How Does Doping Affect the Resistance of a Silicon Beam?

[dvgrizz1]

Homework Statement

Given a silicon beam of diameter 10nm and length 100nm, what would its resistance be if it were doped with a p-type of 10^16/cm^3?

Homework Equations

R= resistivity*length/area
R= length/(qA*electron density* electron mobility)
resistivity of silicon= 0.1 ohm*meters

The Attempt at a Solution

I have enough variables to solve the first equation, but that doesn't take into account the doping at all. However, I'm not sure what to do with electron mobility if I'm supposed to use the second equation. Perhaps there's an equation I'm missing?

 

[KataKoniK]

Thank you for your question. The resistance of a doped silicon beam can be calculated using the equation R = resistivity * length / area, as you mentioned. However, since the beam is doped with a p-type of 10^16/cm^3, the resistivity will be affected.

To account for this, we can use the equation R = length / (q*A*electron density*electron mobility), where q is the charge of an electron, A is the cross-sectional area of the beam, and electron mobility is a measure of how easily electrons can move through the material.

To solve for the resistance, we will need to know the electron density and electron mobility for the given p-type doping level. This information can be found in a table or graph specific to the type and level of doping in silicon.

Once we have these values, we can plug them into the equation and solve for the resistance of the doped silicon beam. I hope this helps. Let me know if you have any further questions.