3. Consider a selective area ion implantation process shown in Fig. 3. The substrate is a p- doped Si wafer with a background Boron (B) dopant concentration of Csub = 106 cm, partially covered by an implantation mask, as shown in Fig. 3(a). Phosphorous (P) ions are implanted into the wafer with a projected range of 100 nm. After implantation, the peak dopant concentration inside the wafer is 1020 cm. The implantation projected range profiles are plotted in Fig. 3(b). (a) What should the ion implantation energy be in order to reach this projected range? (4 points) (b) Write down the full expression of the dopant concentration C(x) as a function of the depth from the wafer surface x, in the unmasked area. (4 points) Note: your expression should have all the numbers plugged in with units. In other words, all parameters in the equation should be expressed in numbers, not symbols. (c) Calculate the total ion implantation dose, defined as the total number of dopant atoms per unit area. (15 points) (d) Assume the implantation mask has the same density as Si (i.e. the implantation dynamics inside the mask are the same as in Si), calculate the minimum mask thickness needed to prevent the doping type of the Si crystal underneath the mask to be reversed. (12 points) (b) Range (A) 2500 2000 1500 1000 500 (a) Range Sigma Phosphorus Arsenic 100 Energy (kV) Antimony 150 600 500 400 300 200 100 200 X Sigma (A) (A) Substrate Range (A) 6000 5000 4000 3000 2000 1000 Implantation mask Implanted ions Range Sigma Boron 100 Energy (kV) Gallium 150 RE 1000 800 600 400 200 200 Sigma (A) Figure 3. (a) Cross-section schematic of ion implantation in a selective area. (b) Projected range profile for different dopants in Si.