High-k Dielectric Materials: Structural Properties and Selection
The role of high-к materials in the field of electronics is well known. Over the last decade or so, there has been an increase in the need for flexible electronics, thus necessitating a paradigm shift in the nature of liigh-k materials. Ceramics are being supplemented with polymers, other soft matter and composites. In this chapter, we discuss the theory of liigh-k materials and the properties of various classes of materials.
In our semiconductor-driven technological society, miniaturization of circuits is a veiy important factor so as to fit in more and more components in a limited surface area. In order to achieve this miniaturization of electrical components, dielectric properties of the constituent devices such as capacitors, memories, sensors, resonators etc. (Tamala, 1999; Lau, 1994; Bai et al., 2000; Facchetti et al., 2005) play an important role. The current industry standard materials don’t meet the criteria for miniaturization, for reasons discussed below. In addition, there is a need for wearable electronics, calling for elasticity of materials used. Thus, there is a need for novel soft matter that can replace current ceramic dielectric materials that are rigid.
High-/: dielectrics are materials in which no steady current can flow through (Landau et al., 2013) as a result of which the static electric field in not zero as is the case in conductors. Dielectrics can be summarized as insulators that can be polarized by the application of electric field. The relationship between relative permittivity er (generally k) and electric polarizability, P, is expressed by Clausius-Mossotti relation (eq 3.1):
where JVj is the concentration and cq is the polarizability of the atom j, which is the sum of electronic, vibrational, and orientation polarization (Kittel, 2005). Ionic and inter-facial polarization are not accounted by Clausius-Mossotti relation, so in a sense it is important to understand polarization so as to understand dielectric constant since polarization is more universal in nature (Zhu, 2014).
Silicon dioxide has been used as a standard material in MOSFET (metal-oxide-semiconductor field-effect transistor) devices, which is a key component of microelectronic circuits. As the size of these MOSFET devices are further reduced, to push more and more devices into a limited area, two problems are seen (1) leakage currents and (2) reliability issues. This leakage current in MOSFETs is due to tunneling effect, where charge carriers flow through the gate barrier. Tunneling probability is inversely proportional to the thickness of the silicon dioxide gate, and hence this puts a limit on the size up to which the silicon dioxide layer can be reduced in thickness. The leakage current issue due to tunneling limits the thickness of Si02 layer in MOSFETs to around at 2-3 nm (Frank et al., 2001).
Another issue with Si02 is the reduced reliability as the thickness is reduced. When charge earners flow through the gate they develop defects and when these defects reach a high enough value, the junction breaks down and the device fails. This issue of reliability is particularly pronounced when the thickness of the Si02 layer is reduced to nanometer ranges. Along with above-mentioned problems, there are few other issues pertaining to Si02 such as when Si02 is used a dielectric medium in between two conducting plates of a capacitor, and the relationship between capacitance C and the thickness of Si02 is given by eq 3.2:
where t0K is the thickness of the gate oxide layer, and A is the area of the capacitor. Thus, the capacitance can be increased for the same voltage by decreasing the thickness of Si02. However, in Si02 the thickness has reached the threshold value and any further reduction in thickness leads to quantum tunneling effects and increase in leakage current. Hence it’s not possible to reduce the thickness of the gate oxide layer.
To tackle the above-mentioned issues, a material that has a higher к value has to be used (Houssa, 2003). Initially, efforts were made to make Si02 work by improving the к value by doping it with impurities like nitrides. These nitrides form oxynitrides and oxide-nitride stacks. Oxynitrides have better resistance toward a leakage current due to increased к value, and this increase is due to change in ionic polarizablity since oxygen is replaced by nitrides. Stacking causes the thin film to get thicker and hence reduces the penetration due to tunneling effect and provides better reliability. Generally, dielectric materials are divided into higli-A- and low-A- materials in reference to the к value of Si02, which has a dielectric constant of 3.9. High-А- materials are made of either ceramics or soft matter such as polymers.