Question 5.1: Consider the contact structure of Figure 5.7(c) consisting o...
Consider the contact structure of Figure 5.7(c) consisting of a pure Al film of indicated geometry over Si. Calculate the depth (y) of Si depletion in the wafer during a processing heat treatment of 1 h at 450°C, where the solubility (S) of Si in Al is 0.5 wt%. The respective densities for Si and Al are \rho_{Si}=2.33 \ and \ \rho_{Al}=2.7
The amount of Si needed to saturate the metal contact structure depends on the Al volume as well as the solubility of Si in Al. Conservation of mass requires that the amount of Si lost beneath the contact window must equal that which enters the metal. For (polycrystalline) Ale(single crystal)Si couples, the diffusivity of Si in Al is given by D=25 \times 10^{-4}exp[-0.79 \ eV/(kT)]cm^{2}/s. By Eqn (5.6),
x^{2}=4Dt (5.6)
the total diffusion length (L) along both sides of the contact at 450°C is calculated to be
L=4\times\left\{(25\times10^{-4}exp\left[-0.79eV/8.62\times10^{-5}\times723\right] )\times3600\right\} ^{1/2}=1.07\times10^{-2}cm(107 \mu m). Therefore,Lwd\rho_{Al}S=wCy\rho_{Si}. Solving, y=\frac{Ld\rho_{Al}S}{(C\rho_{Si})}, substituting \rho_{Al}=2.7,\rho_{Si}=2.33,and assuming w=2µm,d=1µm,and C=5µm, y is calculated to be 0.123 µm.