The concept of tunneling

When changing the gate dielectric material from SiO2 with a dielectric constant εSiO2 to an oxide with higher dielectric constant, k, one can allow for a k/εSiO2 times thicker dielectric and keep the same capacitance as measured from the gate metal. At first glance, a thicker insulator would also be expected to give a lower leakage current. As already touched upon in Section 3.2, additional properties are necessary to fulfill such aspirations. The transmission (tunneling) probability is also strongly dependent on the effective mass of the carrier passing through the oxide and, for a given oxide thickness, on the heights, ΔE, of the energy barriers separating the transistor channel from the gate metal. In choosing a gate oxide with a high dielectric constant as an alternative for SiO2, the first step would be to find a material with high ΔEC and k-values to decrease tunneling. As we will find in this chapter, however, additional properties like image force lowering, traps and the process properties discussed in Chapter 11 also influence the options. Since the quest is to achieve the smallest possible leakage current for a given capacitance, the concept of equivalent oxide thickness (EOT; dEOT) is practical for comparing the leakage currents across different oxides as was demonstrated in Fig. 11.3. Figure 13.1 shows the result of a calculation using the theory to be presented below, where “leakage” is taken as the transmission probability, P, for oxides with different k-values, electron effective masses and barrier heights. Normally, high-k oxides have at least about 50% lower effective masses than SiO2 (Hinkle et al., 2004) and about 50% lower energy offset values (Engström et al., 2007), which decreases the profit of higher k-values as will be discussed in more detail in the following.