Introduction

Al-rich AlGaN alloys are ideal materials for deep ultraviolet (DUV) optoelectronic devices with operating wavelength down to 200 nm due to their large direct band gaps1,2,3,4. They have potential applications in sterilization, water and air purification, biological and chemical agent detection, high-density data storage and medical research5,6. However, the external quantum efficiency of AlGaN-based DUV light-emitting diodes (LEDs) is extremely low around 0.1%7,8. Generally, three main factors, that is, the high dislocation density (1010 cm−2), the low p-type doping efficiency and the AlN-like valence-band maximum (VBM), i.e., the crystal-field split-off hole band as the VBM other than the heavy hole band (see Figure 2.12 in Ref. 9), contribute to this overall small value. We will here focus on improving p-type doping efficiency in Al-rich AlGaN. It is well-known that realizing p-type doping in Al-rich AlGaN is extremely difficult due to the following three major reasons, i.e., the high acceptor activation energy EA, the compensation by nitrogen vacancies and the limited acceptor solubility9. For the most widely used Mg acceptor dopant, its EA increases monotonically with Al composition from 0.16–0.25 eV in GaN to >0.50 eV in AlN9. Therefore, realizing p-type Al-rich AlGaN has become one of the most challenging tasks in the nitride community.

Great efforts have been devoted to improve p-type conduction in group-III nitrides10,11,12,13,14,15,16. Polarization doping has been proposed to increase the hole concentration in compositionally graded AlGaN alloys, in which Mg acceptor is ionized by the polarization field10,11,12. Alternative acceptor-donor co-doping has also been developed to reduce the acceptor activation energy13,14. The non-equilibrium growing with pulse doping has been proved to increase the hole concentration15. Furthermore, Mg δ-doping, a impurity-growth mode by closing Ga and Al flow and leaving N and Mg flow, enhances the p-type conductivity of AlGaN alloys16. To the best of our knowledge, only several experiments are focused on the p-type conduction of Al-rich AlGaN alloys3,9,17,18. The related theoretical work is still absent at present. Our purpose here is to overcome the p-type doping bottlenecks in Al-rich AlGaN.

We note that nanometer scale compositional inhomogeneity has an important influence on the luminescence efficiency of group-III nitride semiconductors6,19,20,21,22,23,24. It has been found that the nanoscale islands or quantum dots observed in AlGaN can improve its internal quantum efficiency6,19,24,25. Moreover, atomic-scale compositional superlattice (SL) has also been observed in Al-rich AlGaN thin films grown by molecular-beam epitaxy (MBE)26. Recent theoretical and experimental works prove that the nanoscale (AlN)m/(GaN)n (m > n) SL, substituting for the Al-rich AlGaN disorder alloy, can convert the VBM from the crystal-field split-off hole to heavy hole band, which directly leads to the increase of the desired transverse electric (TE) polarized light emission efficiency in the DUV spectral region (Ref. 27 and Jiang, X.-h. et al., unpublished data). Compared with Al-rich AlGaN alloy, the SL structure has an obvious advantage because it can combine the high TE polarized light emission efficiency of GaN and the wide energy gap of AlN.

According to the tight-binding approximation, we know that the electronic structures of Mg atom doped in AlGaN can be modified significantly by its nearest and next-nearest (NN) atoms. We will thus pay our attention to the nearest and NN atoms and investigate their influence on Mg electronic structures in nanoscale (AlN)5/(GaN)1 SL (see Figure 1) substitution for Al0.83Ga0.17N disorder alloy. Our following results show that EA decreases if the NN Ga-atom number increases and the Mg-centered tetrahedron volume decreases. The Mg acceptor activation energy can be reduced significantly to 0.26 eV, very close to the EA of GaN, in (AlN)5/(GaN)1 SL by MgGa δ-doping. A high hole concentration in the order of 1019 cm−3 can thus be obtained.

Figure 1
figure 1

Typical structural model of nanoscale (AlN)5/(GaN)1 SL with one GaN monolayer (0.26 nm).

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Results

In order to examine the stability of Mg doped structures, we first calculate the formation energy Ef of Mg acceptor in (AlN)5/(GaN)1 SL and Al0.83Ga0.17N uniform alloy. Generally, Ef of a defect D in charge state q can be calculated as follows28,

where Etot[D(q)] is the total energy of the supercell containing the defect D in charge state q, Etot[bulk] is the total energy in the same supercell without the defect, ni is the atom number of the ith constituent, which has been added to (ni > 0) or removed from (ni < 0) the host material and μi is its chemical potential. EF is the Fermi level referenced to the VBM EV of the bulk. The range of EF is taken to be the band gap of the bulk. A correction term ΔV[D] is introduced in order to align the reference electrostatic potential in the charged defect supercell with that in the bulk. For the finite supercell calculation, a correction term Ecorr is also needed due to the dispersion of the defect level, especially for the shallow level. It can be inferred from the energy difference between the highest occupied state at the Γ point and the average value at several special k points. The chemical potentials μ closely depend on the growth conditions and can be determined by,

Because the group-III nitride semiconductors are usually grown under the N-rich and N-poor conditions26,29,30, which directly determine the kind and concentration of defects in semiconductors, we thus consider these two limited cases to calculate the Mg acceptor formation energy. For the N-rich case, (the energy of N in a N2 molecule). Otherwise, for the N-poor case, μAl(Ga) = μAl(Ga)[bulk], i.e., the energy of Al (Ga) in bulk Al (Ga). The Mg acceptor level ε(0/−1), i.e., the activation energy, is defined as the EF position where the charge states of q = 0 and −1 have equal formation energy and can be calculated from the following formula,

Our calculated formation energies as a function of EF are shown in Figure 2 for MgGa in nanoscale (AlN)5/(GaN)1 SL and MgAl and MgGa in Al0.83Ga0.17N uniform alloy under N-poor and -rich conditions. We can see from Figure 2 that the Ef of Mg0 under p-type condition (EF close to the VBM) is larger than that of Mg1− under n-type condition (EF close to the bottom of the conduction band). We thus can understand that the Mg acceptor concentration is low in thermodynamic equilibrium due to its large Ef in p-type (AlN)5/(GaN)1 SL and Al0.83Ga0.17N alloy, which is consistent with the previous experiment31. The formation energy as a function of EF under N-poor is similar to that under N-rich. The Ef of MgGa and MgAl decreases by 0.94 eV approximately from N-poor to -rich conditions because of the negative formation enthalpy of GaN and AlN. Moreover, we can see from Figure 2(a) that MgGa in (AlN)5/(GaN)1 SL has two stable charge states, i.e., neutral 0 and −1, which induces a shallow acceptor level (0.26 eV). Figure 2(b) shows that Ef of MgGa is about 0.20 eV lower than that of MgAl in Al0.83Ga0.17N uniform alloy. The Mg atom thus tends to replace Ga atom other than Al atom. This can be attributed to the weak bond strength between Ga and N atoms compared to that between Al and N atoms.

Figure 2
figure 2

Formation energy as a function of Fermi level EF for (a) MgGa in nanoscale (AlN)5/(GaN)1 SL and (b) MgAl and MgGa in Al0.83Ga0.17N uniform alloy under N-rich and –poor conditions.

The zero of EF corresponds to the VBM.

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The Mg atom can also substitute Al atom to form an acceptor in (AlN)5/(GaN)1 SL except for the aforementioned MgGa. In order to know the preferable position of Mg0 dopant, we further calculate its formation energy (see Figure 3(a)) for the chosen four special cation positions. The difference of sites 1–4 mainly concentrates on the nearest and NN neighbours of Mg, i.e., local structure around Mg atom (see Figure 3(c)). For the chosen four special positions, the NN Ga-atom numbers NGa are 6, 3, 0 and 0 from site 1 to 4, respectively. We can see from Figure 3(a) that the formation energy Ef increases monotonically from site 1 to 4 in (AlN)5/(GaN)1 SL, which is larger than Ef of Mg0 in GaN and smaller than that in AlN, as it should be. The Ef rapidly increases from site 1 to 2, then slowly increases from site 2 to 4. This is because the Ga-N bond is weaker than the Al-N bond. We can conclude that Mg atom tends to occupy Ga site to form MgGa acceptor in (AlN)5/(GaN)1 SL. This can be realized by means of Mg δ-doping technique, i.e., closing Al flow and leaving Ga and Mg flow16.

Figure 3
figure 3

Mg acceptor formation energy in neutral charge state (a) and its activation energy (b) as a function of Mg-atom site in (AlN)5/(GaN)1 SL. Here four special cation sites, surrounded with different next-nearest Ga atom numbers, are labeled in (c) for 3 × 3 × 3 supercell. For the sake of comparison, Mg acceptor formation energy and activation energy in GaN and AlN are also presented. The lines are guides to the eyes.

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We further calculate Mg acceptor activation energy EA in GaN, AlN and Al0.83Ga0.17N uniform alloy (see Table 1). For the sake of comparison, some previous theoretical and experimental results are also given. We can see from Table 1 that our calculated EA is 0.21 eV in GaN, which is within the range of well-accepted theoretical results (0.198–0.26 eV)32,33,34 and experimental values (0.16–0.25 eV)9,35,36. For Mg dopant in AlN, excellent agreement of EA (0.48 eV) with the previous theoretical calculations (0.40–0.78 eV)14,33,37,38 and experiments (0.5 eV)9,17,39,40 is also confirmed. This clearly indicates that our current calculations with the AM05 exchange-correlation (XC) functional41 are accurate and reliable for the acceptor activation energy. Moreover, we calculate EA of MgGa and MgAl acceptors in Al0.83Ga0.17N uniform alloy and find that they have equal EA (0.44 eV) despite different cation sites occupied by Mg atom, which is in the range of the reported experimental values from 0.40 eV for Al-content x = 0.7 to 0.50 eV for x = 1.09. It is worthwhile to note that, in spite of the Al-site or Ga-site occupied by Mg atom, EA in Al0.83Ga0.17N uniform alloy is always large and approaches the corresponding value of AlN. Therefore, it is extremely difficult to reduce Mg acceptor activation energy in Al-rich AlGaN. We will turn our attention to Mg dopant in (AlN)5/(GaN)1 SL substitution for Al0.83Ga0.17N disorder alloy and seek a new way to reduce EA in the following text.

Table 1 Comparison of Mg acceptor activation energy EA (in unit of eV) with other calculations and experiments in wurtzite GaN, AlN and Al0.83Ga0.17N uniform alloy
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Figure 3(b) shows our calculated Mg acceptor activation energies EA in nanoscale (AlN)5/(GaN)1 SL as a function of Mg-atom position, which are in the range of 0.21 eV in GaN and 0.48 eV in AlN. We can see from Figure 3(b) that EA in site 1 with the NN Ga-atom number NGa = 6 has its smallest value of 0.26 eV, which is very close to the Mg acceptor EA in GaN. Then, EA increases by 0.06 eV from site 1 to 2 with NGa = 3 and has a remarkable increase by 0.11 eV from site 2 to 3 (NGa = 0). The EA keeps a constant approximately from site 3 to 4 (NGa = 0). These results clearly show that NGa or local structure of Mg atom has a significant influence on Mg acceptor EA in SL. By increasing the NN Ga-atom number around Mg dopant, its activation energy EA can be reduced remarkably. We further estimate hole concentration and find that it can reach to 1019 cm−3 in the SL at room temperature. This is extremely important and highly desired for the Al-rich AlGaN-based DUV optoelectronic devices. It is worthwhile to note that the hole concentration can be reduced due to the compensation of donors, such as nitrogen vacancies, which has not been considered in the above estimation. The concentration will be further reduced owing to the high Mg acceptor activation energy if the Ga atoms are not restricted to a single atomic layer.

Discussion

Why does Mg acceptor activation energy sensitively depend on the local structure around Mg dopant and can be reduced significantly in nanoscale (AlN)5/(GaN)1 SL? According to the band offset explaination42,43, Mg activation energy EA is dominated by the position of the VBM state of the host material. The higher the VBM is, the lower the EA is. In our current Mg doping calculations in (AlN)5/(GaN)1 SL, EA has a significant variation with different Mg doping positions, whereas the VBM is always fixed. Obviously, the previous viewpoint cannot explain our results anymore. In order to have a deep understanding for the results of Figure 3(b), we further calculate the partial density of states (PDOS) of Mg atom near the Fermi energy in (AlN)5/(GaN)1 SL for different Mg doping positions (see Figure 4). We can find from Figure 4 that the localization of the Mg defect state sensitively depends on Mg site or local structure around it. The Mg impurity state changes markedly from the delocalized state to highly localized one from site 1 to 4 (see Figure 4(a–d)). According to the definition of shallow and deep levels in semiconductors44, we know that the MgGa acceptor level, corresponding to the delocalized state in site 1, is a shallow level. The acceptor level goes deeper from site 2 to 4 due to the strong localization of the Mg defect state. We thus can understand the results of Figure 3(b). Hence the MgGa acceptor has the strongest delocalization, which results in the smallest acceptor activation energy in the SL.

Figure 4
figure 4

The Mg PDOS near Fermi level EF in p-type (AlN)5/(GaN)1 SL for different Mg doping-sites (see Figure 3(c)).

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Considering that the localization of Mg defect state is closely related to its local structure, we thus pay our attention to the relationship between the local structure and the localization of Mg defect state in order to explore the real physical origin of reducing Mg acceptor activation energy in nanoscale (AlN)5/(GaN)1 SL. Figure 5 shows the local structure around Mg acceptor, i.e., the Mg-centered tetrahedron, for the chosen four different Mg doping-sites. We find that the volumes V of Mg-centered tetrahedrons, indicating the average interaction strength between N and Mg atoms, are 4.317, 4.348, 4.360 and 4.374 Å3 for Mg sites 1–4, respectively. The volume related to site 1 (4) is the smallest (largest). This is owing to the GaN-monolayer strong modulation effect, which is originated from the larger covalent radius of Ga atom than that of Al atom as the NN neighbors of Mg dopant. It is the variation of the local structure that leads to the difference of the interaction between N and Mg atoms, which directly modify the localization of the Mg defect state and Mg acceptor activation energy. The smaller V is, the stronger the N-Mg interaction is. The corresponding Mg defect state thus becomes more delocalization and the activation energy is reduced due to the strong interaction between N and Mg atoms. We thus can understand that the local structure in Figure 5(a) has the smallest volume, the strongest N-Mg interaction, the most obvious delocalization of the Mg defect state (see Figure 4) and the smallest acceptor activation energy among the four different Mg doping-sites (see Figure 3(b)). It is note that the volume of the Mg-centered tetrahedron will increase if some Al atoms substitute Ga atoms in the single GaN layer due to the smaller covalent radius of Al atom, which increases the Mg acceptor activation energy.

Figure 5
figure 5

Local-structure around Mg acceptor for the chosen four different Mg doping-sites (see Figure 3(c)).

The calculated bond/edge length (in Å) and the tetrahedron volume V (in Å3) are indicated.

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In order to have an intuitive picture for the relationship between the Mg acceptor activation energy and its local structure, we give the EA-V plot in Figure 6. It clearly shows that the smaller V is, the smaller the activation energy is. When the volume V has a slight increase from 4.317 to 4.374 Å3 (~1.3%), EA has a remarkable increase from 0.26 to 0.44 eV (~40.9%). Therefore, the local structure around Mg dopant plays a dominating role on the Mg acceptor activation energy. We thus open up a new way to reduce Mg acceptor activation energy in Al0.83Ga0.17N disorder alloy substituted by nanoscale (AlN)5/(GaN)1 SL with MgGa δ-doping. This picture is universal, which can be easily extended to other acceptor dopants in (AlN)m/(GaN)n (m > n) SL and wide-gap semiconductors.

Figure 6
figure 6

Calculated Mg acceptor activation energy as a function of the Mg-centered tetrahedron volume (see Figure 5).

The black line is the fitting curve to the calculated data points.

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In summary, we calculate the formation energy and activation energy of Mg acceptor and investigate the relationship between the local structure around Mg atom and its activation energy in nanoscale (AlN)5/(GaN)1 SL substitution for Al0.83Ga0.17N disorder alloy using first-principles calculations. We find that it is energetically more favourable for Mg atom to substitute Ga atom. The Mg acceptor activation energy sensitively depends on its local structure. The smaller the volume of the local structure is, the smaller the activation energy is. Our calculations show that Mg acceptor activation energy can be reduced significantly from 0.44 eV in Al0.83Ga0.17N disorder alloy to 0.26 eV in (AlN)5/(GaN)1 SL by MgGa δ-doping due to the GaN-monolayer strong modulation. The hole concentration can be significantly enhanced up to 1019 cm−3 in the SL at room temperature. Our results are vital for the realization of AlGaN-based DUV optoelectronic devices. We hope that this study would motivate further investigations in the near future.

Methods

Our first-principles calculations are based on the density functional theory with the generalized gradient approximation (GGA) functional and performed using the Vienna ab initio simulation package (VASP) code45,46,47,48. In our calculations, the AM05 XC functional41 and projector augmented-wave (PAW) method are adopted to obtain accurate lattice constants49. We have built a Al-rich AlGaN supercell with 3 × 3 × 3 wurtzite primitive cells. Two representative Ga distributions are considered. One is nanoscale (AlN)5/(GaN)1 SL with one GaN monolayer and the other is Al0.83Ga0.17N uniform alloy. The SL can be grown by metalorganic vapor phase epitaxy with sources of trimethylaluminum, trimethylgallium and ammonia27. In order to minimize the strain, the supercell without Mg dopant is fully relaxed. Then the relaxed lattice vectors are fixed and the polarization effect is considered in our doping calculations. The N (2s22p3), Mg (3s2), Al (3s23p1) and Ga (3d104s24p1) are treated as valence electrons. The plane-wave basis set with a cutoff energy of 500 eV and the Monkhorst-Pack k-point grid50 of 4 × 4 × 2 have been checked carefully. In our current calculations, the total energy is converged to less than 10−5 eV. The maximum force is less than 0.02 eV/Å to guarantee that the stress is released completely. Based on these parameters, we calculate the lattice constant and valence band width (VBW) of GaN and AlN. Our calculated lattice constants are 3.18 (3.11) Å for a and 5.18 (4.98) Å for c and the VBW is 7.1 (6.0) eV for GaN (AlN), which are in excellent agreement with experiment51.

Considering that the band gap is seriously underestimated in the usual GGA functional, we thus adopt the LDA-1/2 method52,53 to improve our calculations, in which the half ionization is applied to the p-orbital of N atom and d-orbital of Ga atom. We choose the trimming parameter CUT = 2.90 (a.u.) and the power n = 8 for N atom and 1.23 (a.u.) and 100 for Ga atom. This is because our calculated band gaps with these parameters are 3.51 and 6.01 eV for GaN and AlN, which are in good agreement with their experimental values. Our calculated band gaps are 5.24 and 5.56 eV for (AlN)5/(GaN)1 SL and Al0.83Ga0.17N uniform alloy, respectively.