1.
Introduction
Band offsets between two semiconductors AX and BY play a vital role in electronic devices, because they can lead to different electron quantum confinements and determine the spatial distribution of carriers. III–V compound semiconductor materials such as GaX (X = N, P, As, Sb) are important materials for electronic and optoelectronic applications[1–3]. However, the number of the III–V semiconductors and their available material properties are limited. One of the approaches to extend their range of applications is through atomic transmutation, in which, two group III elements (e.g., Ga) are replaced by one group-II element (e.g., Zn), and one group-IV element (e.g., Ge) to systematically obtain new heterovalent II–VI–X2 compounds (e.g., ZnGeX2)[4–8]. These new compounds have the same number of valence electrons as the original III–V compounds, so they are expected to obey the octet rule with the same semiconductor characters. However, although some ternary compounds such as ZnGeN2 and ZnGeP2 have been synthesized and are predicted to have interesting properties for novel applications such as nonlinear optical devices[9, 10], the electronic band structures of these compounds are poorly understood. For example, it is not clear what the relative positions of the conduction band minimums (CBMs) and valence band maximums (VBMs) are between GaX and ZnGeX2 after Ga is replaced by its neighboring Zn and Ge elements and how the band offsets change as the anion atomic number increases from N to P to As to Sb.
In this paper, we systematically calculate the band offsets of heterojunctions GaX/ZnGeX2 (X = N, P, As, Sb) using the first-principles method. We show that the band alignment is type-I for X = P, As, and Sb, that is the VBM of ZnGeX2 is higher than that of GaX and the CBM of ZnGeX2 is lower than that of GaX. Surprisingly, it is type-II for the nitrides because the CBM of ZnGeX2 is higher than GaX. By analyzing the VBM and CBM wavefunction characters, we found that the coupling between anion p and cation d states play a decisive role in determining the position of the valence band maximum, and the increased electronegativity of Ge relative to Ga can explain the lower CBM of ZnGeX2 for X = P, As, and Sb. The anomalous behavior for nitrides can, however, be explained by the strong coulomb interaction between Ge and N ions, which shortens the Ge–N bond length and raises the antibonding CBM energy in ZnGeN2.
2.
Method
X-ray photoemission spectroscopy (XPS) is widely used experimentally to determine the energy difference between the core-level and VBM, and hence to deduce the valence band alignment of two systems[11]. Following the same procedure, the valence band offset (VBO) of heterojunction AX/BY are calculated using the following equations:
$Delta {E_{ m{v}}}{ m (AX/BY)} = Delta E_{{ m{v}}, { m{C}}'}^{ m BY} - Delta E_{{ m{v}}, { m{C}}}^{ m AX} + Delta E_{{ m{C}}, { m{C}}'}^{ m AX/BY},$  | (1) |
where,
$Delta E_{{ m{v}}, { m{C}}}^{ m AX} = E_{ m{v}}^{ m AX} - E_{ m{C}}^{ m AX},$  | (2) |
$Delta E_{{ m{v}}, { m{C}}'}^{ m BY} = E_{ m{v}}^{ m BY} - E_{{ m{C}}'}^{ m BY},$  | (3) |
$Delta E_{{ m{C}}, { m{C}}'}^{ m AX/BY} = E_{{ m{C}}'}^{ m BY} - E_{ m{C}}^{ m AX},$  | (4) |
where
m{v}}, {
m{C}}}^{
m AX}$
m{v}}, {
m{C}}'}^{
m BY}$
m{C}}, {
m{C}}'}^{
m AX/BY}$
The electronic band structure calculations are performed at the experimental lattice constants based on the density functional theory (DFT)[13, 14]. The hybrid functional parametrized by Heyd-Scuseria-Ernzerhof (HSE06)[15], as implemented in the plane-wave basis code VASP[16, 17], is used to calculate the band offsets[18]. The pseudopotential is described by the projector-augmented-wave (PAW) method[19]. The cutoff energy for the wave-function expansion is 500 eV. A Γ centered 6 × 6 × 6 k-point for GaX bulks and 6 × 6 × 3 for ZnGeX2 ternary compounds were used in the calculations. For the structure relaxation the force on each atom was converged to 0.02 eV/?. Table 1 summarizes both the experimental and HSE calculated lattice constants, bond lengths and band gaps of GaX and ZnGeX2 (X = N, P, As, Sb) crystals.
| Crystal | Lattice constant (?) HSE (Exp.) | Bond length (?) HSE (Exp.) | Band gap (eV) HSE (Exp.) |
| GaN | a = b = c = 4.512 (4.50) | 1.954 (1.949) | 3.12 (3.30[20]) |
| GaP | a = b = c = 5.483 (5.45) | 2.374 (2.360) | 2.32 (2.34[21]) |
| GaAs | a = b = c = 5.695 (5.65) | 2.466 (2.448) | 1.35 (1.52[20]) |
| GaSb | a = b = c = 6.154 (6.10) | 2.665 (2.640) | 0.79 (0.81[20]) |
| ZnGeN2 | a = b = 4.572, c = 8.776 | (Ge–N) 1.871, (Zn–N) 2.043 | 3.03 |
| ZnGeP2 | a = b = 5.473 (5.46), c = 10.749 (10.76) | (Ge–P) 2.334 (2.309), (Zn–P) 2.378 (2.398) | 2.02 (2.05[22]) |
| ZnGeAs2 | a = b = 5.711 (5.67), c = 11.226 (11.15) | (Ge–As) 2.446 (2.396), (Zn–As) 2.472 (2.488) | 1.07 (1.15[23]) |
| ZnGeSb2 | a = b = 6.156, c = 12.193 | (Ge–Sb) 2.664, (Zn–Sb) 2.650 | 0.48 |
Table1.
Calculated lattice constants, bond lengths and band gaps of GaX and ZnGeX2 (X = N, P, As, Sb) compounds using HSE functional compared with experimental values.
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| Crystal | Lattice constant (?) HSE (Exp.) | Bond length (?) HSE (Exp.) | Band gap (eV) HSE (Exp.) |
| GaN | a = b = c = 4.512 (4.50) | 1.954 (1.949) | 3.12 (3.30[20]) |
| GaP | a = b = c = 5.483 (5.45) | 2.374 (2.360) | 2.32 (2.34[21]) |
| GaAs | a = b = c = 5.695 (5.65) | 2.466 (2.448) | 1.35 (1.52[20]) |
| GaSb | a = b = c = 6.154 (6.10) | 2.665 (2.640) | 0.79 (0.81[20]) |
| ZnGeN2 | a = b = 4.572, c = 8.776 | (Ge–N) 1.871, (Zn–N) 2.043 | 3.03 |
| ZnGeP2 | a = b = 5.473 (5.46), c = 10.749 (10.76) | (Ge–P) 2.334 (2.309), (Zn–P) 2.378 (2.398) | 2.02 (2.05[22]) |
| ZnGeAs2 | a = b = 5.711 (5.67), c = 11.226 (11.15) | (Ge–As) 2.446 (2.396), (Zn–As) 2.472 (2.488) | 1.07 (1.15[23]) |
| ZnGeSb2 | a = b = 6.156, c = 12.193 | (Ge–Sb) 2.664, (Zn–Sb) 2.650 | 0.48 |
To obtain the core level difference
m{C}}, {
m{C}}'}^{
m AX/BY}$
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Figure1.
(Color online) The crystal structure of superlattice GaX/ZnGeX2 (X = N, P, As, Sb). The Ga, Zn, Ge and X atoms are in light green, purple, gray and blue, respectively.
3.
Results and discussion
Using these procedures discussed, we calculated the band offsets of the GaX/ZnGeX2 heterojunction. The results are shown in Fig. 2.
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Figure2.
Band alignments of (a) GaN/ZnGeN2, (b) GaP/ZnGeP2, (c) GaAs/ZnGeAs2, (d) GaSb/ZnGeSb2 heterojunctions.
Fig. 2 shows that: (i) for all the heterojunctions, the VBM of ZnGeX2 is higher than that of GaX, and the VBO decreases as the atomic number of the anion increases; and (ii) for each heterojunction except GaN/ZnGeN2, the CBM of ZnGeX2 is lower than that of GaX. Thus, there is an anomalous trend in CBM for ZnGeN2 because its CBM is higher than that of GaN.
To understand the calculated results, we first analyze the atomic wavefunction characters of the VBM and CBM states. Take GaAs and ZnGeAs2 as an example. The valence electrons of Ga and As atoms are respectively 3d104s24p1 and 4s24p3. The couplings between different states are drawn schematically according to the chemical trends of atomic energy levels of the elements in Fig. 3. To further distinguish the localization of charge densities, we plot in Fig. 4 the electron charge densities of CBM and VBM in the (
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Figure3.
(Color online) Band edge atomic orbital wavefunctions cubic GaAs and ZnGeAs2.
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Figure4.
Contour plot of electron charge density of VBM and CBM states in (
As the Ga and As atoms approach each other, their valence orbits overlap and hybridize, leading to the formation of bounding and anti-bounding states. As shown in Figs. 3 and 4, CBM is an antibonding state with mostly cationic s character, while VBM is a bonding state with mostly anion p orbital which also couples with cation d orbitals[24]. For VBM of GaX and ZnGeX2, because the Zn 3d has higher orbital energy than Ga 3d (see Table 2), its coupling to the anion p orbital is stronger (see Fig. 4). The stronger p–d coupling[25, 26] in ZnGeX2 pushes upwards the VBM of ZnGeX2, making it higher than that of GaX. This explains why the VBM of ZnGeX2 is higher than that of GaX. Moreover, as the anion atomic number increases, the p–d repulsion decreases due to the increased bond length and p–d energy separation, so the VBO becomes smaller when anion atomic number increases. Meanwhile, the CBM of GaX is more localized on Ga site, whereas it is more on the Ge site in ZnGeX2 (see Fig. 4). Because Ge 4s orbital energy is much lower than the Ga 4s orbital energy, the CBM of ZnGeX2 is expected to be lower in energy than that of the CBM of GaX, as observed in our calculation for X = P, As, Sb. However, CBM is an antibonding state and, therefore, its energy position also depends on the coupling strength of the anion s and cation s orbitals, which increases as the bond length decreases. For more covalent ZnGeSb2, the bond lengths are large. Moreover, the covalent Ge–Sb bond is larger than that of the Zn–Sb bond, suggesting the s–s level repulsion between Ge 4s and Sb 5s orbitals is weak, so the potential effects dominant, thus the CBM of ZnGeSb2 is lower than that of GaSb. As the atomic number of X decreases, the bond length d decreases, thus the CBO decreases.
| Orbit | N | P | As | Sb | Zn | Ga | Ge |
| n s | ?18.49 | ?14.09 | ?14.77 | ?13.16 | ?6.31 | ?9.25 | ?12.03 |
| n p | ?7.32 | ?5.68 | ?5.42 | ?5.08 | ?1.31 | ?2.82 | ?4.13 |
| (n ? 1) d | ? | ? | ?40.60 | ?33.32 | ?10.49 | ?19.18 | ?29.57 |
Table2.
Atomic energy levels (eV) of valence states of elements studied in this paper.
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| Orbit | N | P | As | Sb | Zn | Ga | Ge |
| n s | ?18.49 | ?14.09 | ?14.77 | ?13.16 | ?6.31 | ?9.25 | ?12.03 |
| n p | ?7.32 | ?5.68 | ?5.42 | ?5.08 | ?1.31 | ?2.82 | ?4.13 |
| (n ? 1) d | ? | ? | ?40.60 | ?33.32 | ?10.49 | ?19.18 | ?29.57 |
It is interesting to see that the CBM of ZnGeN2 is higher than that of GaN (Fig. 2), which is in contrast to the common expectation. This anomalous trend can be understood as follows: N is much more electronegative than other group V anions so the coulomb interaction between the nominal Ge4+ and N3? ions is extremely strong. This leads to a much smaller ionic Ge4+–N3? bond length compared to that of Ga3+–N3? and even smaller than that of Zn2+–N3? (see Table 1). The very short Ge–N bond length enhances the coupling between the Ge 4s and N 2s states, pushing the anti-bonding CBM state up in energy, which explains why ZnGeN2 can have an anomalous higher CBM energy than GaN.
4.
Conclusion
In summary, the unusual chemical trends in band offsets of the heterojunctions GaX/ZnGeX2 (X = N, P, As, Sb) are calculated and explained by first-principles theory. The calculated results suggest that for common-anion systems, the VBM of ZnGeX2 is higher than that of GaX; and the VBO decreases when the anion atomic number increases. The CBM of ZnGeX2 is found to be lower than that of GaX for X = P, As, and Sb, and the CBO decreases when the anion atomic number decreases. However, the CBM of ZnGeN2, is higher than that of GaN. Using the orbital hybridization theory, we explained the chemical trend of the band alignments of the four heterojunctions and demonstrated that p–d coupling determines the position of the VBMs. The change of the CBO can be understood by noticing the increased electronegativity of Ge relative to Ga and the variation of anion–cation bond lengths. The anomalous behavior for the nitrides can be explained by the strong coulomb interaction between Ge and N ions, which shortens the ionic Ge–N bond length significantly, thus raised the antibonding CBM energy in ZnGeN2.
Acknowledgement
This work was financially supported by the Major State Basic Research Development Program of China under Grant No. 2016YFB0700700, the National Natural Science Foundation of China (NSFC) under Grants Nos. 11634003, 11474273, 61121491 and U153040, and the Science Challenge Project, under Grant No. TZ20160003. J. W. L. was also supported by the National Young 1000 Talents Plan. H. X. D. was also supported by the Youth Innovation Promotion Association of CAS (No. 2017154).
