A p-n junction is to be created by diffusing boron (B) into an n-type silicon wafer with an existing carrier concentration of 1015/cm3. The location of the junction will be 6μm below the surface of the wafer. The surface concentration of boron will be maintained at 1020/cm3 while the diffusion process is occurring. Assuming the diffusivity of B in Si is 3×10−11 cm2/sec at the process temperature, how many seconds will it take? (Hint: The junction is formed at a location where the boron concentration equals the donor concentration.) Assume no change in donor concentration occurs during the diffusion (ie: no outgassing).
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To find out how many seconds it will take to create the p-n junction, we need to calculate the diffusion length of boron in silicon.
The diffusion length is given by the equation:
xd = √(2Dτ)
where xd is the diffusion length, D is the diffusivity of boron in silicon, and τ is the time.
In this case, the boron diffusivity (D) is given as 3×10^(-11) cm^2/sec and the diffusion length (xd) is 6μm (or 6×10^(-4) cm).
Plugging in the given values, we can solve for τ:
6×10^(-4) = √(2 × 3×10^(-11) × τ)
Squaring both sides of the equation, we get:
(6×10^(-4))^2 = 2 × 3×10^(-11) × τ
Simplifying further:
3.6×10^(-8) = 6×10^(-11) × τ
Dividing both sides by 6×10^(-11), we get:
τ = (3.6×10^(-8))/(6×10^(-11))
τ ≈ 6 seconds
Therefore, it will take approximately 6 seconds to create the p-n junction.