{"id":"energy-bands","level":"matter","name":"Energy bands and carriers","shortName":"Energy bands","role":"Explains how a semiconductor can be electrically controlled.","description":"A crystal offers ranges of allowed electron energies, called bands, separated by forbidden ranges. In silicon, the valence and conduction bands are separated by an energy gap. Supplying energy can create a mobile conduction electron and a corresponding hole in the valence band. The hole is a useful description of an absent electron in the many-electron solid, not a second kind of tiny positive atom. Band diagrams plot energy, sometimes against position; their vertical axis is not physical height. Gate fields and doping reshape the occupancy and alignment of these states. That connection lets materials physics become a voltage-controlled current in a transistor.","specs":[{"label":"Silicon band gap","value":"≈1.1 eV","context":"Near room temperature; varies with temperature."},{"label":"Carrier types","value":"Electrons and holes","context":"Collective semiconductor transport description."},{"label":"Diagram axis","value":"Energy","context":"Band separation is not a spatial distance."}],"interfaces":[{"name":"Temperature and fields","direction":"in","signal":"Energy and electrostatic potential"},{"name":"Carrier population","direction":"out","signal":"Available mobile charge"}],"tradeoff":"A gap enables an off state. Thermal excitation and unwanted leakage prevent ideal isolation.","whyAI":"AI hardware depends on distinct, reliable electrical states. Band engineering supports that distinction before any arithmetic exists.","related":["doping","pn-junction","channel"],"sources":[{"title":"MIT 3.091 — Band Diagrams, Semiconductors, and Doping","url":"https://ocw.mit.edu/courses/3-091-introduction-to-solid-state-chemistry-fall-2018/e1f4e9b940c67f4370ce007a939773c8_MIT3_091F18_REC12.pdf"},{"title":"MIT 3.23 — Semiconductor Statistics and Mass Action","url":"https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/ca2f26ca04b2ccb3eca0c83b73dfa00e_ps7.pdf"}],"scale":"Energy-space schematic; eV rather than meters","kind":"bands","mechanism":["Locate the occupied valence states and available conduction states on an energy diagram.","Add enough energy to create a conduction electron and corresponding valence-band hole.","Change fields or doping to alter state occupancy and transport conditions inside a device."],"misconception":"The gap between bands is an energy interval, not an empty physical layer sandwiched inside silicon.","check":{"question":"What is the vertical distance in an ordinary band diagram?","options":["A physical insulating gap","An electron flight distance","An energy difference"],"answer":2,"explanation":"Band diagrams organize allowed electronic energies. They do not depict bands as material shelves."},"branch":"Atomic foundations","subbranch":"Band structure","science":[{"title":"Thermal carrier generation","equation":"nᵢ = √(N_C N_V) exp[−E_g / (2k_B T)]","explanation":"N_C and N_V describe the effective state densities near the conduction and valence edges. A larger gap suppresses the equilibrium intrinsic carrier population, while higher temperature generally increases it.","assumptions":"Nondegenerate semiconductor in thermal equilibrium; material parameters and band gap can depend on temperature."}],"history":[],"learningObjective":"Distinguish a band gap from a carrier concentration.","engineeringExample":"At fixed temperature, the intrinsic carrier estimate changes exponentially with E_g/(2k_BT); a doped device then needs charge neutrality in addition.","evidenceNotes":"Band diagrams are equilibrium or local approximations and do not specify a transistor operating point.","visualFamily":"device-crosssection","prerequisites":["crystal-lattice"],"labId":"library","scope":"Use the switching investigation to connect physical charge, circuit load and arithmetic; the numerical library has no standalone model of this lesson’s full mechanism.","investigationId":"switching","labScope":"Use the switching investigation to connect physical charge, circuit load and arithmetic; the numerical library has no standalone model of this lesson’s full mechanism."}