Question

# Q4 Phosphorus atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments;the background concentration of Pin this silicon material is known to be 5 × 1019 atoms/m³. The predeposition treatment is to be conducted at 950°C for 45 minutes; the surface concentration of P is to be maintained at a constant level of 4.5 × 1026 atoms/m³. Drive-in diffusion will be carried out at 1200°C for a period of 2.5 h. For the diffusion of P in Si, values of Qa and Do are 3.40 eV and 1.1 × 10^-4 m²/s, respectively.To solve this problem, you will need to make yourself familiar with equations 5.11, 5.12 and 5.13 from the book: C(x, t)=\frac{Q_{0}}{\sqrt{\pi D t}} \exp \left(-\frac{x^{2}}{4 D t}\right) Q_{0}=2 C_{s} \sqrt{\frac{D_{p} t_{p}}{\pi}} x_{j}=\left[\left(4 D_{d} t_{d}\right) \ln \left(\frac{Q_{0}}{C_{B} \sqrt{\pi D_{d} t_{d}}}\right)\right]^{1 / 2} Equation 5.11 (Solution for Fick's 2nd law for drive- in diffusion) Equation 5.12 (predeposition) Equation 5.13 (drive-in diffusion) a) Calculate the value of Qo (total amount of impurities). (3 marks) b) Determine the value of xj (junction depth) for the drive-in diffusion treatment. (3 marks) c) Also, for the drive-in treatment, compute the position x at which the concentration of P atoms is 10^24 m^-3.(3 marks)  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10  Fig: 11