Kelvin Probe Force Microscope - Working Principle

Working Principle

The Kelvin probe force microscope or Kelvin force microscope (KFM) is based on an AFM set-up and the determination of the work function is based on the measurement of the electrostatic forces between the small AFM tip and the sample. The conducting tip and the sample are characterized by (in general) different work functions, which represent the difference between the Fermi level and the vacuum level for each material. If both elements were brought in contact, a net electric current would flow between them until the Fermi levels were aligned. The difference between the work functions is called the contact potential difference and is denoted generally with V_CPD. An electrostatic force exists between tip and sample, because of the electric field between them. For the measurement a voltage is applied between tip and sample, consisting of a DC-bias V_DC and an AC-voltage V_AC sin(ωt) of frequency ω.

Tuning the AC-frequency to the resonant frequency of the AFM cantilever results in an improved sensitivity. The electrostatic force in a capacitor may be found by differentiating the energy function with respect to the separation of the elements and can be written as

where C is the capacitance, z is the separation, and V is the voltage, each between tip and surface. Substituting the previous formula for voltage (V) shows that the electrostatic force can be split up into three contributions, as the total electrostatic force F acting on the tip then has spectral components at the frequencies ω and 2ω.

The DC component, F_DC, contributes to the topographical signal, the term F_ω at the characteristic frequency ω is used to measure the contact potential and the contribution F_2ω can be used for capacitance microscopy.

or contact potential measurements a lock-in amplifier is used to detect the cantilever oscillation at ω. During the scan V_DC will be adjusted so that the electrostatic forces between the tip and the sample become zero and thus the response at the frequency ω becomes zero. Since the electrostatic force at ω depends on V_DC − V_CPD, the value of V_DC that minimizes the ω-term corresponds to the contact potential. Absolute values of the sample work function can be obtained if the tip is first calibrated against a reference sample of known work function. Apart from this, one can use the normal topographic scan methods at the resonance frequency ω independently of the above. Thus, in one scan, the topography and the contact potential of the sample are determined simultaneously.