You don't need the Dirac equation to understand semiconductor physics. Holes are not positrons, and I'm somewhat skeptical of the idea that if positrons had not been discovered or postulated, that the transistor would not have been invented.
Without a doubt, it's really cool that we can say "Hey! We can actually predict that electrons will have spin!", but you don't need to understand that water is made up of hydrogen and oxygen to build a steam engine.
However, if someone can point me to writings by Shockley, Brattain, or Bardeen, or a historical account that indicates otherwise, I'd be happy to read it :)
I assume the article is referring to Fermi-Dirac statistics [1], not the Dirac equation.
That said, the Dirac equation (or relativistic QM more generally) as well as the Feynman path integral (the idea of which originated from a 1933 paper of Dirac) are pretty indispensable in modern condensed matter physics.
1) The article is primarily concerned with Dirac's relativistic formulation of quantum mechanics. This is why they make the claim
'Without understanding the origin of spin, and the Dirac statistics, you wouldn't have mobile phones, computers or anything else that runs on electronics.'
However, Fermi-Dirac statistics can be derived directly from the properties of fermions. True, you can derive the fact that electrons will be fermions because of their spin from the spins-statistics theorem, but you only need to know the Pauli Exclusion principle to get the F-D statistics.
2) My understanding, and speaking with engineers in the field, is that most of the applied industrial research uses empirically derived band structures (which definitely does require Rel. QM to derive from first principles) and regular QM to design devices. This is also the approach I've seen in most semiconductor simulators. However, it is entirely possible that Intel or AMD take a different approach. Not having access to the tools they use, I can't speak to their tech.
However, you seem to be a knowledgeable person, so I'd be more than happy to be informed that I'm full of shit here. :)
> You don't need the Dirac equation to understand semiconductor physics. Holes are not positrons, and I'm somewhat skeptical of the idea that if positrons had not been discovered or postulated, that the transistor would not have been invented.
The MOSFET was patented in 1925 by Julius Edgar Lilienfeld. I don't know if he knew about positrons.
>The MOSFET was patented in 1925 by Julius Edgar Lilienfeld. I don't know if he knew about positrons.
He would not have known anything about positrons. Dirac's major triumph was the prediction of positrons in 1928, before empirical evidence for them existed.
Thank you for reminding me about Lillienfield's patents. It is a good example of why the basic idea of transistors don't require even quantum mechanics (Schroedinger published his equation in 1926). Furthermore, since you need to toss in feedback in anycase, the need for accurately predicting the actual magnitude of gain, is significantly diminished for initial applications. If you read the Art of Electronics, you'll note that one of the things they point out is that you shouldn't base a circuit design that relies too heavily on a particular value of the amplification.
Comments
You don't need the Dirac equation to understand semiconductor physics. Holes are not positrons, and I'm somewhat skeptical of the idea that if positrons had not been discovered or postulated, that the transistor would not have been invented.
Without a doubt, it's really cool that we can say "Hey! We can actually predict that electrons will have spin!", but you don't need to understand that water is made up of hydrogen and oxygen to build a steam engine.
However, if someone can point me to writings by Shockley, Brattain, or Bardeen, or a historical account that indicates otherwise, I'd be happy to read it :)
I assume the article is referring to Fermi-Dirac statistics [1], not the Dirac equation.
That said, the Dirac equation (or relativistic QM more generally) as well as the Feynman path integral (the idea of which originated from a 1933 paper of Dirac) are pretty indispensable in modern condensed matter physics.
[1] https://secure.wikimedia.org/wikipedia/en/wiki/Fermi%E2%80%9...
Two points
1) The article is primarily concerned with Dirac's relativistic formulation of quantum mechanics. This is why they make the claim
'Without understanding the origin of spin, and the Dirac statistics, you wouldn't have mobile phones, computers or anything else that runs on electronics.'
However, Fermi-Dirac statistics can be derived directly from the properties of fermions. True, you can derive the fact that electrons will be fermions because of their spin from the spins-statistics theorem, but you only need to know the Pauli Exclusion principle to get the F-D statistics.
2) My understanding, and speaking with engineers in the field, is that most of the applied industrial research uses empirically derived band structures (which definitely does require Rel. QM to derive from first principles) and regular QM to design devices. This is also the approach I've seen in most semiconductor simulators. However, it is entirely possible that Intel or AMD take a different approach. Not having access to the tools they use, I can't speak to their tech.
However, you seem to be a knowledgeable person, so I'd be more than happy to be informed that I'm full of shit here. :)
> You don't need the Dirac equation to understand semiconductor physics. Holes are not positrons, and I'm somewhat skeptical of the idea that if positrons had not been discovered or postulated, that the transistor would not have been invented.
The MOSFET was patented in 1925 by Julius Edgar Lilienfeld. I don't know if he knew about positrons.
http://en.wikipedia.org/wiki/MOSFET .
>The MOSFET was patented in 1925 by Julius Edgar Lilienfeld. I don't know if he knew about positrons.
He would not have known anything about positrons. Dirac's major triumph was the prediction of positrons in 1928, before empirical evidence for them existed.
Thank you for reminding me about Lillienfield's patents. It is a good example of why the basic idea of transistors don't require even quantum mechanics (Schroedinger published his equation in 1926). Furthermore, since you need to toss in feedback in anycase, the need for accurately predicting the actual magnitude of gain, is significantly diminished for initial applications. If you read the Art of Electronics, you'll note that one of the things they point out is that you shouldn't base a circuit design that relies too heavily on a particular value of the amplification.