Steady state temperature of wafers?

[Obelisk]

Homework Statement

A 50mm wafer, 2mm thick is implanted with Boron at 100keV and 1mA. Considering only conductive cooling, given that thermal resistance is 10K/W, to room temperature of 25oC, determine the steady state wafer temperature and also the time constant for heating

Homework Equations

I know that Net Q = CdT/dt = Qin - ( T - To) / thermal resistance.

The Attempt at a Solution

I can determine Qin by using 1ev = 1.602 X 10^-19 J. But I am stuck on how to proceed. Could someone please help?

 

[MATLABdude]

Homework Statement

A 50mm wafer, 2mm thick is implanted with Boron at 100keV and 1mA. Considering only conductive cooling, given that thermal resistance is 10K/W, to room temperature of 25oC, determine the steady state wafer temperature and also the time constant for heating

Homework Equations

I know that Net Q = CdT/dt = Qin - ( T - To) / thermal resistance.

The Attempt at a Solution

I can determine Qin by using 1ev = 1.602 X 10^-19 J. But I am stuck on how to proceed. Could someone please help?

Okay, how many Boron atoms are impinging on the wafer every second? How much energy do they (collectively) carry?

 

[Obelisk]

The boron atoms would collectively carry 100 X 1.602 X 10 ^ -19 J since 1 keV carries 1.602 X 10 ^ -19 J

How many atoms impinging per second is not given, is this something I can calculate from the information that has been provided in the question? If yes, what equation is required?

Thanks.

 

[MATLABdude]

The boron atoms would collectively carry 100 X 1.602 X 10 ^ -19 J since 1 keV carries 1.602 X 10 ^ -19 J

How many atoms impinging per second is not given, is this something I can calculate from the information that has been provided in the question? If yes, what equation is required?

Thanks.

No, each boron atom carries 100 x 1.602E-19 J. As to the number, here's a hint: why do they tell you the implant current?

 

[Obelisk]

I think I am stalled, really stalled on this one! The only other piece of information that describes / models this physical situation would be:

T = To + (Tf - To) e ^(-t/tau).

I know that I am supposed to obtain Tf as the steady state wafer temperature and tau as the time heating constant. I am blocked, please help!

 

[MATLABdude]

I'll throw you a bone or two. Assume that you have B+ being deposited. Use the current they give you to determine the number of B+ per second.

Next, take a look at the Wikipedia article on Thermal Resistance:
http://en.wikipedia.org/wiki/Thermal_resistance_in_electronics

As for what the time constant is, well, hopefully you have a better thermodynamics background than I do:
http://en.wikipedia.org/wiki/Heat_transfer