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Paste Rheology Correlating With DispensedFinger Geometry

Maximilian Pospischil, Jan Specht, Markus Konig, Matthias Horteis, Carsten Mohr,Florian Clement, and Daniel Biro

Abstract—Dispensing technology in crystalline silicon solar cellmetallization offers the possibility to improve contact finger ge-ometries compared with the dominating screen-printing approach.However, an optimum contact formation strongly depends on pasterheology and process parameters. In this study, a method is intro-duced to predetermine dispensed contact geometries by extract-ing specific rheological parameters from oscillating strain sweeps,allowing for paste optimization prior to printing tests. For thisreason, four different dispensing pastes were processed and com-pared with a commercially available screen-printing paste. Os-cillating strain sweeps were conducted with all pastes, in order todetermine characteristic values for complex shear modulus G∗ andyield stress τy . In the following, p-type Cz-Si solar cells were pro-cessed, which were equipped with dispensed contact fingers usingthe four rheologically investigated dispensing pastes and comparedwith samples with an all screen-printed front-side grid. Effects likepaste spreading or necking could be isolated and referred to thedifferent pastes and printing processes. Various form parametersthat describe specific characteristics of resulting finger geometrieswere introduced. The elastic part G′ of the complex shear modulusG∗ was found to have the major impact on resulting finger widths,aspect ratios, and a macroscopic contact angle between the fingerand the wafer surface.

Index Terms—Contact geometry, dispensing, metallization, rhe-ology, silicon solar cell.

I. INTRODUCTION

INDUSTRIAL crystalline solar cell metallization is still dom-inated by the traditional screen-printing technology. Highly

developed printing equipment and pastes offer a sophisticatedcontact formation process with proven long-term stability. Dis-pensing technology provides the possibility to form more ho-mogenous contacts with similar pastes, reducing side effectslike paste drifting and mesh marks. Furthermore, line defini-tions can be increased at similar finger cross sections, which

Manuscript received March 27, 2013; revised July 18, 2013; accepted July22, 2013. This work was supported by the German Federal Ministry of Envi-ronment, Nature Conservation, and Nuclear Safety within the research project“Gecko” under Contract 0325404.

M. Pospischil, J. Specht, F. Clement, and D. Biro are with the Fraun-hofer Institute for Solar Energy Systems ISE, D-79110 Freiburg, Germany(e-mail: maximilian.pospischil@ise.fraunhofer.de; jan.specht@ise.fraunhofer.de; florian.clement@ise.fraunhofer.de; daniel.biro@ise.fraunhofer.de).

M. Konig, M. Horteis, and C. Mohr are with the Thick Film Materials Di-vision, Business Unit Photovoltaics, Heraeus Precious Metals GmbH & Co.KG, 63450 Hanau, Germany (e-mail: markus.koenig@heraeus.com; matthias.hoerteis@heraeus.com; carsten.mohr@heraeus.com).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JPHOTOV.2013.2278657

reduce optical shading on the front side of the solar cell, asalready indicated by Specht et al. [1]; Chen et al. [2], [3]; andZhu et al. [4]. A record cell efficiency of 20.6% on 125 mm ×125 mm FZ p-type material was achieved at Fraunhofer ISE,Freiburg, Germany, using dispensing technology on Metal WrapThrough-Passivated Emitter and Rear Cell (MWT-PERC) solarcells, which were equipped with a selective emitter structure, aspublished by Lohmuller et al. [5].

Because of the noncontact extrusion approach, dispensingtechnology offers the possibility to adapt paste rheology in awide range in order to further improve contact geometry [6]. Ina previous publication, the influence of finger geometry on cellresults was discussed in detail [7]. The correlation between theoptical finger width and the resulting short-circuit current jsc ,as already stated by Specht et al. [1], could be confirmed as wellas the influence of the actual contact widths. Here, a reducedcontact width allows for higher open-circuit voltages Voc andsignificantly reduces mechanical and electrical contact area, thusreducing contact resistance and fill factor FF. Consequently,highest cell efficiencies were achieved with fingers showingneither paste drifting nor necking.

This paper focuses on the extraction of characteristic rheo-logical parameters from oscillating strain sweeps and the corre-lation between these parameters and dispensed finger geometry,with the aim to be able to predetermine resulting contact geome-tries by rheological investigations during the paste development.

II. PROCEDURE

A. Experimental Setup

This experiment contains a full comparison of four differentdispensing pastes (A–D) specially developed by Heraeus Pre-cious Metals GmbH & Co. KG, Hanau, Germany, as well asa commercial screen-printing reference paste (S) by the samemanufacturer.

As already indicated in [7], paste A was deduced from screen-printing reference paste S that aims to show the difference of thetwo printing processes independent of rheological paste adap-tion. For the dispensing process, rather liquid paste A frequentlyled to paste accumulation at the nozzle outlet, due to its evolvedwetting behavior and, consequently, also did not significantly re-duce paste drifting on the wafer. Thus, Paste B–D were preparedwith increasing stiffness in order to improve printing behaviorand achieve smaller line resolutions on the wafer.

These five pastes were first rheologically investigated by us-ing oscillating strain sweeps in order to extract the most im-portant rheological sizes used in this study. In the following,

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a cell batch of 156 mm × 156 mm p-type Czochralski silicon(Cz-Si) material was processed, which is equipped with an in-dustrial 75-Ω/sq emitter, aluminum printed back surfaces, andpreprinted front-side busbars. The front-side grid was dispensedusing a single nozzle time pressure fluid dispenser as describedby Chen et al. [8] and compared with all screen-printed refer-ence cells using paste S. The resulting finger geometries werethen compared with previously determined rheological data byvarious geometrical characterization methods.

B. Rheological Investigations

In contrast to Newtonian fluids, metal pastes typically showshear thinning as well as thixotropic behavior [6], [8]–[10].Furthermore, highly filled dispersions like metal pastes usuallyare yield stress fluids [11] which means, shear stress τ has toexceed yield stress τy (τ > τy ) to initiate paste flow [8].

Applying stresses below this critical yield stress τ < τy leadsto an elastic deformation, as pastes remain solid.

During this study, rheological experiments were conductedusing an Anton Paar MCR 101 rotational rheometer that isequipped with a D = 25 mm parallel disk setup instead of acone-plate configuration in order to account for the presence offilled media.

These devices record the relation between nonhomogeneousshear strain γ and shear stress τ by tracking the angle of rotationθ and torque M according to the following equations [11]:

γdisk(r) =θr

h(1)

τϕθ,disk =3M

2πR3

[3 +

d ln M

d ln γR

]. (2)

When applying sinusoidal oscillating shear strain

γ = γ0 · sin ωt (3)

with angular frequency ω = 2πf, the corresponding steady-statestress oscillation can be expressed by

τ = τ0 · sin (ωt + δ) (4)

with phase angle δ as a second independent raw parameter.Using a trigonometric addition theorem, the stress wave (4)

can be resolved into two waves, with a π/2 phase shift:

τ = τ ′ + τ ′′ = τ ′0 · sinωt + τ ′′

0 · cos ωt (5)

with

τ ′0 = τ0 · cos δ and τ ′′

0 = τ0 · sin δ. (6)

Consequently, the two stress waves allow the definition oftwo dynamic shear moduli: the in-phase elastic modulus G′ andthe out-of-phase viscous or loss modulus G′′ [11].

G′ =τ ′0

γ0and G′′ =

τ ′′0

γ0. (7)

Frequently, these two dynamic shear moduli are merged intoa complex shear modulus G∗ with

G∗ = G′ + iG′′. (8)

Fig. 1. Complex shear modulus G∗ as a function of actual shear stress τ forstrain sweeps using an Anton Paar MCR 101 rotational rheometer equipped witha 25-mm parallel disk configuration. Pastes A–D resemble specially developeddispensing pastes with increasing values for complex shear modulus G∗ fromA to D. Paste S refers to a commercial screen-printing paste and was used forreference cells in this batch.

Substituting the dynamic shear moduli (7) into (5) leads to

τ = γ0 (G′ sin ωt + G′′ cos ωt) . (9)

By recording the evolution of the storage modulus G′, as wellas the loss modulus G′′, samples can be characterized in termsof elastic and viscous behavior, respectively.

III. RESULTS AND DISCUSSION

A. Oscillating Strain Measurements

During this experiment, pastes were exposed to oscillatingstrain (3) with increasing amplitude γ0 at constant frequencyf = 10 s−1 . By measuring torque and phase angle of the sam-ple, storage modulus G′ (real part of G∗) and loss modulus G′′

(imaginary part of G∗) could be determined. Starting at lowstrain values, pastes indicate linear viscoelastic (LVE) behavior.Here, the values for G′ and G′′ remain rather constant whichoffers the possibility to extract characteristic rheological dataG′

LVE and G′′LVE . With increasing strain, values for G′ and G′′

start decreasing in the yield area. At the intersection of G′ andG′′, the sample clearly becomes liquid.

Plotting the values for G∗ against the amount of shear stress τ ,all examined pastes are clearly distinguishable from one another,comparing them by their yield behavior (see Fig. 1).

In rheology, yielding is defined by yield stress τy and repre-sents a gradual transition between LVE and liquid region of thesample [11]. During dispensing, the amount of shear stress τneeds to exceed τy in order to develop a current profile in thenozzle. Assuming a cylindrical nozzle [8] with diameter d andheight h, a simple balance of acting forces leads to the minimumamount of dispensing pressure pmin required to extrude paste

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POSPISCHIL et al.: PASTE RHEOLOGY CORRELATING WITH DISPENSED FINGER GEOMETRY 3

Fig. 2. Correlation of elastic G′LVE and viscous G′′

LVE shear moduli in theLVE region with yield stress τy ,LVE and flow point τf for four different dis-pensing pastes (A–D) and reference paste S .

with a certain yield stress τy :

pmin =4h

d· τy . (10)

Typically, this value is identified by increasing the amountof shear stress τ in rotational mode until the sample starts toyield and values for strain γ start to increase significantly [11],[12]. In oscillating mode, at least two distinct data points canbe extracted, describing this yield phenomenon: the first at theend of the LVE region, meaning G′ dropping by more than 10%of the plateau value [12], and the second at the intersection ofG′ and G′′, where the sample clearly becomes liquid. These twovalues, which are defined as yield stress τy ,LVE and flow pointτf by Mezger [12], were both extracted and used for comparison(see Fig. 2).

The real part of the complex shear modulus G∗, i.e., thestorage modulus G′, indicates the amount of elasticity in thepaste, the imaginary part G′′ correlates with viscosity. In orderto analyze elastic and viscous paste behavior, the values for G∗

were compared in the LVE area.These values were determined by calculating the mean value

for all data points within a range of ±10% [12] initiated at thosefive adjacent data points having the least standard deviationwithin the curve. By repeating the same measurement procedureseveral times, reproducibility and accuracy could be taken intoaccount.

For all samples, an increasing yield stress τy ,LVE and flowpoint τf corresponds to an increased elasticity and viscosity.Dispensing pastes show increasing values for G′

LVE , G′′LVE as

well as τy ,LVE and τf from A to D. As expected, screen-printingpaste S and derived dispensing paste A show rather similarelastic and viscous behavior. The large difference between yieldstress τy ,LVE and flow point τf indicates a developed yieldregion of all pastes. For further calculations and comparisonwith rotational measurements, values of τf should be used ascritical yield stress (τy ∼ τf ), as pastes are clearly liquid beyondthis value and, thus, develop a flow profile in the nozzle.

Fig. 3. Schematic finger cross section of two typical contact geometries. Pastedrifting is subtracted using the core widths wcr , and contact angle θc is deter-mined using the intersection of 1

4 hf and the finger surface as reference for thesecond leg.

B. Analysis of Finger Geometry

Because of a great diversity of resulting contact finger ge-ometries in this experiment, it is necessary to define some geo-metrical parameters. An ordinary contact finger, as indicated inFig. 3 with contact cross-sectional area Af and total height hf ,is typically defined by its optical width wo , linearly correlatingwith the average covered cell area. The aspect ratio AR is thendefined as ratio between finger height hf and optical width wo :

AR =hf

wo. (11)

In order to be able to separate paste drifting from that amountof paste contributing to finger conductivity, the core width wcrwas defined as width covering 99% of the total finger cross-sectional area Af (see Fig. 3). The contact width wc , conse-quently, correlates linearly with the contact area between fingerand wafer, which is crucial for sufficient mechanical and elec-trical contact formation.

For a better description of wetting behavior during contactformation, a macroscopic contact angle θc is introduced. Inorder to be independent from the wafer surface topography,the horizontal first leg is defined by the average wafer surfaceheight. The second leg implies an useful definition for any kindof contact finger by determining a reference of the second legat the intersection of a horizontal at one quarter of the fingerheight 1

4 hf with the wafer surface.After dispensing pastes A–D through ceramic nozzles with an

outlet diameter of d = 80 μm and processing a screen-printedreference group using paste S, resulting finger widths wererecorded. For each paste group in this batch, three representa-tive solar cells were selected for geometrical analysis. Measure-ments of core widths wcr were taken at three fingers per cell,respectively. Optical width wo was determined by counting pix-els of raw images of the same samples. Finally, cross sections ofseven adjacent fingers on one cell per group, respectively, wereprocessed to evaluate finger height hf , contact width wc , andcontact angle θc .

C. Impact of Paste Elasticity on Finger Geometry

Paste flow within the dispensing unit is strongly influencedby shear dependent viscosity and yield stress [6]. During thefree flow phase between nozzle orifice and wafer, as well asthe actual finger deposition though, paste elasticity has a majorimpact on process parameters and resulting finger geometries

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Fig. 4. Resulting geometrical data of dispensed contact fingers depending onpaste elasticity of four different dispensing pastes (A–D) expressed by storagemodulus G′

LVE . Paste S refers to data of screen-printed samples processed inparallel.

(see Fig. 4). Increased values for elastic shear modulus G′ leadto higher aspect ratios AR and reduced core widths wcr , sincethe ratio between traverse speed and paste flow can be increasedwithout causing line interruptions. For G′

LVE � 1 MPa, wettingbehavior expressed by contact angles θc > 90◦ on the wafer isreduced severely. Thus, contact width wc turned out to be smallerthan core widths wcr for fingers dispensed with pastes C and D.

Finger widths clearly below 50 μm were dispensed withpastes C and D due to their high values of storage modulusG′. Paste A only shows little deviation from screen-printingreference paste S concerning its rheological parameters; thus,finger widths were only reduced slightly, compared with thescreen-printed reference samples.

A larger difference occurs comparing these two samples con-cerning their aspect ratios AR, as well as their contact anglesθc . Here, the advantage of a nonimpact process with hardly anyshear load on the paste during finger deposition is remarkable.Screen-printed reference cells with paste S show rather smallcontact angles θc and, consequently, increased paste spreading.In contrast with the dispensing process, yield stress is surpassed(τ > τy ) during the lift-off phase, and paste becomes liquid,even though it is already in contact with the wafer. Therefore,achievable aspect ratios AR are also limited on screen-printedcells, and are significantly lower than on dispensed samples.

On the other hand, high contact angles of θc > 90◦ as achievedwith pastes C and D reduce mechanical robustness during sin-tering and increase electrical contact resistance due to a smallercontact area but lead to extremely high aspect ratios AR.

A final comparison of resulting contact geometries dependingon specific paste rheology is given by finger cross sections (seeFig. 5).

Comparing these fingers with each other leads to the conclu-sion that paste B was best suited for contact formation on solarcells. Here, a small finger width combined with medium con-tact angles θc gives sufficient mechanical adhesion and provides

Fig. 5. Representative cross section of dispensed front-side contacts usingfour different pastes (A–D) [7].

TABLE IIV PARAMETERS OF DISPENSED (DISP.) AND SCREEN PRINTED (SCREENP.)

SOLAR CELLS USING DIFFERENT PASTES

an optimum tradeoff between shading, contact area, and pasteconsumption.

D. Solar Cell Results

The impact of improving the finger contact geometry on elec-trical cell results was already subject to previous studies [7].Nevertheless, looking at IV-parameters gives a final result com-paring pastes A–D concerning their electrical performance (seeTable I).

Short-circuit current jsc typically increases with decreasingoptical finger width wo as the amount of shaded cell area de-creases (see Fig. 6). However, this effect was partly reduced byan increased number of contact fingers for all dispensed cellscompared with screen-printed reference samples (NA−D = 83versus NS = 68).

Open-circuit voltage Voc shows a similar development as jscalthough here, different influences should be taken into con-sideration. Looking at the one diode model [13], an increase

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POSPISCHIL et al.: PASTE RHEOLOGY CORRELATING WITH DISPENSED FINGER GEOMETRY 5

Fig. 6. Open-circuit voltage Vo c depending on contact width wc and short-circuit current Jsc depending on optical width wo , respectively, for solar cellswith dispensed front contacts using pastes A–D and screen-printed referencesamples with paste S .

in Voc can be partly accounted to an increase in current density(j ∼ jsc) of all dispensed cells compared with the screen-printedreference samples assuming a constant thermal voltage of VT =25.7 mV under standard test conditions:

Voc ≈ VT · (ln jsc − ln j0) . (12)

With respect to IV-parameters from Table I, it can be easilycalculated using (12) that this effect accounts for around 25% ofthe voltage increase for dispensed cells (A–D) compared withthe screen-printed reference samples (S). Consequently, the re-maining 75% can be subjected to a reduced saturation currentdensity j0 which implies less recombination losses on thesecells compared with the screen-printed samples. As describedin detail by, e.g., Fellmeth et al. [14] and Honig et al. [15], themetallized area on the front side strongly contributes to recombi-nation losses in emitter and space-charge-region. This influenceis clearly visible looking at the evolution of Voc (see Fig. 6)regarding the contact width wc that decreases with increasingvalues of storage modulus G′ from paste A to D.

Finally, although pastes C and D performed best in terms ofjsc and Voc , the disadvantage of paste necking was clearly vis-ible when looking at resulting Fill Factors FF (see Table I).Here, a strongly reduced contact area increases the contactresistance although grid resistance could be reduced by 50%for all dispensed cells compared with the screen-printed ref-erence group S [7]. However, additionally increased values ofFF0-pFF in group A at reasonable values of parallel resistance(Rp > 5 kΩ·cm2 ) point to increased recombination losses inthe space-charge-region. Thus, expected maximum Fill Factorvalues did not occur for this group.

Finally, maximum cell efficiencies of η = 18% were reachedby dispensing pastes B and C. Concerning their median cellefficiencies, paste B performed best, due to highest values ofFill Factor FF at reasonably high values for short-circuit currentjsc and open-circuit voltage Voc compared with pastes C and D.The mean cell efficiency of this group exceeded the correspond-ing mean value of the screen-printed reference cells by Δη =

0.4%abs. However, improved contacting behavior of dispens-ing pastes, as well as a further reduction in finger widths, bothhave a strong influence on cell results and may lead to differentrankings of pastes B and C in the future.

IV. CONCLUSION

Dispensing parameters, as well as resulting finger geome-tries, strongly depend on paste rheology. For detailed analysisof these phenomena, rheological data were extracted from oscil-lating strain measurements of five different pastes and correlatedwith resulting finger geometries on texturized Cz-Si substrates.In order to compare geometrical data of various metal fingers,characteristic values like core width, contact width, and opti-cal width were introduced, which can be used again in futurestudies.

Regarding rheology, an increased yield stress τy requireshigher dispensing pressures, which are more difficult to controlin industrial processes. Typically, an increased yield stress τy

goes along with a higher ductility of the paste expressed by thestorage modulus G′ taken from oscillating strain measurementsin the LVE region during this experiment. Furthermore, valuesfor G′ strongly influence resulting macroscopic contact anglesθc at the interface between paste, texturized wafer, and air. Pastedrifting, which is characteristic for screen-printed contact fin-gers, could be isolated by introducing the core width wco . Byswitching the printing process to dispensing, this phenomenonwas reduced but still present when paste A was applied thatis similar to the screen-printing paste S. Aspect ratios AR andcontact angles θc , however, were already significantly increasedjust by switching to dispensing. By using more elastic pastes(B–D), both values were further increased and paste driftingwas prevented completely.

At similar optical widths wo , high contact angles (θc > 90◦),occurring when dispensing very elastic pastes, reduce contactwidth wc , which is necessary for sufficient mechanical adhesionand electrical contact formation. Thus, solar cells dispensed withpastes C and D did not further increase cell efficiencies, andpaste B turned out to form the best contact geometry from anelectrical, optical, as well as mechanical point of view. Applyingthis paste led to a maximum efficiency of η = 18%, which ex-ceeded the best screen-printed reference cell by Δη = 0.4%abs.

In future studies, the impact of surface topography and wet-ting behavior of different textures has to be considered as well,since geometrical finger data depend not only on rheology buton surface characteristics of the substrate as well. Furthermore,finger width of all samples can be further reduced by decreasingthe nozzle diameter. Consequently, this would lead to less silverconsumption and even higher cell efficiencies in the future.

ACKNOWLEDGMENT

The authors would like to thank all coworkers at the Photo-voltaic Technology Evaluation Center (PV-TEC) at FraunhoferISE for processing of the samples, as well as Heraeus PreciousMetals GmbH & Co. KG for their support and supply of devel-opment pastes.

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[11] C. W. Macosko, Rheology: Principles, Measurements and Applications.Poughkeepsie, NY, USA: Wiley/VCH, 1994.

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Maximilian Pospischil studied mechanical engi-neering with the Technical University of Munich (TUMunich), Munich, Germany, and the Technical Uni-versity of Delft, Delft, Netherlands, and received theDiploma degree from the TU Munich in December2009. Since 2010, he has been working toward thePh.D. degree with the “Thermal, PVD and PrintingTechnology/Ind. Cell Structures” Department, Fraun-hofer ISE, Freiburg, Germany. He is currently busywriting his Ph.D. thesis about the development of anindustrial front side metallization process for silicon

solar cells based on dispensing technology.

Jan Specht studied print and media technologywith Stuttgart Media University, Stuttgart, Ger-many. He wrote the diploma thesis about Hotmelt-Screen-Printing for Silicon Solar Cell Metallization.Since then, he has been involved with Printing-, Metallization- and Structuring-Technologies withSilicon Solar Cell Research, Fraunhofer ISE,Freiburg, Germany.

He is currently with Fraunhofer IMS, Duisburg,Germany.

Markus Konig received the Graduate degree in ce-ramics and the Diploma and Ph. D. degrees in materialscience from the Technical University of Darmstadt,Darmstadt, Germany.

He has been working with Heraeus Precious Met-als, Hanau, Germany, on the development of Agpastes for the metallization of photovoltaic devicessince 2010.

Matthias Horteis received the Ph.D. degree inphysics from the University of Constance, Constance,Germany.

He has been working on the metallization of solarcells since 2005, when he joined Fraunhofer ISE,Freiburg, Germany. Since 2011, he is developingscreen print pastes for photovoltaic devices with Her-aeus Precious Metals, Hanau, Germany.

Carsten Mohr is the Business Unit Manager forthe Photovoltaics Business Unit of Heraeus, Hanau,Germany, where, as a Mechanical Engineer by train-ing, he has worked at several positions, includingProduction Engineering, Project Management, En-gineering, Business Development, and Sales in dif-ferent fields such as automotive electronics, sen-sor technology, semiconductor, and precious metalsproducts.

Florian Clement received the Ph.D degree in 2009from the University of Freiburg, Freiburg, Germany.He studied physics with the Ludwigs-Maximilian-University of Munich, Munich, Germany, and theUniversity of Freiburg and received the Diploma de-gree in 2005.

He is currently the Head of the group “MWT solarcells/printing technology,” Fraunhofer ISE, Freiburg,Germany. His research interests include the develop-ment, analysis, characterization, and highly efficientindustrially feasible MWT solar cells with rear side

passivation, i.e., the so-called HIP-MWT devices, and new printing technolo-gies for silicon solar cell processing.

Daniel Biro was born in 1972 and studied physicswith the University of Karlsruhe, Karlsruhe, Ger-many, and the University of Massachusetts Amherst,Amherst, MA, USA. He received the Ph.D. degreefrom the University of Freiburg, Freiburg, Germany,in 2003 in silicon solar cell diffusion technologies.

In 1995, he joined the silicon cell characterizationgroup, Fraunhofer ISE, Freiburg, Germany, where,in 1999, he started working with the silicon solarcell production technology group and in 2004/2005,he coordinated the design and ramp-up of the pro-

duction oriented research platform PV-TEC and is currently the Head of theDepartment “Thermal, PVD and Printing Technology /Ind. Cell Structures.”