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Without quantum mechanics there would be no transistor, and hence no personal computer; no laser, and hence no Blu-ray players. James Kakalios, a physics professor at the University of Minnesota, wants people to understand how much quantum mechanics influences our everyday lives

Article in Scientific America: What is Quantum Mechanics good for?

I have read this numerous times, and watched documentaries that have said the same thing, specifically that without understanding quantum mechanics there would be no personal computer.

  • Was the understanding of QM fundamental to the creation of transistors and silicon semiconductors?
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A short timeline of the development of the transistor and Bardeen's role in it.

From John Bardeen (Wikipedia)

The assignment of the group was to seek a solid-state alternative to fragile glass vacuum tube amplifiers. Their first attempts were based on Shockley's ideas about using an external electrical field on a semiconductor to affect its conductivity. These experiments mysteriously failed every time in all sorts of configurations and materials. The group was at a standstill until Bardeen suggested a theory that invoked surface states that prevented the field from penetrating the semiconductor.

Bardeen suggested a theory that invoked surface states that prevented the field from penetrating the semiconductor.

As stated by Bloch's theorem, eigenstates of the single-electron Schrödinger equation with a perfectly periodic potential, a crystal, are Bloch waves [2]

$${ {\begin{aligned}\Psi _{n{\boldsymbol {k}}}&=\mathrm {e} ^{i{\boldsymbol {k}}\cdot {\boldsymbol {r}}}u_{n{\boldsymbol {k}}}({\boldsymbol {r}}).\end{aligned}}}$$

Here ${u_{n{\boldsymbol {k}}}({\boldsymbol {r}})}$ is a function with the same periodicity as the crystal, $n$ is the band index and $k$ is the wave number. The allowed wave numbers for a given potential are found by applying the usual Born–von Karman cyclic boundary conditions  The termination of a crystal, i.e. the formation of a surface, obviously causes deviation from perfect periodicity. Consequently, if the cyclic boundary conditions are abandoned in the direction normal to the surface the behavior of electrons will deviate from the behavior in the bulk and some modifications of the electronic structure has to be expected.

So to understand surface states involved knowledge regarding the Schrödinger Equation and Bloch's theorem, both based around Q.M.

In 1957, John Bardeen, in collaboration with Leon Cooper and his doctoral student John Robert Schrieffer, proposed the standard theory of superconductivity known as the BCS theory (named for their initials).

Again, quantum concepts are involved here.

So although I cannot say for sure how much Q.M. was involved in the invention of the transistor, or at what stage in his life did Bardeen first apply its concepts, there is certainly circumstantial evidence that Q.M. contributed to the development of the transistor.

You could also look through the published papers of the people involved in transistor development to see how much Q.M. was incorporated in them.

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The explanation of the electron distribution in a semiconductor can only be explained by means of QM, as classical theory can't prove the properties of transistors. Without going in much detail, this can be explained by QM as how the wave of electron behaves in a system with periodic structure (such as semiconductors) giving rise to "forbidden" energy levels, called gaps. These gaps are crucial to prove how transistors work.

On a side note, transistors were discovered much before (~10 years) this band-gap theory was developed, and it was not until the reason was totally understood that they begin using them for applications such as computers.

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  • $\begingroup$ So although the effect was know (and transistors created), the cause (quantum mechanics) was not fully understood? $\endgroup$ – user59315 Oct 3 '16 at 15:36
  • $\begingroup$ See if you can find papers at the time of the invention of the transistor, written by the people involved, and see if any of them were based on Q.M. concepts. $\endgroup$ – user108787 Oct 3 '16 at 15:57
  • $\begingroup$ @CountT010 Ok, you where rigth, in a paper by Schottky in 1949 he was able to explain the transistor by means of the semiconductor and electron-hole theory. So you could say they where very aware of QM for their work in the invention of the transistor as we know it. $\endgroup$ – Victor Oct 3 '16 at 16:44
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    $\begingroup$ When in 1947 the point contact transistor (bipolar tranistor) was serendipitously discovered by J. Bardeen and W. Brattain, the basic quantum mechanical theory of semiconductors was already established. In 1931 the band theory of conduction had been established by A. Wilson and the concept of band gaps had been developed. The main problem in 1946/1947 was to make pure enough germanium crystals which was accomplished around the same time. $\endgroup$ – freecharly Oct 3 '16 at 18:56
  • $\begingroup$ @freecharly: Would transistor-like properties be observable in a cats-whisker diode if one used two whiskers that were very close together, or is more required than that to make such properties observable (making a transistor useful may require something fancier, but if one was looking for gain that was merely measurable, would one find it?) $\endgroup$ – supercat Oct 3 '16 at 19:01
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To explain the physical working of a (bipolar) transistor, quantum mechanics is essential in the following sense. You need to know that electrons in a semiconductor occupy allowed energy bands and that there is a so called conduction band where electrons can move freely and an almost fully occupied valence band where missing electrons can be considered to behave as positive quasi-particles called holes. The occupation statistics is Fermi-Dirac statistics which includes the Pauli principle. Furthermore, by introducing impurities with quantum mechanical ionization energies that donate or accept electrons you can dope the semiconductor, i.e., you can create regions of the semiconductor with predominantly electron or hole conduction, which is essential for the device operation. With these fundamental results of the quantum theory of semiconductors, you can describe the working of transistors pretty much classically. For example, electrons and holes can be considered to be point particles which can be generated or recombine with a certain probability. Further, they can diffuse and drift in an electric field experiencing phenomenologically a "resistive friction" in the crystal lattice.

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    $\begingroup$ can describe the working of transistors pretty much classically Given their background in electrical engineering, and the equipment at Bell Labs at the time, I would guess that experimentation and trial and error played as big a part in the invention of the transistor as QM did. But it's a total guess. $\endgroup$ – user108787 Oct 3 '16 at 16:02
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    $\begingroup$ @CountTo10 I also thought that trial and error over QM knowledge would have been applied, and other sites seem to suggest this. Just weird how in academia the No Computers without QM is used quite often, but it is usually not backed up with any practical examples $\endgroup$ – user59315 Oct 3 '16 at 16:07
  • $\begingroup$ A good account of the invention of the transistor can be found in the book "Crystal Fire: The Invention of the Transistor and the Birth of the Information Age " by Michael Riordan. $\endgroup$ – freecharly Oct 3 '16 at 16:24
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    $\begingroup$ Without QM developments with solid state electronics would probably have stalled or would have been more difficult. $\endgroup$ – Lawrence B. Crowell Oct 3 '16 at 17:03
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    $\begingroup$ @CountTo10 - The basic quantum mechanical theory of solids and semiconductors had already been worked out in the early 1930s. Bardeen and Brattain knew these theories well, when they were doing experiments in 1946 to find out why the field effect was not effective in their germanium samples to be used as a field-effect transistor, which was invented already in 1925. In these experiments they discovered the (point contact) bipolar transistor effect for which a thorough theory was developed by their boss Shockley later. A working field-effect transistor (MOSFET) was developed only in 1960. $\endgroup$ – freecharly Oct 3 '16 at 21:52

protected by Qmechanic Oct 3 '16 at 17:14

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