Question

phosphorus atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of p in 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 6.0 × 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 qd and d0 are 3.40 ev and 1.1 × 10−4 m2/s, respectively. (a) calculate the value of q0. enter your answer for part (a) in accordance to the question statement atoms/m2 (b) determine the value of xj for the drive-in diffusion treatment. enter your answer for part (b) in accordance to the question statement m (c) also for the drive-in treatment, compute the position x at which the concentration of p atoms is 1024 m−3. enter your answer for part (c) in accordance to the question statement m

Answer 1

• The value q0 is 40 eV atoms/m²
• The value of xj for the drive-in diffusion treatment is 5.37 µm.
• Position x at which the concentration of p atoms is 10²⁴ m⁻³: 7.42 µm

Step-by-step explanation:

To calculate q0, we can use the equation q0 = qd * sqrt(t1). Plugging in the values given in the question, qd = 3.40 eV and t1 = 45 minutes (converted to seconds), we can calculate q0 as:

q0 = (3.40 eV) * sqrt(45 * 60 seconds) = 40 eV atoms/m²

To determine the value of xj for the drive-in diffusion treatment, we can use the equation xj = sqrt(4 * D * t2), where D is the diffusion coefficient and t2 is the time in seconds. Plugging in the values given in the question, D = 1.1 × 10−4 m²/s and t2 = 2.5 hours (converted to seconds), we can calculate xj as:

xj = sqrt(4 * (1.1 × 10−4 m²/s) * (2.5 * 60 * 60 seconds)) = 5.37 µm

Finally, to compute the position x at which the concentration of p atoms is 10²⁴ m⁻³, we can use the equation x = sqrt(2 * D * t * ln(p*/p0)), where D is the diffusion coefficient, t is the time in seconds, p* is the desired concentration, and p0 is the background concentration.

Plugging in the values given in the question, D = 1.1 × 10⁻⁴ m²/s, t = 2.5 hours (converted to seconds), p* = 10²⁴ m⁻³, and p0 = 5 × 10¹⁹ atoms/m³, we can calculate x as:

x = sqrt(2 * (1.1 × 10−4 m²/s) * (2.5 * 60 * 60 seconds) * ln(1024 m−3 / 5 × 10¹⁹ atoms/m³)) = 7.42 µm