Defect Energy Levels in HfO 2 , ZrO 2 , La 2 O 3 and SrTiO 3
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Defect Energy Levels in HfO2, ZrO2, La2O3 and SrTiO3 K Xiong, P W Peacock, J Robertson Engineering Dept, Cambridge University, Cambridge CB2 1PZ, UK Abstract Defect energy levels of oxygen vacancies in various high K oxides HfO2, ZrO2, La2O3 and SrTiO3 have been calculated using methods which give the correct band gap, such as the screened exchange and weighted density approximation. Introduction Wide band gap oxides with a high dielectric constant (K) are required to replace silicon dioxide as the gate dielectric in future complementary metal oxide semiconductor (CMOS) integrated circuits, in order to maintain a sufficiently low leakage current [1]. The oxides must satisfy certain criteria such as thermal stability and band offsets [2]. The choice at present has narrowed to HfO2 and its silicate alloys. Unfortunately, the properties of these oxides are much poorer than SiO2 in other ways, such as having a higher defect density and an interface with Si which seems to possess more defects. Furthermore, transistors made with high K gate oxides have threshold voltage shifts and reduced mobilities [3-6] some of which could be attributed to the presence of trapped charge at these defects. Consequently, it is important to be able to identify the nature of these defects and to be able to optimise the processing conditions in order to minimise their concentrations. Electron spin resonance (ESR) has been used to try to identify the defects in HfO2 layers on Si. The majority of studies have found centres like Pb centres associated with the Si-oxide interface. Kang et al [7] have identified centres in bulk oxide by using a corona charging method which presumably converts defects from their diamagnetic to paramagnetic state. They observed three defects, the oxygen vacancy, the Hf3+ centre and the superoxy radical or oxygen interstitial. These three centres are similar to those previously found in bulk ZrO2 by ESR by Matta et al [8]. Foster et al [9,10] have previously calculated the formation energies of the oxygen vacancy and oxygen interstitial in ZrO2 and HfO2. They also calculated the electrical levels, but corrected for errors. Results Here, we calculate the energy levels of defects using the plane wave pseudopotential method using the CASTEP code [11]. This method uses the local density approximation (LDA) to calculate the exchange-correlation energy in the electronic Hamiltonian. The LDA gives a good representation for the total energy and the occupied states. However, it is well known to severely under-estimate the band gap of semiconductors. This is because of discontinuity in the exchange-correlation potential across the gap. The generalised gradient approximation (GGA) gives no improvement on the bands gap problem. The LDA gap problem is often approximately fixed by rigidly shifting the conduction bands upwards to give the experimental band gap. However, this method is
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unsuitable for the situation where there are defect levels in the gap, because it is not known if the defect levels are associated w
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