Semiconductors - Drift/Mobility & Temperature

[Marcin H]

Homework Statement

Homework Equations

The Attempt at a Solution

I am having problems with all parts of this problem, but I'll start with part A. Comparing the 2 equations I see that Ca could be 3/2 based off the hint, but I am not sure why or how it would be 3/2 or -3/2. The problem does not specify if this is for lattice scattering or impurity scattering. Either way I am not sure how to compare the 2 equations above. And as for Cb it seems like it can only be 1. I don't see how cb can be an equation unless we have to solve the equation above for Cb assuming Ca is ±3/2.

 

[mfb]

The problem does not specify if this is for lattice scattering or impurity scattering.

(A) is about the density of electrons and holes, it has nothing to do with scattering.

Does n(T) increase with increasing T according to 3-26?
Which sign does c_a need to reproduce this?
How much does n(T) increase if T doubles (for example)? Can you derive which c_a reproduces this?

And as for Cb it seems like it can only be 1.

Right.

I don't see how cb can be an equation unless we have to solve the equation above for Cb assuming Ca is ±3/2.

A parameter cannot be an equation. That's like asking how a color can be a fruit.
You can compare the equations at different temperatures to set up multiple equations that all have to be true and solve for the two unknown parameters that way, but doing it by inspection is quicker.

 

[Marcin H]

Oh, right. I was confusing concentration with mobility.

Does n(T) increase with increasing T according to 3-26?
Yes, n(T) increases with increasing T, so Ca would have to be +(3/2)

As for Cb is the hint just to trick us? Why do they say it's an equation if Cb just equal to 1?And for parts B and C, I don't know if I am overthinking it, but if we are using the same equation for the electron mobility of intrinsic silicon as we did for copper, then why would the relationship between mobility and temperature change between the 2 materials? Why even ask part c? Does lattice scattering vs impurity scattering have anything to do with this?

 

[mfb]

Oh, I didn't see the "is an equation" hint. Actually, it is not an equation, but it is not 1 either, I misread the problem statement before.

Plug in T=300 K in the first equation: Now the carrier density at 300 K appears both on the left and right side, so you can cancel them. The fraction is 1 by construction, so which value does the exponent at the right side need?

Does n(T) increase with increasing T according to 3-26?
Yes, n(T) increases with increasing T, so Ca would have to be +(3/2)

Right.

And for parts B and C, I don't know if I am overthinking it, but if we are using the same equation for the electron mobility of intrinsic silicon as we did for copper, then why would the relationship between mobility and temperature change between the 2 materials?

You can't use the semiconductor equations for copper, it is not a semiconductor.

The difference between semiconductor and metal becomes relevant in (c).

 

[Marcin H]

Oh, I didn't see the "is an equation" hint. Actually, it is not an equation, but it is not 1 either, I misread the problem statement before.

Plug in T=300 K in the first equation: Now the carrier density at 300 K appears both on the left and right side, so you can cancel them. The fraction is 1 by construction, so which value does the exponent at the right side need?Right.You can't use the semiconductor equations for copper, it is not a semiconductor.

The difference between semiconductor and metal becomes relevant in (c).

Plugging in 300K into that equation gives me 1 = e^(-(Eg/2kT)Cb). So solving for Cb would give me 0 taking the natural log of both sides. Not sure if this is correct or what it tells us if it is 0.EDIT*

Also, for part b and c what are we supposed to use to find the mobility then? What are they trying to get at by saying that the mobility follows that of the equation used for copper.

 

[mfb]

c_b is not meant as a factor here, it is written in a misleading way. Just see what you have to modify to make the equation right.

The mobility and concentration are completely different things, you need both to calculate the resistance.

 

[Marcin H]

I'm lost here. What is the right equation? Am I supposed to plug in T=300k into equation 3-26 and compare those?

 

[mfb]

That will certainly help.

 

[Marcin H]

What values should I use for the effective mass of electrons/holes in equation 3-26? Also, is the h in that equation h(bar)? Or something else?

 

[mfb]

What values should I use for the effective mass of electrons/holes in equation 3-26?

You don't need values for them, they cancel anyway.

Also, is the h in that equation h(bar)? Or something else?

It is the Planck constant, not divided by 2pi, but this will cancel as well.