Monday, January 13, 2014

KP Fundamentals

Overview of Kelvin Probe Method
  • Background
    • Kelvin method invented by Lord Kelvin over a century ago
  • Work Function - energy required to remove an electron from material 
    • indicates surface conditions such as
      • absorbed, evaporated layers, surface reconstruction, surface charging, oxide layer imperfections, surface and bulk recombinations
  • Use a reference surface to study a sample electrode
  • the two are conductors that form a parallel plate capacitor at the tip
  • Capacitance - C = ε A/D
    • ε is the permittivity of the material in between plates, A is area connected as capacitor, D is distance between two conductors
  • C = Q/V
    • C is capacitance, Q is charge, v is voltage
  • Q = V ε A / D
    • As long as it is possible to determine voltage difference charge can be calculated, ε = permittivity of free-space if instrument is in vacuum
    • Null method - apply external voltage V1 to probe. If V1 is equal to Voltage on probe then V is 0, so no current is flowing to or from the probe

  • Current Nullification method
    • Probe is vibrated in sinusoid and is perpendicular to the surface
    • Distance between plates D = D0 + D1sin(ωt)
    • D1 is the amplitude of oscillation
  • Find new capacitance
    • C = ε A/[D0 + D1sin(ωt)]
  • Find Current generated
    • I = V dC/dt
    • I = V d (ε A/[D0 + D1sin(ωt)]) /dt
    • I = V ε A [D1ωsin(ωt)]/[D0 + D1sin(ωt)]2
    • Then we nullify this current by bringing Voltage to 0

  • This is the solution to noise difficulties that come from null field method
  • Distance D is maintained due to parallel movement of probe
    • Capacitance remains constant as permittivity and area doesn’t change
    • Therefore we are looking for the variations in surface potential/charge
    • Current I is generated I = (dV/dt) C
  • Drawbacks
    • This results in an averaged potential measurement
    • Given some potential function, the instrument will measure the enclosed charge averaged over the size of the measuring tip
  • Resultant Error
    • If diameter of measured potential > diameter of tip error results = 2 times the size of the tip
    • If diameter of measured potential = diameter of tip error results = 2 times the size of the measured potential
    • If diameter of measured potential < diameter of tip error results = 2 times the size of the measured potential
  • To get accurate measurements the probe must be both close to the surface and small in comparison to measured charge to minimize edge effects

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