Question

A phosphorus diffusion has a surface concentration of 5 x 10¹⁸ /cm³, and the background concentration of the p-type wafer is 1 x 10¹⁵ /cm³. The Dt product for the diffusion is 10-⁸ cm².

Find the junction depth for a Gaussian distribution.

Answer 1

To find the junction depth for a Gaussian distribution in phosphorus diffusion in a p-type wafer, the given surface concentration, background concentration, and the Dt product are used in the formula derived from a Gaussian distribution profile.

Step-by-step explanation:

The question pertains to semiconductor physics, specifically to the process of phosphorus diffusion in a p-type silicon wafer and finding out the junction depth associated with a Gaussian distribution. To calculate the junction depth where the concentration equals the intrinsic level (approximately equal to the background concentration for p-type material), we use the concept of the Gaussian distribution. The equation for the junction depth (xj) in a Gaussian distribution is given by:

xj = √(2 * Dt * ln(Nsurface/Nbackground))

Where:

• Dt is the diffusion coefficient multiplied by time (product for diffusion)
• Nsurface is the surface concentration
• Nbackground is the background concentration
• ln is the natural logarithm function

Given:

• Nsurface = 5 x 10ⁱ⁸ /cm³
• Nbackground = 1 x 10ⁱ⁵ /cm³
• Dt = 10⁻⁸ cm²

Plugging the values into the junction depth equation we get:

xj = √(2 * 10⁻⁸ cm² * ln(5 x 10ⁱ⁸ /cm³ / 1 x 10ⁱ⁵ /cm³))

Solving for xj will provide the junction depth for the phosphorus diffusion in the silicon wafer.