligible beyond the surface for both cases, while the presence of oxygen beyond the surface, as shown to be between 9% and 5% from a 4 nm to 16 nm depth, remains in the aged film. The concentration of oxygen is seen to be higher at all milling depths when compared to the as-deposited case, suggesting a transition to a more oxygen-rich film with aging. Furthermore, chemical state analysis using the ALSCOF library gives some indication of the film transitioning from silicon nitride to silicon oxy-nitride, based on the concentration levels detected. If only silicon nitride is considered, a 1:1 ratio between Si and N is observed beyond the surface.
The precursor used (BTBAS) is known to be capable of growing silicon oxy-nitride, as well as silicon nitride with various concentration ratios, depending on the growth conditions. 40 Initial work with the atomic concentration ratios of the freshly grown films shows a considerably lower oxygen concentration by 5%-7%, suggesting a transition to a more oxygen-rich film with aging. This could be the cause of the thickness and band offset shifts observed with aging. Increases in film thickness will reduce the conductivity of a passivating contact, but this could be mitigated by growing a thinner initial film. Decreases in band offset ratio (and so hole-selectivity) would be detrimental to the performance of a passivating contact, but it is encouraging that ΔE C /ΔE V remains greater than 1, even after aging. An assessment of the passivation, carrier tunneling, and selectivity properties of these ultrathin dielectrics will be reported in a follow-up study. Here, the potential of SiNx nanofilms to act as selective contacts is presented using specific contact resistivity (ρc) measurements as well as analytical calculations and device simulations.

D. Specific contact resistivity of silicon nitride nanolayers
Maintaining a low ρc is a crucial factor for pursuing high performance carrier-selective contacts. In essence, ρc is a quantitative metric that characterizes the passage of electrical current through a carrier-selective contact. To measure ρc of an Ohmic contact, the Cox and Strack method (CSM) and transfer length method (TLM) are generally used. [41][42][43] These methods rely on using the currentvoltage characteristics to extract the resistivity of the contact. The TLM technique measures the resistance via current flow only in the inversion layer of the contact, whereas current flows vertically in the CSM technique [as shown in Fig. 8(a)] under an applied voltage. The CSM technique is advantageous as the current distributes homogeneously below the contact rather than distributing exponentially directly below the contact as in the TLM technique. Nonetheless, in cases where hole transport materials and substrates are Schottky heterojunctions rather than Ohmic, the traditional approaches fail to accurately extract ρc due to rectification effects. 44 To tackle this, an expanded CSM technique that can effectively separate the contact resistivity from Schottky contacts has been reported and successfully used. 44 This combines the traditional CSM approach with Cheung's method to extract an effective ρc [44][45][46] and is used in our work.
As shown in Fig. 8(a), current flows longitudinally in the device under a varied applied voltage. From Fig. 8(a), the total resistance, R T , is comprised of where R C is the contact resistance, R S is the spreading resistance in the substrate, and R O is the residual resistance. The spreading resistance is defined as where d is the diameter of the circular electrode and ρ and t are the resistivity and thickness of the substrate, respectively. The contact resistance is defined as To eradicate the rectification effects from the current-voltage characteristics of potential non-Ohmic contacts, we can extract R T by combining the traditional CSM approach with 44 d(V) d(ln(I)) = R T I + nq kT , where I is the current, V is the voltage, n is the ideality factor of the substrate, q is the electrical charge, k is the Boltzmann constant, and T is the temperature. The current-voltage characteristics with varying top electrode diameters between 1 mm and 2 mm are shown in Fig. 8(b). From the current-voltage characteristics, R T is determined by using Eq. (6) [ d(V) d(ln(I)) vs I]. Following this, R S and R C are calculated using Eqs. (4) and (3), respectively. Consequently, we can determine ρc, by plotting R C (where R C = R T − R S ) against 1/S (where S = πd 2 /4) and extracting the gradient. Figure 8(c) shows this plot for a 2 nm SiN tunneling layer. In Fig. 8(d), ρc is shown as a function of SiN thickness between 1 nm and 4 nm.
Using a SiNx thickness of 1 nm, ρc as low as 0.52 Ω cm 2 is achieved. This was found to increase up to 0.95 Ω cm 2 , 3.6 Ω cm 2 , and 8.2 Ω cm 2 when using a SiNx layer thickness of 2 nm, 3 nm, and 4 nm, respectively. The general trend between increasing dielectric layer thickness resulting in a higher ρc in this type of contact is re-emphasized. The dependency of ρc on dielectric tunneling layer thickness is generally a trade-off between other contact quality metrics such as carrier lifetime.
To promote hole-selectivity and avoid Schottky barrier formation, multiple mechanisms can be used. First, a dielectric tunneling layer can be used that when interfaced with silicon, achieves favorable band alignments, which promotes majority carrier transport from the substrate to the external circuit. Another way is to use a ARTICLE scitation.org/journal/apm large work function metal that exceeds the work function of the silicon substrate, promoting upward band bending. A third way is to modulate the surface carrier concentration to further promote hole transport. This can be achieved using a material with a large fixed positive charge density, as typically done in (p)TOPCon with ptype polycrystalline silicon. Using analytical calculations and device simulations, we now look at the probability of hole tunneling at similar SiNx thicknesses shown in Fig. 8, with direct comparisons to TOPCon.

E. Silicon nitride nanolayers as hole-selective contacts
Thin film passivating contacts are dependent on current transport through what would classically be considered insulators. While there is a debate on the exact nature of current transport through the dielectric film, it is generally accepted that tunneling plays a significant role for layers <2 nm. [47][48][49] Using the Wentzel-Kramers-Brillouin (WKB) approximation, the tunneling probability of carriers depends strongly on the barrier height (Δϕ b given in eV), effective mass, m * , and the dielectric thickness, t. This dependency is described by Eq. (7) 50 for the carrier tunneling probability, Pt, The intrinsic carrier selectivity of the dielectric, S h , can be calculated as the ratio of the tunneling probability of holes to the tunneling probability of electrons, 51 To calculate the tunneling probabilities in SiO 2 , the conduction band barrier ΔE C was set to 3.2 eV, while the valence band barrier ΔE V was 4.7 eV. 52 The effective masses for electrons and holes were set to 0.4 and 0.58, respectively. 52,53 As the effective masses have a direct effect on the tunneling probability and current, a more detailed analysis of this parameter is provided in the supplementary material. The band alignment found in this work was used for calculations in SiNx, with ΔE C = 1.77 eV and ΔE V = 1.09 eV. For SiNx, the electron and hole effective masses were both set to 0.5. 54 The band offset values are visualized in Fig. 9(a), highlighting the smaller bandgap of SiNx compared to SiO 2 , and the band alignment of the dielectric in relation to a crystalline silicon absorber. Figure 9(b) compares the tunneling probability and selectivity of SiO 2 and (as-deposited) SiNx. The SiNx has larger hole tunneling probabilities for all thicknesses due to the smaller valence band offset, and it clearly favors hole tunneling as opposed to the electron-selective SiO 2 . For a hole tunneling probability of 10 −8 , a SiNx layer of ∼2.4 nm is required providing 150 times more hole tunneling than electron tunneling. A probability of 10 −8 is equivalent to that of electrons in a typical 1.4 nm SiO 2 for (n)TOPCon devices. [55][56][57] For an SiO 2 layer to achieve a similar hole tunneling probability, a 1.1 nm layer would be required, which exhibits preferential electron tunneling. This highlights the benefits of SiNx for hole-selective contacts. The exact values presented here depend on the effective masses used for the calculation. Despite the m * used, the SiNx layer is still seen to outperform oxides in terms of hole tunneling. The reader is referred to the analysis included in the supplementary material for further details.
Sentaurus TCAD simulations were conducted to elucidate the effect that tunneling probability has in the current transfer dynamics across SiNx nanolayers. Tunneling across the dielectrics was simulated using Sentaurus's nonlocal tunneling model that implements Schenk and Heiser's approach, 58 with the extensions in Refs. 59 and 60. Mobility was modeled using Klaassen's mobility model, 61,62 while Schenk's low injection model was used for bandgap narrowing. 63 In passivated contacts, a highly doped poly silicon layer is often deposited on the tunneling dielectric layer, with the metal contact deposited last, as illustrated in Fig. 10(a). The wafer resistivity was set to 1 Ω cm, the poly Si doping density to 6 × 10 19 cm −3 , and a diffusion of Boron acceptors was set at the surface of the wafer with a 0.15 μm depth factor using a Gaussian profile. Figures 10(b) and 10(c) compare the tunneling current for the selected thicknesses of as-deposited SiNx and SiO 2 , respectively. The curves show that, for a device with a SiNx nanolayer, the current is limited by the resistivity of the base when the thickness is below 2 nm. In a hole tunneling SiO 2 structure, the layer thickness must be under 0.7 nm for the total resistance to be limited by the base. Considering other values reported for m * in SiO 2 , the limiting thickness increases to 1.1 nm. Still substantially thinner than that of a nitride nanolayer. In Fig. 10, it is also evident that the hole current density depends more strongly in the SiO 2 thickness than in the case of SiNx. Figures 10(b) and 10(c) show current densities spanning four orders of magnitude. In the SiNx structure, a thickness of 2.2 nm produces an industrially practical contact resistance of 100 mΩ cm 2 . Implementing an equivalent contact with SiO 2 would require a 1 nm nanolayer. This highlights a key advantage of SiNx as the film thickness does not require as rigorous control as for SiO 2 . From Figs. 9 and 10, it is clear that the favorable band alignment of SiNx translates into high hole tunneling current and high selectivity in the contact structures. Using ALD to deposit SiNx gives extremely accurate control of thicknesses, allowing the structures to be tailored to maximize the selectivity, while maintaining sufficient current.

IV. CONCLUSION
We show a highly controllable, Å-scale growth of SiNx films using atomic layer deposition and explore their hole-selectivity using a photoemission-based method to determine the band alignments at the SiNx/Si interface. The film thicknesses determined immediately after growth are seen to rise by 2 Å-5 Å over a period of 48 h after which the thickness stabilizes. A band offset ratio (ΔE C /ΔE V ) of 1.62 ± 0.24 is determined for freshly grown samples. However, the holeselectivity reduces during aging with a final ΔE C /ΔE V value of 1.22 ± 0.18. Despite the reduction in band offset ratio, a larger barrier to electrons than to holes remains, and therefore, these films show promise for applications in hole-selective contacts for silicon solar cells. A specific contact resistivity as low as 0.52 Ω cm 2 is achieved with sub-2 nm SiNx layers. Calculations of tunneling probability and selectivity of ALD SiNx are shown to demonstrate this potential. SiNx exhibits greater tunneling probability for holes than electrons, which results in a favorable hole-selectivity. In comparison to SiO 2 , greater tunneling probabilities are calculated, which corresponds to higher current densities in the structure. Future studies will investigate the effective masses, passivation, and contacting quality of this material to further assess its suitability for fabricating hole-selective contacts for high-efficiency PV applications.

SUPPLEMENTARY MATERIAL
See the supplementary material for the consideration of carrier effective mass on tunneling, further discussion of the TCAD simulation parameters, and the XPS spectra for the aged SiNx/Si specimen.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.