Chapter 6 Calculations of electronic structure and density of states in the wurtzite
6.4 Density of states
We calculated the total DOS of ZMO alloys by summation over all bands using a Gaussian function with a broadening parameter of 0.01 eV, e.g., due to temperature
broadening around 77K. Shown in Fig. 6-4, we obtained the similar DOS for the concentration ranging from 0 to 10%, while the DOS of upper valence bands were
slightly broadened and decreased as increasing Mg incorporation (dash line). Imai et al.
[24] used the first-principle pseudopotential method to show that the bond of Zn-O is
more ionic than Zn-S due to the probability of electron lingering between Zn and O is much smaller than between Zn and S. Similar to those obtained by Li et al. [25] using
the first-principle calculation, the increasing probability of electron lingering between cation and anion with increasing Mg composition suggest that in the ZMO alloys the
electrons from O2p orbital are less localized around the oxygen atom to cause reduction of electronegative characteristic of oxygen and ionization energy of acceptors.
Fig. 6-4 Total density of states of various Mg concentrations in the wurtzite Zn
1-xMg
xO alloys: (a) 0%, (b)
10%, (c) 20%, and (d) 30%. The dash line presented discrepancy between ZnO and Zn
1-xMg
xO alloys
structure.
Shown in Figs. 6-4(c) and 6-4(d), we found both the DOS of the upper valence band near - 2.7 eV and the uppermost conduction bands near 19 eV increase as Mg
composition increases. Because the weighting of Mg’s atomic orbital increases with increasing Mg concentration in the VCA method, we believe that the Mg3s orbital mainly
contributes extra density of modes to the upper valence band and the Mg3p orbitals principally contribute extra density of modes to the uppermost conduction bands. We
also shown the anion-atom p-orbitals wave function for top valence band and cation-atom s-orbitals wave function for lowest conduction band at Γ point in Table
6-1 and Table 6-2, respectively. Additionally, the DOS of the near lowest conduction band increases with more localized wavefunction as increasing Mg incorporation.
Consequently, the more overlap of wavefunctions of the neighboring cation atoms results in narrowing the width of conduction band so that the larger effective mass. The
wavefunction overlapping determines the rate of quantum tunneling of an electron from one ion to another so that the electrons hop slower from one ion to an adjacent one in the
lattice with increasing Mg concentration that shows the larger effective electron mass.
Table 6-1 Anion-atom p-orbitals wave function for top valence band at Γ point
Table 6-2 Cation-atom s-orbitals wave function for lowest conduction band at Γ point
6.5 Summary
In conclusion, using sp3 semi-empirical tight-binding model under virtual-crystal approximation, we have calculated the electronic band structure and the total density of states for the wurtzite structure of Zn1-xMgxO alloys semiconductor. We observed
enlarging band gap and increasing electron effective mass that agree with the
experimental results as increasing Mg composition up to x = 0.3. From the calculated total density of states, due to extra density of modes coming from Mg3s and Mg3p
orbitals as introducing more Mg composition, the increasing electron effective mass is a result of more orbital overlap of cation sites. In addition, the O2p is less localized
around the oxygen atom to cause reducing electronegative characteristic of oxygen.
Mg incorporation (%) s-orbitals wave function weight
0 10 20 30
0.68285 0.68296 0.68304 0.68312
Mg incorporation (%)p-orbitals wave function weight
0 10 20 30
0.61208 0.6108 0.60964 0.60844
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Chapter 7 Electronic band structures and surface states of ZnO finite well structures
Zinc oxide (ZnO) is a promising material due to its large direct band gap (3.4 eV at 5K) and large exciton binding energy of 60 meV [1], all of which are advantageous for
short-wavelength light-emitting diode [2,3] and low-threshold laser [4, 5] applications at room temperature. It is known that the optical properties and the performance of
photonic devices are mainly determined by their electronic density of states (DOS), which can be modified by the quantum confinement effects. ZnO nanostructures have
superior optical properties over its bulk crystal, for instance, the low-dimensional ZnO nanostructures, such as QDs [6-8], nanoparticles [9, 10], nanobelts [11], nanowires [12,
13], and quantum wells [14, 15], have been widely investigated. In particular, the
quantum confinement [16-19] causes the band gap and the effective masses of electron
and hole having strong dependence on the size. Another difference was found that the intensity of the below-band-gap emission relative to that of the band edge emission
increases as reducing the crystalline size. Recently, Shaish et al. [20] showed that intensity ratio of below-band-gap (surface state) and band-edge luminescence in ZnO
nanowires depend on the wire radius. The weight of this surface luminescence increases as the wire radius decreases at the expense of the band-edge emission. Pan et al. [21]
also predicated a significant increase in the intensity ratio of the deep level to the near band edge emission with ever-increasing nanorod surface-aspect ratio. Thus, in
quantum-size nanostructures, the surface-recombination may entirely quench band-to-band recombination, presenting an efficient sink for charge carriers that unless
deactivated may be detrimental for electronic devices. Nevertheless, it is still lack of theoretical study on the influences of the crystalline size on electronic structure and
surface states in ZnO.
In comparison of simulation methods for nanostructures, the application of the ab
initio calculation, a self-consistent method such as using local density approximation
(LDA), to study electronic band structures of nanostructures or disordered alloys
generally requires using very large supercells in order to mimic the distribution of local chemical environments. It is very computationally demanded. On the other hand, the
tight-binding (TB) theory is a versatile and simple method to calculate the electronic properties of solids. Additionally, due to the transferability of the TB parameters, the
method has been readily applied to systems with broken translational invariance such as low-dimensional structures [29, 30], clusters [31, 32] and alloys [24, 33]. Accordingly,
in this chapter, we used TB method to investigate the electronic stricture and surface states of ZnO finite well structures considering non-relaxed and non-reconstructed
surfaces along <0001> and <1-100> growth directions.