Contact Resistance Homework: Aluminium Contacts & Silicon Wafer

[Obelisk]

Homework Statement

Aluminium contacts {100} p-doped silicon (10ohm/square) which has been implanted into a 200mm wafer (1 mm thick) by 100keV phosphorus at 7X10^15. What will be the resistance of a 1um^2 contact and will it be ohmic?

Homework Equations

Rc = Pc/A

The Attempt at a Solution

I determined Pc = thickness X Sheet Resistance

But then, when I apply the given equation to obtain Rc, I am not getting answers in ohm-cm2 which should be the units of Rc.

If I can get help with finding Rc, I can figure out if it is ohmic or not but I am stuck here. Please help!

 

[Jhero]

Thank you for your question. In order to calculate the resistance of a 1um^2 contact, we first need to determine the sheet resistance of the implanted silicon. This can be calculated using the given information about the doping concentration (7X10^15) and the thickness of the wafer (1 mm). Once we have the sheet resistance, we can use the equation you provided, Rc = Pc/A, to calculate the contact resistance.

However, it is important to note that the units of Rc will not be in ohm-cm2, but rather in ohms. This is because the sheet resistance (Pc) is already in units of ohms per square, so when we divide it by the area (A) of the contact (1 um^2), we will simply get the resistance in ohms.

To determine if the contact is ohmic, we can compare the calculated resistance to the sheet resistance of the implanted silicon. If the contact resistance is significantly lower than the sheet resistance, then it is likely that the contact is ohmic. However, if the contact resistance is similar or higher than the sheet resistance, then it may not be ohmic.

I hope this helps. If you have any further questions or need clarification, please don't hesitate to ask. Good luck with your calculations!