Type of atomic force microscopy
Photoconductive atomic force microscopy (PC-AFM) is a variant of atomic force microscopy that measures photoconductivity in addition to surface forces.
Background.
Multi-layer photovoltaic cells have gained popularity since mid 1980s. At the time, research was primarily focused on single-layer photovoltaic (PV) devices between two electrodes, in which PV properties rely heavily on the nature of the electrodes. In addition, single layer PV devices notoriously have a poor fill factor. This property is largely attributed to resistance that is characteristic of the organic layer. The fundamentals of pc-AFM are modifications to traditional AFM and focus on the use of pc-AFM in PV characterization. In pc-AFM the major modifications include: a second illumination laser, an inverted microscope and a neutral density filter. These components assist in the precise alignment of the illumination laser and the AFM tip within the sample. Such modifications must complement the existing principals and instrumental modules of pc-AFM so as to minimize the effect of mechanical noise and other interferences on the cantilever and sample.
The original exploration of the PV effect can be accredited to research published by Henri Becquerel in 1839. Becquerel noticed the generation of a photocurrent after illumination when he submerged platinum electrodes within an aqueous solution of either silver chloride or silver bromide. In the early 20th century, Pochettino and Volmer studied the first organic compound, anthracene, in which photoconductivity was observed. Anthracene was heavily studied due to its known crystal structure and its commercial availability in high-purity single anthracene crystals. The studies of photoconductive properties of organic dyes such as methylene blue were initiated only in the early 1960s owing to the discovery of the PV effect in these dyes. In further studies, it was determined that important biological molecules such as chlorophylls, carotenes, other porphyrins as well as structurally similar phthalocyanines also exhibited the PV effect. Although many different blends have been researched, the market is dominated by inorganic solar cells which are slightly more expensive than organic based solar cells. The commonly used inorganic based solar cells include crystalline, polycrystalline, and amorphous substrates such as silicon, gallium selenide, gallium arsenide, copper indium gallium selenide and cadmium telluride.
With the high demand of cheap, clean energy sources persistently increasing, organic photovoltaic (OPV) devices (organic solar cells), have been studied extensively to help in reducing the dependence on fossil fuel and containing the emission of green house gases (especially CO2, NOx, and SOx). This global demand for solar energy increased 54% in 2010, while the United States alone has installed more than 2.3 GW of solar energy sources in 2010. Some of the attributes which make OPVs such a promising candidate to solve this problem include their low-cost of production, throughput, ruggedness, and their chemically tunable electric properties along with significant reduction in the production of greenhouse gases. 
For decades, the researchers have believed that the maximum power conversion efficiency (PCE) would most likely remain below 0.1%. Only in 1979 Tang reported a two-layer, thin-film PV device, which ultimately yielded a power conversion efficiency of 1%. Tang's research was published in 1986, which allowed others to decipher many of the problems which limited the basic understanding of the process involved in the OPVs. In later years, the majority of the research focused on the composite blend of poly(3-hexylthiopehene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM). This, along with the research performed on fullerenes, dictated the majority of studies pertaining to OPV for many years. In more recent research, polymer-based bulk heterojunction solar cells, along with low band-gap donor-acceptor copolymers have been created for PCBM-based OPV devices. These low band-gap donor-acceptor copolymers are able to absorb a higher percentage of the solar spectrum as compared to other high efficiency polymers. These copolymers have been widely researched due to their ability to be tuned for specific optical and electrical properties.
To date, the best OPV devices have a maximum power conversion efficiency of approximately 8.13%. This low power conversion efficiency is directly related to discrepancies in the film morphology on the nano-scale level. Explanations of film morphology include recombination and/or trapping of charges, low open circuit voltages, heterogeneous interfaces, grain boundaries, and phase-separated domains. Many of these problems arise from the deficient knowledge of electro-optical properties on the nano-scale level. In numerous studies, it has been observed that heterogeneities in the electrical and optical properties influence device performance. These heterogeneities which occur in OPVs are a result the manufacturing process, such as annealing time, which is explained below. Research has mainly consisted of discovering exactly how this film morphology affects the device performance.
Until recently, microscopy methods used in the characterization of these OPVs consisted of atomic force microscopy (AFM), transmission electron microscopy (TEM) and scanning transmission X-ray microscopy (STXM). These methods are very useful in the identification of the local morphology on the film surface, but lack the ability to provide fundamental information regarding local photocurrent generation and ultimately on the device performance. To obtain information which links the electrical and optical properties, the use of electrical scanning probe microscopy (SPM) is an active area of research. Electrostatic force microscopy (EFM) and scanning Kelvin probe microscopy (SKPM) have been utilized in the studies of electron injection and charge trapping effects, while scanning tunneling microscopy (STM) and conductive atomic force microscopy (c-AFM) have been used to investigate electron transport properties within these organic semiconductors. 
Conductive AFM has been widely used in characterizing the local electric properties in both photovoltaic fullerene blends and organic films, but no reports have shown the use of c-AFM to display the distribution of photocurrents in organic thin films. The most recent variation of SPM devices include (tr-EFM) and photoconductive AFM (pc-AFM) . Both these techniques are capable of obtaining information regarding photo-induced charging rates with nano-scale resolution. The advantage of pc-AFM over tr-ERM is present in the maximum obtainable resolution by each method. pc-AFM can map photocurrent distributions with approximately 20 nm resolution, whereas tr-EFM was only able to obtain between 50 and 100 nm resolution at this time. Another important factor to note is although the tr-EFM is capable of characterizing thin films within organic solar cells, it is unable to provide the needed information regarding the capacitance gradient nor the surface potential of the thin film.
The origin of PC-AFM is due to the work performed by Gerd Binnig and Heinrich Rohrer on STM for which they were awarded the Nobel Prize in physics in 1986. They fabricated an instrument called scanning tunneling microscope (STM) and demonstrated that STM provides surface topography on the atomic scale. This microscopy technique yielded resolutions which were nearly equal to scanning electron microscopy (SEM).
Theory.
The fundamental principles of photoconductive atomic force microscopy (pc-AFM) are based on those of traditional atomic force microscopy (AFM) in that an ultrafine metallic tip scans the surface of a material to quantify topological features. 
The working premises for all types of AFM techniques are largely dependent on the fundamentals of the AFM cantilever, metallic tip, scanning piezo-tube and the feedback loop that transfers information from lasers that guide the motion of the probe across the surface of a sample. The ultra-fine dimensions of the tip and the way the tip scans the surface produces lateral resolutions of 500 nm or less. In AFM, the cantilever and tip functions as a mass on a spring. When a force acts on the spring (cantilever), the spring response is directly related to the magnitude of the force. "k" is defined as the force constant of the cantilever.
Hooke's law for cantilever motion:
formula_1
The forces acting on the tip are such that the spring (cantilever) remains soft but responds to the applied force, with a detectable resonant frequency, "fo". In Hooke's law, "k" is the spring constant of the cantilever and "mo" is defined as the mass acting on the cantilever: the mass of the cantilever itself and the mass of the tip. The relationship between "fo" and the spring constant is such that "k" must be very small in order to make the spring soft. Since "k" and "mo" are in a ratio, the value of "mo" must also decrease to increase the value of the ratio. Manipulating the values in this way provides the necessary high resonance frequency. A typical "mo" value has a magnitude of 10−10 kg and creates an "fo" of approximately 2 kHz.
Expression for resonant frequency of a spring:
formula_2
Several forces affect the behavior of the cantilever: attractive and repulsive Van der Waals forces, and electrostatic repulsion. Changes in these forces are monitored by a guide laser that is reflected off the back of the cantilever and detected by a photodetector. Attractive forces between the atoms on the sample surface and the atom at the AFM tip draw the cantilever tip closer to the surface. When the cantilever tip and the sample surface come within a range of a few angstroms repulsive forces come into play as a result of electrostatic interactions. There is also a force exerted from the cantilever pressing down on the tip. The magnitude of the force exerted by the cantilever is dependent upon the direction of its motion, whether it is attracted or repelled from the sample surface When the tip of the cantilever and the surface come into contact, the single atom at the point of the tip and the atoms on the surface exhibit a Lennard-Jones potential. The atoms exhibit attractive forces until a certain point and then experience repulsion from one another. The term "ro" is the separation at which the sum of the potentials between the two atoms is zero 
Force on AFM tip in terms of Lennard-Jones potential:
formula_3
Modifications of this early work have been implemented to perform AFM analysis on both conducting and non-conducting materials. Conductive atomic force microscopy (c-AFM) is one such modification technique. The c-AFM technique operates by measuring fluctuations in current from the biased tip and sample while simultaneously measuring changes in the topographical features. In all techniques of AFM, two modes of operation can be used: contact mode and non-contact mode. In c-AFM resonant contact mode is used to obtain topographical from current that is measured between the biased AFM tip and the sample surface. In this type of operation, the current is measured in the small space between the tip and the sample surface. This quantification is based on the relationship between the current traveling through the sample and layer thickness. In the previous equation, Aeff is the effective emission area at the injecting electrode, "q" is the electron charge, "h" is the Planck constant, "m"eff / "m"0 = 0.5, which is the effective mass of an electron in the conduction band of a sample, "d" is the sample thickness and "Φ" is the barrier height. The symbol, "β", the field enhancement factor, accounts for the non-planar, geometry of the tip used.
Relationship between conducting current and sample layer thickness:
formula_4
The accuracies of all AFM techniques rely heavily on a sample scanning tube, the piezo-tube. The piezo-tube scanner is responsible for the direction of tip displacement during a sample analysis, and is dependent on the mode of analysis. The piezo components are either arranged orthogonally or manufactured as a cylinder. In all techniques, sample topography is measured by the movement of the x and y piezos. When performing non-contact mode pc-AFM, the piezo-tube keeps the probe from moving in the x and y direction and measures the photocurrent between the sample surface and conducting tip in the z-direction. 
The principles of the piezo-tube is dependent upon how the piezo-electric material reacts with an applied voltage to either the interior or exterior of the tube. When voltage is applied to the two electrodes connected to the scanner, the tube will expand or contract causing motion to the AFM tip in the direction of this movement. This phenomenon is illustrated as the piezo-tube becomes displaced by an angle, θ. As the tube is displaced, the sample that, in traditional AFM is fixed to the tube generates lateral translation and rotation relative to the AFM tip, thus movement of the tip is generated in the x and y directions When voltage is applied of the inside of the tube, movement in the z-direction is implemented.
The relationship between the movement of the piezo-tube and the direction of the displacement of the AFM tip assumes that the tube is perfectly symmetric. When no voltage is applied