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Electrons and holes in semiconductors: intrinsic/extrinsic silicon, donors & acceptors, mass action

Electrons and holes are mobile charged particles in semiconductors that determine the operation of electrical components like MOS transistors, diodes, switches, capacitors, and integrated resistors. Mobile conduction electrons are free to move throughout the silicon crystal. Holes are voids in electron shells that behave like mobile, positively charged particles. If you remember acid-base chemistry of aqueous solutions from first-year chemistry, then by analogy it is easy to understand silicon doping and electron/hole concentrations. In pure water or intrinsic silicon, pairs of particles of opposite charge are generated by thermal energy and disappear by recombination. In water, H+ and OH- ions are created by splitting H2O molecules; in silicon, mobile electrons and holes are generated by elevation of electrons from the valence band to the conduction band. If you add a strong acid like hydrochloric acid to water, it completely dissociates into H+ and Cl- ions, thus greatly increasing the H+ ion concentration and decreasing OH-. Likewise, if you add arsenic to silicon, the arsenic atoms donate mobile electrons to the silicon crystal, greatly increasing them while decreasing the holes. Conversely, adding NaOH to water increases OH- and decreases H+, as adding boron to silicon increases holes and decreases mobile electrons. The law of mass action applies to both materials. In water, the product of the H+ and OH- concentrations, measured in moles per liter, is 10**-14. In silicon, the product of mobile electron and hole concentrations, measured in particles per cubic centimeters, is 10**20. This is at room temperature. At higher temperatures, more energy is available to generate charged particles and the equilibrium concentrations of mobile charges are higher; and conversely for lower temperatures. One important difference is that in water, both the positive and negative charges are mobile, whereas in silicon, only the generated holes or electrons are mobile; the dopant atoms are immobile. As a result, non-uniform doping profiles produce electric fields in silicon, even without any external voltage applied, due to diffusion of the mobile particles from regions of high to low concentration. The video shows the resistance in ohms of a 1-cm cube of silicon between two opposite faces, which is numerically equivalent to the resistivity value of the material in ohm-cm. For mobile carriers to be created, electrons must have enough thermal energy at the prevailing temperature to escape from the covalent bond between adjacent silicon atoms. The energy band model explains the numbers of electrons and holes in intrinsic silicon and why donors and acceptor atoms are fully ionized at room temperature. For more about the energy band model: https://www.chu.berkeley.edu/wp-conte... Silicon unit cell:    • Silicon & diamond unit cell atomic mo...   CMOS inverter operation:    • CMOS Tech: NMOS and PMOS Transistors ...   (C) 2024 Gray Chang