Theoretical Study on Leakage Current in MOS with High-K Dielectric Stack: Effects of In-plane-Longitudinal Kinetic Energy Coupling and Anisotropic Masses

Abstract

A model of leakage current in Al/HfO 2 /SiO 2 /Si MOS (metal-oxide-semiconductor) capacitors is given by adopting the tunnel current model in SiGe-based heterojunction bipolar transistors. The velocity of an electron in the metal gate, which originates from the coupling between longitudinal and transverse (in-plane) kinetic energies, and the anisotropic mass of the substrate were included in the leakage current model. It was found that the leakage current obtained by including the gate electron velocity is lower than that calculated without the coupling effect and the leakage current decreases with an increasing gate electron velocity. However, the leakage current is not significantly influenced by the silicon substrate orientation. If a measured leakage current in the high-K dielectric stack MOS with Si(100) substrate were much higher than that in the MOS with Si(111) as observed in the conventional MOS, then the gate electron phase velocity in the latter would be higher. A small increase of the equivalent oxide thickness (EOT) of HfO 2 will decrease the tunnel current appreciably and tunnel current oscillations become visible as the EOT becomes thicker. Oscillatory behavior of the tunnel current is due to resonance states in the quantum well formed in high-K dielectric stack at high electric fields.

Numerical Simulation of Tunneling Current in an Anisotropic Metal-Oxide-Semiconductor Capacitor

“…This is because the gate electron velocity causes an effective potential barrier V eff (z) higher than the barrier V(z) as already explained in Refs. [3,[28][29].…”

“…It means that the usage of HfSiO x N as the gate oxide can reduce the tunneling current as explained in Refs. [3] and [18]. Figure 6 depicts the electron transmittance as a function of the incident angle of electron (in degree) with respect to the barrier over the range from -80° to 80° in 2. longitudinal-transverse kinetic energy.…”

“…[3] in computing tunneling currents in TiN/HfSiO x N/SiO2/p-Si MOS capacitors. The description of an electron in an anisotropic material under the parabolicband effective mass approximation is used as a first step in the model which is described as [21].…”

“…In order to fulfill these aims, it is required a thinner SiO 2 gate oxide. However, a vast tunneling current arises and power dissipation becomes significantly high when the gate oxide thickness is less than 1.5 nm [3]. In order to solve these problems, it is needed a high-κ dielectric with equivalent electrical oxide thickness but higher physical thicknesses to replace SiO 2 [4][5][6][7].…”

“…Since having good dielectric properties and good thermal stability on silicon substrates, Hf-based silicates are the promising candidate to replace SiO 2 compared to other high-κ materials [8][9][10]. The gate oxides anticipated to substitute SiO 2 are a stack of an ultrathin SiO 2 and a high-κ layer, which is known as a high-κ gate stack, because an ultrathin SiO 2 often grows during fabrication process [3]. …”