2.3.1.3 Dielectrics

Non-conducting, insulating materials are called dielectrics and provide a band gap ${\mathcal{E}_{\mathrm{G}}}$ which is typically larger than 4 eV. Figure 2.10 shows a typical band edge diagram for a semiconducting material. Here, the energy levels ${\mathcal{E}_{\mathrm{C}}}$ , ${\mathcal{E}_{\mathrm{V}}}$ , and ${\mathcal{E}_{\mathrm{F}}}$ are the conduction band energy, the valance band energy, and the FERMI level, respectively. The FERMI level is defined as the energy for which the occupation probability is exactly $1/2$ . The activation of an electron from the valence band to the conduction band requires the energy of the band gap. This type of energy can be either of potential, kinetic, or thermodynamic nature.

Figure: 10: Idealized band diagram which shows a semiconducting material with the different energy levels resulting from the band structure. The FERMI level $\mathcal{E}_{\mathrm{F}}$ which determines the energy level where occupation probability is one half. If $\mathcal{E}_{\mathrm{F}}$ is closer to the conduction band than to the valence band, the material behaves more like a semiconducting material than an insulator.

Natural quantities to describe dielectrics are the conductivity $\sigma$ , the band gab ${\mathcal{E}_{\mathrm{G}}}$ , the relative dielectric constant ${{\varepsilon_{\mathrm{r}}}}$ , the break-down voltage, and the melting, respectively the boiling point for fluid dielectrics. For modern semiconductor devices, the conductivity and the break-down voltage have lost importance because the design can control the internal voltage distribution very well and the conductivity of the insulating material are considered together with their leakage behavior including tunneling effects in gate dielectrics.

For thicker dielectric layers, the capacitances are more important than the conductivities because the impact of cross talk between different interconnect lines is mainly determined by the capacitive coupling. This phenomenon can be investigated only if the final chip layout has been designed.

The relative dielectric constant ${\varepsilon_{\mathrm{r}}}$ is the most important quantity in microelectronics to characterize the insulation material since the capacitive coupling of two structures should be either ideally if the current flow has to be controlled, e.g. in a transistor or has to be avoided to reduced cross talk between interconnect structures. However, the constant has certain limits in both directions: If no matter is present the relative dielectric constant has its lower bound with ${{\varepsilon_{\mathrm{r}}}}{=}1$ . The upper bound is given by the crystal structure of the material. Some materials, such as Perovskites and PZTs [140], provide extremely high relative dielectric constants. As a drawback, these materials often show a quite low stability in terms of the repolarisation and temperature. However, in certain applications these materials can be applied as well.

$\mathrm{SiO_2}$ has been used in a wide range of applications because it is easy and cheap to produce and is rather stable in electrical and thermal terms, and very chemically resistant. Therefore, $\mathrm{SiO_2}$ is very often used for instance as insulation material in control gates in transistors where a rather high dielectric constants would be required. But due to the low costs and simpleness of the fabrication of $\mathrm{SiO_2}$ , this material is still used as gate dielectrics and as passivation and insulation layers in interconnect structures to encapsulate the interconnecting lines from each other. In the latter example, a very low dielectric constant is the optimum for the overall device performance.

There are many materials which provide better electrical behavior than $\mathrm{SiO_2}$ , but none of them can be as reliably produced within existing economical limits as $\mathrm{SiO_2}$ . Therefore, the ${\mathrm{Si}}$ technology is very commonly used and has generated a considerably big market for such fabrication machinery, which even further reduces its COO. If new material compounds have to be considered in terms of fabrication, additional materials have to be acquired, which are mostly very rare in high purity. Furthermore, the deposition and etching of such materials often requires new chemical environments and new machinery to handle these chemical reactions.

Despite of the huge costs, the enhanced electrical requirements given by the semiconductor road map demand the introduction of new materials which have either lower or higher relative dielectric constants ${\varepsilon_{\mathrm{r}}}$ to fulfill the industry's needs for future down scaling.

Sofar, enormous efforts have been made to supply the newly developed technology nodes with novel materials that require only minor changes to the standard ${\mathrm{Si}}$ process flow. Material types, which have succeeded in reducing COO are the low-$\kappa$ and high-$\kappa$ materials. The offer different ${\varepsilon_{\mathrm{r}}}$ values compared to $\mathrm{SiO_2}$ and are used to adjust the capacitive coupling through material selection.

The dielectrics can be grouped according to their chemical structure in oxides, nitrides, carbides, halogenides, polymers, and organic materials. In addition, there are plenty of mixtures and doped material which provide advantageous material properties for certain purposes.

The group of oxides include the well known compounds $\mathrm{SiO_2}$ , ${\mathrm{Al_2O_3}}$ , and germanium oxide which can be either $\mathrm{GeO}$ or $\mathrm{GeO_2}$ where germanium dioxide is thermally more stable. Other commonly used oxides for new semiconductor structures are ${\mathrm{BeO}}$ , ${\mathrm{ZrO_2}}$ , ${\mathrm{HfO_2}}$ , and ${\mathrm{Ta_2O_5}}$ which are mainly used as high-$\kappa$ materials within FEOL structures like gate stacks for transistors or capacitors for memory cells. Special types of oxides are the high-$\kappa$ compounds Perovskites and lead zirconium titanites (PZT). They provide high values of ${\varepsilon_{\mathrm{r}}}$ but have a very limited thermal budget because above the CURIE^2.37 temperature the spontaneous polarization vanishes according to a mechanical relaxation of the crystals.

The nitride group includes ${\mathrm{TiN}}$ , ${\mathrm{TaN}}$ , and ${\mathrm{Si_3N_4}}$ which excels with their hardness. Unfortunately, the member materials are quite brittle compared to most of the oxides. Important advantages of nitrides are that nitrides can be built on top of a metal layer and that according to the stability of the nitride compound, the nitride layer can be used to seal certain regions for instance to avoid the diffusion of a particular metal to its surrounding semiconducting or insulating materials.

Carbides are another group of dielectrics where ${\mathrm{SiC}}$ is the most important representative. Because its advantageous crystal structure, this material can be used as a substrate material like Si, Ge, or ${\mathrm{Al_2O_3}}$ . However, ${\mathrm{SiC}}$ is very brittle, extremely hard, and chemically very robust. Hence, it is also used for BEOL structures for instance as etch stop layers in interconnect stacks.

Beside the already mentioned materials types, there are plenty of polymers and organic compounds which include polyimide, poly-tetra-fluorine-ethylene (PTFE), organosicate glasses, and other polymers. Those materials are often used as low-$\kappa$ materials in BEOL structures as interlayer dielectrics (ILD) and some even as substitute for semiconducting materials.

For BEOL structures dielectric layers are often doped to improve particular properties such as to harden the material compound, decrease the relative permittivity, or to reduce the diffusion constant for a certain atom species [148]. Typical representatives for this type are ${\mathrm{SiON}}$ , ${\mathrm{SiOC}}$ , ${\mathrm{SiOF}}$ , ${\mathrm{SiCN}}$ . They appear in the interconnect structures of leading edge high performance devices.

A critical issue in alternative materials is their temperature stability both during fabrication and during operation. For instance the phase stage of the Perovskites and PZT crystal structures that provides the high ${\varepsilon_{\mathrm{r}}}$ value is only thermally stable below the CURIE temperature ${T_{\mathrm{c}}}$ . For these materials the CURIE temperature determines the temperature limit for operation and the thermal budget during device fabrication. Figure 2.11 shows the principal assembly of a unit cell of a certain PZT material. In the mechanically relaxed stage, the crystal shows a face centered cubic structure where the Ti atom is exactly located in the center of the cubic unit cell.

Figure 2.11: Temperature impact on the crystal structure of the high-$\kappa$ material PZT. Below the CURIE temperature ${T_{\mathrm{c}}}$ , the crystal structure of PZT offers not enough space for a cubic centered ${\mathrm{Ti}}$ or ${\mathrm{Zr}}$ atom (a). Hence, spontaneous polarization is observed. However, above ${T_{\mathrm{c}}}$ the thermal energy is sufficient to enable a stable energetic minimum in which the cubic centered atom is at its forseen position in the center of the atomic unit cell.

However, under certain conditions of pressure and temperature, the unit cell deforms in such a way that the Ti atom has too little space in the center of the unit cell and flips therefore either slightly to the upper or to the lower side. Hence, the space charge does no longer vanish but shows a spontaneous polarization. This stage provides a meta-stable energetic minimum of the crystal structure.

This is demonstrated in Figure 2.11 where an applied electric field in the vertical direction enables the Ti atom to slip from the upper side to the lower side of the center of the unit cell. This effect of flipping the Ti atom provides the high ${\varepsilon_{\mathrm{r}}}$ value. However, with every flip of the Ti atom, energy is absorbed by the crystal and causes hysteresis loss and with increasing number of flips the ${\varepsilon_{\mathrm{r}}}$ number will be slightly reduced due to mechanical relaxations. Nevertheless, the number of possible flips is enormous according to the current reliability concerns according to the ITRS. But if the temperature is increased above a certain threshold value (CURIE temperature), the thermal energy is sufficient for the advantageous crystal structure to mechanically relax. As a consequence, the high ${\varepsilon_{\mathrm{r}}}$ vanishes and drops back to approximately 1 in the global energetic minimum of this crystal structure.

Low-$\kappa$ materials can be used to reduce capacitive coupling like cross talk or influence charges in adjacent interconnect lines. Materials with ${\varepsilon_{\mathrm{r}}}$ values lower than 2.5 are called extreme low-$\kappa$ (ELK) materials. Typical ELK materials reach values around 2.4 by using doped $\mathrm{SiO_2}$ . Examples are ${\mathrm{SiOC}}$  [149,150,148,151], ${\mathrm{SiON}}$ , or ${\mathrm{SiOF}}$  [152,153]. Alternatively, values in the regime between 1.6 and 1.9 have been reported using air gaps [154,155,156]. Polymers like aromatic polymers [21] reach values of ${{\varepsilon_{\mathrm{r}}}}{=} 2.7$ . A typical range for organic silicate glasses OSG is ${{\varepsilon_{\mathrm{r}}}}{=} 2.3-3.1$  [21], whereby the low values for the latter materials can be obtained if a porous low methyl variant of OSG is used [21].

As additional layers for etch stop and passivation purposes, the materials ${\mathrm{Si_3N_4}}$ and ${\mathrm{SiCN}}$ can be used where carbon doped nitride offers a lower ${\varepsilon_{\mathrm{r}}}$ than the commonly used ${\mathrm{Si_3N_4}}$  [151]. To account for the high mechanical stress in these material stacks used in BEOL structures, additional layers of ${\mathrm{Al_2O_3}}$ can significantly reduce the mechanical stress but have higher ${\varepsilon_{\mathrm{r}}}$ values than $\mathrm{SiO_2}$  [157,158].