Eur. Phys. J. Appl. Phys. 40, 59–63 (2007) DOI: 10.1051/epjap:2007129
THE EUROPEAN PHYSICAL JOURNAL APPLIED PHYSICS
The conduction band alignment of HfO2 caused by oxygen vacancies and its effects on the gate leakage current in MOS structures L.F. Mao1,a , Z.O. Wang1 , J.Y. Wang2 , and C.Y. Zhu1 1 2
School of Electronics & Information Engineering, Soochow University, 178 Gan-jiang East Road, Suzhou 215021, P.R. China Institute of Microelectronics Peking University, Beijing 100871, P.R. China Received: 2 May 2007 / Accepted: 9 July 2007 c EDP Sciences Published online: 31 August 2007 – Abstract. Based on the first-principles simulations, the oxygen vacancies in the ultrathin HfO2 layer as the gate dielectric in a metal-oxide-semiconductor structure is found to result in the conduction band offset alignment around the vacancy. Thus an increase in the gate leakage current tunneling current comes when the oxygen vacancies appear in the HfO2 layer wherever the oxygen vacancies locate. The relative increase in the tunneling current caused by the oxygen vacancies slightly change with the increasing oxide thickness for a low oxide electric field. PACS. 73.40.Gk Tunneling – 73.40.Qv Metal-insulator-semiconductor structures – 74.50.+r Tunneling phenomena; point contacts, weak links, Josephson effects
1 Introduction It is well-known that as scaling trends shrinking the thickness of the gate dielectrics in transistors, the most commonly used gate dielectric, silica, will likely fail to meet industry requirement of an insulating barrier due to the defect-assisted leakage current and the quantummechanical tunneling current. In recent years, a major thrust of the development in the semiconductor industry is searching for the new materials that could replace SiO2 as the gate dielectric in complementary metal-oxidesemiconductor (CMOS) technology. HfO2 is a hard material with a relatively high dielectric constant and wide bandgap. HfO2 -related research is increasing rapidly because it can be used as the gate dielectric in microelectronic devices for substituting silicon dioxide (e.g. [1–14] and references therein). Therefore a model that can describe the behaviour of the oxygen vacancies in HfO2 and characterize its effects on the gate leakage current is necessary. HfO2 shows a rich variety of the crystal structures depending on the pressure, temperature, impurity content, growth condition, and epitaxial strain. Tetragonal phase of HfO2 is shown to exist in thin films of HfO2 deposited on silicon [1,2]. Moreover, the (001) surface of t-HfO2 at the silicon interface forms a lattice with a mismatch of 5% and with the minimum number of the dangling bonds. Hence we chose tetragonal HfO2 for this study. However it a
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is almost impossible to effectively grow HfO2 on Si without formation of interfacial SiO2 or silicate-like layer. But in this paper, we focus on the oxygen behaviour of the oxygen vacancies in HfO2 layer. Thus, for simplicity, such an interfacial layer is not considered in this paper. In this work, first principles simulations are used to study how the oxygen vacancies in the t-HfO2 layer affects the planar macroscopic potential at the position of the vacancies, how it affects the conduction band near the vacancy based on the analysis of the planar macroscopic potentials, and how the tunneling current through the t-HfO2 layer changes when the oxygen vacancies appears in the t-HfO2 layer.
2 Method The Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimizer has the ability to perform cell optimization, including optimization at fixed external stress [15]. Thus the structural and electronic parameters of structures of hafnia without and with the oxygen vacancies in this work were relaxed by using the BFGS update scheme. The plane wave pseudopotential method within the density functional theory under the PBE (Perdew-Burke-Ernzerhof) generalized gradient approximation was used to calculate the total energy and electron structure, and the detailed description can be found in reference [17]. Pseudo-wave-functions were expanded in plane waves up to a kinetic energy cutoff of 260 eV, and the Brillouin
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The European Physical Journal Applied Physics
zone was sampled by a Monkhorst-Pack mesh of k points with a k-point spacing of 0.04 ˚ A−1 . A convergence criterion of 0.00005 eV was used for the electronic energy in the geometry optimization of HfO2 . The relaxed structure of the HfO2 supercell were performed by using the BFGS update scheme until the maximum force on the atoms was less than 0.1 eV/˚ A, the maximum displacement was less than 0.0005 ˚ A, and the maximum stress was less than 0.5 GPa. In order to determine the valence band alignment around the oxygen vacancy in the t-HfO2 layer, the local potentials have been calculated in the first-principles simulations of HfO2 . Thus a microscopic planar potential along the z-direction V tot (z) is obtained. Thus the macroscopic average potential V tot (z)can be obtained as [16]: V tot (z) =
1 L
z+L/2
z−L/2
V tot (z ) dz
(1)
where L is the length of a single period in the tetragonal HfO2 . The macroscopic average potentials away from the interface correspond to the macroscopically averaged bulk potential. Thus the potential shift ∆V tot can be used to determine the valence band offset (for example [18,19] and its references): δEv = ∆V tot + δEV BM
(2)
where ∆EV BM is the difference in the energies of the valence band maxima of the two bulk materials measured with respect to their respective bulk potentials. In this work, the tunneling current is calculated by using the following equation [20]: ∞ ∞ qm∗ J= D (E ) [f (E) − f (E)]dE dEx x r l 2π 2 3 0 Ex (3) where D(Ex ) is the transmission probability when the longitudinal electron energy is Ex . fr and fl are the distribution functions in the right and the left contact, m∗ is the effective electron mass. The Fermi-Dirac distribution was used in the tunneling current calculations, and the maximum of the longitudinal electron energy was set at 20kB T (15kB T was used in the tunneling current calculations in reference [21], kB is the Boltzmann constant, and T is the temperature). The temperature used in the tunneling current calculation in this work is 300 K. The entire oxide can be assumed to be composed of many supercells, (some with oxygen vacancies and the others without oxygen vacancies). And thus the tunneling current through the t-HfO2 layer with dilute vacancies can be calculated according to the following expression: J = Jv Sv + J0 S0
(4)
where Sv is the area of the t-HfO2 layer which corresponds the part being composed of supercells with the oxygen vacancy, Jv is the tunneling current through such a t-HfO2 layer of a unit area, S0 is the area which corresponds this
Fig. 1. The planar averages of microscopic and macroscopic potential along the z-direction, which is perpendicular to the perfect oxide/the defect oxide interface; (b) the planar average macroscopic potential and its Gaussian fitting.
part being the perfect oxide, J0 is the tunneling current through the perfect oxide of a unit area. By using equation (4), the effects of the arbitrary vacancy concentration (
