Theoretical and experimental studies of electric field distribution in N-polar GaN/AlGaN/GaN heterostructures Open Access

GaN-based heterostructures are interesting due to the fact that piezoelectric polarization and spontaneous polarization originating from the wurtzite crystal structure can be utilized in devices such as field effect transistors.^1–5 To date, most of theoretical and experimental works on GaN-based transistors have been focused on Ga-polar devices,^6–10 primarily due to the relatively easy growth of GaN crystals along this crystallographic direction. Since Rajan et al. demonstrated a series of N-polar GaN/AlGaN/GaN transistors,¹¹ research in the area of N-polar heterostructures has gained momentum and a few other groups fabricated such heterostructures.^12–14 However, the issue of electric field distribution in N-polar GaN/AlGaN/GaN heterostructures was not explored experimentally up till now. On the other hand, theoretical studies of this issue can be controversial since different values of Fermi-level position at N-polar GaN surface have been reported so far.^15–17 This quantity is one of the boundary conditions which should be known for theoretical calculations of electric field distribution in GaN-based heterostructures. Therefore, it is very interesting to perform combined theoretical and experimental studies of electric field distribution in N-polar GaN/AlGaN/GaN heterostructures similar to those which have been done for Ga-polar structures.^18,19 Such studies are the aim of this paper.

The N-polar GaN(channel)/AlGaN/GaN(buffer) heterostructure was grown by plasma-assisted molecular beam epitaxy (PAMBE) in the VG90 reactor under metal-rich conditions at 730 °C. The N-polar GaN substrate used for epitaxy was fabricated by hydride vapour phase epitaxy (St. Gobain Crystal). During the MBE growth, nitrogen was supplied by a plasma source and the growth rate was 0.35 μm/h. A 500 nm-thick GaN buffer layer was deposited directly on N-polar GaN substrate. Next, a 20 nm thick AlGaN layer and a 20 nm thick GaN(channel) layer were deposited. Contactless electroreflectance (CER) and photoreflectance (PR) measurements were performed with a bright configuration set-up²⁰ in an ambient air at room temperature.

Figure 1 shows CER and PR spectra measured for N-polar GaN(channel)/AlGaN/GaN(buffer) heterostructure at room temperature. In CER spectrum a strong resonance followed by Franz-Keldysh oscillation (FKO) is visible at ∼3.4 eV. Such signal can be attributed to GaN. Very similar resonance is observed in PR spectrum, but besides the GaN-related transition, a strong PR signal is observed at ∼3.8 eV. This signal is associated with an optical transition in AlGaN layer. This transition is also followed by FKO, but in this case, the FKO period is much longer due to a large electric field in AlGaN layer. The AlGaN-related transition is not observed in CER spectrum since the built-in electric field in AlGaN layer is not modulated during CER measurements. This phenomenon is associated with the fact that a two dimensional electron gas (2DEG) exists at the GaN(channel)/AlGaN interface in the investigated heterostructure. The 2DEG screens the band bending modulation inside the GaN(channel)/AlGaN/GaN(buffer) heterostructure and, therefore, only a part of sample between the surface and the sheet of 2DEG is probed by CER. Very similar phenomenon was observed for Ga-polar AlGaN/GaN heterostructures.^18,19,21 This means that the GaN-related signal, which is observed in CER spectrum, is associated with the GaN(channel) layer. From the period of GaN-related FKO, it is possible to determine the built-in electric field inside GaN(channel) layer. Since the magnitude of electric field modulation in PR and in CER spectroscopy is very weak (i.e., in CER measurements most of AC voltage drops in the air gap between the top electrode and the surface since there is no contact between them¹⁶) the standard and widely applied formula^22–24 can be used to analyze the FKO signal.

Figure 2 shows the analysis of GaN- and AlGaN-related FKO for the investigated heterostructure similarly as in Refs. 18 and 19. For GaN, the built-in electric field has been determined to be 0.22 ± 0.02 and 0.20 ± 0.02 MV/cm from CER and PR measurement, respectively, which is the same within experimental uncertainty. For AlGaN, the electric field has been estimated to be 0.98 ± 0.10 MV/cm.

In order to find the electric field distribution in N-polar GaN(channel)/AlGaN/GaN(buffer) heterostructure, the experimental values of electric field in GaN(channel) and AlGaN layer have been compared with the theoretical calculations of electric field distribution in such heterostructure performed for various boundary conditions (i.e., different Fermi-level position at GaN surface and in GaN(buffer) layer; the latter corresponds to different residual carrier concentration in GaN(buffer) layer).

Since the distribution of electric field in GaN(channel)/AlGaN/GaN(buffer) heterostructure results from polarization effects and the distribution of free carriers along the growth direction, including 2DEG distribution at the GaN(channel)/AlGaN interface, the one-electron Schrodinger equation with proper boundary conditions has to be solved in order to find this distribution. One boundary condition (the Fermi-level position at GaN surface) is implemented in the first trial potential, while the second boundary condition (the Fermi-level position in GaN(buffer) layer, which corresponds to the residual carrier concentration in this layer) is implemented after the first iteration of self-consistent calculations. In each iteration, the trial potential is corrected by a correction potential, which is associated with the distribution of free carriers. This potential is determined by solving the Poisson equation. The parameters for calculations have been taken from Ref. 25.

Figure 3 shows the calculated electric field distribution for two situations where the boundary conditions were varied independently. In the first situation (see Fig. 3(a)), the Fermi-level position at the surface of GaN(channel) layer is varied and its position in GaN(buffer) layer is pinned. This set of calculations clearly shows that the built-in electric field in GaN(channel) layer strongly depends on the position of Fermi-level at GaN surface while the built-in electric field in AlGaN and GaN(buffer) layer does not change with this boundary condition. In the second situation (see Fig. 3(b)), the Fermi-level position at GaN(channel) surface was pinned 0.3 eV below the conduction band, and its position in GaN(buffer) layer was varied according to the carrier concentration in GaN(buffer) layer given in this figure. In this case, it is clearly observed that the residual carrier concentration in GaN(buffer) strongly changes the band bending in this layer, as should be expected, but it also strongly influences the built-in electric field in AlGaN layer and changes the band bending in GaN(channel) only a little.

From electrical measurements of N-polar GaN layers, we know that the residual carrier concentration in this material is ∼10¹⁷cm⁻³. Therefore, the Fermi-level position in GaN buffer layer can be treated as a boundary condition, which is more or less known for these heterostructures. In order to determine the electric field distribution in the investigated heterostructure, we have to calculate the electric field in GaN(channel) and AlGaN layer for various Fermi-level positions at GaN surface and compare the calculated values with those determined experimentally for the investigated sample. Those calculations have been performed for various residual doping levels in GaN(buffer) layer.

Figure 4 shows a comparison of built-in electric field in GaN(channel) and AlGaN layer of the investigated heterostructure obtained from measurement (thick grey horizontal lines) with theoretical calculations performed for various Fermi-level positions at GaN surface and different residual electron concentration in GaN(buffer) layer. It is clearly visible that the built-in electric field in AlGaN layer strongly depends on residual doping and weakly depends on the Fermi-level position at GaN surface. The agreement between the theoretical predictions and experimental value of electric field in AlGaN layer is observed when the residual doping in GaN(buffer) is between 1.0 and 1.5 × 10¹⁷cm⁻³, which is in a good agreement with the estimation of electron concentration in N-polar GaN layers grown at similar conditions. Regarding electric field in GaN(channel) layer, it is visible that this field is varying strongly with the shift in Fermi-level position at the surface while the influence of residual doping on electric field in this layer is rather weak in the considered range of carrier concentration. Finally, we can conclude that the agreement between the theoretical calculations and the experimental data for GaN and AlGaN layer is observed for the same Fermi-level position at GaN surface, that is, ∼0.3 eV below the CB in GaN. Such a surface boundary condition is in good agreement with the Fermi-level position of 0.27 eV determined for N-polar GaN surface in Van Hoof structures studied by CER spectroscopy.¹⁶ For Ga-polar AlGaN/GaN heterostructures of various thicknesses of AlGaN layer capped by a thin (∼3 nm) GaN layer, the surface boundary condition has been found to be ∼0.55 eV below the conduction band of GaN.^18,19 In this case it has also been found that this boundary condition is consistent with the Fermi-level position of ∼0.4–0.6 eV below CB determined by CER spectroscopy for Ga-polar Van Hoof GaN structures.^16,26 Therefore, the Fermi-level position at N-polar GaN surface in GaN(channel)/AlGaN/GaN(buffer) heterostructure determined in this work can be treated as a surface boundary condition for calculations of electric field distribution in GaN(channel)/AlGaN/GaN(buffer) heterostructures of various thicknesses of GaN(channel) and AlGaN layers. Such calculations are shown in Figs. 5 and 6. In addition, the 2DEG concentration at the GaN(channel)/AlGaN interface is plotted in these figures.

After analyzing the results in Figs. 5 and 6, it is clearly visible that thicknesses of GaN(channel) and AlGaN layer have to be in proper range in order to obtain a channel with the 2DEG of a given concentration. To achieve the 2DEG concentration of ∼10¹³ cm², the thickness of GaN(channel) layer should be in the range of ∼20–30 nm. The same is with the thickness of AlGaN layer. On one hand, this layer cannot be too thin since the concentration of 2DEG would be too low, see inset in Fig. 5(b). On the other hand, this layer cannot be too thick since a channel for holes can be formed at the AlGaN/GaN(buffer) interface, see band profile for heterostructures with AlGaN layer thicker than 35 nm in Fig. 6(a). Finally, it is also worth noting that a formation of 2DEG at the GaN(channel)/AlGaN interface strongly depends on the Fermi-level position at GaN surface, and therefore, such heterostructures can be very promising for chemical field effect transistors (ChFET),²⁷ where the Fermi-level at GaN surface (in this case it will be a functionalized chemical gate) is tuned by chemical particles interacting with this gate. Such an interaction would change 2DEG concentration, which should be observed in transistor electrical/I-V characteristics. In general, the same idea is utilized in Ga-polar ChFET,²⁷ but N-polar ChFET should be more sensitive since the 2DEG is closer to the chemical gate and its concentration dependence on Fermi-level position at the chemical gate is stronger. This issue is very well illustrated in Fig. 7 where the concentration of 2DEG is plotted vs. the Fermi-level position on N-polar GaN surface for GaN(channel)/AlGaN(20 nm)/GaN(buffer) heterostructure. It is visible that the shift of Fermi-level at GaN surface by ∼0.5 eV (or even less in heterostructures with thinner GaN(channel)) is able to switch conductivity in GaN(channel) off. This also suggests that the formation of 2DEG at the GaN(channel)/AlGaN interface will strongly depend on capping of GaN(channel) by SiN or AlGaN.

In conclusion, the electric field distribution in N-polar GaN(channel)/AlGaN/GaN(buffer) heterostructures with various thicknesses of GaN(channel) and AlGaN layer has been calculated with the surface boundary condition determined experimentally for N-face GaN(20 nm)/AlGaN(20 nm)/GaN(buffer) heterostructure. In this way, the range of layer thickness for which 2DEG is formed at the GaN(channel)/AlGaN interface has been determined. Moreover, the surface boundary condition estimated in this work (i.e., the position of Fermi-level ∼0.3 eV below CB) is in a good agreement with previous experimental study of Fermi-level position at N-polar GaN surface in Van Hoof structures which has been found to be 0.27 eV below CB.¹⁶ In addition, it has been shown that the formation of 2DEG at the GaN(channel)/AlGaN interface strongly depends on Fermi-level position at GaN surface and hence this structure is very promising in ChFET.

This work was performed within the grant of the National Science Centre (No. 2011/03/B/ST3/02633).