SiNx/(Al,Ga)N interface barrier in N-polar III-nitride transistor structures studied by modulation spectroscopy

Contactless electroreflectance studies coupled with numerical calculations are performed on in-situ SiNx capped N-polar III-nitride high electron mobility transistor (HEMT) structures with a scaled channel thickness in order to analyse the built-in electric field in the GaN channel layer. The experimentally obtained field values are compared with the calculated field versus channel thickness curves. Furthermore, the experimental and theoretical sheet carrier densities, ns, are evaluated. While a gradual decrease in carrier concentration with decreasing channel thickness is expected for N-polar structures, experimentally a sudden drop in the ns values is observed for samples with very thin channels. The additional loss in charge was associated with a change in the SiNx/AlGaN interface Fermi level at very thin channel thicknesses.

www.nature.com/scientificreports/ scattering from charged interface states with increasing field in the channel 25 , which can lead to a significant increase in sheet resistance if not accounted for 23,24 .
Modulation spectroscopy is a technique that allows to gain insight into built-in electric fields in semiconductor structures through Franz-Keldysh oscillation (FKO) appearing in optical spectra in presence of medium to high fields 26,27 . In all of the structures in this study a built-in electric field arising from polarization properties of III-nitrides is expected to be present in subsequent layers. Of particular interest is the GaN channel built-in electric field since it influences the two dimensional electron gas (2DEG) density. This field itself is dependent not only on polarization effects but also on the surface or, in case of SiN x capped structures, interface Fermi level position 28 . Therefore it seems practical to first study the Fermi level position of bare and capped structures to understand the effect of SiN x capping.
In this work contactless electroreflectance (CER) spectroscopy is applied to study the built-in electric field in the GaN channel of N-polar HEMTs with different GaN channel thicknesses and cap layers. Extracted field values are then compared with numerical calculations of the GaN channel field dependency on channel thickness with varied interface Fermi level position (i.e. interface barrier height). From the comparison it is observed that a shift from 0.5 to 1.3 eV in the Fermi level position occurs when the sheet carrier density decreases beyond a critical value when reducing the channel thickness. At the same channel thickness a sudden drop in carrier concentration was observed in electrical measurements.

Structures studied
Three series of structures were prepared for this study that shared a common stack design as follows: a 1.4 μm thick semi-insulating GaN base layer was deposited on a C-plane sapphire. Next a backbarrier was prepared that consisted of a 20 nm thick graded Al x Ga 1-x N layer with x = 0.05 → 0.38 and a 10 nm thick Al 0.38 Ga 0.62 N film. On top of the backbarrier a 0.7 nm thick AlN interlayer was introduced to decrease carrier scattering. Finally a GaN channel layer of varied thickness was deposited and capped with a 2.6 nm thick Al 0.46 Ga 0.54 N cap layer (absent in two of the 1st series structures). As a dielectric a SiN x film was introduced on top. Details on individual samples are given in Table 1. Samples were grouped in three series. The 1st series with and without the top AlGaN and/or SiN x layers was prepared to serve as a reference series that provided a comparison between capped and uncapped structures, sample stacks are shown in Fig. 1a-d. The 2nd and 3rd series were grown for carrier concentration studies and they share the design with the stack shown in Fig. 1d but with a varied GaN channel layer thickness and additional backbarrier doping.

Results and discussion
Hall measurement results obtained for samples from 2nd and 3rd series, presented in Table 1, show a predictable decrease in carrier concentration with narrowing of the GaN channel when the thickness is changed from 20 to 15 nm (2nd series) or from 12 to 10.5 nm (3rd series). However, in both series, the concentration suddenly drops 3 times (3rd series) or becomes unmeasurable (2nd series). The sudden increase in resistivity was previously associated with the circumstance, that in N-polar GaN/AlGaN heterostructures the decrease in charge with decreasing channel thickness is coupled with a significant reduction in electron mobility.
Since the field in the GaN channel strongly depends on the Fermi level position on the outer boundary of a structure, be it its surface or an interface with a capping dielectric, first samples with and without SiN x and/ or Al 0.46 Ga 0.54 N layers were studied by CER. Figure 2a shows spectra recoded for the 1st series of structures. A band-to-band transition followed by FKO originating from the GaN channel is visible in CER spectra recorded for all samples. Clearly, FKO extrema shift towards higher energies with addition of Al 0.46 Ga 0.54 N and/or SiN x indicating an increase in field values. The assessment of the field, shown in Fig. 2b, was done in a conventional way by analysing the energetic position of FKO extrema 26,27 . Without SiN x and Al 0.46 Ga 0.54 N layers the built-in electric field in the GaN channel layer is 0.73 MV/cm. An addition of SiN x and/or Al 0.46 Ga 0.54 N causes the field to change due to a shift of the surface/interface Fermi level and/or creation of polarization-induced charges. In www.nature.com/scientificreports/ the SiN x capped structure a slight increase in the field to 0.83 MV/cm is observed. Fields values in structures with the Al 0.46 Ga 0.54 N layer, both capped and uncapped, is also higher at 1.13 MV/cm and 1.00 MV/cm, respectively. In order to translate the obtained field values to barrier height numerical calculations of dependency of builtin electric field on the surface/interface Fermi level position were performed, the results are shown in Fig. 2c. Crossings of calculated curves with horizontal lines indicating experimental field values show the respective Fermi level position. It can be seen that for GaN a surface barrier of ~ 0.4 eV is observed. This is a similar value to 0.3 eV reported previously for air ambient exposed N-polar GaN [28][29][30] . Quite unexpectedly a lower surface barrier of ~ 0.35 eV is estimated for the uncapped Al 0.46 Ga 0.54 N terminated structure. In ultra-high vacuum (UHV) conditions a higher initial barrier for GaN and a gradual increase in surface barrier in AlGaN alloys were observed by x-ray photoelectron spectroscopy (XPS) previously 22 . The discrepancy may be related to surface oxidation of samples under study within this work and N-polar nitrides are known to be easily oxidated 30 . SiN x capping shifts the Fermi level slightly away from the CB edge in both structures with and without the Al 0.46 Ga 0.54 N layer  www.nature.com/scientificreports/ to ~ 0.5 eV. Such an effect of SiN/AlGaN interface barrier stabilisation was reported in Ref. 22 and, since for SiN x capped structures ambient composition should not have any effect, a comparison between aim ambient (here) and UHV conditions (Ref. 22 ) is not unjustified. Similar CER studies were performed for both 2nd and 3rd series, consisting of full structures with a top Al 0.46 Ga 0.54 N layer and capped by SiN x that were previously studied by Hall effect measurements. The resulting CER spectra with FKO extrema marked are shown in Fig. 3a,b, respectively. In both series an expected increase in FKO period, i.e. increase of the built-in electric field, can be seen with narrowing of the GaN channel. Analysis of FKO yielded field values of 0.50, 0.71, and 1.68 MV/cm for structures with 20, 15, and 10 nm GaN channel thickness (2nd series) and 0.91, 1.20, and 1.80 MV/cm for structures with 12, 10.5, and 9 nm GaN channel thickness (3rd series). It can be immediately noticed that the field increase between 15 and 10 nm (10.5 and 9 nm) is much steeper than between 20 and 15 nm (12 and 10.5 nm) channel thickness. To better understand the observed effect a dependency of channel field on channel thickness was calculated for SiN x /Al 0.46 Ga 0.54 N barrier of 0.5 eV and several other values. It can be seen in Fig. 4 that the experimental points follow the 0.5 eV line only up to a certain thickness of 10 nm where a jump occurs to ~ 1.3 eV for two structures that showed lowered or unmeasurable carrier concentration. However, the channel thickness itself cannot be a factor that causes such a drastic change in surface barrier height and, in turn, carrier concentration. N-polar HEMTs are known to be highly scalable with carrier concentrations in excess of 10 13 cm −2 even with channel thickness below 6 nm 23,31 and, therefore, a different mechanism must be responsible for the observed carrier concentration drop.
Having established the SiN x /Al 0.46 Ga 0.54 N interface Fermi level position for all samples, calculations of the carrier concentration dependency on the GaN channel thickness were performed and are shown in Fig. 5. Two interface barrier heights were selected that correspond to the ones deducted above, namely 0.5 eV and 1.3 eV, and for each barrier two curves were calculated with doping level in the barrier of 4 × 10 18 cm −3 and 5 × 10 18 cm −3 that correspond to doping levels in 2nd and 3rd series, respectively. Results of Hall measurements of four samples that show high carrier concentration nicely follow the calculated curves for a barrier height of 0.5 eV following a gradual decreasing carrier concentration with narrowing of the GaN channel. The predicted carrier concentration for the 9 nm sample (3rd series) at a barrier height of 0.5 eV is 0.87 × 10 13 cm −2 . The experimentally obtained carrier concentration of 3.19 × 10 12 cm −2 is, however, even lower than the calculated value of 4.66 × 10 13 cm −2 . Regarding the 10 nm sample (2nd series) that was too resistive for Hall measurements its predicted carrier concentration at barrier of 0.5 eV was 0.71 × 10 13 cm −2 , and at 1.3 eV, a barrier that corresponds to CER measurements, www.nature.com/scientificreports/ calculations show 0.33 × 10 13 cm −2 . As was observed for the former sample the real concentration is probably even lower causing the Hall measurement to be unsuccessful. In order to understand this change in barrier height a discussion of previous reports is necessary. Two interface barrier heights were reported for N-polar SiN x /GaN. In Ref. 22 it was estimated by XPS that the barrier is ~ 0.3 eV in case of bulk-like films . An earlier paper on SiN x passivated GaN/AlGaN heterostructures reports a ~ 1.0 eV barrier deducted from C-V studies 21 . At the same time the latter report gives an insight on the SiN x / GaN interface state density providing a value of 4.5 × 10 12 cm −2 and stating that this interface charge is contained within 0.21 eV around the 1.0 eV surface state. These results suggest that two separate surface states exist at the SiN x /Al 0.46 Ga 0.54 N interface. Here we propose a model that describes the rapid decrease in carrier concentration for channel thicknesses below a "critical" value based on filling of these levels by carriers and subsequent changes in the band diagrams. Figure 6 shows three cases of surface state occupancy and resulting band profiles of a N-polar HEMT structure identical to the ones studied experimentally within this paper with a GaN channel thickness and built-in electric field d and F, respectively, and a barrier doping level n Si . Two surface states are considered. In the first case the interface barrier is set at 0.5 eV, i.e., in the upper interface state. In the intermediate case a slight increase in the barrier height is depicted that results from a downward Fermi level shift within the upper state. The last case shows a band diagram that results from a further downward shift of the interface Fermi level to the lower interface state at 1.3 eV. At constant d and n Si the field values are F 1 < F 2 < F 3 . Carrier concentration follows with n S1 > n S2 > n S3 . Now a situation of decreasing d at constant n Si will be considered. With a narrowing of the channel the field F increases and the separation between carriers filling the upper surface state and the triangular potential well (TPW) at the GaN/AlGaN interface decreases promoting a carrier transfer from the surface state towards TPW. At a certain point the upper interface state is depleted of carriers hence the Fermi level shifts to the lower state. This in turn causes a significant change in the GaN channel band bending (i.e., the field increases) and a subsequent drop in n s . While it may seem that in the intermediate case n s should increase due to carrier transfer  www.nature.com/scientificreports/ it actually decreases because of gradually increasing GaN channel field. The second case to consider is decreasing n Si at a constant thickness d. With a decrease in doping concentration there will be less carriers in the channel while the TPW itself does not change. Empty states in TPW will attract carriers from the upper interface state causing them to migrate along the built-in electric field. Again there will be initial gradual change in the surface barrier height within the upper interface state range of energies and a subsequent shift to the lower state when all carriers are removed from the upper one.
Comparing the model and experimental data for both the 2nd and 3rd series reducing the channel thickness results in a gradual reduction in carrier concentration down to a certain thickness. Below that thickness a sudden drop of the measured n s values below the predicted ~ 0.7 × 10 12 cm −2 or ~ 0.9 × 10 12 cm −2 , respectively, assuming a Fermi level position of 0.5 eV, can be observed. At the same time, a change in the interface barrier was observed for the two samples with the narrowest channel in respective series. Taking n Si as a variable one may compare the 10.5 nm sample from the 3rd series and the 10 nm sample from the 2nd series. While the channel thickness is not identical it is very close and the only significant difference is the doping level in the barrier at 5 × 10 18 cm −3 for the 3rd series sample and 4 × 10 18 cm −3 for the 2nd series sample. It can be seen from Hall measurements that a higher backbarrier doping allows the 3rd series to maintain a high carrier concentration while the other one shows a complete collapse. The proposed model allows also to explain why the 2nd series 15 nm structure maintains a high carrier concentration at 0.87 × 10 13 cm −2 while the 3rd series 9 nm structure does not keep its predicted concentration of similar 0.88 × 10 13 cm −2 . The reason here is the difference in the GaN channel builtin electric field. For a narrower channel and the interface barrier of 0.5 eV the calculated field is 1.1 MV/cm, compare to actual 0.7 MV/cm seen experimentally in the structure with a 15 nm channel. A higher field will provide more potential for the interface carriers to migrate towards TPW.
Basing on the proposed model the apparent discrepancy in the SiN x /GaN interface Fermi level position reported in Refs. 21,22 can be explained. In a bulk-like material studied in Ref. 22 only a weak surface band bending exists that results from the interface states occupancy by carriers coming from the bulk. In this case the upper state is at least partially filled by electrons originating from the unintentional background n-type doping that is common in N-polar GaN. This results in a low surface barrier of ~ 0.3 eV. The much higher interface barrier of 1.0 eV reported in Ref. 21 results from the built-in electric field present in GaN/AlGaN/GaN structures that draws the SiN x /GaN electrons towards the potential well present at the GaN/AlGaN interface emptying the upper interface state and shifting the Fermi level to the lower one.
In order to better understand the mechanism of Fermi level switching between two SiN x /(Al)GaN interface states more studies are needed to determine e.g. the density of interface states and their origin. It also seems important to fully describe the conditions at which the surface barrier stays low ensuring a high 2DEG concentration. Similar studies for other combinations of dielectric/III-nitride structures also seem important since various materials are proposed for gate dielectrics.  www.nature.com/scientificreports/ built-in electric field, and (2) a decrease in backbarrier doping that reduces the 2DEG density while leaving the potential well intact that attracts carriers from surface states.

Methods
Sample growth. All samples investigated in this study were grown by metal-organic chemical vapour deposition (MOCVD). C-plane sapphire substrates with 4° misorientation towards sapphire-a-plane were used to achieve smooth N-polar (Al,Ga)N films 4 . A 1.4 μm thick semi-insulating (S.I.) GaN base layer was first deposited using the procedure reported previously. For all samples, the backbarrier layer consisted of a 20 nm thick graded Al x Ga 1−x N layer with x = 0.05 → 0.38 and a 10 nm thick Al 0.38 Ga 0.62 N film, followed by a 0.7 nm thick AlN interlayer, a GaN channel layer with thickness varying from 9 to 20 nm, a 0 or 2.6 nm thick Al 0.46 Ga 0.54 N cap layer, and a 0 or 5 nm thick in-situ SiN x film. The graded Al x Ga 1−x N layers were doped with Si to achieve n-type doping of 4 × 10 18 cm −2 (1st and 2nd series) or 5 × 10 18 cm −2 (3rd series). The SiN x film was grown at 1,030 °C using disilane and ammonia flows of 4.46 μmol/min and 268 mmol/min, respectively.
2DEG concentration measurements. Van der Pauw Hall measurements with indium contacts were performed at room temperature to determine the carrier concentrations.

Contactless electroreflectance measurements.
For CER measurements the samples were mounted in a capacitor with a half-transparent top electrode made from a copper-wire mesh. An air gap of ~ 0.5 mm was kept between the sample surface and the top electrode. An alternating voltage of ~ 3 kV provided the band bending modulation. Other relevant details on CER can be found in Refs. 32,33 .

Calculations.
A commercial package nextnano++ was used for band profile and carrier concentration calculations 34 that provides solutions for coupled Schrödinger-Poisson equations.

Data availability
The datasets generated during and/or analysed during this study are available from the corresponding author on reasonable request.