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Unformatted text preview: II. Diodes We start our study of nonlinear circuit elements. These elements (diodes and transistors) are made of semiconductors. A brief description of how semiconductor devices work is first given to understand their i − v characteristics. You will see a rigorous analysis of semiconductors in the breadth courses. 2.1 Energy Bands in Solids In every atom, the nucleus (positively charged) is surrounded by a cloud of electrons. Initially scientists envisioned the atomic structure to be similar to the solar system: the nucleus in the center (similar to the sun), electrons revolving on orbits around the nucleus (similar to planets), and the electric attraction force between the nucleus and electrons being similar to the gravitational force between the sun and planets. However, according to Maxwell’s equations, electrons that revolve around a nucleus should emit electromagnetic radiation. As such, the electrons should lose energy gradually and their orbit should decay (in a fraction of a second!). This means that there is a mechanism that would not allow the electrons to lose energy gradually and is one of main reasons that the quantum theory was developed. According to quantum theory, electrons revolving around an atom can have only discrete levels of energy as is shown below. Electrons are not allowed to gradually lose or gain energy. They can only “jump” from one level to another (by absorbing or emitting a quanta of energy, usually a photon). Furthermore, there are only a finite number of electrons that are allowed in each state (Pauli’s Principle). Therefore, both the energy levels for electrons and the number of electrons at each energy level are specified. Because any system would tend to be in a minimum energy state, electrons in an atom start by “filing” the lowest energy level. Once all allowable slots is filled, electrons start filling the next energy level and so on. Therefore, the electronic structure include “filled” energy levels (all slots are taken by electrons), “empty” energy levels (positions are available but no electron is present), and “partially filled” levels (there are some electrons but there is also room for more electrons). Isolated Atoms A Solid ECE65 Lecture Notes (F. Najmabadi), Fall 2009 24 When atoms are arranged in a solid, the inter-spacing between atoms can become comparable to the size of electron orbitals of each atom (electrons at each energy level are confined to a region in space called the orbital and the higher energy levels have larger orbital sizes). In this case, the outer orbitals merged into energy bands. Electrons in these bands are not tied to an atom, rather they are free to move around the solid (if space is available per Pauli’s Principle). In addition, instead of discrete energy levels, these “shared” electrons can have continuous values of energy within a “band” of energy. As before, there are range of energies that no electron can occupy. These range of energies are called “Forbidden Gaps.” (see thethat no electron can occupy....
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- Spring '08
- Transistor, Diode Circuits, F. Najmabadi