22 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 1, JANUARY 2014

Optical and Electrical Simulation of μc-Si:H SolarCells: Effect of Substrate Morphology

and Crystalline FractionDo Yun Kim, Rene A. C. M. M. van Swaaij, and Miro Zeman

Abstract—Hydrogenated microcrystalline silicon (μc-Si:H) is animportant material for high-efficiency multijunction solar cells.Due to its complex microstructural properties, it is difficult to de-scribe the electronic behavior clearly. In this study, we measureopto-electronic properties including the mobility gap of μc-Si:Hfilms in solar cells, as well as physical properties such as the crys-talline fraction profile. The height distribution function of the ZnOsubstrates is obtained by AFM scans, which is used for optical sim-ulation. All the parameters that we obtained from measurementswere used as input parameters of a model in the ASA simulator.We obtained a good fit between measurements and simulations

Index Terms—Microcrystalline silicon, mobility gap, optical andelectrical simulation, solar cells, TCO morphology.

I. INTRODUCTION

HYDROGENATED amorphous silicon (a-Si:H) is an im-portant material for thin-film solar cell technology. For a

better understanding, much effort has been devoted to computermodeling of a-Si:H devices. To date, computer modeling hasbeen quite well established and a fairly good match between ex-periment and simulation results has been demonstrated, therebyenabling good interpretation of the device operation [1]–[4].Even though hydrogenated microcrystalline silicon (μc-Si:H) isalso regarded as a key material for micromorph solar cells, lesswork has been carried out on computer modeling of μc-Si:Hsolar cells. In spite of its importance, the electronic propertiesof μc-Si:H are not completely understood due to its complicatedmicrostructure, as illustrated in Fig. 1(a). In reality, during thevery early stages of μc-Si:H film growth, an incubation layeris formed, followed by microcrystallites growing with differentsizes, amorphous tissues surrounding the crystals, grain bound-aries, cracks, dislocations, etc.

For the modeling of μc-Si:H, two different methods are used.The first model considers amorphous and crystalline regions,and grain boundaries separately. Depending on their fraction,each factor can affect opto-electrical properties significantly

Manuscript received June 16, 2013; revised August 17, 2013; acceptedSeptember 10, 2013. Date of publication November 14, 2013; date of cur-rent version December 16, 2013. This work was supported by the EuropeanCommission under Grant 283501 in the framework of the FP7 project “FastTrack.”

The authors are with Photovoltaic Materials and Devices Laboratory,Delft University of Technology, 2628 CD Delft, The Netherlands (e-mail:D.Kim@tudelft.nl; R.A.C.M.M.vanSwaaij@tudelft.nl; M.Zeman@tudelft.nl)

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.2013.2287770

Fig. 1. Schematic representation of (a) μc-Si:H solar cell in reality and(b) μc-Si:H solar cell in the effective medium approximation.

and to a different extent. This approach, however, needs inputparameters for each phase, which are difficult to obtain as thesematerial parameters are extracted from general measurements.

The second model uses the effective medium approach(EMA), treating μc-Si:H as if it is a single-phase material insteadof considering each respective phase, as illustrated in Fig. 1(b).This approach ignores detailed information of the componentmaterials; however, this is a simple and time-saving method.

To achieve highly efficient μc-Si:H solar cells, securing thematerial quality is regarded as a key factor. In addition, lightmanagement techniques are taken into account for the sameobjective. Proper light management is generally achieved bytuning the substrate morphology. In the literature, it has beenreported that film growth is strongly dependent on the substratemorphology [5]. It has been demonstrated that μc-Si:H grownon highly textured substrates, beneficial for increasing the pho-tocurrent through light trapping, has many cracks in the growthdirection, suppressing the efficiency.

In this context, it is necessary to figure out how material pa-rameters of μc-Si:H change under different conditions in orderto develop an accurate simulation model that fits the experimen-tal results well, such that solar-cell behavior can be character-ized properly and design can be optimized. Therefore, in thiscontribution, we carry out optical and electrical simulations ofμc-Si:H solar cells deposited on different substrates by usingthe ASA simulator that has been developed at the Delft Uni-versity of Technology (TU Delft) [6]. For these simulations,the effective medium approximation is adopted to describe theμc-Si:H.

2156-3381 © 2013 IEEE

KIM et al.: OPTICAL AND ELECTRICAL SIMULATION OF μc-Si:H SOLAR CELLS 23

TABLE IVARIOUS ZnO SUBSTRATES FROM DIFFERENT INSTITUTE

II. EXPERIMENTAL AND SIMULATION PROCEDURES

In this study, various samples were investigated and char-acterized, including TCO substrates; p, i and n-type μc-Si:Hlayers; and solar cells., These layers and devices were fabri-cated by Forschungszentrum Julich (FZJ), Ecole polytechniquefederale de Lausanne (EPFL), and TU Delft. In Table I, vari-ous types ZnO substrates used in this study are tabulated. TheZnO:Al from FZJ (crater-like shape), hereafter called ZJL, isfabricated by sputtering, and ZnO:B from EPFL (pyramidalshape), hereafter referred to as ZEP1 to ZEP3 depending on theRMS roughness (σRMS ), is fabricated by low-pressure chemicalvapor deposition (LPCVD).

Atomic force microscopy (AFM) scans of 256 × 256 pointsover an area of 10 μm × 10 μm on the ZnO substrates, n-layers,and back ZnOs of p-i-n solar cells were taken to obtain the heightdistribution functions, z(x, y), which in turn are used for opticalsimulations that are based on the scalar scattering model as de-scribed by Jager et al. [7]. With this model, the angular intensitydistribution (AID) function is calculated. This model is com-bined with the ASA simulator. Optical film properties, such asthe refractive index and extinction coefficient of μc-Si:H layers,are characterized for use as practical and reliable input parame-ters in our simulations. For the description of μc-Si:H, we haveadopted the EMA. μc-Si:H is a heterogeneous material that con-sists of a-Si:H, silicon crystals, grain boundaries, voids, cracks,etc., and the contribution to the optical properties of each com-ponent is difficult to ascertain. Using the EMA, the properties ofthe μc-Si:H layers that we measured are regarded to represent theentire (or average) properties of the μc-Si:H layers. The electri-cal properties of films and devices are also measured to be usedas input parameters for electrical modeling, where we followedthe percolation approach as used by Pieters et al. [8]. In addition,we assumed the infinite surface recombination velocity, becausepractically no excess minority carriers reach the contacts adjoin-ing the doped layers. Because of the very low carrier lifetimesin the doped layer, the excess minorities recombine before theycan reach the contact surface [9]. For comparison of simulationto experimental external solar cell results, quantum efficiency(QE), illuminated current density versus voltage (J–V ) charac-teristics, and temperature-dependent dark J–V characteristicsof solar cells from FZJ, hereafter called SJL, EPFL, hereafterreferred to as SEP1 to 3, and TU Delft, hereafter named SDFT,are measured. The SJL and SEP solar cells have the structureof Front ZnO/p-μc-Si/ i-μc-Si/n-μc-Si/Back ZnO/Back metalcontact. The SDFT solar cell also has the same structure, exceptfor the back ZnO, which was omitted. All of the solar cells hadthe same i-layer thickness of around 1.1 μm. The detailed PV

TABLE IIPHOTOVOLTAIC PARAMETERS OF SOLAR CELLS ON DIFFERENT SUBSTRATES

USED IN THIS STUDY FOR SIMULATIONS

Fig. 2. SEM images of (a) ZEP3, (b) Ag/Cr/Al back contact and cross-sectionof the (c) SEP3 and (d) SEP1.

parameters of the solar cells used in this simulation are tabulatedin Table II. The maximal standard deviation in the measured pa-rameters is 2 mV for the VOC , 0.05 mA/cm2 for the JSC , 0.01for the FF, and 0.07% for η. From the temperature-dependentdark J–V, the voltage-dependent dark current activation energyis calculated, from which in turn the mobility gap, Eμ , of theintrinsic layer in a p-i-n device is obtained using a model devel-oped by Pieters et al. [8]. According to this model this activationenergy is described by

Ep-i-na =

Eμ − V

2+ 3kT. (1)

III. RESULTS AND DISCUSSION

In Fig. 2(a) and (b), scanning electron microscope (SEM)images of the front ZnO with σRMS of 158 nm, Ag/Cr/Al backcontact of the p-i-n uc-Si:H solar cell on that ZnO substrate areshown as an example. From this figure, it can be clearly seenthat the surface morphology maintains a similar shape even afterthe deposition of p-i-n- solar cells followed by Ag/Cr/Ar backcontact. The difference between the Fig. 2(a) and (b) is obviouslysmall. After the deposition of the p-i-n μc-Si:H solar cells on twodifferent ZnO substrates, as shown in Fig. 2(c) and (d), whichare SEP3 and SEP1, respectively, the roughness hardly becomessmaller and the morphology of the front TCO is almost copied.Since there is a big change in refractive index between thefront TCO/p-Si, n-Si/back TCO, and the back TCO/Ag/Cr/Alback contact, there must be much reflection at those interfaces.Hence, in order to take into account these phenomena, we alsomeasured the height functions at those surfaces and used them

24 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 1, JANUARY 2014

Fig. 3. AFM images of (a) ZEP3, (b) ZEP2, (c) ZEP1, and (d) ZJL.

in our simulations. On the other hand, it can be seen from thecross-section images, that a difference in the growing surfaceof those two solar cells is apparent. In the literature, it has beenshown that solar cells on ZnO substrates with rough morphologycan have many cracks generated at the sharp and steep valleysof the ZnO [10]–[14]. This can explain the fact that the SEP3on the ZEP3 of σRMS of 158 nm has Jsc induced by betterscattering, but lower VOC and FF because of a higher crackdensity with respect to SEP1 on the ZEP1 of σRMS of 113 nm.We shall discuss this further in this paper.

In Fig. 3(a)–(d), AFM images of ZnO substrates are shown.The ZEP1 is the as-deposited ZnO:B by LPCVD and has thehighest σRMS among these substrates. The σRMS is then reducedto a value as low as 113 nm by performing Ar plasma treatmentin EPFL. In contrast, the ZJL is etched by etchant solution toform textured surfaces in FZJ.

With increasing σRMS of ZEP from 113–158 nm, the hazeratios in transmission (HT ) of all ZnO substrates increase con-tinuously, as shown in Fig. 4(a). In Fig. 4(b), the AID of theZnO substrates is shown at the wavelength of 600 nm. Here,the specular transmission component is higher for ZnO withlower σRMS and the diffuse transmission component is higherfor ZnO with higher σRMS . Both results directly indicate betterlight scattering with σRMS . The height distribution function ofz(x, y) as obtained from AFM scans of these surfaces is usedas input in the optical simulation for tracing the propagationof scattered light. The measurements (markers) are remarkablyconsistent with the simulation results (shown by lines), as de-picted in Fig. 4(a) and (b), which validates the application ofthis optical model to device simulation.

Film growth of μc-Si:H depends to a large extent on the depo-sition conditions. In addition, the growth is strongly influencedby the surface morphology of the underlying substrate. Sev-eral authors have shown [15], [16] that the crystalline fractionincreases along the growth direction and that the film growthoften starts with an amorphous incubation layer. In this context,we examined the crystalline fraction profile of μc-Si:H solarcells and films, which were fabricated on ZnO substrates having

Fig. 4 (a). Haze ratio and (b) AID in transmission of TCO layers. Markers areexperimental results and the lines are simulation results.

different σRMS . We determined the crystalline fraction profileof μc-Si:H p-i-n solar cells and layers by alternating Ramanmeasurements and reactive ion etching. From the Raman mea-surements, the crystalline fraction (XC ) was determined usingthe flowing relation:

XC =I510 + I518

I480 + I510 + I518(2)

where Ii denotes an integrated intensity of Raman spectra ati cm−1 [17].

Dry etching was carried out using a reactive ion etcher witha gas mixture of CF4 , SF6 , and N2 . The depth profiles of XC

of p-i-n solar cells and intrinsic μc-Si:H layers on differentsubstrates are shown in Fig. 5(a) and 5(b). It is noteworthy thateven at a position of ∼50 nm from the TCO, XC of all thesolar cells is 40–55 %, whereas XC of Si films on glass is 15–40%. The XC of individual films is substantially lower thanin the solar cells and continues to increase with thickness. Thedifference in XC is induced by the presence of p-μc-Si:H layer,which obviously turns out to promote crystalline growth. Themeasurements also reveal that the crystalline fraction of solarcells and i-layers are strongly affected by σRMS of substrates.With high σRMS substrates the overall XC of devices stays low.In general, if XC of i-μc-Si:H increases, the VOC decreases [18].In contrast, the VOC of SEP1 is higher than that of SEP2 andSEP3 (see Table II), even though their XC shows an increasingtrend as confirmed from Fig. 5. Given that the XC of the solarcells decreases while the TCO morphology (see Fig. 3) becomesrougher, this feature would be strongly related to the presence

KIM et al.: OPTICAL AND ELECTRICAL SIMULATION OF μc-Si:H SOLAR CELLS 25

Fig. 5 (a). Dependence of crystalline fraction profile of p-i-n devices fromdifferent institutes. (b) Intrinsic μc-Si:H films from EPFL on different substrates.

of cracks. The decreasing FFs of the solar cells with σRMS alsosupport this.

We approximated a constant XC of the i-μc-Si:H layers ofthose solar cells in the simulations by selecting XC at the middleof the i-μc-Si:H layers. Similar to the work of Pieters et al. [8],the XC is used to rescale effective density of states (DOS) ofi-layer, following the percolation assumption in which electronictransport dominantly takes place through clusters of crystallites(percolation path) [19]–[21]. Thus, a low crystalline fractionindicates low effective DOS in this simulation. This is valid es-pecially when the μc-Si:H has crystallites over the percolationthreshold. Several authors have shown theoretically and exper-imentally that percolation occurs when the crystalline fractionof μcSi:H is around 20–30% [21]–[24]. In particular, Hammaet al. showed that the conductivity of μc-Si:H films jumped upmore than three orders of magnitudes when XC reached 30%and the conductivity stayed constant even though XC increasedup to 76% [24].

In order to determine the Eμ of p-i-n devices, we measureddark J–V curves as a function of temperature (from 40 ◦C to100 ◦C at 10 ◦C intervals). The temperature was set with accu-racy of ±0.5 ◦C. For accurate measurements, we used a Keith-ley 6517 A electrometer. With this electrometer the current wasmeasured with an accuracy better than 0.01%; the voltage is setwith an accuracy of 0.15%. In general, the n-μc-Si:H layer is soconductive that it is not possible to measure precise current inthe low-voltage region, which ultimately makes it difficult to ob-tain Eμ . Therefore, the n-μc-Si:H layer outside of the effective

Fig. 6. Dark current activation energy Ep -i-na of (a) SEP1, (b) SEP3, (c) SJL,

and (d) SDFT solar cells.

solar cell is etched after the deposition of the metal back contact.Using this structure, parasitic leakage current is largely reducedin the low-voltage region. The dark current activation energycurves of SEP1, SEP3, SJL, and SDFT are shown in Fig. 6.Fitting this result to (1) shows that the Eμ of the intrinsic layersin the p-i-n devices are around 1.20, 1.19, 1.15, and 1.21 eVfor SEP1, SEP3, SJL, and SDFT, respectively. For SEP1 andSEP3, the difference between the obtained mobility gaps turnsout to be negligible, even though their XC showed quite bigdifference: ΔXC at the middle of these cells is approximately10%.

From the dark J–V measurements, we found that the cur-rent density at room temperature of the μc-Si:H solar cells wasaround ∼10−5 mA/cm2 at a voltage of 0.02 V, whereas that oftypical a-Si:H solar cells is ∼10−8 mA/cm2 as shown by Kindet al. [25]. They also showed that Eμ of a-Si:H solar cells isabout 1.69 eV, which is obviously higher than our results. Theseresults are clear indications that the current of our μc-Si:H solarcells flows through percolation paths made up by the crystallineSi phase, thus strongly supporting the validity of the percolationassumption in this study.

Subsequently, optical and electrical simulations were carriedout using ASA simulator for the μc-Si:H solar cells, using the pa-rameters obtained by measurements: the wavelength-dependentcomplex refractive index; the thickness of each layer; the heightdistribution function of the TCOs, n-layers, and back ZnOs; theactivation energy of the p- and n-layers; the dark current activa-tion energy (thereby Eμ ); and the XC of the i-layer in a p-i-ndevice [thereby re-scaled densities of states at the conductionand valence band edge (Nc0/v0)]. In addition, other parame-ters such as electron and hole mobilities (μe/h ), band tail width(Etail) and electron affinity of μc-Si:H are taken from Pieterset al. (see [8] and references therein); we assumed a constantband tail width of 31 meV. The defect density (Ndb) of the in-trinsic layer and the cross section for electron (n) or hole (p)capture, of a positively charged (+), neutral (0), or negatively

26 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 1, JANUARY 2014

Fig. 7. Simulations and measurements of (a) QEs and (b) illuminated J–Vcurves of SEP1, (c) QEs and (d) illuminated J–V curves of SEP3, (e) QEs and(f) illuminated J–V curves of SJL, and (g) QEs and (h) illuminated J–V curvesof SDFT.

charged (–) gap state (σ+/0/−n/p ) are varied for fitting simulation

results to experiment results. As a result, we obtained excellentfits, as shown in Fig. 7. The slight deviation of the QEs at longerwavelengths between experimental and simulation results orig-inate from the extinction coefficients, because μc-Si:H has verylow absorption coefficient in the long wavelength region and,therefore, it is hard to measure this accurately.

Important material parameters used in this simulation, suchas the Eμ , μe/h , Nc0/v0 , Ndb , and σ

+/0/−n/p , are tabulated in

Table III. These values are similar to those obtained in theliterature [8], [26]. Although the ZJL has the lowest σRMS andthereby lower HT , the SJL on the ZJL shows higher JSC thanthe SEP on the ZEP due to the lower Eμ of i-layer of the SJLof 1.15 eV as obtained by dark current activation energy. Thisresult is in line with the higher XC of the SJL as confirmed byRaman. The lower VOC of the SJL in this simulation originatesfrom both the reduced Eμ and increased XC (thus effectiveDOS).

TABLE IIIINPUT PARAMETERS FOR SIMULATIONS

Furthermore, our simulation results showed that the defectdensity of SEP3 was much higher (1.0 × 1016 cm−3) than thatof SEP1 (5.8 × 1015 cm−3). The defect density mainly affectsthe slope of dark J–V curves and FF in the simulation results.Therefore, we changed this value carefully to match the results.This also supports our speculation discussed previously regard-ing the generation of cracks depending on substrate morphology,which resulted in lower VOC even with lower XC .

IV. CONCLUSION

In this study, μc-Si:H films and solar cells were deposited onZnO substrates having different σRMS for optical and electricalsimulation with percolation assumption. The height functionof the ZnO substrates is obtained by AFM scans on the sub-strates and used for the optical model together with complexrefractive index and the thickness of ZnO substrates. The XC

depth profiles of μc-Si:H films and solar cells were measuredby Raman spectroscopy and the XC of the middle of intrinsiclayers was chosen to rescale effective DOS. We observed thatthe XC of the solar cells is significantly influenced by σRMS .For the determination of the Eμ of the intrinsic μc-Si:H layer inp-i-n devices, temperature dependent dark J–V measurementswere carried out. All experimentally obtained parameters wereused as input parameters for the optical and electrical modelsin the ASA simulator. We demonstrated that experimental andsimulation results are in good agreement. Although the ZJL haslower HT than the ZEP, the JSC of the SJL was higher due to itslower Eμ . This result suggests that Eμ determines to a signifi-cant extent the JSC . From experiments and simulation results,we found that the VOC is largely affected by σRMS of substrates,thereby possibly cracks, as well as XC of the solar cells.

ACKNOWLEDGMENT

The authors would like to thank Dr. M. Meier and Dr. M.Ghosh of the Forschungszentrum Julich, and S. Hanni, M.Stuckelberger, and Dr. M. Despeisse of IMT’s PV-lab (EPFL)for preparation of the samples. We would like to thank Dr. A.Campa from the University of Ljubljana for sharing his ideason optical measurements.

KIM et al.: OPTICAL AND ELECTRICAL SIMULATION OF μc-Si:H SOLAR CELLS 27

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Do Yun Kim was born in Seoul, Korea, in 1982.He received the B.Sc and M.Sc. degrees in materialsscience and engineering in 2007 and 2009, respec-tively, both from Yonsei University, Seoul, Korea.He received the Ph.D degree in physical electronicson silicon-based multijunction solar cells, under thesupervision of Prof. M. Konagai, in 2012 from theTokyo Institute of Technology, Tokyo, Japan. His re-search interests include the characterization and mod-eling of silicon-based thin-film multijunction solarcells. Since 2012, he has been a Postdoctoral Re-

searcher at the Photovoltaics Materials and Devices Laboratory, the Delft Uni-versity of Technology, Delft, The Netherlands.

Rene A. C. M. M van Swaaij was born in Maastricht,the Netherlands, in 1966. He received the M.Sc. andPh.D. degrees in physics in 1990 and 1995, respec-tively, both from Utrecht University, Utrecht, TheNetherlands.

In 1997, he joined the Delft University of Technol-ogy, Delft, The Netherlands, to work on amorphous-silicon-based solar cells. In 2002, he was appointed anAssociate Professor within Electronic Components,Technology, and Materials (ECTM). Since January 1,2009, he has been with the Photovoltaic Materials and

Devices Group, Department of Electrical Sustainable Energy Delft Universityof Technology. His research interests include the fast deposition of amorphoussilicon layers and the physics underlying the operation of amorphous silicon so-lar cells. He has authored and co-authored more than 80 journal and conferencepapers.

Miro Zeman was born in Slovakia in 1957. Hereceived the B.Sc and Ph.D. degrees in materialsscience in 1981 and 1989, respectively, both fromthe Slovak University of Technology, Bratislava,Slovakia.

In 1989, he became a member of the Solar CellGroup, Delft University of Technology, Delft, TheNetherlands. In 2009, he was appointed a Full Profes-sor with the Delft University of Technology for theChair of Photovoltaic Materials and Devices in theDepartment of Electrical Sustainable Energy. Since

1989, he has been in charge of more than 30 Dutch and six European projectsdealing with the development of thin-film solar cells and technology for theirfabrication. He has authored and co-authored more than 130 scientific publi-cations and contributed to two scientific books. In 2006, he co-founded thenonprofit organization Slovak Renewable Energy Agency in Slovakia. His re-search interests include the development of novel concepts for the improvementof thin-film silicon solar cell performance and modeling of devices based onamorphous semiconductors.