# What is the doping and hole concentration?

Tags:
1. Apr 27, 2015

### unscientific

1. The problem statement, all variables and given/known data

(a) Show law of mass action.
(b) Find dopant concentration and hole concentration.

2. Relevant equations

3. The attempt at a solution

Part(a)

Bookwork.

Part(b)

Letting the doping concentration be $D$, we have:
$$D = n - p$$
For $I = n_{intrinsic} = p_{intrinsic}$, we have:
$$D^2 + 4I^2 = (n+p)^2 = (n-p)^2 + 4np$$

Which gives us the result
$$n = \frac{1}{2}\left( \sqrt{D^2 + 4I^2} + D \right)$$
$$p = \frac{1}{2}\left( \sqrt{D^2 + 4I^2} - D \right)$$

For the doping to work at 750K, I estimate the doping concentration to be $D \approx n_{intrinsic} = \sqrt{np}$.
At 750 K,
$$D = \sqrt{np} = 1.7 \times 10^{23}$$
At 300K,
$$I = \sqrt{np} = 1 \times 10^{19}$$

Since $D >> I$, we have
$$p \approx \frac{I^2}{D} = 6 \times 10^{14}$$

Is this right?

2. May 2, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. May 4, 2015

bumpp

4. May 7, 2015

### unscientific

bumppp

5. May 10, 2015

### unscientific

bumpp dope

6. May 14, 2015

### unscientific

bumping on dope

7. May 16, 2015

### unscientific

bumping dope concentration?

8. May 18, 2015

### unscientific

bump on dopant concentration

9. May 22, 2015

### unscientific

bumpp

10. May 23, 2015

BUMPP