Question

In a sample of silicon, the hole concentration starts at 8.1×10¹²/cm³ at x=0, and then drops off exponentially as x increases with a diffusion length of Lp=43.7μm. What is the diffusion current density due to holes at x=0 in mA/cm²? Use: Dp=15.9 cm²/s and q=1.6×10⁻¹⁹C (Note that diffusion length is used in this exponential similar to how a time constant is used in an RC circuit. So the equation exp(−x/Lp) gives the exponential drop off as x increases here.) Answer:

Answer 1

The diffusion current density due to holes at x=0 is 5.565 mA/cm². This was calculated by applying the formula for diffusion current density, utilizing the given values for hole concentration, diffusion constant, and charge of the hole.

Step-by-step explanation:

To find the diffusion current density due to holes at x=0, we use the equation for diffusion current density Ip, which is given by:

Ip = q * Dp * dp/dx

We know the hole density p drops off exponentially as a function of x, so the spatial derivative dp/dx at x=0 is given by -(p0/Lp), where p0 is the initial hole concentration and Lp is the diffusion length.

Substituting the given values p0 = 8.1×1012 cm−3, Dp = 15.9 cm2/s, Lp = 43.7 µm, and q = 1.6×10−19 C, we get:

Ip = (1.6×10−19 C) * (15.9 cm2/s) * (-(8.1×1012 cm−3) / (43.7×10−6 cm))

Ip = -5.565 mA/cm2, which is the magnitude of the diffusion current density due to holes at x=0 (neglecting the sign, which indicates the direction of current flow).