Question

Consider silicon T=300K. Assume the hole concentration is given by p=10¹⁶ e⁻ˣ/ᴸp (cm⁻³ ), Where Lp=10⁻³ cm. Calculate the hole diffusion current density at (a) x=0, (b) x=10⁻³ cm. Assume Dp=10cm²/s.

Answer 1

The question involves calculating the hole diffusion current density in silicon at 300K, assuming a specified hole concentration and given diffusion constant. Using Fick's first law and the gradient of the given hole concentration expression, the current densities at x=0 and x=10^-3 cm can be found.

Step-by-step explanation:

The student's question is related to hole diffusion current density in a semiconductor at a certain temperature, which falls under the subject of Physics, specifically semiconductor physics. To solve for the diffusion current density, we use Fick's first law of diffusion, which states that the diffusion current density (Jp) is proportional to the negative gradient of the hole concentration (p). The equation is given by Jp = -Dp dp/dx.

Given the hole concentration as p=1016 e-x/Lp (cm-3), where Lp=10-3 cm, and the diffusion constant Dp as 10 cm2/s, we'll calculate Jp for:

• (a) x=0
• (b) x=10-3 cm

To calculate the current density, we first find the gradient of p with respect to x, which is dp/dx = -1016/Lp e-x/Lp. Substituting the values of x, we can find Jp for both positions a and b.

Here, we are not considering any additional given cross-sectional area, length, or other values from the attached unrelated examples since they don't pertain to the question at hand.