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Engineering LibreTexts

2.4.4 Summary to: Conductors - Special Applications

  • Page ID
    2772
  • [ "article:topic", "Richardson equation" ]

    Thermionic emission provides electron beams. The electron beam current (density) is given by the Richardson equation:

    \[j=A\cdot T^2 \cdot \text{exp}\left(-\frac{E_A}{kT}\right)\]

    • Atheo = 120 A · cm–2 · K–2 for free electron gas model 
      Aexp  (20 - 160) A · cm–2 · K–2
    • EA = work function  (2 - >6) eV
    • Materials of choice: WLaB6 single crystal

    High field effects (tunneling, barrier lowering) allow large currents at low T from small (nm) size emitter

    Needs UHV!

    There are several thermoelectric effects for metal junctions; always encountered in non-equilibrium.

    Seebeck effect: 
    Thermovoltage develops if a metal A-metal B junction is at a temperature different form the "rest", i.e. if there is a temperature gradeient
    Essential for measuring (high) temperatures with a "thermoelement"
    Future use for efficient conversion of heat to electricity ???
    Peltier effect:
    Electrical current I through a metal - metal (or metal - semiconductor) junction induces a temperature gradient I, i.e. one of the junction may "cool down".
    Used for electrical cooling of (relatively small) devices. Only big effect if electrical heating ( I2) is small.