High-k materials

From the cellular phone to the personal digital assistant, miniaturization is omnipresent in our everyday life.

In electronics, this trend is translated into Moore's law, which is often state as the doubling of transistor performance and quadrupling of the number of devices every three years.

This phenomenal progress has been achieved through the scaling of the metal-oxide-semiconductor field-effect transistor (MOSFET) to smaller and smaller physical dimensions.

The narrowest feature on present-day integrated circuits is the gate oxide, the thin dielectric layer that forms the basis of field-effect device structures. The roadmap of the Semiconductor Industry Association, which provides the targets for further improvements of MOS devices, indicates that the thickness of SiO₂ (the present gate dielectric) should be smaller than 10 Å, which represents a layer of about five Si atoms across. The use of such a thin SiO₂ layer is precluded by severe leakage problems. Current research is therefore focusing on the replacement of SiO₂ by high-k materials. The increase of the dielectric constant (k) compared to SiO₂ permits to use a gate with a larger physical thickness (t_phys) while achieving the same capacitance as devices with a smaller equivalent thickness (t_eq) of SiO₂:

t_eq=k_ox/k t_phys

where k_ox is the dielectric constant of SiO₂. The larger physical thickness solves the potential leakage problems as well as other issues related to the penetration of the gate dopants in the substrate when very thin films are used.

However, replacing the SiO₂ with a material having a different dielectric constant is not as simple as it may seem. The material bulk and interface properties must be comparable to those of silicone dioxide, which are remarkably good. For instance, thermodynamic stability with respect to silicon, stability under thermal conditions relevant to microelectronic fabrication, low diffusion coefficients, and thermal expansion match are quite critical. With these objectives in mind, recent research on high-k dielectrics has primarily focused on metal oxides and their silicates. Among these, the group IVb transition metals Zr and Hf have generated a substantial amount of investigations.

In the framework of the quest for high-k materials to replace conventional SiO₂ as the gate dielectric in MOS devices, first-principles calculations constitute a valuable tool to understand the behavior of novel materials at the atomic scale without requiring empirical data. This is particularly interesting for the early stages of research when relatively little experimental data are available. In terms of its predictive accuracy, density-functional theory (DFT) has proved to be very appropriate to study the ground-state properties of the electronic system, such as the structural, vibrational, and dielectric properties on which this topical review will focus.

However, DFT has one important drawback associated to the high computational cost of the calculations that are required, which limits both the length and time scales of the phenomena which can be modeled. Nowadays, it is possible to treat systems containing up to hundreds of atoms within the most widespread DFT approach based on plane-wave basis sets and pseudopotentials. For the high-k materials, it is important to note that transition-metal and first-row elements (e.g. oxygen) generally present an additional difficulty when treated with plane-wave basis sets. Namely, their valence wave functions are generally strongly localized around the nucleus and may require a large number of basis functions to be described accurately, thus further limiting the size of the system that can be investigated. Identifying an oxide with a large dielectric constant which is thermodynamically stable in contact with silicon is only one part of the problem. To be a good insulating layer, the conduction band offset of the oxide with respect to silicon has to be greater than 1 eV. In order to study the electronic properties, it is necessary to go beyond the framework of DFT whose predictions show some systematic deviations with respect to experiments (band-gap underestimated, band dispersion poorly described). The electronic excitations or quasiparticles, as measured in photoemission and tunneling experiments correspond to the creation or annihilation of an electron and can be obtained using the GW approximation.