Abstract
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[
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[
where,
where
The electronic band structure calculations are performed at the experimental lattice constants based on the density functional theory (DFT)[
To obtain the core level difference
Figure 1.(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.
Figure 2.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 (
Figure 3.(Color online) Band edge atomic orbital wavefunctions cubic GaAs and ZnGeAs2.
Figure 4.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[
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).
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