# Atomic Layer Deposition (ALD) of Metal Gates for CMOS
## 1 Introduction
### High-\(\kappa\) Dielectric and Effective Oxide Thickness (Eot)  
The solution to the issues above is to use an alternative dielectric which has a dielectric constant, or \(\kappa\)-value, higher than SiO\({}_{2}\) and allows physical thickness larger than SiO\({}_{2}\) without tradeoff in gate capacitance. For a simplified model, the capacitance between the gate and the channel can be expressed as  
\[C=\frac{\varepsilon_{0}\kappa S}{t} \tag{2}\]  
where \(\kappa\) is the dielectric constant, \(\varepsilon_{0}\) the permittivity of free space (= 8.85 \(\times\) 10\({}^{-3}\) fF/fm), \(S\) the area, and \(t\) the thickness of the dielectric. For SiO\({}_{2}\), \(\kappa\) is around 3.9. If a high \(\kappa\) material is used as gate dielectric, a thicker layer could give the same capacitance density, or for a high-\(\kappa\) layer of a given thickness (\(t_{\text{high-}k}\)), the capacitance density generated equals to that of a SiO\({}_{2}\) layer of \(t_{ox}\), This \(t_{ox}\) is called equivalent oxide thickness (\(EOT\))  
\[EOT=\frac{3.9}{\kappa}t \tag{3}\]  
For example, to retain an \(EOT\) of 1 nm for a dielectric with a \(\kappa\)-value \(\sim\)20, the physical thickness of the high-\(\kappa\) could be \(\sim\)5 nm. The increase of the physical thickness could help to suppress the gate leakage. First industrial application of alternative dielectric concept was to alloy nitrogen into SiO\({}_{2}\) to form so-called silicon oxynitrides, whose \(\kappa\) value is slightly higher than SiO\({}_{2}\) and thus allows larger physical thickness than SiO\({}_{2}\). The \(\kappa\)-value of pure Si\({}_{3}\)N\({}_{4}\) is around 7, compared to that of SiO\({}_{2}\) about 4. That of SiO\({}_{x}\)N\({}_{y}\) is between 4 and 7, depending on the nitrogen concentration in the films. Encouraging results in leakage current reduction, boron diffusion control, and reliability enhancement were demonstrated by using SiO\({}_{x}\)N\({}_{y}\) to replace SiO\({}_{2}\) of the same \(EOT\)[7; 8; 9]. The leakage suppression of SiO\({}_{x}\)N\({}_{y}\) depends on the layer composition. A work done by [PERSON] and [PERSON] [10], for instance, demonstrated a 100\(\times\) leakage current reduction using a layer with a SiO\({}_{2}\): Si\({}_{x}\)N\({}_{y}\) ratio of 1:1 and \(EOT\) of 1.7 nm. The advantages of SiO\({}_{x}\)N\({}_{y}\) lie in that it guaranties the safety in contamination control, because nitrogen is a widely used element in IC production and the compatibility to conventional poly-Si. It has been found that the addition of N to SiO\({}_{2}\) can form Si-O-N network bonding and greatly block the boron diffusion through the dielectric [11; 12]. The reason for using SiO\({}_{x}\)N\({}_{y}\) instead of pure Si\({}_{3}\)N\({}_{4}\) is that the former shows much better channel mobility [13]. The mobility degradation attributes to the pentavalent N at interface, which induces defects and aggravate the interface scattering. For SiO\({}_{x}\)N\({}_{y}\) layers, especially those with graded N concentration, the interface defects density could be much less than the pure SiN\({}_{x}\). The SiO\({}_{x}\)N\({}_{y}\) dielectric was used for a few technology nodes. By increasing the N concentration node by node, the scaling strategy was successfully extended from 130 nm node to 65 nm node. The SiO\({}_{x}\)N\({}_{y}\) solution can only temporarily alleviate the gate leakage crisis. When \(EOT\) is below 1.3 nm, it does not work anymore and a new alternative has to be found from \"real\" high-\(\kappa\) candidates [14]. A high-\(\kappa\)dielectric must have a high \(\kappa\)-value, large enough band offsets with Si, and be thermally stable when contacted with the gate electrode and Si, and its impact to channel mobility must be acceptably small [15; 16; 17]. Figure 5 lists the dielectric properties of most important gate dielectric candidates. Among all of them, SiO\({}_{2}\) has the lowest dielectric constant and the largest conduction and valence band offsets. For the others, the band offsets decrease when the k-value increases.