characterization and optimization of absorbing plasma-enhanced chemical vapor deposited...

Characterization and optimization ofabsorbing plasma-enhanced chemical vapordeposited antireflection coatings for silicon photovoltaics

Parag Doshi, Gerald E. Jellison, Jr., and Ajeet Rohatgi

We have optimized plasma-enhanced chemical vapor deposition ~PECVD! of SiN-based antireflection~AR! coatings with special consideration for the short-wavelength ~,600 nm! parasitic absorption in SiN.Spectroscopic ellipsometry was used to measure the dispersion relation for both the refractive index n andthe extinction coefficient k, allowing a precise analysis of the trade-off between reflection and absorptionin SiN-based AR coatings. Although we focus on photovoltaic applications, this study may be useful forphotodetectors, IR optics, and any device for which it is essential to maximize the transmission of lightinto silicon. We designed and optimized various AR coatings for minimal average ~spectrally! weightedreflectance ~^Rw&! and average weighted absorptance ~^Aw&!, using the air mass 1.5 global solar spectrum.In most situations ^Rw& decreased with higher n, but ^Aw& increased because k increased with n. For thepractical case of a single-layer AR coating for silicon under glass, an optimum refractive index of ;2.23~at 632.8 nm! was determined. Further simulations revealed that a double-layer SiN stack with an n 52.42 film underneath an n 5 2.03 film gives the minimum total photocurrent loss. Similar optimizationof double-layer SiNySiO2 coatings for silicon in air revealed an optimum of n 5 2.28 for SiN. Todetermine the allowable tolerance in index and film thickness, we generated isotransmittance plots,which revealed more leeway for n values below the optimum than above because absorption begins toreduce photocurrent for high n values. © 1997 Optical Society of America

Key words: Antireflection coatings, plasma-enhanced chemical vapor deposition, silicon, silicon ni-tride, photovoltaics, solar cells, absorption.

1. Introduction

Plasma-enhanced chemical vapor deposition ~PECVD!of SiN and SiO2 dielectrics has become increasinglypopular for photovoltaic applications. Not only dothese films serve as durable antireflection ~AR!coatings that are impervious to moisture ~un-like alternatives such as ZnSyMgF2 coatings!, theyalso provide efficient surface and bulk defectpassivation1–4 through the hydrogen species avail-able in the film.5,6 In addition, PECVD films canbe deposited extremely rapidly ~10–50 nmymin! atlow enough temperatures ~200–500 °C! to prevent

P. Doshi and A. Rohatgi are with University Center of Excellencefor Photovoltaics Research and Education, Department of Electri-cal and Computer Engineering, Georgia Institute of Technology,Atlanta, Georgia 30332. G. E. Jellison is with Solid State Divi-sion, Oak Ridge National Laboratory, Oak Ridge, Tennessee37831.

Received 25 November 1996; revised manuscript received 30May 1997.

0003-6935y97y307826-12$10.00y0© 1997 Optical Society of America

7826 APPLIED OPTICS y Vol. 36, No. 30 y 20 October 1997

minority-carrier lifetime degradation or unwanteddiffusion of metallic impurities from contacts. Fi-nally, well-designed PECVD processes are compati-ble with other in situ processes such as plasmaetching of silicon7–9 and hydrogen plasma treatmentsto promote passivation of bulk defects.10,11

In this paper we present the optimization of thesePECVD coatings for silicon antireflection through acombination of spectroscopic ellipsometry measure-ments to determine refractive index n and extinctioncoefficient k and detailed calculations of reflectance,absorptance, and transmittance for various SiN-based AR coating options. To our knowledge this isthe first attempt at quantifying the effect of parasiticabsorption in SiN, although Saitoh and co-workers12

considered the complex refractive index of SiN.They, however, computed the effect of the complexindex only on reflectance, without including the ef-fects of absorption on the reduction of short-circuitcurrent density. Instead this study focuses on cal-culating and decoupling the loss in photocurrent re-sulting from unwanted reflection and absorption. Inaddition, we exploit the ability to tune through a wide

range of optical constants ~by varying the gas com-position in the PECVD plasma! to characterize manySiN films and determine the maximum tolerable in-dex before absorption begins to increase the totalphotocurrent loss. Thus the SiN coatings weretuned to maximize the transmission of light into pla-nar silicon for various situations including silicon inair or under glass. It is important to note that thecharacterization and analysis of the films and ARcoatings investigated in this study are relevant notonly to photovoltaic devices but also to photodetec-tors, infrared optics, and any application in which itis essential to maximize the transmission of light intosilicon over a broad range of wavelengths.

2. Sample Preparation

SiN films were deposited on polished silicon samplesin the Plasma-Therm PECVD system operating at13.6 MHz. Deposition conditions included a pres-sure of 0.9 Torr, power of 20 W, and temperature of300 °C. The refractive index n of SiN was varied bycontrolling the SiH4 to NH3 flow-rate ratio. For thisstudy ten SiN films were analyzed in the range of n 52.0 to n 5 2.5 because this generally covers the op-timum range for single- and double-layer PECVD ARcoatings for silicon. To obtain the wavelength de-pendence ~dispersion relation! of n and k, we per-formed spectroscopic ellipsometry measurements onthese ten films. Spectroscopic ellipsometry mea-surements at 632.8 nm for these ten films gave indexvalues of n 5 2.03, 2.12, 2.20, 2.23, 2.25, 2.28, 2.33,2.35, 2.42, 2.55. Similar measurements for PECVDSiO2 films were not acquired because SiO2 is not lossy~k 5 0!. Instead the dispersion relation of SiO2 wascomputed by Conrady dispersion formula13:

n~l! 5 N 1Bl

1C

l3.5 , (1)

where for SiO2, N 5 1.447, B 5 0.00374, C 50.00057, and l is the wavelength in micrometers.Equation ~1! gives a fairly constant index, varyingonly from 1.451 at 1100 nm to 1.465 at 400 nm. TheSellmeier formulation for SiO2 gives nearly identicalvalues, differing by ,0.0015 in index at any wave-length. Ellipsometer readings of SiO2 films at 632.8nm were in agreement with these formulations.

3. Spectroscopic Ellipsometry

Spectroscopic ellipsometry measurements were madewith a two-channel spectroscopic polarization modu-lation ellipsometer14 from 250 to 840 nm. This in-strument measures the associated ellipsometricparameters

N 5 cos~2C!, (2a)

S 5 sin~2C!sin~D!, (2b)

C 5 sin~2C!cos~D!, (2c)

where C and D are the standard ellipsometric anglesrepresenting the change in amplitude and phase

shift, respectively, upon reflection. The ellipsomet-ric data were first converted to the r representation,

r 5rp

rs5 tan~C!exp~i z D! 5

C 1 iS1 1 N

, (3)

where rp~rs! is the complex reflection coefficient forlight polarized parallel ~perpendicular! to the plane ofincidence.

The ellipsometric r data were then fit to a four-medium model consisting of airyroughnessyamor-phous SiNysilicon. We approximated the roughnesslayer by using the Bruggeman effective medium ap-proximation,15 assuming that it consisted of 50% air,50% SiN. We parameterized the amorphous siliconlayer with five fittable parameters by using the for-mulation of Jellison and Modine.16 In this formula-tion, the imaginary part of the dielectric function is aproduct of the Tuac joint density of states and theLorentz formula for a collection of noninteracting at-oms and is given by

e2TL~E! 5AE0C~E 2 Eg!

2

~E2 2 E02!2 1 C2E2

1E

E . Eg

5 0 E # Eg. (4)

The four fittable parameters are the amplitude A,the band gap Eg, the Lorentz resonant energy E0, andthe broadening factor C. The real part of the dielec-tric function is determined by a Kramers–Kronig in-tegration,

e1~E! 5 e1~`! 1 S2pDP *

Eg

` je2~j!

j2 2 E2 dj, (5)

where an additional fitting parameter e1~`! has beenadded. This integral can be solved in closed formand is given in Ref. 16. Finally, n and k can becalculated:

n~E! 5 Re$@e1~E! 2 i z e2TL~E!#1y2% , (6a)

k~E! 5 Im$@e1~E! 2 i z e2TL~E!#1y2% . (6b)

Altogether, there are seven parameters to be fitted:the two film thicknesses and the five parameters usedto describe the dielectric function for the SiN film.Table 1 shows the seven fitted parameters for the tenSiN films characterized in this study. In the fittingprocedure we incorporate experimental errors anduse the reduced x2 as the figure of merit; therefore theseven fittable parameters are determined along withthe correlated and uncorrelated error.17,18 In almostall cases the reduced x2 , ;1, indicating that themodel does fit the data quite well. Table 1 alsoshows that the correlated errors for the film thicknessare very small, ranging from only 1 to 3 Å. Thecorrelated errors are usually the largest because theyinclude the uncertainties of the model fitting. Theuncorrelated errors were only 0.5 6 0.1 Å.

Using Eqs. ~4!–~6! with the fitted parameters inTable 1 @and the closed form of Eq. ~5! from Ref. 16#, wecalculated the refractive index n ~Fig. 1! and extinc-

20 October 1997 y Vol. 36, No. 30 y APPLIED OPTICS 7827

tion coefficient k ~Fig. 2! for each film. Note that thevalues of n and k represent an extrapolation from 840to 1200 nm. ~Because there are no critical pointsnear these wavelengths, this is a reasonable extrap-olation.! Within the wavelengths of interest both nand k decrease with wavelength, and the increase inn is accompanied by an increase in k. It is clear thatthe wavelength dependence of n and k cannot beneglected. The refractive index varies by as much

Table 1. Fitted Parameters from the Spectroscopic Ellipsometry Dataof the 10 Films

n~632.8nm!

drough

~Å!

d~SiN!~Å!

d ~SiN!Correlated

Error~Å!

Eg

~eV!A

~eV!E0

~eV!C

~eV! e1~`! x2

2.03 24 491 3 2.76 70 8.15 6.12 1.40 0.772.12 22 589 2 2.50 93.3 7.75 9.47 1.10 0.162.20 22 606 1 2.37 93.7 6.28 8.03 1.41 0.192.23 33 568 2 2.34 105 6.90 9.50 1.11 0.722.25 27 563 2 2.32 98 6.39 8.16 1.31 0.842.28 34 595 1 2.30 106 6.36 8.96 1.31 0.612.33a 35 516 2 2.14 108 6.33 9.50 1.16 0.902.35a 32 549 2 2.14 113 6.12 9.50 1.12 2.142.42 30 739 1 2.18 117.1 5.23 7.09 1.30 0.452.55 33 668 1 2.12 126.4 4.78 6.22 1.36 0.51

aThese two films experienced a 750 °Cy10-s rapid thermal an-neal.

as 0.5 over the wavelength range shown, and k is highat shorter wavelengths but vanishes when the photonenergy is below the bandgap energy ~Eg! of the film.

The correlated errors in the refractive index ~Dn!,the extinction coefficient ~Dk!, and ad were alsosmall. Table 2 shows these errors for one of thesamples @n~632.8 nm! 5 2.42#. The error in n isroughly constant ~1.2%–1.4%!, whereas the error in kdecreases as k becomes smaller ~but the percent errorincreases!. Because these are correlated errors,they are an overstatement of the errors in n and k.The error in exp~2ad! is also small ~0.3–4.6%! anddecreases for higher wavelengths. Because onlywavelengths above 400 nm will be included for coat-ing optimization ~explained below!, this error neverexceeds 2.1%. Similar errors were also determinedfor the lower-index @n~632.8 nm! 5 2.03# film. Thusthe actual error propagated into the photocurrentloss and optimum thickness calculations are expectedto be quite small.

4. Simulation Procedure

Once the dispersion relation was determined for theten SiN films, optimization of these absorbing ARcoatings was possible. To obtain optical constants~n and k! for silicon, we employed external data filesintended for use with the PC-1D19 semiconductor de-vice simulator ~namely, SI.INR and SI.ABS!. The

Fig. 1. Index of refraction for SiN films measured from spectroscopic ellipsometry data.

Table 2. Correlated Errors for the n~632.8! 5 2.42 Filma

l~nm!

Dn Dk

ada D~ad! exp~-ad!

D@exp~-ad!#

Absorptance % Error Absorptance % Error Absorptance % Error

270 0.036 1.4 0.017 1.8 0.05 0.072 0.004 0.072 4.6350 0.035 1.3 0.010 2.1 0.02 0.352 0.006 0.352 2.1500 0.030 1.2 0.002 5.7 0.003 0.949 0.003 0.949 0.30800 0.029 1.2 0 0 0 0 0 0 0

aAll ad errors were calculated for a thickness of 600 Å.


Fig. 2. Extinction coefficient for SiN films measured from spectroscopic ellipsometry data.

silicon refractive-index data originated from Ref. 20,and silicon absorption coefficient data were obtainedfrom Green’s21 interpolation of data in Ref. 22. Weobtained the value for k from the silicon absorptioncoefficient data by using the simple relation

k 5al

4p, (7)

where a is the absorption coefficient and l is thewavelength. The goal of optimizing the AR coatingsfor a photovoltaic device is to maximize the short-circuit current density Jsc, or equivalently, to reducethe photocurrent loss resulting from reflection andabsorption, referred to as Jpcl in this paper. Losses

associated with the AR coating system can be com-puted as

Jpcl 5 q (l

@Nph~l!uAM1.5GR~l!IQE~l!#

1 q (l

@Nph~l!uAM1.5GA~l!IQE~l!# 5 Jpclurefl 1 Jpcluabs,

(8)

where q 5 1.6 3 10219, Nph~l!uAM1.5G is the number ofphotonsycm2ys at each wavelength available to thecell under a 1-sun illumination according to the airmass 1.5 global solar spectrum, R is the front surfacereflectance, A is the absorptance, and IQE is the in-ternal quantum efficiency ~ratio of photocurrent col-lected to photocurrent absorbed within the cell!.Note that in Eq. ~3! the component of photocurrent

Fig. 3. Distribution of photocurrent density available under ~1-sun! air mass 1.5 global solar spectrum used for spectral weighting ofreflectance, absorptance, and transmittance.


Fig. 4. Plots of reflectance plus absorptance ~or one transmittance! for SiN single-layer AR coatings under glass. Thickness wasoptimized for each index as shown in Table 2. Dotted curves with open symbols show reflectance only, no absorption.

loss resulting from reflection and absorption is di-vided into two separate terms. Because the IQEvaries from cell to cell, we assumed a 100% IQE overthe wavelengths of 400–1100 nm and zero IQE else-where to estimate the optimum coating system usefulfor all cells. Therefore the calculations in this studyrepresent the maximum photocurrent loss over the400–1100-nm range, which would have to beweighted by the IQE ~#1! of an existing cell to eval-uate the actual photocurrent loss of any particulardevice.

The evaluation of AR coating systems was per-formed by calculation of the average reflectance, ab-sorptance, and transmittance weighted by the solarspectrum in this study. The equations for reflec-tance and transmittance can be found in many texts~e.g., Ref. 23!, and for these calculations a softwarepackage, called CAMS,24 was used. The factors forweighting the optimization with the solar spectrum~see Fig. 3! were calculated from the relative powerdensity of the air mass 1.5 global solar spectrum ateach wavelength ~PC-1D file AM15G.SPC!. Thesedata were first scaled up to equal a 1-sun ~0.1 Wycm2!illumination to give P~l! and then divided by theenergy ~in electron volts! per photon, Eph, to yield thephotocurrent density Jpc ~in amperes per square cen-timeter! available at each wavelength. Thus theweighting factors are directly proportional to thenumber of photons at a particular wavelength:

Jpc~l! 5 qNph~l!uAM1.5G 5qP~l!uAM1.5G

Eph~l!

5qP~l!uAM1.5G

hcl

5P~l!uAM1.5G

1.24~eV!yl~mm!. (9)


Next the CAMS software was used to compute the av-erage weighted reflectance ^Rw&, absorptance Âw&,and transmittance ^Tw& according to

^Yw& ;(

l5400nm

1100nm

Y~l!Jpc~l!

(l5400nm

1100nm

Jpc~l!

, (10)

where Y is the quantity of interest ~R, A, or T! andJpc~l! is the weighting factor shown in Fig. 3. Thedenominator in Eq. ~10! is 41.46 mAycm2, whichnormalizes the weighting factors and is the total pho-tocurrent available from 400 to 1100 nm for the 1-sun, air mass 1.5 global spectrum. The figure ofmerit for a coating system is ^Tw& because this is thequantity to maximize in order to achieve minimalphotocurrent loss. Using the definition in Eq. ~10!and R~l! 1 A~l! 1 T~l! 5 1 results in

^Tw& 5 1 2 ~^Rw& 1 Âw&!. (11)

So, by weighting R, A, and T as defined in Eq. ~4! andmaking IQE 5 1, the photocurrent loss in Eq. ~8!simplifies to

Jpcl 5 ~^Rw& 1 Âw&! (l5400nm

1100nm

Jpc~l!

5 ~1 2 ^Tw&! (l5400nm

1100nm

Jpc~l!. (12)

Thus the procedure for optimization required deter-mination of the thickness of the individual layers thatmaximizes ^Tw&. We did this by varying the filmthickness of each of the ten films ~for each situation!and computing ^Tw&.

Table 3. Single Layer AR Coatings of SiN, Under Glass

Index~632.8 nm!

OptimizedThickness

~Å!^Rw&~%!

^Aw&~%!

^Tw&~%!

Photocurrent Loss ~mAycm2!

Reflected Absorbed Total

Uncoated — 19.02 0.00 80.98 7.89 0.00 7.892.03 760 6.00 0.03 93.97 2.49 0.01 2.502.12 720 5.14 0.38 94.48 2.13 0.16 2.292.20 690 4.52 0.94 94.54 1.87 0.39 2.262.23a 680a 4.37a 1.03a 94.60a 1.81a 0.43a 2.24a

2.25 680 4.30 1.15 94.55 1.78 0.48 2.262.28 670 4.16 1.34 94.50 1.72 0.56 2.282.33 650 3.98 2.42 93.60 1.65 1.00 2.652.35 650 3.97 2.62 93.41 1.65 1.09 2.732.42 630 4.09 2.66 93.25 1.70 1.10 2.802.55 590 4.45 3.53 92.02 1.85 1.46 3.312.40, k 5 0b 645 3.68 0.00 96.32 1.53 0.00 1.53DLAR 2.42y2.03c 400y480 2.96 1.74 95.30 1.23 0.72 1.95

aValues represent optimum SiN single-layer coating under glass.bThis “unrealistic” coating represents a constant 2.40 index to show the ideal film if absorption is neglected.cValues are for double-layer antireflection case.

5. Results and Discussion

A. Coatings Under Glass ~n 5 1.5!

Because solar cells require encapsulation with glassas the top layer facing the Sun, the optimization ofPECVD AR coatings under glass is most practical.The analysis in this section assumes that the siliconis in optical contact with the glass. The most com-mon PECVD AR coating option involves a singlelayer of SiN. Table 2 shows the results of the anal-ysis in which the thickness of each of the ten SiNfilms was varied to obtain the maximum ^Tw&. Forcomparison Table 2 also shows an ideal film with aconstant 2.40 index without absorption ~k 5 0!. Theideal case represents the quarter-wave optimum ARcoating for silicon under glass ~n 5 ~nglassnSi!

1y2; nd 54l!. Figure 4 shows the reflectance plus ab-

sorptance ~or one minus transmittance! for several ofthese AR coatings. The dotted curves ~with openmarkers! show the reflectance only to separatelyhighlight the parasitic absorption in each coating.Although stoichiometric SiN with an index of ;2.0 ismost commonly used because of its almost negligibleabsorption, its reflectance ~^Rw& 5 6.0%! is high be-cause of the poor match with glass ~see Table 3 andFig. 4!. Increasing the index to 2.42 lowers ^Rw& to4.1% because it is close to the optimum quarter-waveAR coating; however, the high absorption loss of 1.1mAycm2 makes this high-index film a poor choice aswell. Given the trade-off in reflectance and absorp-tion, the optimum SiN single-layer coating underglass was found to be an index of 2.23 and thicknessof 680 Å, which gave the greatest ^Tw& 5 94.6%, re-sulting in a photocurrent loss of 2.24 mAycm2. Thus

Fig. 5. Isotransmittance curves for SiN single-layer AR coatings under glass. Curves are labeled with the amount of additionalphotocurrent loss from the optimum, which is at n 5 2.23 and a thickness of 680 Å.


Table 4. Single-Layer SiN, in Air

Index~632.8 nm!

OptimizedThickness

~Å!^Rw&~%!

^Aw&~%!

^Tw&~%!



Uncoated — 34.17 0.00 65.83 14.17 0.00 14.172.03a 780a 7.98a 0.02a 92.00a 3.31a 0.01a 3.32a

2.12 740 8.54 0.33 91.13 3.54 0.14 3.682.20 720 9.25 0.80 89.95 3.84 0.33 4.172.23 710 9.46 0.89 89.65 3.92 0.37 4.292.25 700 9.64 0.99 89.37 4.00 0.41 4.412.28 690 9.97 1.15 88.88 4.13 0.48 4.612.33 680 10.43 2.12 87.45 4.32 0.88 5.202.35 680 10.60 2.28 87.12 4.39 0.95 5.342.42 660 11.64 2.29 86.07 4.83 0.95 5.782.55 630 13.31 3.05 83.64 5.52 1.26 6.782.0, k 5 0b 790 7.38 0.00 92.62 3.06 0.00 3.06

aValues represent optimum single-layer SiN coatings in air.bThis “unrealistic” coating represents a constant 2.0 index to show the ideal film if absorption is neglected.

accurate characterization of the film’s extinction co-efficient proved crucial in determining the maximumindex that can be used. Without the k values, onewould conclude that high-index values as great as2.40 ~see Table 3! would be optimal based purely onreflectance; however, if employed, absorption wouldseverely degrade cell efficiency. It is important tonote that the calculations do not include the extra 4%reflectance loss at the air–glass interface, whichwould decrease the photocurrent available between400 and 1100 nm by 1.66 mAycm2 ~4% of 41.46 mAycm2!. Also not included is the shading of a front gridcontact because this factor varies considerably amongcell designs and contact schemes and is not importantfor this study.

Improvement is possible by use of a double-layerAR ~DLAR! coating under glass. This could be done

by depositing a high-index SiN film below a lower-index SiN film. Table 3 shows that an optimized2.42y2.03 DLAR coating results in an additional 0.3mAycm2 of photocurrent compared with the bestsingle-layer AR coating. This DLAR coating is quitepractical and cost effective because both of the coat-ings can be easily deposited in the same PECVDchamber without removal of the silicon wafers.Such a coating system also has advantages in termsof bulk and surface defect passivation through therelease of the atomic hydrogen that is abundantlyavailable in the as-deposited PECVD SiN.5,6 Re-cently, Cai et al.25 showed ~by Fourier transform in-frared spectroscopy measurement of Si–H and N–Hbond concentrations! that the high-index films con-tain a greater amount of hydrogen than lower-indexfilms and that these high-index films also release a

Fig. 6. Plots of reflectance plus absorptance ~or one minus transmittance! for SiN single-layer AR coatings in air. Thickness wasoptimized for each refractive index as shown in Table 3. Dotted curves with open symbols show reflectance only, no absorption.


Table 5. SiNySiO2 Double-Layer AR Coatings, in Air

SiN Index~632.8 nm!

Optimum SiNThickness

~Å!

Optimum SiO2

Thickness~Å!

^Rw&~%!

^Aw&~%!

^Tw&~%!



2.03 670 890 5.41 0.04 94.55 2.24 0.02 2.262.12 660 950 4.12 0.41 95.47 1.71 0.17 1.882.20 630 970 3.10 0.99 95.91 1.29 0.41 1.702.23 630 980 2.85 1.08 96.07 1.18 0.45 1.632.25 620 980 2.71 1.20 96.09 1.12 0.50 1.622.28a 610a 980a 2.46a 1.38a 96.16a 1.02a 0.57a 1.59a

2.33 590 990 2.12 2.42 95.46 0.88 1.00 1.882.35 590 990 2.05 2.61 95.34 0.85 1.08 1.932.42 570 1000 1.86 2.66 95.48 0.77 1.10 1.872.55 540 1020 1.84 3.49 94.67 0.76 1.45 2.212.55, k 5 0b 575 1100 1.54 0.00 98.46 0.64 0.00 0.64

aValues represent optimum double-layer SiNySiO2 coatings in air.bThis “unrealistic” coating represents a constant 2.55 index to show the ideal index if absorption is neglected.

greater amount of hydrogen after a postdepositionrapid thermal anneal. In addition, the lower-indexfilm on the top serves as a good capping layer, pre-venting outdiffusion of hydrogen. It is important tonote, however, that evidence of bulk hydrogenation ishighly material specific. Thus, depending upon thematerial, this DLAR may represent the optimal coat-ing option.

It is well known that, in practice, films may not bedeposited precisely at the optimum index and thick-ness. For this reason it is important to know theallowable tolerance in index and thickness. Figure5 shows a plot of isotransmittance curves for single-layer SiN AR coatings under glass. The optimum isshown at an index of 2.23 and thickness of 680 Å, anddeviations from the optimum result in additionalphotocurrent loss. For example, to yield a photocur-rent loss less than 0.1 mAycm2 greater than the op-

timum, the thickness must be maintained between620 and 760 Å at an index of 2.23. The curves in Fig.5 also indicate the tolerable deviation in index. Toyield a photocurrent loss less than 0.05 mAycm2 fromthe optimum, the index must be maintained between2.12 and 2.28. Notice also that the curves are asym-metric around the optimum index. The asymmetryis due to the increased absorption in higher-indexSiN films. Thus there is significantly more toler-ance with n values lower than the optimum, whereashigh-index values quickly result in undesirable ab-sorption loss.

B. Coatings in Air ~n 5 1.0!

A similar analysis can be done for AR coatings in air,which is the common situation for laboratory cells.Table 4 shows the optimization of single-layer SiNAR coatings in air. The reflectance plus absorptance

Fig. 7. Plots of reflectance plus absorptance ~or one minus transmittance! for SiNySiO2 double-layer AR coatings in air. Thickness wasoptimized for each refractive index as shown in Table 4. Dotted curves with open symbols show reflectance only, no absorption.


Fig. 8. Isotransmittance curves for the case of SiNySiO2 double-layer AR coatings with the SiN refractive index fixed at 2.28 at 632.8 nm.Curves are labeled with the additional photocurrent loss from the optimum, which is at thickness values of 610 Å for SiN and 980 Å forSiO2.

plots in Fig. 6 show that the optimum choice of indexis obvious. In this case the 2.03 index maximizes^Tw&. This index is far superior to the others be-cause it simultaneously represents the quarter-waveoptimum AR coating for silicon in air and preventsthe absorption loss that accompanies the high-indexfilms.

The PECVD coating system that is perhaps themost widely used in the laboratory involves a double-layer SiNySiO2 coating first introduced by Chen etal.26 Table 5 shows the optimization of this DLARcoating option. Figure 7 shows a plot of reflectanceplus absorptance for these optimized coatings. Allcoatings exhibit an undesirable hump in the heavilyweighted 500–700-nm wavelength range. This

hump steadily decreases only when the SiN indexincreases. Unfortunately, a high index such as 2.42absorbs a considerable amount of photocurrent ~al-most 1 mAycm2! below 600 nm. Thus backing offslightly with an index of 2.28 minimizes the totalphotocurrent loss to ;1.6 mAycm2. Reducing theindex further to 2.03 eliminates absorption butmakes the reflectance intolerably high, especially inthe critical 500–700-nm range ~as shown in Fig. 7!.The calculations in Table 5 also reveal that, if absorp-tion can be neglected, the ideal constant index film isn 5 2.55. Again, the measured k values were essen-tial for determining the highest maximum allowableindex for optimization.

Simulations were also performed to illustrate the

Fig. 9. Isotransmittance curves for SiNySiO2 double-layer AR coatings in air. Curves are labeled with the amount of additionalphotocurrent loss from the optimum, which is at n 5 2.28 and thickness of 610 Å for SiN. SiO2 thickness was fixed at 980 Å.


Fig. 10. Best double-layer AR coatings for silicon in air. Thickness of each layer was optimized as shown in Tables 4–6. Slightreduction of the “hump” ~in the 500- to 700-nm range! occurs by replacing SiO2 with MgF2. Passivating 10-nm oxide shows almost noincrease in reflectance.

allowable tolerance in film thickness and index of theSiNySiO2 double-layer AR coating. Figure 8 showsisotransmittance curves that depict the allowabletolerance in the thickness of the n 5 2.28 SiN andSiO2 films. As in Fig. 5, the curves are labeledaccording to the additional photocurrent loss result-ing from deviations from the optimum ~located at athickness of 610 Å for SiN and 980 Å for SiO2!.The curves show that fairly large thickness devia-tions from optimum to as high as 650 Å for SiN and6100 Å for SiO2 are allowable to maintain addi-tional photocurrent loss below 0.1 mAycm2. Itmust be said, however, that these tolerances be-come more strict as the index deviates from theoptimum value of 2.28. Because there is a greatertolerance in the SiO2 thickness, it was held to 980 Åto produce Fig. 9, which is a plot of isotransmittancecurves displaying the tolerance in SiN index andthickness. As observed in Fig. 5, parasitic absorp-

tion makes the curves asymmetric about the opti-mum index. Thus there is much more leeway for nvalues below 2.28 than above.

As stated above, the double-layer SiNySiO2 ARcoating did have an undesirable hump in reflectancein the critical 500–700-nm wavelength range. Fig-ure 10 shows that a slight reduction in the hump ispossible when the SiO2 is replaced with MgF2 ~which,however, is permissible only for laboratory cells, be-cause MgF2 dissolves in water!. Table 6 indicatesslightly less than 0.1 mAycm2 improvement with thismodification. Another important case to consider isthat of depositing films on top of a thin SiO2 layer,directly on top of the silicon, which is commonly usedfor high-quality front-surface passivation. Table 7shows that a 10-nm SiO2 layer can be used withoutan appreciable increase in photocurrent loss; how-ever, the thickness of the SiN layer must be reducedby roughly the thickness of the passivating oxide.

Table 6. SiNyMgF2 Double-Layer AR Coatings, in Air

SiN Index~632.8 nm!


~Å!

Optimum MgF2

Thickness~Å!

^Rw&~%!

^Aw&~%!

^Tw&~%!



2.03 710 1000 4.66 0.03 95.31 1.93 0.01 1.942.12 680 1030 3.56 0.41 96.03 1.48 0.17 1.652.20 650 1050 2.76 0.98 96.26 1.14 0.41 1.552.23a 640a 1050a 2.57a 1.07a 96.36a 1.07a 0.44a 1.51a

2.25 630 1050 2.47 1.19 96.34 1.02 0.49 1.522.28 620 1050 2.29 1.37 96.34 0.95 0.57 1.522.33 610 1050 2.04 2.45 95.51 0.85 1.02 1.862.35 600 1050 2.03 2.62 95.35 0.84 1.09 1.932.42 590 1080 1.98 2.67 95.35 0.82 1.11 1.932.55 560 1100 2.20 3.50 94.30 0.91 1.45 2.36

aValues represent optimum double-layer SiNyMgF2 coatings in air.


Table 7. Ten-nm SiO2 1 SiNyMgF2 Double Layer AR Coatings, in Air

SiN Index~632.8 nm!


~Å!

Optimum MgF2

Thickness~Å!

^Rw&~%!

^Aw&~%!

^Tw&~%!



2.03 600 1020 5.09 0.04 94.87 2.11 0.02 2.132.12 560 1040 3.99 0.40 95.61 1.65 0.17 1.822.20 530 1050 3.15 0.95 95.90 1.31 0.39 1.702.23 520 1050 2.94 1.04 96.02 1.22 0.43 1.652.25 510 1050 2.83 1.11 96.02 1.17 0.46 1.652.28a 500a 1060a 2.61a 1.33a 96.06a 1.08a 0.55a 1.63a

2.33 480 1060 2.30 2.33 95.37 0.95 0.97 1.922.35 470 1060 2.27 2.50 95.23 0.94 1.04 1.982.42 450 1070 2.16 2.52 95.32 0.90 1.04 1.982.55 410 1080 2.18 3.25 94.57 0.90 1.35 2.25

aValues represent optimum double-layer 10-nm SiO2 1 SiNyMgF2 double-layer coatings in air.

6. Summary and Conclusions

We have presented a methodology for optimizingSiN-based PECVD antireflection coatings for siliconphotovoltaic devices. This first required performingspectroscopic ellipsometry measurements to obtainaccurate refractive index and extinction coefficientdata as a function of wavelength for a wide range ofSiN films. Next computations of reflectance, ab-sorptance, and transmittance spectrally weighted bythe solar spectrum allowed minimization of the totalphotocurrent loss for various coating options.

From the film characterization and simulations ithas been shown that the optimization cannot bebased solely upon reflectance, because parasitic ab-sorption within SiN plays a major role. In most sit-uations high-index films minimized reflectance butincreased absorption. Given this trade-off, an opti-mum SiN index of 2.23 ~at 632.8 nm! was found for asingle-layer coating under glass. We simulated fur-ther improvement by using a double-layer coatingconsisting of a 2.42 index below a 2.03 index underglass. In addition to superior antireflection, thisdouble-layer coating can be advantageous for passi-vation of bulk defects within the solar cell becausehigher-index SiN films have recently been reported tohave a greater hydrogen content and seem to releasea greater amount of this hydrogen into the bulk.25

Double-layer SiNySiO2 AR coatings for silicon in airwere also optimized. In this case a 2.28 index wasfound to give the optimum results.

Calculations were also done to determine the al-lowable tolerance in index and thickness for coatingsunder glass and in air. Isotransmittance plots re-vealed an absorption-induced asymmetry about theoptimum index. Because the SiN k values werefound to increase with index, much greater leewayexists for n values below the optimum than above.Because of the fairly large flexibility in the choice ofindex to achieve the maximum transmission of lightinto a solar cell, the final choice may be governed bythe films’ ability to passivate surface and bulk de-fects. It is therefore necessary to investigate theimpact of the films’ optical parameters on defect pas-sivation. Thus a detailed study accounting for re-


flection, absorption, front surface passivation, andbulk defect passivation is ultimately required to gainthe maximum benefits of PECVD dielectrics and com-plete the optimization for photovoltaic applications.

This research was supported by Sandia NationalLaboratories subcontract AO-6162 and by the OakRidge National Laboratory, managed by LockheedMartin Energy Research Corporation for the U.S. De-partment of Energy under contract DE-AC05-960R22464.

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