Optical Properties of Wurtzite GaN and ZnO Quantum Dots
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Optical Properties of Wurtzite GaN and ZnO Quantum Dots Vladimir A. Fonoberov and Alexander A. Balandin Nano-Device Laboratory, Department of Electrical Engineering, University of California-Riverside, Riverside, California 92521, U.S.A. ABSTRACT We have investigated exciton states in wurtzite GaN/AlN and ZnO quantum dots. A strong piezoelectric field in GaN/AlN quantum dots is found to tilt conduction and valence bands, thus pushing the electron to the top and the hole to the bottom of the GaN/AlN quantum dot. As a result, the exciton ground state energy in GaN/AlN quantum dots with heights larger than 3 nm exhibits a red shift with respect to bulk GaN energy gap. It is shown that the radiative decay time in GaN/AlN quantum dots is large and increases from 0.3 ns for quantum dots with height 1.5 nm to 1.1×103 ns for the quantum dots with height 4.5 nm. On the contrary, the electron and the hole are not separated in ZnO quantum dots. Moreover, a relatively thick “dead layer” is formed near the surface of ZnO quantum dots. As a result, the radiative decay time in ZnO quantum dots is small and decreases from 73 ps for quantum dots with diameter 1.5 nm to 29 ps for the quantum dots with diameter 6 nm. INTRODUCTION Wurtzite GaN/AlN and ZnO quantum dots (QDs) have recently attracted attention as promising nanostructured materials for optoelectronic applications. Optical properties of QDs strongly depend on the QD size. Although the band gap energy for GaN and ZnO is nearly the same (about 3.5 eV), the optical properties of GaN/AlN and ZnO QDs are different. The main difference in the optical properties of these QDs comes from the presence of strong strain and piezoelectric fields in GaN/AlN QDs and absence of those fields in ZnO QDs (see Refs. [1-3]). In this paper we carry out a rigorous calculation of exciton states in both types of QDs. The results of our calculations are compared with available experimental data and the difference in the optical spectra of GaN/AlN and ZnO QDs is discussed. THEORY In order to calculate exciton states in wurtzite GaN/AlN QDs we use the theoretical model from Refs. [1-3]. The model allows us to takes into account the strain and piezoelectric fields present in the GaN/AlN QDs. It also explicitly includes degeneracy and anisotropy of conduction and valence bands. Since the radius of the region of electron and hole localizations in the considered GaN/AlN QDs is less than the exciton Bohr radius of bulk GaN (~ 2 nm), we first calculate separate electron and hole states in those QDs and then consider the electron-hole Coulomb interaction as a perturbation. The electrostatic piezoelectric potential V p (r ) , generated by the sum P (r ) of the spontaneous and the strain-induced polarizations, is found by solving the Maxwell equation: ∇ ⋅ ( εˆstat (r )∇V p (r ) − 4π P(r ) ) = 0 ,
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where εˆstat (r ) is the dielectric tensor. Electron states are found as the eigenstates of the one-band envelope-function equation with the following Hamiltonian Hˆ e = Hˆ S (re ) + H e(ε ) (re ) +
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