Solar Energy Materials & Solar Cells 102 (2012) 167–172

Contents lists available at SciVerse ScienceDirect

Solar Energy Materials & Solar Cells

0927-02

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journal homepage: www.elsevier.com/locate/solmat

Surface potential imaging of PV cells with a Kelvin probe

Chris Yang n, Yury Pyekh, Steven Danyluk

The G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

a r t i c l e i n f o

Article history:

Received 29 November 2011

Received in revised form

7 March 2012

Accepted 8 March 2012Available online 1 April 2012

Keywords:

Surface potential

Delta surface potential

Surface band bending

Kelvin probe

Defects

48/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.solmat.2012.03.006

esponding author. Tel.: þ1 404 894 3594; fax

ail address: chris.yang@marc.gatech.edu (C. Y

a b s t r a c t

This paper describes a Kelvin probe based inspection technique which measures surface potentials (SP)

at various illumination conditions and derives the delta surface potential (DVSP) and surface band

bending (f) of photovoltaic (PV) cells. The DVSP is the difference of surface potential measured in light

and dark conditions respectively. The delta surface potential (DVSP) is related to charge injection and

carrier lifetime, while the surface band bending (f) is associated with the surface condition. A white

light and short wavelength light illuminations are used to distinguish the bulk effects from that of the

surface.

A scanning vibrating Kelvin probe system was built to image PV cells with and without illumination.

Experiments were performed on both single crystalline silicon (sc-Si) and multi-crystalline silicon (mc-

Si) cells. It is found that the sc-Si cells possess a higher DVSP but a lower f than that of mc-Si cells. The

average DVSP and f are 350 mV and 50 mV for the sc-Si cells, and 280 mV and 110 mV for the mc-Si

cells. Process defects on a surface could affect both parameters, and it is found that the DVSP is not

uniform and could be reduced to 170 mV at a defect on the mc-Si cells. The high DVSP and low fs are

expected to contribute to the high conversion efficiency on a cell.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

Full wafer inspection and characterization of PV cells duringmanufacturing are essential factors toward increasing the solarconversion efficiency with low manufacturing costs. For multi-crystalline silicon cells, the conversion efficiency is presentlyaround 16% for commercial modules and about 20% for researchcells [1]. However, these efficiencies are still much lower than the29% theoretical efficiency [2]. The conversion efficiency of a PVcell depends on materials, design, and processes. For a givenmaterial type, cell processing is critical because the processvariation can significantly reduce the cell efficiency. The processvariation and defects can also further degrade the PV module’sperformance.

PV cell efficiency is determined by exposing the cell to a knownirradiation (e.g., 1 sun) and then measuring the maximum power[3,4]. This method yields the average efficiency of the cell, butcannot pinpoint defects or provide insight into cell details. Defectsin solar cells include dislocations, impurities, interface states, localcharges, grain boundaries, and shunts, among other issues, depend-ing on both material and process conditions. All defects affect theminority carrier lifetimes and cell efficiency [5–7]. Several methods

ll rights reserved.

: þ1 404 385 0812.

ang).

have been developed for specifically measuring carrier lifetime,including SPV, m–PCD, EBIC, and DLTS [8–13]. These microscopicinspection techniques are quite valuable in understanding thefundamental physics of cell defects. For example, the high resolu-tion imaging provided by a scanning Kelvin probe microscopy(SKPM) can clearly reveal local surface potential variations at grainboundaries, cell junction, or other defects [13–18]. With light-assisted technique, defects can be further measured under eithersteady or non-steady status. However, from the perspective of cellprocessing, it is desirable to have a large scale, full-sized cellmeasurement technique which can relate the processing conditionto the cell performance.

In this paper, we are reporting on a scanning Kelvin probesystem in conjunction with illumination designed to measure andmap the surface potential of full-sized PV cells. The Kelvin probeis a non-contact, non-destructive sensor that produces a signalwith the probe not physically connected to the surface. The Kelvinprobe has been widely used in surface science for measuring avariety of parameters such as adsorption, surface charging, graintextures, dopants, contaminants, and their influence on the sur-face potential, among other factors [9]. The scanning systemdeveloped here is an outcome of earlier research work done onnon-vibrating Kelvin probes [19,20]. This new system can mea-sure the surface potential and extract two critical performanceparameters, the delta surface potential (DVSP) and surface bandbending (f) on full-sized cells. Experiments were conducted onboth single crystalline silicon (sc-Si) and multi-crystalline silicon

C. Yang et al. / Solar Energy Materials & Solar Cells 102 (2012) 167–172168

(mc-Si) cells. Experimental results are reported herein and thecorrelation with the cell processing is discussed.

2. Principle of operation

The Kelvin probe technique measures the work function of ametal or the surface potential on a semiconductor in a non-contact method. It operates on the principle of contact potentialdifference (CPD) that is developed between two surfaces whenplaced in proximity and connected externally to allow for electronflow between the solids [21]. Electrons will flow from a materialof higher Fermi energy to a surface with the lower Fermi energyand the surface potential adjusts as the Fermi energy is equalized.Charges accumulate and an electrical field builds up on the twoopposite surfaces, as shown in Fig. 1a, as they are brought in closeproximity. The contact potential difference (VCPD) equals the workfunction difference as given by

VCPD ¼ ej jðjm�jpÞ ð1Þ

where jm and jp are the work functions of the sample and proberespectively, as shown in Fig. 1a. The VCPD can be measured with avibrating probe via a nulling technique where a feedback voltageis provided to make the current flow zero. At the null point, thefeedback potential equals VCPD, and the electrical field betweenthe surfaces is zero. The probe signal (VP) at the nulling point isthen equivalent to VCPD as

VP ¼ VCPD ¼ ej jðjm�jpÞ ð2Þ

The work function of the sample being investigated can beobtained if that of the probe is known. Practically, the workfunction of the probe can be known from a calibration procedureon multiple pure and stable samples in the same condition.

A PV cell is a planar semiconductor diode that responds tolight and generates excess charge carriers in the cell. As the cell isilluminated, a potential is created from charges which arediffused and separated by the p/n junction. The surface potentialmeasured by the Kelvin probe is the sum of the potentialgradients across the cell structure, including the substrate, p/njunction, dielectric layer, and top surface [21]. For the case of acell in the dark, i.e. without external carrier injection, as shown inFig. 1b, the surface potential for the cell can be written as

VspðdarkÞ ¼jsiþVbiþVdiþfs ð3Þ

where jsi is the work function of the silicon substrate, Vbi is thebuilt-in potential at the p/n junction, Vdi is the equivalent

++++

----

Ef1

Ef2

Energy

eVcpdEf1

+++++

-----

Vdi

φ

Fig. 1. Band energy model for various configurations of probes and samples (a) a meta

surface in light; top figures show the physical configuration, and the bottom figures sh

potential across the dielectric layer, and fs is the surface potentialband bending. The potential at the dielectric layer can be

represented as Vdi ¼Qeq

Cdi, where Qeq is the equivalent charge in

the dielectric layer and Cdi is the capacitance of thedielectric layer.

When the PV cell is illuminated with white light as shown inFig. 1c, excess electrons and holes are created throughout thethickness of the cell. The effective charges collected at a surfacewill bring about an open circuit potential, if the cell is notconnected to an external load. In the case of spot illuminationused in this paper, the open circuit potential is also function of thespatial distribution of charges. Therefore, a measurement of localsurface potential will not only represent the intrinsic properties,such as the charge generation and recombination lifetimes, ofmaterial, but also reflect the characteristic of charge re-distribu-tion. The lateral distribution of charges can be effectively used tolocate defects on a surface. The surface potential under a spotillumination can be described as

VspðlightÞ ¼jsiþVbiþVdiþVLoc ð4Þ

where VLoc is the open circuit potential at the illuminated spot.

Subtracting Eq. (3) from Eq. (4) yields the delta surface potential(DVsp) as

DVsp ¼ VspðlightÞ�VspðdarkÞ ¼ VLoc�fs ð5Þ

It can be seen that the delta surface potential is a function oflocal surface potential which relates with defect and surfacestates. The band bending in the Eq. (5) can be further excludedby short wavelength illumination. Excess charges created near thetop surface will introduce a flat band in the short wavelengthillumination [9]. The surface potential at a flat band condition is

Vspðlight,sÞ ¼jsiþVbiþVdi ð6Þ

The surface band bending (fs) can be obtained by subtractingthe voltage obtained in the dark and short wavelength lightconditions. Subtracting Eq. (6) from Eq. (3) gives

fs ¼ VspðdarkÞ�Vspðlight,sÞ ð7Þ

In this paper, we provide experimental measurements ofsurface potentials under different illumination conditions andthen render the delta surface potential and band bending by thesesubtracting processes. Full-sized wafer images are created onboth sc-Si and mc-Si cells.

Ef2

n

p

Vbi

n

++++++

------

hν

n

n

VocEf1

Vdi

Ef2

p p

p

l surface, (b) a p/n junction near the surface in the dark, (c) a p/n junction near the

ow the Fermi levels and band structures.

C. Yang et al. / Solar Energy Materials & Solar Cells 102 (2012) 167–172 169

3. Scanning system

An x–y–z scanning Kelvin probe system was developed tomeasure and map the surface potential distribution of a PV cell atvarious illuminations, as shown in Fig. 2. A Kelvin probe ismounted on the z-axis and scanned along the x,y axes at apredetermined height, while a PV cell is held in position on astationary platform. The x,y axes are driven by stepper motorswhich have a travel distance of 250 mm at a 0.4 mm resolution.The spacing between the probe and the cell is monitored by afiber optic displacement sensor. The entire scanning station isenclosed in a light shielded chamber, and the light irradiation as aspot is provided through an optical fiber. The illuminationintensity is 100 mW/cm2 at the fiber cable output, and theillumination spot size is 30 mm2 in diameter at the incident angleof 601. The short wavelength illumination is provided with samelight source but through a 400 nm band pass filter inserted in theoptic path, which reduces the light intensity to 1 mW/cm2 at thefiber output. Both the Kelvin probe and fiber optic sensor signalsare recorded with Lab-view based operation system, and thesurface images are created using Matlab software.

The Kelvin probe has a probe tip diameter of 4.6 mm and avibrating frequency of 1200 Hz. The spacing between the probeand the cell is held at 1.2 mm. The work function of the Kelvinprobe tip is pre-calibrated with multiple references of metal filmscoated on silicon. A linear equation is extracted from the calibra-tion procedure to correlate the Kelvin probe signal with absolute

Fig. 2. Schematic diagram of the Kelvin probe scanning system.

Fig. 3. SP map of a sc-Si cell in the dark (a) and light (b) conditions. B

work function. All data reported in the paper are absolute surfacepotential of PV cells based on this prior calibration.

Crystalline silicon PV cells of 156�156 mm2, including singlecrystalline silicon (sc-Si) cells and multi-crystalline silicon (mc-Si)cells, were measured. The cells are processed with standardprocess until a silicon nitride antireflection layer and metalcontacts. Surface scans are taken on an area of 146�146 mm2

with a 5 mm edge exclusion.

4. Results

4.1. Single crystalline silicon (sc-Si) cells

Fig. 3 shows the surface potential (SP) map of a sc-Si cell indark and light conditions respectively. It can be seen that the SPdistribution is not uniform, and there is a macro non-uniformpattern over the entire cell. Higher SP exists at the cell perimeterand a lower SP in the center part of the cell. The SP increases withlight illumination, but the variability in the SP distributionpattern remains. The average SP on the cell is approximately4.50 and 4.85 V for the dark and light measurements respectively.

In addition to the macro scale variation, there is also local,spot-type non-uniformity which shows either even lower orhigher SP than majority of surface. The low SP spots are randomlydistributed on the cell, while the high SP spots are more close toperimeter and busbars. As a matter of fact, the high SP spots havesimilar potential with busbars, which indicates the possiblemetallic contamination at the spots. The existence of metalresidue on the high SP spots outside busbars was confirmed in aseparate microscopy examination. The SP maps further show thevariations along the busbars. On the other side, the spreaddistribution of the low SP spots indicates a likely chargingembedded in dielectric layer or at silicon interface. It is clear thatSP mapping can indicate the variability in the cell processing ormetal firing.

The delta surface potential is calculated by subtracting thedark image from the light image and shown in the DVsp map inFig. 4. It can be seen that the DVsp shows a different distributionpatterns, with a lower DVsp at the bottom half than the top half ofthe cell. There also exists a local scale variation on the cells, withextremely low DVsp value at several spots. Fig. 4 shows a traceplot of DVsp across a low SP spot along the designated line MM0 inthe DVsp map. It can be seen that the DVsp is not constant along

oth images are scaled in the same color range from 4.2 to 4.9 V.

0.20

0.25

0.30

0.35

0.40

0

DV

sp (

V)

Distance (mm)20 40 60 80 100 120 140

Fig. 4. The DVsp map of the sc-Si cell (a) and a trace plot along the line MM0 (b).

Fig. 5. SP map of a mc-Si cell in the dark (a) and light (b) conditions. Both images are scaled in the same color range from 4.2 to 4.7 V.

C. Yang et al. / Solar Energy Materials & Solar Cells 102 (2012) 167–172170

the line, and the DVsp is only approximately 0.23 V at the spot. Thelow DVsp spot is like a shunting defect which reduces the cellefficiency.

4.2. Multi crystalline silicon (mc-Si) cells

The SP map of a mc-Si cell is shown in Fig. 5. It can be seen thatthere is a different pattern of SP distribution on mc-Si cell thanthe sc-Si cell. The overall SP distribution is quite uniform on mc-Sicells, but there is a pattern of grain-related variation. The SPdifference among crystalline grains is up to 50 mV in the darkimage. As the cell is illuminated, the SP difference among grains isreduced due to average effect of charge redistribution. However,the light image shows a different variability. A few of low SP spotsis found on the right side of the cell in the light image. The lowerSP in the light image indicates a possible interface defect on themc-Si cell. On the other hand, the SP profile on busbars on the mc-Si cells is much more uniform, showing sharp straight edges. Onlya few of metal contamination is observed outside busbars. Theaverage SP on the mc-Si cell is 4.25 and 4.53 V for the dark andlight respectively.

The DVsp map of the mc-Si cell is shown in Fig. 6. It can be seenthat DVsp is not uniform as well. There is a slightly higher DVsp onthe left half of the cell than on the right half in general. There is

also a very low DVsp spot on right-hand side of the cell. A traceplot shown in Fig. 6 clearly indicates there is only 0.17 V DVsp onthe spot. A 50 mV offset between the right and left halve of thecell is also observed in the trace plot. It is clear that the defect atthis spot has a big impact on the cell performance, which affects alarge surrounding area on the spot. The average DVsp is approxi-mately 0.28 V on the mc-Si cell.

4.3. Surface band bending fs images

The surface band bending of the cells was measured with a400 nm wavelength light irradiation. Fig. 7 shows the surfaceband bending maps of both sc-Si and mc-Si cells. It can be seenthat both types of cells show a relatively uniform distribution ofsurface band bending on the whole surface, except for the celledges. The average fs are 50 mV and 110 mV for sc-Si and mc-Sicells respectively. However, significant lower fs value is alsofound at the same area on mc-Si cell as indicated by DVsp map. Itis clear that the defect at this location affects both fs and DVsp onthe cell.

Table 1 summarizes the experimental results, including thesurface potential, change in surface potential, and surface bandbending, of PV cells measured. There is a good consistency amongthe same types of cells. All three mc-Si cells show lower SP than

0.15

0.2

0.25

0.3

0.35

0

ΔVsp

(V)

Distance (mm)20 40 60 80 100 120 140

Fig. 6. The DVsp map of the mc-Si cell (a) and a trace plot along the line NN0 (b).

Fig. 7. Surface band bending maps of sc-Si cell (a) and mc-Si cell (b).

Table 1Comparison of different performance metrics for two types of cells.

Vdark (V) Vlight (V) DVsp (mV) f (mV)

Ave std Ave std Ave std Ave Std

sc-Si A 4.397 0.069 4.751 0.065 354.5 9.4 39.7 0.6

sc-Si B 4.597 0.040 4.948 0.042 350.5 8.8 58.5 0.5

mc-Si A 4.226 0.028 4.533 0.032 307.0 21.1 117.2 1.7

mc-Si B 4.260 0.037 4.534 0.029 274.3 34.3 110.6 2.4

mc-Si C 4.272 0.039 4.534 0.038 262.1 28.8 111.1 1.3

C. Yang et al. / Solar Energy Materials & Solar Cells 102 (2012) 167–172 171

the sc-Si cells in both dark and light conditions. A correspondinglylower delta surface potential is also found on the mc-Si cells. Onthe contrary, higher surface band bending is observed on the mc-Si cells. It is clear that a higher DVsp and lower fs contribute to ahigher conversion efficiency in the sc-Si cells.

5. Discussions

A PV cell is essentially a diode that is expected to be uniformover the entire cell. However, non-uniformity may be brought upby defects or process variation. In many cases, these defects will

either cause electricity loss if it is minor, or become a currentdrain if the defect is severe. Identifying these defects is critical toPV cell and module operation. Presently, there are a few micro-scopic inspection techniques available for PV measurements;however, the macro-scale inspection techniques that can relateprocessing to cell performance are still lacking. Here we areintroducing an inspection method based on a conventional Kelvinprobe for full-sized cells imaging. The large probing gap of thescanning system can further eliminate the probe tip-inducedvariation due to a reduced electrical field between the probeand cell surface. Experiments have demonstrated the capability ofmeasuring a variety of process defects on PV cells.

It should also be noted that the Kelvin probe uses thecapacitive coupling for signal detection. The measured signalswill definitely vary depending on the material and the outmostlayer on a surface. In the case of PV cells, which have multiplelayers and different structures, the probe signals vary correspond-ingly to either metal or silicon on the top surface of cells. If theprobe is on the busbars, the Kelvin probe will basically yield thework function of metals. If the probe is on silicon with a dielectriclayer, it will then render the surface potential of semiconductorsubstrate, which couples with charges in the dielectric layer. Thesurface variations at the silicon dielectric interface and metalcontacts are clearly visible in the maps. In fact, there is a large

C. Yang et al. / Solar Energy Materials & Solar Cells 102 (2012) 167–172172

variability in the metal contact firing, and some contaminants arefound to be electrical current draining sites. The silicon interfacedefects and charges in the dielectric layer are also observed onboth sc-Si and mc-Si cells.

While single wavelength illumination is generally used inother light-assisted inspection techniques, various light sourcesare implemented here to allow for detecting different defects oncells. Specifically, the white light illumination is used for throughcell defects, while the short wavelength light is used exclusivelyfor surface defects. The spot light illumination used here canfurther help identify local defects as a result of lateral distributionof photo-carriers. The two types of illuminations will generallyrender different images because of different defects detected.However, there may be similar features on two different images iflarge surface defects exist. This similarity indicates the possibilityof detecting all process-related macroscopic defects with thewhite light illumination.

The surface band bending is related to surface treatment in acleaning process. A positively or negatively charged surface maybe produced from a chemical reaction. Due to its negative effecton charge recombination, a surface needs to be passivated withneutral charges. It can be seen that the surface band bendingimaging provides a viable way to evaluate a cleaning process.However, there may exist different surface band bending fordifferent types of cells. The high surface band bending indicatesthe necessity of surface treatment to improve cell performance.

The defects discussed above are primarily electrical ones thatrelate to cell efficiency. There are also mechanical types of defectsthat impact the stability and reliability of cells or modules. In fact,the mechanical defects such as micro-cracks will also introduceelectrical field discontinuity in the cracking area. This character-istic may indicate a possibility of detecting surface cracks withthe present scanning system.

6. Conclusions

A scanning Kelvin probe system has been successfully devel-oped for mapping large, full-sized PV cells at various illuminationconditions. The scanning system can measure surface potential,delta surface potential, and surface band bending. The surfaceeffect is distinguished from the bulk by short wavelength lightand white light. The inspection capabilities have been demon-strated on both sc-Si and mc-Si cells.

Experiments indicate that the surface potentials in the darkand light are about 4.50 and 4.85 V for sc-Si cells, and 4.25 and4.53 V for mc-Si cells. The DVsp is about 350 mV and 280 mV, andfs is 50 mV and 110 mV, for sc-Si cells and mc-Si cells respec-tively. The high DVSP and low fs contribute to high conversionefficiency on sc-Si cells.

Acknowledgments

This project is supported by NSF (Grant no.1042187). Authorswould like thank Dr. A Rohatgi’s group for cell preparation andDr. S. Melkote for discussions.

References

[1] M.A. Green, K. Emery, Y. Hishikawa, W. Warta, E.D. Dunlop, Solar cellefficiency tables (Version 38), Progress in Photovoltaic: Research and Appli-cations 19 (2011) 565–572.

[2] I. Tobias, C. del Canizo, J. Alonso, Crystalline Silicon Solar Cells and Modules,in: A. Luque, S. Hegedus (Eds.), Handbook of Photovoltaic Science andEngineering, John Wiley & Sons, West Sussex, England, 2005, pp. 269–270.

[3] B. von Roedern, Physics of Photovoltaic Materials, in: C.J. Cleveland,R.U. Ayres (Eds.), Encyclopedia of Energy, 5, Elsevier Inc., Amsterdam, 2004,pp. 47–59.

[4] S. Ashok, K.P. Pande, Photovoltaic measurements, Solar Cells 14 (1985) 61–81.[5] A.A. Istratov, H. Hieslmair, O.F. Vyvenko, E.R. Weber, R. Schindler, Defect

recognition and impurity detection techniques in crystalline silicon for solarcells, Solar Energy Materials and Solar Cells 72 (2002) 441–451.

[6] M. Takihara, T. Takahashi, T. Ujihara, Minority carrier lifetime in polycrystal-line silicon solar cells studied by photoassisted Kelvin probe force micro-scopy, Applied Physics Letters 93 (2008) 021902-1–3.

[7] M. Langenkamp, O. Breitenstein, Classification of shunting mechanisms incrystalline silicon solar cells, Solar Energy Materials and Solar Cells 72 (2002)433–440.

[8] W. Melitz, J. Shen, A.C. Kummel, S. Lee, Kelvin probe force microscopy and itsapplication, Surface Science Reports 66 (2011) 1–27.

[9] L. Kronik, Y. Shapira, Surface photovoltage phenomena: theory, experiment,and applications, Surface Science Reports 37 (1999) 1–206.

[10] T. Takahashi, Photoassisted Kelvin probe force microscopy on multicrystal-line Si solar cell materials, Japanese Journal of Applied Physics 50 (2011).08LA05-1-8.

[11] K. Dirscherl, I. Baikie, G. Forsyth, A. van der Heide, Utilisation of a micro-tipscanning Kelvin probe for non-invasive surface potential mapping of mc-Sisolar cells, Solar Energy Materials and Solar Cells 79 (2003) 485–494.

[12] A. Castaldini, D. Cavalcoli, A. Cavallini, M. Rossi, Scanning Kelvin probe andsurface photovoltage analysis of multicrystalline silicon, Materials Scienceand Engineering: B 91–92 (2002) 234–238.

[13] M. Wilson, A. Savtchouk, J. Lagowski, K. Kis-Szabo, F. Korsos, A. Toth,R. Kopecek, V. Mihailetchi, QSS-mPCD measurement of lifetime in siliconwafers: advantages and new applications, Energy Procedia 8 (2011) 128–134.

[14] Y. Rosenwaks, R. Shikler, T. Glatzel, S. Sadewasser, Kelvin probe forcemicroscopy of semiconductor surface defects, Physical Review B: CondensedMatter and Materials Physics 70 (2004) 85320-1–7.

[15] S. Saraf, Y. Rosenwaks, Local measurement of semiconductor band bendingand surface charge using Kelvin probe force microscopy, Surface Science 574(2005) L35–L39.

[16] A. Breymesser, V. Schlosser, D. Peiro, C. Voz, J. Bertomeu, J. Andreu,J. Summhammer, Kelvin probe measurements of microcrystalline silicon ona nanometer scale using SFM, Solar Energy Materials and Solar Cells 66(2001) 171–177.

[17] C.S. Jiang, A. Ptak, B. Yan, H.R. Moutinho, J.V. Li, M.M. Al-Jassim, Microelec-trical characterizations of junctions in solar cell devices by scanning Kelvinprobe force microscopy, Ultramicroscopy 109 (2009) 952–957.

[18] A. Doukkali, S. Ledain, C. Guasch, J. Bonnet, Surface potential mapping ofbiased pn junction with kelvin probe force microscopy: application to cross-section devices, Applied Surface Science 235 (2004) 507–512.

[19] C. Korach, J. Streator, S. Danyluk, Measurement of perfluoropolyether lubricantthickness on a magnetic disk surface, Appl. Phys. Lett. 79 (2001) 698–700.

[20] Y. Yang, S. Danyluk, Kelvin probe study on the perfluoropolyether film onmetals, Tribology Letters 10 (2001) 211–216.

[21] D.K. Schroder, Semiconductor Material and Device Characterization, third Ed.,Wiley-IEEE Press, New York, 2006, pp. 526-532.