What is the doping and hole concentration?

[unscientific]

Homework Statement

(a) Show law of mass action.
(b) Find dopant concentration and hole concentration.[/B]

Homework Equations

The Attempt at a Solution

Part(a)[/B]
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?

 

[unscientific]

bumpp

 

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bumppp

 

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bumpp dope

 

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bumping on dope

 

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bumping dope concentration?

 

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bump on dopant concentration

 

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bumpp

 

[unscientific]

BUMPP