Kelvin probe force microscopy (KPFM), also known as surface potential microscopy, is a noncontact variant of atomic force microscopy

Atomic force microscope

Atomic force microscopy or scanning force microscopy is a very high-resolution type of scanning probe microscopy, with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit...

 (AFM) that was invented in 1991. With KPFM, the work function

Work function

In solid-state physics, the work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface...

 of surfaces can be observed at atomic

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

 or molecular

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 scales. The work function relates to many surface phenomena, including catalytic activity

Catalysis

Catalysis is the change in rate of a chemical reaction due to the participation of a substance called a catalyst. Unlike other reagents that participate in the chemical reaction, a catalyst is not consumed by the reaction itself. A catalyst may participate in multiple chemical transformations....

, reconstruction of surfaces, doping and band-bending of semiconductor

Semiconductor

A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...

s, charge trapping in dielectric

Dielectric

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...

s and corrosion

Corrosion

Corrosion is the disintegration of an engineered material into its constituent atoms due to chemical reactions with its surroundings. In the most common use of the word, this means electrochemical oxidation of metals in reaction with an oxidant such as oxygen...

. The map of the work function produced by KPFM gives information about the composition and electronic state of the local structures on the surface of a solid.

KPFM is a scanning probe method where the potential

Electric potential

In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...

 offset between a probe tip and a surface can be measured using the same principle as a macroscopic Kelvin probe. The cantilever in the AFM is a reference electrode

Reference electrode

A reference electrode is an electrode which has a stable and well-known electrode potential. The high stability of the electrode potential is usually reached by employing a redox system with constant concentrations of each participants of the redox reaction.There are many ways reference...

 that forms a capacitor with the surface, over which it is scanned laterally at a constant separation. The cantilever is not piezoelectrically driven at its mechanical resonance

Resonance

In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

 frequency ω₀ as in normal AFM although an alternating current (AC) voltage is applied at this frequency.

When there is a direct-current (DC) potential difference between the tip and the surface, the AC+DC voltage offset will cause the cantilever to vibrate. The origin of the force can be understood by considering that the energy of the capacitor formed by the cantilever and the surface is


plus terms at DC. Only the cross-term proportional to the V_DC·V_AC product is at the resonance frequency ω₀. The resulting vibration of the cantilever is detected using usual scanned-probe microscopy methods (typically involving a diode laser and a four-quadrant detector). A null circuit is used to drive the DC potential of the tip to a value which minimizes the vibration. A map of this nulling DC potential versus the lateral position coordinate therefore produces an image of the work function of the surface.

A related technique, electrostatic force microscopy

Electrostatic force microscope

Electrostatic force microscopy is a type of dynamic non-contact atomic force microscopy where the electrostatic force is probed. . This force arises due to the attraction or repulsion of separated charges. It is a long-ranged force and can be detected 100 nm from the sample...

 (EFM), directly measures the force produced on a charged tip by the electric field emanating from the surface. EFM operates much like magnetic force microscopy

Magnetic force microscope

Magnetic force microscope is a variety of atomic force microscope, where a sharp magnetized tip scans a magnetic sample; the tip-sample magnetic interactions are detected and used to reconstruct the magnetic structure of the sample surface. Many kinds of magnetic interactions are measured by MFM,...

 in that the frequency shift or amplitude change of the cantilever oscillation is used to detect the electric field. However, EFM is much more sensitive to topographic artifacts than KFPM. Both EFM and KPFM require the use of conductive cantilevers, typically metal-coated silicon

Silicon

Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...

 or silicon nitride

Silicon nitride

Silicon nitride is a chemical compound of silicon and nitrogen. If powdered silicon is heated between 1300° and 1400°C in an atmosphere of nitrogen, trisilicon tetranitride, Si3N4, is formed. The silicon sample weight increases progressively due to the chemical combination of silicon and nitrogen...

.

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. When both elements are brought in contact, a net electric current will flow between them until the Fermi levels are aligned. The potential is called the contact potential (difference) denoted generally with . An electrostatic force between tip and sample builds up, resulting from the net charge transfer. 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(ω₂t) of frequency ω₀ at the second resonance frequency of the AFM cantilever


Tuning the AC-frequency to the second resonance frequency of the cantilever results in an improved sensitivity and allows the independent and simultaneous imaging of topography and the contact potential.
As a result of these biasing conditions, an oscillating electrostatic force appears, inducing an additional oscillation of the cantilever with the characteristic frequency ω₂. The general expression of such electrostatic force not considering coulomb forces due to charges can be written as


The electrostatic force can be split up into three contributions, as the total electrostatic force F acting on the tip has spectral components at the frequencies ω₂ and 2ω₂.


The DC component, F_DC, contributes to the topographical signal, the term
F_ω2 at the characteristic frequency ω₂ is used to measure the contact potential and the contribution F_2ω2 can be used for capacitance microscopy.




For contact potential measurements a lock-in amplifier

Lock-in amplifier

A lock-in amplifier is a type of amplifier that can extract a signal with a known carrier wave from an extremely noisy environment . It is essentially a homodyne with an extremely low pass filter...

is used to detect the cantilever oscillation at ω₂. 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 oscillation frequency ω₂ becomes zero and at the same time response at frequency 2ω₂ become maximum. Since the electrostatic force at ω₂ depends on V_DC - V_CPD, the value of V_DC which minimizes the ω₂-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.