Quantum physics
“I think it is safe to say that no one understands quantum mechanics.”
Physicist Richard P. FeynmanTo say that the invention of semiconductor devices was a revolution would not be an exaggeration.
Not only was this an impressive technological accomplishment, but it paved the
way for developments that would indelibly alter modern society. Semiconductor devices made
possible miniaturized electronics, including computers, certain types of medical diagnostic and
treatment equipment, and popular telecommunication devices, to name a few applications of
this technology.
But behind this revolution in technology stands an even greater revolution in general science:
the field of quantum physics. Without this leap in understanding the natural world, the
development of semiconductor devices (and more advanced electronic devices still under development)
would never have been possible. Quantum physics is an incredibly complicated realm
of science. This chapter is but a brief overview. When scientists of Feynman’s caliber say that
“no one understands [it],” you can be sure it is a complex subject. Without a basic understanding
of quantum physics, or at least an understanding of the scientific discoveries that led to its
formulation, though, it is impossible to understand how and why semiconductor electronic devices
function. Most introductory electronics textbooks I’ve read try to explain semiconductors
in terms of “classical” physics, resulting in more confusion than comprehension.
Many of us have seen diagrams of atoms that look something like Figure 2.1.
Tiny particles of matter called protons and neutrons make up the center of the atom; electrons
orbit like planets around a star. The nucleus carries a positive electrical charge, owing to the presence of protons (the neutrons have no electrical charge whatsoever), while the atom’s
balancing negative charge resides in the orbiting electrons. The negative electrons are attracted
to the positive protons just as planets are gravitationally attracted by the Sun, yet the
orbits are stable because of the electrons’ motion. We owe this popular model of the atom to the
work of Ernest Rutherford, who around the year 1911 experimentally determined that atoms’
positive charges were concentrated in a tiny, dense core rather than being spread evenly about
the diameter as was proposed by an earlier researcher, J.J. Thompson.
Rutherford’s scattering experiment involved bombarding a thin gold foil with positively
charged alpha particles. Young graduate students H. Geiger and E. Marsden
experienced unexpected results. A few Alpha particles were deflected at large angles. A few
Alpha particles were back-scattering, recoiling at nearly 180o. Most of the particles passed
through the gold foil undeflected, indicating that the foil was mostly empty space. The fact
that a few alpha particles experienced large deflections indicated the presence of a minuscule
positively charged nucleus
Rutherford scattering: a beam of alpha particles is scattered by a thin gold foil.
Although Rutherford’s atomic model accounted for experimental data better than Thompson’s,
it still wasn’t perfect. Further attempts at defining atomic structure were undertaken,
and these efforts helped pave the way for the bizarre discoveries of quantum physics. Today our
understanding of the atom is quite a bit more complex. Nevertheless, despite the revolution of
quantum physics and its contribution to our understanding of atomic structure, Rutherford’s
solar-system picture of the atom embedded itself in the popular consciousness to such a degree
that it persists in some areas of study even when inappropriate.
Consider this short description of electrons in an atom, taken from a popular electronics
textbook:
Orbiting negative electrons are therefore attracted toward the positive nucleus,
which leads us to the question of why the electrons do not fly into the atom’s nucleus.
The answer is that the orbiting electrons remain in their stable orbit because of two
equal but opposite forces. The centrifugal outward force exerted on the electrons
because of the orbit counteracts the attractive inward force (centripetal) trying to
pull the electrons toward the nucleus because of the unlike charges.
Figure 2.2: Rutherford scattering: a beam of alpha particles is scattered by a thin gold foil.
Although Rutherford’s atomic model accounted for experimental data better than Thompson’s,
it still wasn’t perfect. Further attempts at defining atomic structure were undertaken,
and these efforts helped pave the way for the bizarre discoveries of quantum physics. Today our
understanding of the atom is quite a bit more complex. Nevertheless, despite the revolution of
quantum physics and its contribution to our understanding of atomic structure, Rutherford’s
solar-system picture of the atom embedded itself in the popular consciousness to such a degree
that it persists in some areas of study even when inappropriate.
Consider this short description of electrons in an atom, taken from a popular electronics
textbook:
Orbiting negative electrons are therefore attracted toward the positive nucleus,
which
In keeping with the Rutherford model, this author casts the electrons as solid chunks of
matter engaged in circular orbits, their inward attraction to the oppositely charged nucleus
balanced by their motion. The reference to “centrifugal force” is technically incorrect (even
for orbiting planets), but is easily forgiven because of its popular acceptance: in reality, there
is no such thing as a force pushing any orbiting body away from its center of orbit. It seems
that way because a body’s inertia tends to keep it traveling in a straight line, and since an
orbit is a constant deviation (acceleration) from straight-line travel, there is constant inertial
opposition to whatever force is attracting the body toward the orbit center (centripetal), be it
gravity, electrostatic attraction, or even the tension of a mechanical link.
The real problem with this explanation, however, is the idea of electrons traveling in circular
orbits in the first place. It is a verifiable fact that accelerating electric charges emit
electromagnetic radiation, and this fact was known even in Rutherford’s time. Since orbiting
motion is a form of acceleration (the orbiting object in constant acceleration away from normal,
straight-line motion), electrons in an orbiting state should be throwing off radiation like mud
from a spinning tire. Electrons accelerated around circular paths in particle accelerators called
synchrotrons are known to do this, and the result is called synchrotron radiation. If electrons
were losing energy in this way, their orbits would eventually decay, resulting in collisions with
the positively charged nucleus. Nevertheless, this doesn’t ordinarily happen within atoms.
Indeed, electron “orbits” are remarkably stable over a wide range of conditions.
Furthermore, experiments with “excited” atoms demonstrated that electromagnetic energy
emitted by an atom only occurs at certain, definite frequencies. Atoms that are “excited” by
outside influences such as light are known to absorb that energy and return it as electromagnetic
waves of specific frequencies, like a tuning fork that rings at a fixed pitch no matter how
it is struck. When the light emitted by an excited atom is divided into its constituent frequencies
(colors) by a prism, distinct lines of color appear in the spectrum, the pattern of spectral
lines being unique to that element. This phenomenon is commonly used to identify atomic elements,
and even measure the proportions of each element in a compound or chemical mixture.
According to Rutherford’s solar-system atomic model (regarding electrons as chunks of matter
free to orbit at any radius) and the laws of classical physics, excited atoms should return energy
over a virtually limitless range of frequencies rather than a select few. In other words, if
Rutherford’s model were correct, there would be no “tuning fork” effect, and the light spectrum
emitted by any atom would appear as a continuous band of colors rather than as a few distinct
lines.
A pioneering researcher by the name of Niels Bohr attempted to improve upon Rutherford’s
model after studying in Rutherford’s laboratory for several months in 1912. Trying to
harmonize the findings of other physicists (most notably, Max Planck and Albert Einstein),
Bohr suggested that each electron had a certain, specific amount of energy, and that their orbits
were quantized such that each may occupy certain places around the nucleus, as marbles
fixed in circular tracks around the nucleus rather than the free-ranging satellites each were
formerly imagined to be. In deference to the laws of electromagnetics and accelerating
charges, Bohr alluded to these “orbits” as stationary states to escape the implication that
they were in motion.
Although Bohr’s ambitious attempt at re-framing the structure of the atom in terms that
agreed closer to experimental results was a milestone in physics, it was not complete. His
mathematical analysis produced better predictions of experimental events than analyses belonging
to previous models, but there were still some unanswered questions about why electtrons should behave in such strange ways. The assertion that electrons existed in stationary,
quantized states around the nucleus accounted for experimental data better than Rutherford’s
model, but he had no idea what would force electrons to manifest those particular states. The
answer to that question had to come from another physicist, Louis de Broglie, about a decade
later.
De Broglie proposed that electrons, as photons (particles of light) manifested both particlelike
and wave-like properties. Building on this proposal, he suggested that an analysis of
orbiting electrons from a wave perspective rather than a particle perspective might make more
sense of their quantized nature. Indeed, another breakthrough in understanding was reached The atom according to de Broglie consisted of electrons existing as standing waves, a phenomenon
well known to physicists in a variety of forms. As the plucked string of a musical
instrument vibrating at a resonant frequency, with “nodes” and “antinodes” at stable
positions along its length. De Broglie envisioned electrons around atoms standing as waves
bent around a circle.Electrons only could exist in certain, definite “orbits” around the nucleus because those
were the only distances where the wave ends would match. In any other radius, the wave should destructively interfere with itself and thus cease to exist.
De Broglie’s hypothesis gave both mathematical support and a convenient physical analogy
to account for the quantized states of electrons within an atom, but his atomic model was still
incomplete. Within a few years, though, physicistsWerner Heisenberg and Erwin Schrodinger,
working independently of each other, built upon de Broglie’s concept of a matter-wave duality
to create more mathematically rigorous models of subatomic particles.
This theoretical advance from de Broglie’s primitive standing wave model to Heisenberg’s
matrix and Schrodinger’s differential equation models was given the name quantum mechanics,
and it introduced a rather shocking characteristic to the world of subatomic particles: the
trait of probability, or uncertainty. According to the new quantum theory, it was impossible
to determine the exact position and exact momentum of a particle at the same time. The
popular explanation of this “uncertainty principle” was that it was a measurement error (i.e.
by attempting to precisely measure the position of an electron, you interfere with its momentum
and thus cannot know what it was before the position measurement was taken, and vice
versa). The startling implication of quantum mechanics is that particles do not actually have
precise positions and momenta, but rather balance the two quantities in a such way that their
combined uncertainties never diminish below a certain minimum value.
This form of “uncertainty” relationship exists in areas other than quantum mechanics. As
discussed in the “Mixed-Frequency AC Signals” chapter in volume II of this book series, there
is a mutually exclusive relationship between the certainty of a waveform’s time-domain data
and its frequency-domain data. In simple terms, the more precisely we know its constituent
frequency(ies), the less precisely we know its amplitude in time, and vice versa.
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