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 SiNx and/or Al0.46Ga0.54N 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 Al0.46Ga0.54N and/or SiNx 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 extrema26,27. Without SiNx and Al0.46Ga0.54N layers the built-in electric field in the GaN channel layer is 0.73 MV/cm. An addition of SiNx and/or Al0.46Ga0.54N causes the field to change due to a shift of the surface/interface Fermi level and/or creation of polarization-induced charges. In the SiNx capped structure a slight increase in the field to 0.83 MV/cm is observed. Fields values in structures with the Al0.46Ga0.54N 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 built-in 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 GaN28,29,30. Quite unexpectedly a lower surface barrier of ~ 0.35 eV is estimated for the uncapped Al0.46Ga0.54N 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) previously22. The discrepancy may be related to surface oxidation of samples under study within this work and N-polar nitrides are known to be easily oxidated30. SiNx capping shifts the Fermi level slightly away from the CB edge in both structures with and without the Al0.46Ga0.54N layer to ~ 0.5 eV. Such an effect of SiN/AlGaN interface barrier stabilisation was reported in Ref.22 and, since for SiNx 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 Al0.46Ga0.54N layer and capped by SiNx 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 SiNx/Al0.46Ga0.54N 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 1013 cm−2 even with channel thickness below 6 nm23,31 and, therefore, a different mechanism must be responsible for the observed carrier concentration drop.
Having established the SiNx/Al0.46Ga0.54N 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 × 1018 cm−3 and 5 × 1018 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 × 1013 cm−2. The experimentally obtained carrier concentration of 3.19 × 1012 cm−2 is, however, even lower than the calculated value of 4.66 × 1013 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 × 1013 cm−2, and at 1.3 eV, a barrier that corresponds to CER measurements, calculations show 0.33 × 1013 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 SiNx/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 SiNx passivated GaN/AlGaN heterostructures reports a ~ 1.0 eV barrier deducted from C-V studies21. At the same time the latter report gives an insight on the SiNx/GaN interface state density providing a value of 4.5 × 1012 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 SiNx/Al0.46Ga0.54N 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 nSi. 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 nSi the field values are F1 < F2 < F3. Carrier concentration follows with nS1 > nS2 > nS3. Now a situation of decreasing d at constant nSi 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 ns. While it may seem that in the intermediate case ns should increase due to carrier transfer it actually decreases because of gradually increasing GaN channel field. The second case to consider is decreasing nSi 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 ns values below the predicted ~ 0.7 × 1012 cm−2 or ~ 0.9 × 1012 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 nSi 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 × 1018 cm−3 for the 3rd series sample and 4 × 1018 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 × 1013 cm−2 while the 3rd series 9 nm structure does not keep its predicted concentration of similar 0.88 × 1013 cm−2. The reason here is the difference in the GaN channel built-in 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 SiNx/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 SiNx/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 SiNx/(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.