Physical Models of Semiconductor Quantum Devices

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The exercises are focussed on the theory and the basic understanding of the operation of special devices, as single-electron transistor, resonant tunneling diode, pn-diode, bipolar transistor, MOSFET, and laser. Numerical simulations of such devices are performed with an advanced simulation package Sentaurus-Synopsys. This enables to understand the physical effects by means of computer experiments. Further reading will be recommended in the lecture.


These quantum numbers for electrons are symbolized by the letter l. An older convention for subshell description used letters rather than numbers. The letters come from the words sharp , principal not to be confused with the principal quantum number, n , diffuse , and fundamental.

Magnetic Quantum Number: The magnetic quantum number for an electron classifies which orientation its subshell shape is pointed. These different orientations are called orbitals. Think of three dumbbells intersecting at the origin, each oriented along a different axis in a three-axis coordinate space. Valid numerical values for this quantum number consist of integers ranging from -l to l, and are symbolized as m l in atomic physics and l z in nuclear physics.

Lecture 7: Compound Semiconductor Materials Science (Becoming the Quantum Mechanic!)

Spin Quantum Number: Like the magnetic quantum number, this property of atomic electrons was discovered through experimentation. Spin quantum numbers are symbolized as m s in atomic physics and s z in nuclear physics.

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The physicist Wolfgang Pauli developed a principle explaining the ordering of electrons in an atom according to these quantum numbers. His principle, called the Pauli exclusion principle , states that no two electrons in the same atom may occupy the exact same quantum states.

That is, each electron in an atom has a unique set of quantum numbers. This limits the number of electrons that may occupy any given orbital, subshell, and shell. A common method of describing this organization is by listing the electrons according to their shells and subshells in a convention called spectroscopic notation. In this notation, the shell number is shown as an integer, the subshell as a letter s,p,d,f , and the total number of electrons in the subshell all orbitals, all spins as a superscript.

Thus, hydrogen, with its lone electron residing in the base level, is described as 1s 1. A helium atom has two protons in the nucleus, and this necessitates two electrons to balance the double-positive electric charge. Consider the next atom in the sequence of increasing atomic numbers, lithium:. If we examine the organization of the atom with a completely filled L shell, we will see how all combinations of subshells, orbitals, and spins are occupied by electrons:.

Often, when the spectroscopic notation is given for an atom, any shells that are completely filled are omitted, and the unfilled, or the highest-level filled shell, is denoted. For example, the element neon shown in the previous illustration , which has two completely filled shells, may be spectroscopically described simply as 2p 6 rather than 1s 2 2s 2 2p 6. Lithium, with its K shell completely filled and a solitary electron in the L shell, may be described simply as 2s 1 rather than 1s 2 2s 1. The omission of completely filled, lower-level shells is not just a notational convenience.

It also illustrates a basic principle of chemistry: that the chemical behavior of an element is primarily determined by its unfilled shells. Both hydrogen and lithium have a single electron in their outermost shells 1s 1 and 2s 1 , respectively , giving the two elements some similar properties. Both are highly reactive, and reactive in much the same way bonding to similar elements in similar modes.

Physical Models of Semiconductor Quantum Devices

It matters little that lithium has a completely filled K shell underneath its almost-vacant L shell: the unfilled L shell is the shell that determines its chemical behavior. Elements having completely filled outer shells are classified as noble , and are distinguished by almost complete non-reactivity with other elements. These elements used to be classified as inert , when it was thought that these were completely unreactive, but are now known to form compounds with other elements under specific conditions.

Since elements with identical electron configurations in their outermost shell s exhibit similar chemical properties, Dmitri Mendeleev organized the different elements in a table accordingly. Such a table is known as a periodic table of the elements , and modern tables follow this general form in. Dmitri Mendeleev, a Russian chemist, was the first to develop a periodic table of the elements. Although Mendeleev organized his table according to atomic mass rather than atomic number, and produced a table that was not quite as useful as modern periodic tables, his development stands as an excellent example of scientific proof.

Seeing the patterns of periodicity similar chemical properties according to atomic mass , Mendeleev hypothesized that all elements should fit into this ordered scheme. This is how science should work: hypotheses followed to their logical conclusions, and accepted, modified, or rejected as determined by the agreement of experimental data to those conclusions.

Any fool may formulate a hypothesis after-the-fact to explain existing experimental data, and many do. What sets a scientific hypothesis apart from post hoc speculation is the prediction of future experimental data yet uncollected, and the possibility of disproof as a result of that data.

Theory of Semiconductor Quantum Devices |

To boldly follow a hypothesis to its logical conclusion s and dare to predict the results of future experiments is not a dogmatic leap of faith, but rather a public test of that hypothesis, open to challenge from anyone able to produce contradictory data. Thus, if a hypothesis successfully predicts the results of repeated experiments, its falsehood is disproven. Quantum mechanics, first as a hypothesis and later as a theory, has proven to be extremely successful in predicting experimental results, hence the high degree of scientific confidence placed in it. Many scientists have reason to believe that it is an incomplete theory, though, as its predictions hold true more at micro physical scales than at macro scopic dimensions, but nevertheless it is a tremendously useful theory in explaining and predicting the interactions of particles and atoms.

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As you have already seen in this chapter, quantum physics is essential in describing and predicting many different phenomena. In the next section, we will see its significance in the electrical conductivity of solid substances, including semiconductors. Simply put, nothing in chemistry or solid-state physics makes sense within the popular theoretical framework of electrons existing as discrete chunks of matter, whirling around atomic nuclei like miniature satellites.

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Home Textbook Vol. Table of Contents. Feynman To say that the invention of semiconductor devices was a revolution would not be an exaggeration. Atom Many of us have seen diagrams of atoms that look something like Figure below. Rutherford atom: negative electrons orbit a small positive nucleus. Rutherford scattering: a beam of alpha particles is scattered by a thin gold foil.

BohrModel Bohr hydrogen atom with orbits drawn to scale only allows electrons to inhabit discrete orbitals. De Broglie Hypothesis De Broglie proposed that electrons, as photons particles of light manifested both particle-like and wave-like properties. Rent the eBook. FAQ Policy.

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