ok by equilibrium I mean whatever temperature that may be. I dont know what that is. I guess its defined as something but im not sure.
I thought that at 0K there will be 0 EHP's but the arsenic free electrons would still be available for conduction right? I was under the impresion that there would still be some minimal conduction at 0K due to the extra electrons having nowhere to go other than the conduction band.
my point was this - if at 0K, there will be no holes at all so p=0.
But if there are still a few free electrons (from arsenic) n=some small value
and therefore np=0
an intrinsic semiconductor at 0K will have p=0 AND n=0, so np=0
so in fact, the relation np=ni^2 does hold. But is it correct that at ANY temperature the added electrons are always in the conduction band, even if they are effectively useless at low temperature?
Here is my thought process (if you have the time to read it)
1. take tiny piece of silicon made up of 4 si atoms only and cool it to 0 Kelvin
2. n=0 and p=0
3. increase temperature, and np=ni^2 (here we assume that the ni value is increasing to a value corresponding to the current temperature) so the relationship holds.
- lets assume that 2 atoms ionize and so we have 2 free electrons and 2 holes so ni^2 = 4 = np
4. remove one si atom and replace with arsenic. We now have 3 silicon atoms and one arsenic.
5. Cool to 0 Kelvin.
- n=1 and p=0 and therefore np=0 - ok good.
6.increase temperature to the same point where 2 electron hole pairs were previously created in the intrinsic silicon...(where we had n=2, p=2 and ni^2=4)
7. Now we have the arsenic electron plus the 2 silicon electrons (from EHP formation) and n=3 and p=2 and np=6 which is wrong!
- so im aware that in order to equal 4 p must be 4/3 !
Hence where my problems are arising from
I do see from what you said that every arsenic atom reduces the probability of an intrinsic EHP forming.
So is it the case that this probability is reduced by just the right amount that when analysed over time the average n=3 and p=4/3 ? that would almost make sense for me
sorry im aware that was quite convoluted!
This is my take on what you have said. I think you got everything pretty much correct, apart from the ni bit. Remember the ni constant is for intrinsic semiconductor material, this is what the (I) is. It is independent of doping levels. So you can't use it for anything else.
Without getting too much into it, you maybe better to think about band-gap energy levels. So for an electron to reach the conduction band it has to have enough energy. The energy needed depends on the type of semiconductor material and the strength of the bond the electron has with the atom. Remember that although adding arsenic adds one free electron to the mix, it will only break free if it has enough energy. Room temperature generally does this.
Think about getting a ping pong ball and a straw and place the ball on a tilted table. Stretch a piece of tape across the table and label the bottom half of the table Valence and the top half conduction. Blow through the straw and try and move the ball into the conduction band area. If takes a certain amount of blow (energy). Now go and stand in the freezer for an hour and try again. You won't have enough blow (energy) to move the ball very far. This is the best way I can explain it.
Basically it's the contraction and expansion of the crystal lattice at low and high temperatures that cause the band gap energy to go up and down, making it harder or easier (more or less energy) for the electrons to move away.
Ratch will correct me if I have somthing not quite right.
Adam
