A p-n junction is obtained at a depth of 3×10−3 cm by diffusion of antimony (Sb) into p-type germanium. What is the acceptor concentration in the bulk Ge, if diffusion was carried out for three hours at 790∘ C?
Given:
Constant Sb surface concentration is 8×1018 cm3
The diffusivity of Sb in Ge at 790∘ C is 4.8×10−11 cm2/sec
Write answer in units of cubic centimeters, in scientific notation up to two decimal points
To find the acceptor concentration in the bulk Ge, we can use Fick's second law of diffusion. The equation is:
C(x, t) = C0 * (1 - erf(x / (2 * sqrt(D * t))))
Where:
- C(x, t) is the concentration at depth x and time t
- C0 is the surface concentration
- D is the diffusion coefficient
- t is the time
- x is the depth
Given values:
- Surface concentration (C0) = 8x10^18 cm^3
- Diffusion coefficient (D) = 4.8x10^(-11) cm^2/sec
- Depth (x) = 3x10^(-3) cm
- Time (t) = 3 hours = 3 x 60 x 60 seconds = 10800 seconds
Let's substitute these values into the equation:
C(3x10^(-3) cm, 10800 sec) = 8x10^18 cm^3 * (1 - erf(3x10^(-3) cm / (2 * sqrt(4.8x10^(-11) cm^2/sec * 10800 sec))))
Using a scientific calculator, we can evaluate this expression to find the acceptor concentration in the bulk Ge.