Electrostatic force microscope
Encyclopedia
Electrostatic force microscopy (EFM) is a type of dynamic non-contact atomic force microscopy where the electrostatic force is probed. ("Dynamic" here means that the cantilever
is oscillating and does not make contact with the sample). This force arises due to the attraction or repulsion
of separated charge
s. It is a long-ranged force and can be detected 100 nm from the sample. For example, consider a conductive cantilever tip and sample which are separated a distance
usually by a vacuum. A bias voltage between tip and sample is applied by an external battery forming a capacitor, C, between the two. The capacitance of the system depends on the geometry of the tip and sample. The total energy stored in that capacitor is 
. The battery works to maintain a constant voltage, 
, between the capacitor plates (tip and sample). By definition, taking the negative gradient of the energy gives the force. The z component of the force (the force along the axis connecting the tip and sample) is thus:
.
The electrostatic force can be probed by changing the voltage, and that force is parabolic with respect to the voltage. One note to make is that
is not simply the voltage difference between the tip and sample. Since the tip and sample are often not the same material, and furthermore can be subject to trapped charges, debris, etc., there is a difference between the work function
s of the two. This difference, when expressed in terms of a voltage, is called the contact potential difference,
This causes the apex of the parabola to rest at 
. Typically, the value of 
is on the order of a few hundred millivolts. Forces as small as piconewtons can routinely be detected with this method.
With an electrostatic force microscope, like the atomic force microscope
it is based on, the sample can be immersed in liquid.
Cantilever
A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is resisted by moment and shear stress. Cantilever construction allows for overhanging structures without external bracing. Cantilevers can also be constructed with trusses or slabs.This is in...
is oscillating and does not make contact with the sample). This force arises due to the attraction or repulsion
Repulsion
Repulsion is a 1965 British psychological thriller film directed by Roman Polanski, based on a scenario by Gérard Brach and Roman Polanski. It was Polanski's first English language film, and was shot in Britain, as such being his second film made outside his native Poland. The cast includes...
of separated charge
Charge (physics)
In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers.-Formal definition:...
s. It is a long-ranged force and can be detected 100 nm from the sample. For example, consider a conductive cantilever tip and sample which are separated a distance
usually by a vacuum. A bias voltage between tip and sample is applied by an external battery forming a capacitor, C, between the two. The capacitance of the system depends on the geometry of the tip and sample. The total energy stored in that capacitor is . The battery works to maintain a constant voltage, , between the capacitor plates (tip and sample). By definition, taking the negative gradient of the energy gives the force. The z component of the force (the force along the axis connecting the tip and sample) is thus:.The electrostatic force can be probed by changing the voltage, and that force is parabolic with respect to the voltage. One note to make is that
is not simply the voltage difference between the tip and sample. Since the tip and sample are often not the same material, and furthermore can be subject to trapped charges, debris, etc., there is a difference between the work functionWork 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...
s of the two. This difference, when expressed in terms of a voltage, is called the contact potential difference,
This causes the apex of the parabola to rest at . Typically, the value of is on the order of a few hundred millivolts. Forces as small as piconewtons can routinely be detected with this method.With an electrostatic force microscope, like the atomic force microscope
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...
it is based on, the sample can be immersed in liquid.