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'''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.<ref name="tangten"/> At the time, research was primarily focused on single-layer [[Photovoltaic effect|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.

[[File:mypcafm.gif|thumb|right|upright=3.0|Animation representing sampling process of pc-AFM.]]

The original exploration of the PV effect can be accredited to research published by [[Henri Becquerel]] in 1839.<ref name="span">{{cite journal|author=H. Spanggaard, F.C. Krebs|journal= Solar Energy Materials & Solar Cells|doi=10.1016/j.solmat.2004.02.021 |year=2004|volume=83|page= 125|title=A brief history of the development of organic and polymeric photovoltaics|issue=2–3}}</ref> 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]].<ref name="AEB">{{cite journal|author=A. E. Becquerel|journal= Compt. Rend. Acad. Sci. |year=1839|volume= 9|page= 145}} {{cite journal|author=A.E. Becquerel|journal= Compt. Rend. Acad. Sci. |year=1839|volume=9|page=561}}</ref> In the early 20th century, Pochettino and Volmer studied the first organic compound, [[anthracene]], in which photoconductivity was observed.<ref name="span" /><ref name="poch">{{cite journal|author=A. Pochettino|journal= Acad. Lincei Rend. |year=1906|volume= 15|page= 355}}</ref><ref name="vol">{{cite journal|author=M. Volmer|journal=Ann. Physik |year=1913|volume=40|page= 755}}</ref> Anthracene was heavily studied due to its known crystal structure and its commercial availability in high-purity single anthracene crystals.<ref name="math">{{cite journal|author=A. M. Mathieson, J.M. Robertson, V.C. Sinclair|doi=10.1107/S0365110X50000641|journal= Acta. Crystallogr. |year=1950|volume= 3|page= 245|title=The crystal and molecular structure of anthracene. I. X-ray measurements|issue=4}}{{cite journal|author=V.C. Sinclair, J.M. Robertson, A.M. Mathieson|journal= Acta. Crystallogr. |year=1950|volume= 3|page= 251|doi=10.1107/S0365110X50000653|title=The crystal and molecular structure of anthracene. II. Structure investigation by the triple Fourier series method|issue=4}}</ref><ref name="sloan">{{cite journal|author=G.J. Sloan|journal=Mol. Cryst. |year=1966|volume= 1|page= 161}}{{cite journal|author=G.J. Sloan|journal= Mol. Cryst. |year=1967|volume= 1|page= 323}}{{cite journal|author=G.J. Sloan, J.M. Thomas, J.O. Williams|journal= Mol. Cryst. Liq. Cryst.|year= 1975|volume= 30|page= 167|doi=10.1080/15421407508082852|title=Basal Dislocations in Single Crystals of Anthracene }}</ref> 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.<ref name="bube">{{cite book|author=R.H. Bube|title= Photoconductivity of solids|publisher= Wiley|place= New York|year= 1960}}</ref><ref name="anth">{{cite journal|author= S. Anthoe|journal= Rom. Rep. Phys.|year=2002|volume=53|page= 427}}{{cite journal|author=G.A. Chamberlain|doi=10.1016/0379-6787(83)90039-X|journal=Sol. Cells|year= 1983|volume= 8|page= 47|title=Organic solar cells: A review}}</ref> In further studies, it was determined that important biological molecules such as [[chlorophylls]], [[carotenes]], other [[porphyrins]] as well as structurally similar [[phthalocyanine]]s also exhibited the PV effect.<ref name="span" /> Although many different blends have been researched, the market is dominated by inorganic [[solar cell]]s 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 CO<sub>2</sub>, NO<sub>x</sub>, and SO<sub>x</sub>). 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.<ref name="laird">{{cite web|author=L. Laird|title= Growth in Solar means Growth in Ohio|url=http://blog.energy.gov/blog/2010/10/06/growth-solar-means-growth-ohio|publisher= Energy.gov|year= 2010}}</ref> 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]].<ref name="ping">{{cite journal|author=L.S.C. Pingree, O.G. Reid, D.S. Ginger|doi=10.1002/adma.200801466|journal=Adv. Mater.|year=2010|volume=21 |issue=1|page= 19|title=Electrical Scanning Probe Microscopy on Active Organic Electronic Devices}}</ref> 
For decades, the researchers have believed that the maximum power conversion efficiency (PCE) would most likely remain below 0.1%.<ref name="span" /> Only in 1979 Tang reported a two-layer, [[thin-film]] PV device, which ultimately yielded a power conversion efficiency of 1%.<ref name="tangten">{{cite journal|author=Tang, C.W. |journal=Appl. Phys. Lett.|year= 1986|volume= 48|page=183|doi=10.1063/1.96937|title=Two-layer organic photovoltaic cell|issue=2|bibcode = 1986ApPhL..48..183T }}</ref> 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.<ref name="ping" /><ref name="xin">{{cite journal|author=H. Xin, O.G. Reid, G. Ren, F.S. Kim, D.S. Ginger, S.A. Jenekhe|journal= ASC Nano|year=2010|volume=4 |issue=4|pages=1861–1872}}</ref><ref name="bull">{{cite journal|author=T.A. Bull, L.S.C. Pingree, S.A. Jenekhe, D.S. Ginger, C.K. Luscombe|journal= ACS Nano|doi=10.1021/nn800878c|year=2010|volume=3|issue=3|pages= 627–636|title=The Role of Mesoscopic PCBM Crystallites in Solvent Vapor Annealed Copolymer Solar Cells|pmid=19228011}}</ref><ref name="hama">{{cite journal|author=B.H. Hamadani, S. Jung, P.M. Haney, L.J. Richter, N.B. Zhitenev|journal=Nano Lett.|year=2010|volume=10|page= 1611|doi=10.1021/nl9040516|title=Origin of Nanoscale Variations in Photoresponse of an Organic Solar Cell|issue=5|bibcode = 2010NanoL..10.1611H }}</ref><ref name="pingthree">{{cite journal|author=L.S.C. Pingree, O.G. Reid, D.S. Ginger|journal=Nano Lett.|year=2010|volume=9 |issue=8|page= 2946|doi=10.1021/nl901358v|title=Imaging the Evolution of Nanoscale Photocurrent Collection and Transport Networks during Annealing of Polythiophene/Fullerene Solar Cells|bibcode = 2009NanoL...9.2946P }}</ref><ref name="guide">{{cite journal|author=M. Guide, X.D. Dang, T.Q. Nguyen|journal=Adv. Mater. |year=2011|doi=10.1002/adma.201003644|title=Nanoscale Characterization of Tetrabenzoporphyrin and Fullerene-Based Solar Cells by Photoconductive Atomic Force Microscopy|pages=n/a–n/a}}</ref><ref name="coff">{{cite journal|author=D.C. Coffey, O.G. Reid, D.B. Rodovsky, G.P. Bartholomew, D.S. Ginger|journal=Nano Lett.|year=2007|volume=7 |issue=3|page= 738|doi=10.1021/nl062989e|title=Mapping Local Photocurrents in Polymer/Fullerene Solar Cells with Photoconductive Atomic Force Microscopy|bibcode = 2007NanoL...7..738C }}</ref> In more recent research, polymer-based bulk [[heterojunction]] solar cells, along with low [[Band gap|band-gap]] donor-acceptor copolymers have been created for PCBM-based OPV devices.<ref name="xin" /><ref name="bull" /> 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.<ref name="bull" /> These copolymers have been widely researched due to their ability to be tuned for specific optical and electrical properties.<ref name="bull" />
To date, the best OPV devices have a maximum power conversion efficiency of approximately 8.13%.<ref name="shar">{{cite journal|author=A. Sharma, G. Andersson, D.A. Lewis. |journal=Phys. Chem. Chem. Phys.|year=2011|volume= 13|page= 4381|doi=10.1039/C0CP02203A|title=Role of humidity on indium and tin migration in organic photovoltaic devices|issue=10 |bibcode = 2011PCCP...13.4381S }}</ref> 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.<ref name="bull" /><ref name="shah">{{cite journal|author=Shaheen, S. E.; Ginley, D. S.; Jabbour, G. E. |title=Organic-Based Photovoltaics: Toward Low-Cost Power Generation |url=http://www.calpoly.edu/~rechols/Phys422/MRS2005Intro.pdf|journal=MRS Bull.|year=2005|volume=30|page= 10}}</ref><ref name="hop">{{cite journal|author=Hoppe, H.; Sariciftci, N. S. |title=Organic Solar Cells: An Overview|url=http://www.lios.at/Publications/2004/2004-021.pdf |doi=10.1557/JMR.2004.0252 |journal=J. Mater. Res.|year=2004|volume=19|page= 1924|issue=7|bibcode = 2004JMatR..19.1924H }}</ref><ref name="hopp">{{cite journal|author=Hoppe, H.; Sariciftci, N. S. |title=Morphology of Polymer/Fullerene Bulk Heterojunction Solar Cells |doi= 10.1039/B510618B|year=2006|volume=16|page= 45|journal=Journal of Materials Chemistry}}</ref><ref name="corn">{{cite journal|doi=10.1002/1521-4095(200107)13:14<1053::AID-ADMA1053>3.0.CO;2-7|author=Cornil, D. Beljonne, J. P. Calbert, J. L. Bredas|journal=Adv. Mater.|year=2001|volume=13|page= 1053}}</ref><ref name="moons">{{cite journal|author=E. Moons|journal=J. Phys. Condens. Matter|year=2002|volume=14|page= 12235}}</ref><ref name="mayer">{{cite journal|author=A. C. Mayer, S. R. Scully, B. E. Hardin, M. W. Rowell, M. D. McGehee|journal= Mater. Today|doi=10.1016/S1369-7021(07)70276-6|year=2007|volume=10|page= 28|title=Polymer-based solar cells|issue=11}}</ref><ref name="jaq">{{cite journal|author=|journal=J. Phys. Chem. B|year=2007|volume=111|page= 7711|doi=10.1021/jp073626l|title=Time-Resolved Electric Force Microscopy of Charge Trapping in Polycrystalline Pentacene|last1=Jaquith|first1=Michael|last2=Muller|first2=Erik M.|last3=Marohn|first3=John A.|issue=27}}</ref> 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.<ref name="ping" /> 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 [[X-ray microscope|scanning transmission X-ray microscopy]] (STXM).<ref name="keme">{{cite journal|author=|journal=J. Phys. Chem. B|year=2004|volume=108|page= 18820|doi=10.1021/jp0464674|title=Three-Dimensional Inhomogeneities in PEDOT:PSS Films|last1=Kemerink|first1=M.|last2=Timpanaro|first2=S.|last3=De Kok|first3=M. M.|last4=Meulenkamp|first4=E. A.|last5=Touwslager|first5=F. J.|issue=49}}</ref> 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 force microscope|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.<ref name="poch" /><ref name="keme" /><ref name="nardes">{{cite journal|author=A. M. Nardes, M. Kemerink, R. A. J. Janssen, J. A. M. Bastiaansen, N. M. M. Kiggen, B. M. W. Langeveld, A. J. J. M. van Breemen, M. M. de Kok|journal=Adv. Mater.|doi=10.1002/adma.200602575|year=2007|volume=19|page= 1196|title=Microscopic Understanding of the Anisotropic Conductivity of PEDOT:PSS Thin Films|issue=9}}</ref><ref name="ion">{{cite journal|author=C. Ionescu-Zanetti, A. Mechler, S. A. Carter, R. Lal|journal=Adv. Mater.|year=2004|volume=16|page= 385|doi=10.1002/adma.200305747|title=Semiconductive Polymer Blends: Correlating Structure with Transport Properties at the Nanoscale|issue=5}}</ref><ref name="pingtwo">{{cite journal|author=L. S. C. Pingree, B. A. Macleod, D. S. Ginger|journal=J. Phys. Chem. C|year=2008|volume=112|page= 7922|doi=10.1021/jp711838h|title=The Changing Face of PEDOT:PSS Films: Substrate, Bias, and Processing Effects on Vertical Charge Transport|issue=21}}</ref><ref name="lin">{{cite journal|author=H.-N. Lin, H.-L. Lin, S.-S. Wang, L.-S. Yu, G.-Y. Perng, S.-A. Chen, S.-H. Chen|journal=Appl. Phys. Lett.|year=2002|volume=81|page= 2572|doi=10.1063/1.1509464|title=Nanoscale charge transport in an electroluminescent polymer investigated by conducting atomic force microscopy|issue=14|bibcode = 2002ApPhL..81.2572L }}</ref><ref name="leeone">{{cite journal|author=H. J. Lee, S. M. Park|journal=J. Phys. Chem. B|year=2004|volume=108|page= 1590|doi=10.1021/jp035766a|title=Electrochemistry of Conductive Polymers. 30. Nanoscale Measurements of Doping Distributions and Current−Voltage Characteristics of Electrochemically Deposited Polypyrrole Films|issue=5}}</ref><ref name="kdo">{{cite journal|author=K. D. O'Neil, B. Shaw, O. A. Semenikhin|journal=J. Phys. Chem. B|year=2007|volume=111|page= 9253|doi=10.1021/jp071564t|title=On the Origin of Mesoscopic Inhomogeneity of Conducting Polymers|issue=31}}</ref>	
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.<ref name="keme" /> The most recent variation of SPM devices include (tr-EFM) and photoconductive AFM (pc-AFM) .<ref name="keme" /> Both these techniques are capable of obtaining information regarding photo-induced charging rates with nano-scale resolution.<ref name="keme" /> 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&nbsp;nm resolution, whereas tr-EFM was only able to obtain between 50–100&nbsp;nm resolution at this time.<ref name="keme" /> 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.<ref name="giri">{{cite journal|author=R. Giridharagopal, G. Shao, C. Groves, D.S. Ginger. |title=New Scanning Probe Techniques for Analyzing Organic Photovoltaic Materials and Devices |publisher=Asylum Research Atomic Force Microscopes|year= 2010|url=http://www.asylumresearch.co.uk/Applications/Photovoltaics/Photovoltaics.shtml}}</ref>
[[File:Pcafmcoff.jpg|thumb|350 px|Chemical schematic of pc-AFM instrumentation (left) with local topography and photocurrent maps<ref name="coff"/>]]

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.<ref name="binn">{{cite journal|author=Binning, H. Rhorer, Ch. Gerber, E. Weibel|journal=Phys. Rev. Lett.|doi=10.1103/PhysRevLett.49.57|year=1982|volume= 49 |issue=1|pages= 57–60|title=Surface Studies by Scanning Tunneling Microscopy|bibcode=1982PhRvL..49...57B}}</ref> This microscopy technique yielded resolutions which were nearly equal to scanning electron microscopy (SEM).<ref name="binn" />

==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.<ref name="Skoog">{{cite book|author=Skoog, D.A., et al. |title=Principle of Instrumental Analysis|edition= 6|year=2007|pages=616–618}}</ref><ref name="Explorer">{{cite journal|author=Explorer Instrument Operation Maual Chapter 1 Scanning Probe Microscopy}}</ref><ref name="Atkins">{{cite book|author=Atkins, P., De Paula, J.|title=Atkins’ Physical Chemistry|isbn=0-19-954337-2|edition= 8}}</ref><ref name="Brugger">{{cite book|author=Brugger, J.|title= Nanotechnology for Engineers| chapter =1|page= 28}}</ref><ref name="Binning">{{cite journal|journal=Phys. Rev. Lett. |volume=56|issue= 9|year=1986|pages= 930–933|doi=10.1103/PhysRevLett.56.930|title=Atomic Force Microscope|last1=Binnig|first1=G.|last2=Quate|first2=C. F.|pmid=10033323|last3=Gerber|first3=C|bibcode=1986PhRvL..56..930B}}</ref><ref name="DePaula">{{cite book|author=Atkins, P, DePaula, J.|isbn=1-4292-1813-4 |title=Elements of Physical Chemistry|edition=5|year=2009}}</ref>	
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&nbsp;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.<ref name="Explorer" /><ref name="Atkins" /> ''k'' is defined as the force constant of the cantilever.

<center>'''[[Hooke's law]] for cantilever motion:'''<ref name="Explorer" /><ref name="Atkins" /></center>

<center><math> f = - kd </math></center>

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, ''f<sub>o</sub>''. In Hooke's law, ''k'' is the spring constant of the cantilever and ''m<sub>o</sub>'' is defined as the mass acting on the cantilever: the mass of the cantilever itself and the mass of the tip. The relationship between ''f<sub>o</sub>'' and the spring constant is such that ''k'' must be very small in order to make the spring soft. Since ''k'' and ''m<sub>o</sub>'' are in a ratio, the value of ''m<sub>o</sub>'' must also decrease to increase the value of the ratio. Manipulating the values in this way provides the necessary high resonance frequency. A typical ''m<sub>o</sub>'' value has a magnitude of 10<sup>−10</sup> kg and creates an ''f<sub>o</sub>'' of approximately 2&nbsp;kHz.<ref name="Binning" />

<center>'''Expression for [[resonant frequency]] of a spring:'''</center>

<center><math>f_o = \frac{1}{2\pi }\sqrt{\frac{k}{m_o}}</math></center>

Several forces affect the behavior of the [[cantilever]]: attractive and repulsive [[Van der Waals forces]], and [[electrostatic repulsion]].<ref name="Atkins" /> Changes in these forces are monitored by a guide laser that is reflected off the back of the cantilever and detected by a [[photodetector]].<ref name="Skoog" /><ref name="Explorer" /> Attractive forces between the atoms on the sample surface and the atom at the AFM tip draw the cantilever tip closer to the surface.<ref name="coff"/> 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]].<ref name="Atkins" /><ref name="DePaula" /> 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<ref name="Atkins" /> 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 ''r<sub>o</sub>'' is the separation at which the sum of the potentials between the two atoms is zero <ref name="Atkins" /><ref name="DePaula" /> 

<center>'''Force on AFM tip in terms of [[Lennard-Jones potential]]''':<ref name="Atkins" /><ref name="DePaula" /></center> 

<center><math>f={\operatorname{-d}V\over\operatorname{d}r}={24\varepsilon_o\over r_o}\left[{2}{r_o\over r}^{12}-{r_o\over r}^{6}\right]</math></center>

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.<ref name="ping" /> In all techniques of AFM, two modes of operation can be used: contact mode and non-contact mode.<ref name="Skoog" /> 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.<ref name="ping" /> In this type of operation, the current is measured in the small space between the tip and the sample surface.<ref name="ping" /> This quantification is based on the relationship between the current traveling through the sample and layer thickness.<ref name="Olbrich">{{cite journal|author=Olbrich, A. et al.|journal=Appl.Phys. Lett.|volume= 73|year= 1998 |pages=3114–3116|doi=10.1063/1.122690|title=Conducting atomic force microscopy for nanoscale electrical characterization of thin SiO[sub 2]|issue=21 |bibcode = 1998ApPhL..73.3114O }}</ref> In the previous equation, A<sub>eff</sub> is the effective emission area at the injecting electrode, q is the electron charge, h is planck’s constant, ''m<sub>eff</sub>'' / ''m<sub>0</sub>'' =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.<ref name="Olbrich" /> The symbol, ''β'', the field enhancement factor, accounts for the non-planar, geometry of the tip used.<ref name="Olbrich" /> 

<center>'''Relationship between conducting current and sample layer thickness:'''<ref name="Olbrich" /></center>

<center><math> I=A_{eff}\left( \frac{q^2 m_o}{8\pi h m_{eff}} \right )\left ( \frac{1}{t\left ( E^2 \right )} \right )\left ( \frac{\beta^2 V^2 }{\phi d^2} \right )e^\left (\left ( \frac{\left ( 8\pi \right )\left ( 2m_{eff}q \right )^\frac{1}{2}}{\left ( 3h \right )} \right )\left ( \nu \left ( E \right ) \right )\left ( \frac{d}{\beta V } \right )\left ( \phi^\frac{1}{3} \right ) \right ) </math></center>

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.<ref name="Skoog" /><ref name="Explorer" /> 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.<ref name="Skoog" /><ref name="Explorer" /> 
[[File:Afmfig3.jpg|thumb|Sample scanning piezo-tube in AFM<ref name="Xiao">{{cite journal|author=Xiaojun, T. ''et al.'' |journal=Ultramicroscopy |volume=105|year=2005|pages=336–342|doi=10.1016/j.ultramic.2005.06.046|title=System errors quantitative analysis of sample-scanning AFM }}</ref>]] 
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<ref name="Xiao"/> 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.<ref name="Xiao" /> When no voltage is applied to the tube the z-axis bisects the tube, sample and sample stage symmetrically. When a voltage is applied to the exterior of the tube (x and y motion), the expansion of the tube can be understood as a circular arc. In this equation, the ''r'' term indicates the outside radius of the piezo-tube, ''R'' is the curvature radius of the tube with applied voltage, ''θ'' is the bend angle of the tube, ''L'' is the initial length of the tube and ''ΔL'' is the extension of the tube after the voltage is applied.<ref name="Xiao" /> The change in length of the piezo-tube, ''ΔL'', is expressed as the intensity of the electric field applied to the exterior of the tube, the voltage along the x-axis, U<sub>x</sub>, and the thickness of the wall of the tube.

<center>'''Expressions for bend geometry of piezo-tube:'''<ref name="Xiao" /></center>

<center><math>L-\Delta L = \left ( R-r \right )\Theta </math></center>

<center><math>L+\Delta L = \left ( R+r \right )\Theta </math></center>

<center>'''Length displacement in terms of exterior electric field:'''<ref name="Xiao" /></center>

<center><math>\Delta L = Ed_{31} = \left ( \frac{d_{31}L}{t} \right )U_x</math></center>

<center>'''Expression for tube displacement, ''θ'':'''<ref name="Xiao" /></center>

<center><math>\Theta = \frac{L}{R} = \left ( \frac{d_{31}L}{t_{r}} \right )U_x</math></center>

With the calculation of ''θ'', the displacement of the probe in the x and z directions can be calculated as:

<center>'''Expressions for probe displacement in the x- and z-directions:'''<ref name="Xiao" /></center> 

<center><math>dx = (R+\chi )\left ( 1-cos\Theta \right )+\left ( D_{ss} +D_{sp}\right )U_{x}</math></center>

<center><math>dz = \left ( \left ( R + \chi \right )sin\Theta - L \right )+\left ( D_{ss} + D_{sp} \right )\left ( cos\Theta -1 \right )</math></center>

Another fundamental concept of all AFM is the [[feedback loop]]. The feedback loop is particularly important in non-contact AFM techniques, particularly in pc-AFM. As previously mentioned, in non-contact mode the cantilever is stationary and the tip does not come into physical contact with the sample surface.<ref name="Skoog" /> The cantilever behaves as a spring and oscillates at its resonance frequency. Topological variance causes the spring-like oscillations of the cantilever to change amplitude and phase in order to prevent the tip from colliding with sample topographies.<ref name="Explorer" /> The non-contact feedback loop is used to control that changes in the oscillations of the cantilever.<ref name="Explorer" /> 
The application of AFM on non-conducting samples (c-AFM) has in recent years evolved into the modification used for analysis of morphologies on the local scale, particularly morphologies at heterojunctions of multilayered samples.<ref name="ping" /><ref name="coff"/><ref name="Dangone">{{cite web|author=Dang, X.D., Nguyen, T.Q.|title= Photoconductive AFM of Organic Solar Cells|work= Asylum Research Atomic Force Microscopes. 2010 |url=http://www.asylumresearch.com/Applications/PhotoconductiveAFM/PhotoconductiveAFM.shtml}}</ref><ref name="Sakaguchi">{{cite journal|author=Sakaguchi, H. ''et al.'' |journal=Jpn. J. Appl. Phys.|volume=38|doi=10.1143/JJAP.38.3908 |year=1999|pages= 3908–3911|title=Nanometer-Scale Photoelectric Property of Organic Thin Films Investigated by a Photoconductive Atomic Force Microscope|bibcode = 1999JaJAP..38.3908S }}</ref><ref name="grovestwo">{{cite journal|author=Groves, C. ''et al.'' |journal=Accounts of Chemical Research|volume= 43|issue= 5|year=2010|pages=612–620|doi=10.1021/ar900231q|pmid=20143815|title=Heterogeneity in polymer solar cells: local morphology and performance in organic photovoltaics studied with scanning probe microscopy}}</ref> Photoconductive atomic force microscopy (pc-AFM) is particularly prevalent in the development of organic photovoltaic devices (OPV).<ref name="ping" /><ref name="Sakaguchi" /><ref name="grovestwo" /> The fundamental modification of c-AFM to pc-AFM is the addition of an illumination source and an inverted microscope that focuses the laser to a nanometer-scale point directly underneath the conductive AFM tip.<ref name="coff" /><ref name="Dangone" /> The main concept of the illumination laser point is that it must be small enough to fit within the confines of ultra-thin films. These characteristics are achieved by using a monochromatic light source and a laser filter.<ref name="coff" /><ref name="Dangone" /> In the OPV application, applying the illumination laser to the confines of ultra-thin films is further assisted by the recent development of the bulk heterojunction (BHJ) mixture of electron donating and accepting material in the film.<ref name="grovestwo" />
The combination of the conductive tip and illumination laser provides photocurrent images with vertical resolutions in the range of 0 to 10 pA when overlaid with the topographical data obtained.<ref name="coff" /><ref name="Dangone" /><ref name="dant">{{cite journal|author=Dante, M., Peet, J., Nguyen, T.Q.|journal= J. Phys. Chem. C|year=2008|volume=112|pages= 7241–7249|doi=10.1021/jp712086q|title=Nanoscale Charge Transport and Internal Structure of Bulk Heterojunction Conjugated Polymer/Fullerene Solar Cells by Scanning Probe Microscopy|issue=18}}</ref> Also unique to this modification are the spectra data gathered by comparing the current between the tip and sample to a variety of parameters including: laser wavelength, applied voltage and light intensity.<ref name="Dangone" /> The pc-AFM technique was also reported to detect local surface oxidation at a vertical resolution of 80&nbsp;nm.<ref name="Olbrich" />
[[File:Photocurone.jpg|thumb|left|Photocurrent resolutions compared with a traditional topographical image. Reproduction granted by The American Chemical Society. License Number: 2656610690457<ref name="coff" />]]

==Instrumentation==
The instrumentation involved for pc-AFM is very similar to that necessary for traditional AFM or the modified conductive AFM. The main difference between pc-AFM and other types of AFM instruments is the illumination source that is focused through the inverted [[microscope objective]] and the [[neutral density filter]] that is positioned adjacent to the illumination source.<ref name="ping" /><ref name="coff" /><ref name="Dangone" /><ref name="dant" /> The technical parameters of pc-AFM are identical to those of traditional AFM techniques.<ref name="ping" /><ref name="coff" /><ref name="Skoog" /><ref name="Dangone" /><ref name="dant" /> This section will focus on the instrumentation necessary for AFM and then detail the requirements for pc-AFM modification. 
The main instrumental components to all AFM techniques are the conductive AFM cantilever and tip, the modified [[piezo]] components and the sample substrate.<ref name="Skoog" /><ref name="geisse">Geisse, N. AFM and combined optical techniques. Application Note 12 Asylum research</ref> The components for photoconductive modification include: the illumination source (532&nbsp;nm laser), filter and inverted microscope. When modifying traditional AFM for pc application, all components must be combined such that they do not interfere with one another and so that various sources of noise and mechanical interference do not disrupt the optical components.<ref name="geisse" />
[[File:Afmfig6.jpg|thumb|Schematic of AFM sample analysis components. Reproduction granted by The American Chemical Society. License Number: 265674124703<ref name="coff" />]] 
In traditional instrumentation, the stage is a cylindrical piezo-tube scanner that minimizes the effect of [[Noise (electronics)|mechanical noise]].<ref name="geisse" /><ref name="park">{{cite web|author=Park Systems Inc. |title=Development of Crosstalk Eliminated (XE) Atomic Force Microscopy|url=http://www.parkafm.com/AFM_technology/technology.php|year=2008}}</ref> Most cylindrical piezos are between 12 and 24&nbsp;mm in length and 6 and 12&nbsp;mm in diameter.<ref name="mayer" /> The exterior of the piezo-tube is coated with a thin layer of conducting metal so that this region can sustain an [[electric field]].<ref name="mayer" /> The interior of the cylinder is divided into four regions (x and y regions) by non-conducting metallic strips.<ref name="Skoog" /><ref name="park" /> Electrical leads are fixed to one end and the exterior wall of the cylinder so that a current can be applied. When a voltage is applied to the exterior, the cylinder expands in x and y direction. Voltage along the interior of the tube causes cylinder expansion in the z-direction and thus movement of the tip in the z-direction.<ref name="Skoog" /><ref name="geisse" /><ref name="park" /> The placement of the piezo tube is dependent upon the type of AFM performed and the mode of analysis. However the z-piezo must always be fixed above the tip and cantilever to control the z-motion.<ref name="Explorer" /> This configuration is most often seen in the c-AFM and pc-AFM modifications to make room for additional instrumental components which are placed below the scanning stage.<ref name="geisse" /> This is particularly true for pc-AFM, which must have the piezo-components arranged above the cantilever and tip so that the illumination laser can transmit through the sample.

{{Clarify|date=June 2011}}with applied voltage<ref name="sun">{{cite journal|author=Sun, Q. ''et al.'' |journal=Rev. Sci. Instrum.|volume= 77|page= 13701|doi=10.1063/1.2162455|year=2006|title=Noninvasive determination of optical lever sensitivity in atomic force microscopy|bibcode = 2006RScI...77a3701H }}</ref>

In some configurations, the piezo components can be arranged in a tripod design. In this type of set-up, the x, y and z components are arranged orthogonally to one another with their apex attached to a movable pivot point.<ref name="Explorer" /> Similar to the cylindrical piezo, in the tripod design the voltage is applied to the piezo corresponding to the appropriate direction of tip displacement.<ref name="Explorer" /> In this type of set-up the sample and substrate are mounted on top of the z-piezo component. When the x and y piezo components are in use, the orthogonal design causes them to push against the base of the z-piezo, causing the z-piezo to rotate about a fixed point.<ref name="Explorer" /> Applying voltage to the z-piezo causes the tube to move up and down on its pivot point.<ref name="Explorer" /> 
[[File:Afmpiezofig1.jpg|thumb|Diagram of the tripod piezo<ref name="mats">Materials Evaluation and Engineering Inc. Handbook of Analytical Methods For Materials. (2009)</ref>]]
The other essential components of AFM instrumentation include the AFM tip module, which includes: the AFM tip, the cantilever, and the guiding laser.<ref name="Skoog" />
When the piezo-tube is positioned above the cantilever and tip, the [[Laser|guiding laser]] is focused through the tube and onto a mirror that rests on tip of the cantilever.<ref name="mats"/> The guiding laser is reflected off of the mirror and detected by a photodetector. The laser senses when the forces acting on the tip change. The reflected laser beam from this phenomenon reaches the [[detector]].<ref name="Skoog" /><ref name="park" /> The output from this detector acts as a response to the changes in force and the cantilever adjusts the position of the tip, while keeping constant the force that acts on the tip.<ref name="Skoog" /><ref name="park" /><ref name="mats"/>

The instrumentation of conductive AFM (c-AFM) has evolved with the desire to measure local electrical properties of materials with high resolutions. The essential components are: the piezo-tube, the guide laser, the conducting tip, and cantilever. Although these components are identical to traditional AFM their configuration is tailored to measuring surface currents on the local scale. 
As mentioned previously, the piezo-tube can be placed either above or below the sample, depending on the application of the instrumentation. In the case of c-AFM, repulsive contact mode is the predominantly used to obtain electrical current images from the surface as the sample moves in the x and y direction. Placing the z-piezo above the cantilever allows for better control of the cantilever and tip during analysis.<ref name="Explorer" />
The material that comprises the conductive tip and cantilever can be customized for a particular application. Metal-coated cantilevers, gold wires, all-metal cantilevers and [[diamond]] cantilevers are used.<ref name="osh">{{cite journal|author=O’Shea, S.J. ''et al.'' |journal=Rev. Sci. Instrum.|issue= 3|year= 1995|pages= 2508–1512|doi=10.1063/1.1145649 |volume=66|title=Characterization of tips for conducting atomic force microscopy|bibcode = 1995RScI...66.2508O }}</ref> In many cases diamond is the preferred material for cantilever and/or tip because it is an extremely hard material that does not [[oxidize]] in ambient conditions.<ref name="osh" /> The main difference between the instrumentation of c-AFM and STM is that in c-AFM the bias voltage can be directly applied to the nanostructure (tip and substrate).<ref name="tank">{{cite journal|author=Tanaka, I. ''et al.'' |journal=Appl. Phys. Lett. |volume=74|issue= 6|year=1999|pages= 844–846|doi=10.1063/1.123402|title=Imaging and probing electronic properties of self-assembled InAs quantum dots by atomic force microscopy with conductive tip|bibcode = 1999ApPhL..74..844T }}</ref> In STM, on the other hand, the applied voltage must be supported within the vacuum tunneling gap between the STM probe and surface.<ref name="Skoog" /><ref name="tank" /> When the tip is in close contact with the sample surface the application of bias voltage to the tip creates a vacuum gap between the tip and the sample that enables the investigation of electron transport through nanostructures.<ref name="tank" />
[[File:Afmgold.jpg|thumb|Repulsive contact between the Au-plated conductive AFM tip and the sample<ref name="wold">{{cite journal|author=Wold, D.J. et al.|journal= J. Am. Chem. Soc.|year=2000|volume= 122|pages= 2970–2971|doi=10.1021/ja994468h|title=Formation of Metal−Molecule−Metal Tunnel Junctions:  Microcontacts to Alkanethiol Monolayers with a Conducting AFM Tip|issue=12}}</ref>]]
The main components and instrumentation of c-AFM instrumentation are identical to that required for a pc-AFM module. The only modifications are the illumination source, filter and inverted microscope objective that are located beneath the sample substrate. In fact, most pc-AFM instruments are simply modified from existing cp-AFM instrumentation. The first report of this instrumental modification came in 2008. In that paper, Lee and coworkers implemented the aforementioned modifications to examine the resolution of photocurrent imaging. Their design consisted of three main units: a conductive mirror plate, steering mirror and laser source.
The main difficulty with the previously existing c-AFM instrumentation is the inability of the technique for characterizing [[photonic]] devices.<ref name="lee">{{cite journal|author=Lee, J. et al. |journal=Ultramicroscopy|doi=10.1016/j.ultramic.2008.04.077 |volume=108 |year=2008|pages= 1090–1093|title=Construction of pcAFM module to measure photoconductance with a nano-scale spatial resolution|issue=10|pmid=18562107}}</ref> Specifically, it is difficult to measure changes in local and nano-scale electrical properties that result from the photonic effect.<ref name="lee" /> The optical illumination component (laser) was added to the c-AFM module in order to make such properties visible. Early in development, the main concerns regarding pc-AFM include: physical configuration, laser disturbance and laser alignment.<ref name="lee" /> Although many of these concerns have been resolved pc-AFM modules are still widely modified from c-AFM and traditional AFM instruments.

The first main concern deals with component configuration and whether or not there is physically enough space for modification in the cramped c-AFM module. The component configuration must be such the addition of the laser illumination component does not cause disturbance to other units.<ref name="lee" /><ref name="mad">{{cite journal|author=Madl, M. ''et al.'' |journal=Semicond. Sci. Technol. |volume=25 |year=2010|pages= 1–4}}</ref> Interaction between the illumination laser and the guiding laser was also a concern. First attempts to address these two issues was to place a prism between the sample tip and the surface such that the prism would allow the illumination laser to reflect at the interface between the prism and the laser and thus be focused to a localized spot on the sample surface.<ref name="Sakaguchi" /><ref name="lee" /> However, lack of space for the prism and the production of multiple light reflections when introducing a prism required a different concept for configuration.

The module constructed by Lee et al. implemented a tilted mirror plate that was positioned underneath the sample substrate. This conductive mirror was tilted at 45° and successfully reflected the illuminating laser to a focused spot directly underneath the conductive tip.<ref name="lee" /> The steering mirror was employed as a means of controlling the trajectory of the laser source, with this addition the position of the reflected beam on the sample could be easily adjusted for placement underneath the AFM tip.<ref name="lee" /> The illumination laser source was a diode-pumped solid-state laser system that produced a wavelength of 532&nbsp;nm and a spot of 1&nbsp;mm in the sample.
[[File:Pcafmassemb.jpg|thumb|pc-AFM module with conducting mirror]]
The addition of the mirror and laser underneath the sample substrate results in a higher scanning level due to raising the sample substrate. This configuration has no effect on any other instrument component and does not affect AFM performance.<ref name="lee" /> This result was confirmed by identical topographical images that were taken with and without the placement of the mirror and laser. This particular set-up required the separation of the x, y and z piezo-scanners The separation of piezo-tubes accounts for the elimination of x-z cross-coupling and scanning-size errors, which is common in traditional AFM.<ref name="lee" />

In addition there was no evidence of laser interferences between the guiding laser and the irradiation laser. The guiding laser, at a wavelength of 650&nbsp;nm, hits the mirror on the back of the conducting cantilever from vertical trajectory and is reflected away from the cantilever towards the position sensitive [[photodetector]] (PSPD).<ref name="lee" /> The illumination beam, on the other hand, travels from underneath the sample platform and is reflected into position by the reflecting mirror. The angle of the mirror plate ensures that the beam does not extend past the sample surface.<ref name="lee" />

The conductive AFM tip was easily aligned over the reflected illumination beam. The laser spot in the sample was reported to be 1mm in size and can be found using the AFM recording device.<ref name="lee" /> A convenience of this technique is that laser alignment is only necessary for imaging in the z-direction because the photocurrents are mapped in this direction.<ref name="lee" /> Therefore, normal AFM/c-AFM can be implemented for analysis in the x and y directions.
The instrumental module proposed by Lee et al. produced spot sizes from the illumination laser of 1&nbsp;mm in thicknesses. Recent applications have altered Lee’s design in order to decrease spot size while simultaneously increasing the intensity of this laser. Recent instrumentation has replaced the angled mirror with an inverted microscope and a neutral density filter.<ref name="ping" /><ref name="coff" /><ref name="Dangone" /><ref name="grovestwo" /><ref name="dant" /> In this device the x and y piezos, illumination laser and inverted microscopy are confined underneath the sample substrate, while the z-piezo remains above the conductive cantilever.<ref name="ping" /><ref name="coff" /><ref name="Dangone" /><ref name="grovestwo" /><ref name="dant" /><ref name="west">{{cite journal|author=Westenhoff, S. et al. |journal= J. Am. Chem. Soc. |volume=130|issue=41|page=13653|doi=10.1021/ja803054g|year=2008|title=Charge Recombination in Organic Photovoltaic Devices with High Open-Circuit Voltages|last2=Howard|first2=Ian A.|last3=Hodgkiss|first3=Justin M.|last4=Kirov|first4=Kiril R.|last5=Bronstein|first5=Hugo A.|last6=Williams|first6=Charlotte K.|last7=Greenham|first7=Neil C.|last8=Friend|first8=Richard H.}}</ref> In the applications of Ginger et al. a neutral-density filter is added to increase laser attenuation and the precision of laser alignment is enhanced by the addition of the inverted microscope. 

One of the most common pc-AFM setups incorporates a light source, which emits in the visible spectrum along with an [[indium tin oxide]] (ITO) semi-conductive layer (used as the bottom [[cathode]]).<ref name="span" /> The use of a gold plated silicon AFM probe is often used as the top anode in pc-AFM studies. This [[electrode]] which carries relatively small current within it, is able to generate nano-scale holes within the sample material to which the two electrodes are able to detect the relatively small change in conductance due to the flow from the top electrode to the bottom electrode.<ref name="Dangone" /> The combination of these elements produced laser intensities in the range of 10 to 108 W/m<sup>2</sup> and decreased the size of the laser spot to sub-micrometer dimensions making this technique useful for the application of nm thin OPV films.<ref name="ping" /><ref name="grovestwo" /><ref name="west" />
[[File:Pingreeafmpic.jpg|thumb|left|Representation of pc-AFM instrumentation and sample substrate<ref name="ping" />]]

==Applications==
Although there is significant insight as to how OPVs work, it is still difficult to relate the device’s functionality to local film structures.<ref name="keme" /> This difficulty may be attributed to the minimal current generation at a given point within OPVs.<ref name="ping" /> Through pc-AFM, OPV devices can be probed at nano-scale level and can help to increase our fundamental knowledge of mechanisms involved in OPVs at nano-scale level.<ref name="dant" /> pc-AFM is capable of gathering information such as the mapping of photocurrents, differences in film morphology, determination of donor-acceptor domains, current density-voltage plots, quantum efficiencies, and approximate charge carrier mobilities.<ref name="ping" /><ref name="pingthree" /><ref name="grovestwo" /><ref name="dant" /><ref name="dangthree">{{cite journal|author=X.-D. Dang, A.B. Tamayo, J. Seo, C.V. Hoven, B. Walker, T.-Q. Nguyen|journal=Adv. Func. Mater.|doi=10.1002/adfm.201000799|year=2010|volume=20|page= 3314|title=Nanostructure and Optoelectronic Characterization of Small Molecule Bulk Heterojunction Solar Cells by Photoconductive Atomic Force Microscopy|issue=19}}</ref><ref name="dantethree">{{cite journal|author=M. Dante, A. Garcia, T.-Q. Nguyen|journal= J. Phys. Chem. C|year=2010|volume=113|page= 1596|doi=10.1021/jp809650p|title=Three-Dimensional Nanoscale Organization of Highly Efficient Low Band-Gap Conjugated Polymer Bulk Heterojunction Solar Cells|issue=4}}</ref><ref name="hov">{{cite journal|author=C.V. Hoven, X.-D. Dang, R.C. Coffin, J. Peet, T.-Q. Nguyen, G.C. Bazan|doi=10.1002/adma.200903677|journal=Adv. Mater.|year=2010|volume=22|page= E63|title=Improved Performance of Polymer Bulk Heterojunction Solar Cells Through the Reduction of Phase Separation via Solvent Additives|issue=8}}</ref><ref name="dangfour">{{cite journal|author=X.-D. Dang, A. Mikhailovsky, T.-Q. Nguyen|journal=Appl. Phys. Lett.|doi=10.1063/1.3483613|year=2010|volume=97|page= 113303|title=Measurement of nanoscale external quantum efficiency of conjugated polymer:fullerene solar cells by photoconductive atomic force microscopy|issue=11|bibcode = 2010ApPhL..97k3303D }}</ref><ref name="ogr">{{cite journal|author=O.G. Reid, K Munechika, D.S. Ginger|journal=Nano Lett.|year=2008|volume=8|page= 1602|doi=10.1021/nl080155l|title=Space Charge Limited Current Measurements on Conjugated Polymer Films using Conductive Atomic Force Microscopy|issue=6|bibcode = 2008NanoL...8.1602R }}</ref><ref name="odou">{{cite journal|author=O. Douheret, L. Lutsen, A. Swinnen, M. Breselge, K. Vandewal, L. Goris, J. Manca|journal=Appl. Phys. Lett.|year=2006|volume=89|page= 032107|doi=10.1063/1.2227846|title=Nanoscale electrical characterization of organic photovoltaic blends by conductive atomic force microscopy|issue=3|bibcode = 2006ApPhL..89c2107D }}</ref> One of the other notable characteristics of pc-AFM is its ability to provide concurrent information regarding the topological and photocurrent properties of the device at nano-scale.<ref name="guide" /> Using this concurrent sampling method, the sample handling is minimized and can provide more accurate results. In a study by Pingree et al., pc-AFM was used to measure how spatial deviations in the photocurrent generation developed with different processing techniques.<ref name="pingthree" /> The authors were able to compare these photocurrent variations to the duration of the annealing process.<ref name="pingthree" /> They have concluded that lengthening the annealing time allows for improved nano-scale phase separation as well as created a more ordered device.<ref name="pingthree" /> Actual times for the annealing process vary depending on the properties of the polymers used.<ref name="pingthree" /> The authors have shown that external quantum efficiency (EQE) and power conversion efficiency (PCE) levels reach a maximum at certain annealing times whereas while the electron and hole mobility’s do not show the corresponding trends.<ref name="pingthree" /> Therefore, while lengthening the annealing time can increase the photocurrents within the OPV, there is a practical limit to after which the benefits may not be substantial.<ref name="pingthree" />

In more recent studies, pc-AFM has been employed to gather information regarding the photoactive regions from the use of [[quantum dots]].<ref name="madl">{{cite journal|author=M. Madl, W. Brezna, G. Strasser, P. Klang, A.M. Andrews, M.I. Bodnarchuk, M.V. Kovalenko, M. Yarema, W. Heiss, J. Smoliner|journal=Physica Status Solidi (c) |year=2011|volume= 8 |issue=2|page= 426}}</ref> Because if their relative ease of use, along with size-tunable excitation attributes, quantum dots have commonly been applied as sensitizers in [[optoelectronic]] devices.<ref name="madl" /> The authors have studied the photoresponse of sub-surface foundations such as buried [[indium arsenide]] (InAs) quantum dots through the implementation of pc-AFM.<ref name="madl" /> Through the use of pc-AFM, information regarding quantum dot size, as well as the dispersion of quantum dots within the device, can be recorded in a non-destructive manner.<ref name="madl" /> This information can then be used to display local variances in photoactivity relating to heterogeneities within the film morphology.<ref name="madl" />

==Sampling==
Sample preparation of the OPV is of the utmost importance when performing pc-AFM studies. The sampling substrate is recommended to be conductive, as well as transparent, to the light source which is irradiated upon it.<ref name="taub">{{cite web|author=M. Taub, B. Menzel, G. Khanna, E. Lilleodden|title= SPM Training Manual, Vers. 2.0|publisher= Laboratory for Advanced Materials, Stanford University|year=2003}}</ref> Numerous studies have used [[indium tin oxide|ITO]]-coated glass as their conductive substrate. Because of high cost of ITO, however, there have been attempts to utilize other semiconducting layers, such as [[zinc oxide]] (ZnO) and carbon nanotubes as an alternative to ITO.<ref name="hop" /><ref name="lee" /> Although these semiconductors are relatively inexpensive, high quality ITO layers are still being used extensively for PV applications. Poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate), more commonly known as [[PEDOT:PSS]], is a transparent, polymeric conductive layer which is usually placed between the ITO and the active OPV layer. The PEDOT:PSS is a conductive polymer is stable over various applied charges.<ref name="dam">{{cite book|author=D. Damjanovic|url=http://books.google.com/books?id=88W3fMqNkRwC&printsec=frontcover|isbn=012369431|title= The Science of Hysteresis|year=2006|volume=3|editors= I. Mayergoyz and G. Bertotti|publisher= Elsevier}}</ref> In most studies, PEDOT:PSS is spin-coated onto the ITO-coated glass substrates directly after plasma cleaning of the ITO.<ref name="taub" /> Plasma cleaning, as well as halo-acid etching, have been shown to improve the surface uniformity and conductivity of the substrate.<ref name="ping" /> This PEDOT:PSS layer is then annealed to the ITO prior to spin-coating the OPV layer onto the substrate. Studies by Pingree et al. have shown the direct correlation between annealing time and both peak and average photocurrent generation.<ref name="pingthree" /> Once this OPV film is spin-coated onto the substrate, it is then annealed at temperatures between 70 and 170 °C, for periods up to an hour depending on the procedure as well as OPV being used.<ref name="xin" /><ref name="bull" /><ref name="hama" /><ref name="pingthree" /><ref name="coff" /><ref name="shah" /><ref name="taub" /><ref name="dam" />

[[File:contactvsnon.jpg|thumb|Deviation of the laser spot on photo diode caused by changes in sample topography.]]

==An example of OPV fabrication==
A recently developed OPV system based on tetrabenzoporphryin (BP) and either [6,6]-phenyl-C<sub>61</sub>-butyric acid methyl ester (PCBM) is explained in detail as follows.<ref name="dam" /> In this study, the precursor to BP (1,4:8,11:15,18:22,25-tetraethano-29H,31H-tetrabenzo[b,g,l,q]porphyrin (CP) solution is applied as the starting film, and was thermally annealed which caused the CP to convert into BP.<ref name="dam" /> The BP:fullerene layer serves as the undoped layer within the device. For surface measurements, the undoped layer is rinsed with a few drops of chloroform and spin-dried until the BP network is exposed at the donor/acceptor interface.<ref name="dam" /> For bulk heterojunction characterization, an additional fullerene solution is spin-coated onto the undoped layer, a thin layer of lithium fluoride is then deposited followed by either an aluminum or gold cathode which is thermally annealed to the device.<ref name="xin" /><ref name="hama" /><ref name="shah" /><ref name="dam" /> The thin layer of lithium fluoride is deposited to help prevent the oxidation of the device.<ref name="angus">{{cite book|author=Macleod, H A|title= Thin-Film Optical Filters|edition= 3|isbn=1-4200-7302-8|place=London|publisher= Institute of Physics|year=2001}}</ref> Controlling the thickness of these layers plays a significant role in the generation of the efficiency of the PV cells. Typically, the thickness of the active layers is usually smaller than 100&nbsp;nm to produce photocurrents. This dependence on layer thickness is due to the probability that an electron is able to travel distances on the order of exciton diffusion length within the applied electric field. It should be noted that many of the organic semiconductors used in the PV devices are sensitive to water and oxygen.<ref name="ping" /> This is due to the likelihood of photo-oxidation which can occur when exposed to these conditions.<ref name="ping" /> While the top metal contact can prevent some of this, many studies are either performed in an inert atmosphere such as nitrogen, or under [[ultra-high vacuum]] (UHV).<ref name="ping" />

[[File:Tetrabenzoporphryin.png|thumb|left|Chemical structure of tetrabenzoporphryin (BP)]] 
[[File:CPmolecule.PNG|thumb|Chemical structure of (1,4:8,11:15,18:22,25-tetraethano-29H,31H-tetrabenzo[b,g,l,q]porphyrin (CP).]]
[[File:PCBM.png|thumb|Chemical structure of [[phenyl-C61-butyric acid methyl ester]] (PCBM)]]
Once the sample preparation is complete, the sample is placed onto the scanning stage of the pc-AFM module. This scanning stage is used for x-y piezo translation, completely independent of the z-direction while using a z-piezo scanner. The piezo-electric material within this scanner converts a change in the applied potential into mechanical motion which moves the samples with nanometer resolution and accuracy. There are two variations in which the z-piezo scanner functions; one is contact mode while the other is tapping mode. 

Many commercial AFM cantilever tips have pre-measured resonant frequencies and force constants which are provided to the customer. As sampling proceeds, the cantilever tip’s position changes, which causes the scanning laser wavelength (650&nbsp;nm) to deviate from its original position on the detector.<ref name="leeone" /><ref name="taub" /> The z-piezo scanner then recognizes this deviation and moves vertically to return the laser spot to its set position.<ref name="leeone" /> This vertical movement by the z-piezo scanner is correlated to a change in voltage.<ref name="leeone" /> Sampling in contact mode relies upon intermolecular forces between the tip and surface as depicted by [[Van der Waals force]]. As the sampling begins, the tip is moved close to the sample which creates a weakly attractive force between them. Another force which is often present in contact mode is capillary force due to hydration on the sample surface. This force is due to the ability of the water to contact the tip, thus creating an undesirable attractive force. [[Capillary force]], along with several other sources of tip contamination, are key factors in the decreased resolution observed while sampling

[[File:Afmtiptwo.jpg|thumb|left|Decreased resolution caused by rounding of the AFM tip.]]

There are considerations which need to be taken into account when determining which mode is optimal for sampling for a given application. It has been shown that sampling in contact mode with very soft samples can damage the sample and render it useless for further studies.<ref name="shah" /> Sampling in non-contact mode is less destructive to the sample, but the tip is more likely to drift out of contact with the surface and thus it may not record data.<ref name="leeone" /> Drifting of the tip is also seen due to piezo hysteresis, which causes displacement due to molecular friction and polarization effects due to the applied electric field.
It is important to note the correlation between resolution and curvature of tip radius. Early STM tips used by Binning and Rohrer were fairly large, anywhere between some hundred nm to 1&nbsp;µm in radius.<ref name="binn" /> In more recent work, the tip radius of curvature was mentioned as 10–40&nbsp;nm.<ref name="hama" /><ref name="pingthree" /><ref name="coff" /><ref name="taub" /> By reducing the radius of curvature of the tip, it allows for the enhanced detection of deviations within the OPVs surface morphology. Tips often need to be replaced due to tip rounding, which leads to a decrease in the resolution.<ref name="leeone" /> Tip rounding occurs due to the loss of outermost atoms present at the apex of the tip which can be a result of excessive force applied or character of the sample.<ref name="leeone" />

Because of the extremely small radius of the AFM tip, the illumination source is allowed to be focused tighter, thus increasing its efficiency. Typical arrangements for pc-AFM contain a low powered, 532&nbsp;nm laser (2–5&nbsp;mW) whose beam is reflected off mirrors located beneath the scanning stage.<ref name="ping" /><ref name="xin" /><ref name="bull" /><ref name="hama" /><ref name="pingthree" /><ref name="coff" /><ref name="shah" /> Through the use of a [[charge-coupled device]] (CCD), the tip can easily be positioned directly over the laser spot.<ref name="taub" /> [[Xenon arc lamp]]s have also been widely used as illumination sources, but are atypical in recent work.<ref name="guide" /> In a study by Coffey et al., lasers of two different wavelengths (532&nbsp;nm and 405&nbsp;nm) are irradiated onto the same sample area.<ref name="coff" /> With this work, they have shown images with identical contrast which proves that the photocurrent variations are less related to spatial absorbance variation.<ref name="coff" />

[[File:Photocurrent.jpg|thumb|The variation in the photocurrent from two different illumination sources.|Different illumination sources show nearly identical photocurrent maps<ref name="coff" />]] Most sampling procedures often begin by obtaining the [[dark current]] images of the sample. Dark current is referred to as the photocurrent generation created by the OPV in the absence of an illumination source. The cantilever and tip are simply rastered across the sample while topographic and current measurements are obtained. This data can then be used as a reference to determine the impact the illumination process exhibits on the OPV. Short circuit measurements are also commonly performed on the OPV devices. This consists of engaging the illumination source at open current (that is applied potential to the sample is zero). Nguyen and workers noted that a positive photocurrent reading correlated to the conduction of holes, while a negative reading correlated to the conduction of electrons.<ref name="dam" /> This alone allowed the authors to make predictions regarding the morphology within the cell. The current density for the forward and reverse bias can calculated as follows:<ref name="guide" />
<center>'''Current density equation:'''</center>

<center><math>J = \frac{8}{9}\varepsilon_o\varepsilon_r\mu \frac{V^3}{L^3}</math></center>

where ''J'' is the current density, ''ε<sub>o</sub>'' is the permittivity of a vacuum, ''ε<sub>r</sub>'' is the relative permeability of the medium, ''µ'' is the mobility of the medium, ''V'' is the applied bias and ''L'' is the film thickness in nanometers.<ref name="dam" /> The majority of the organic materials have relative permeability values of ~3 in their amorphous and crystalline states.<ref name="dant" /><ref name="afmu">AFM Instrumentation. AFM University, Atomic Force Microscopy Education Resource Library. Web. 21 Apr. 2011. <http://www.afmuniversity.org/></ref><ref name="angus" />

[[File:Annealed films.jpg|thumb|Unannealed film: (a) current-voltage plot under 632 nm laser with platinum AFM tip, (b) pc-AFM under short circuit representation, and (c) dark current-voltage plots. Annealed film: (d) illuminated current-voltage characteristics, (e) pc-AFM short circuit representation, and (f) dark current-voltage plots.|Effects of annealing<ref name="bull" />]]
[[File:Current mappingkmk.jpg|thumb|left|a) Superimposed photocurrent map and three-dimensional film topography collected from a conductive AFM tip (diamond coated) while under short circuit conditions. (b) Reduced scan area which depict local current-voltage measurements in (c).|Current density maps<ref name="hama" />]] 
The range of bias commonly applied is usually limited to between −5 V to +5 V for most studies.<ref name="sloan" /><ref name="xin" /><ref name="bull" /><ref name="hama" /><ref name="pingthree" /><ref name="coff" /><ref name="shah" /><ref name="lee" /> This can be achieved by applying a forward bias or [[reverse bias]] to the sample through the spotted gold contact. By adjusting this bias, along with the current passing through the cantilever, one can adjust the repulsive/attractive forces between the sample and the tip. When a reverse bias is applied (tip is negative relative to the sample), the tip and the sample experience attractive forces between them.<ref name="pingthree" /> This current density measurement is then combined with the topographical information previously gathered from the AFM tip and cantilever. The resulting image displays the local variations in morphology with the current density measurements superimposed onto of them.

Several methods have been employed to help reduce both mechanical and acoustic vibrations within the system. Mechanical vibrations are mainly attributed to traffic in and out of a building Other sources of mechanical vibrations have often been seen in the higher stories of a building due to reduced damping from building supports. This source of vibrational noise is easily controlled through the use of a vibration isolation table. Acoustical vibrations are far more common than mechanical vibrations. This type of vibration is a result of air movement near the instrument such as fans or human voices. Several methods have been developed to help reduce this source of vibration. An easy solution for this is separating the electronic components from the stage. The reason for this separation of components is due to the cooling fans within the electrical devices. While operating, the fans lead to a constant source of vibrational noise within the system. In most cases, other methods still need to be employed to help reduce this source of noise. For instance, the instrument can be placed within a sealed box constructed of acoustic dampening material. Smaller stages also result in less surface area for acoustic vibrations to collide with, thus reducing the noise recorded. A more in depth solution consists of removing all sharp edges on the instrument. These sharp edges can excite resonances within the piezo-electric materials which increase the acoustic noise within the system.<ref name="dangthree" />

==See also==
{{colbegin|2}}
*[[Atomic force microscopy]]
*[[Scanning tunneling microscope]]
*[[Scanning probe microscopy]]
*[[Conductive atomic force microscopy]]
{{colend}}
{{clear}}

==References==
{{reflist|30em}}

[[Category:Scanning probe microscopy]]
[[Category:Semiconductor analysis]]
[[Category:Intermolecular forces]]
[[Category:Scientific techniques]]