# The tunneling effect question

1. Oct 14, 2009

### tkm2002

1. The problem statement, all variables and given/known data
Suppose a tunneling current in an electronic device goes through a potential-energy barrier. The tunneling current is small because the width of the barrier is large and the barrier is high. To increase the current most effectively, what should you do?
a. Reduce the width of the barrier.
b. Reduce the height of the barrier.
c. Either choice (1) or choice (2) is equally effective.
d. Neither choice (1) nor choice (2) increases the current
2. Relevant equations

3. The attempt at a solution
should I use this equation?
T ≈ e^(-2CL) , L is he width of the barrier.
c^2 = 2m(U-E)/(h/2pi) , U is the height of the barrier ; E is the energy of electron ;m is the mass of electro; h is plank constant

I am not understand why the answer is a.

2. Oct 14, 2009

### gabbagabbahey

Yes, use those equations. What happens if you cut 'U' in half? What happens if you cut 'L' in half?....So which has the greater effect?

3. Oct 15, 2009

### tkm2002

I do not know how to calculate and compare it

4. Oct 15, 2009

### gabbagabbahey

Call the initial U, $U_0$ and the initial L, $L_0$....what does that make the initial transmission coefficient? What doe the transmission coefficient become when you plug in $U=U_0/2$ and $L=L_0$? How about when you plug in $U=U_0$ and $L=L_0/2$

5. Oct 16, 2009

### tkm2002

But I do not how to compare them
http://img98.imageshack.us/img98/6779/89062472.jpg [Broken]

$T_0$ = e^2CL
$T of L_0/2$ = $T_0$^1/2
I do not how to write $T of U_0/2$ in terms of $T_0$

Last edited by a moderator: May 4, 2017
6. Oct 17, 2009

### gabbagabbahey

Well, the largest effect that the first one will have is to reduce the exponent by a factor of $\sqrt{2}$ (when E=0)....While the second one reduces the exponent by a factor of 2...

P.S. You are missing the negative signs in your exponents!

7. Oct 19, 2009

### tkm2002

I am not very understand.
Can you express the equation?