4th European hotovoltaic Solar Energy Conference, 1-5 September 9, Hamburg, Germany LOCK-IN THERMOGRAHY ON CRYSTALLINE SILICON ON GLASS (CSG) THIN FILM MODULES: INFLUENCE OF ELTIER CONTRIBUTIONS H. Straube, O. Breitenstein, J.-M. Wagner Max lanck Institute of Microstructure hysics Weinberg, D-61 Halle, Germany ABSTRACT: In this contribution we escribe electro-thermal moeling of a CSG thin film silicon solar cell uner pulse bias. The moel is aime at extracting cell parameters locally through comparison with lock-in thermography (LIT) results over a wie voltage range. The cell is ivie into a number of volume elements for Spice electronics simulations. The results are image an convolute with the appropriate point sprea function for a highly heat conuctive silicon layer on a thick glass substrate. eltier effects must be taken into account since p an n type holes are separate from each other an are resolve in the thermograms. Values for the test moule s area ioe saturation currents, nonlinear ege shunts, an series resistance resulting from a manual fit of experimental an simulate thermograms are presente. Keywors: Characterization, olycrystalline Si-Films, Lock-in Thermography, eltier Effect 1 INTRODUCTION Dark lock-in thermography (DLIT) has proven to be a successful tool to quantify loss mechanisms in monoan multi-crystalline solar cells [1]. It gives images of the local power istribution (mw/m²) in the sample. The interpretation of thermograms of thin film moules such as CSG [], however, is more ifficult than that of stanar cells, ue to the more complex patterning an particularly ue to strong eltier contributions at the s. This was seen while stuying ege recombination heating at the laser grooves separating cells. Two observations were mae. Firstly, at low voltages, holes close to these eges were foun to present a negative DLIT signal. This means that here the eltier cooling is locally stronger than contributions from heat issipation at the junction, sheet an resistances. Since the eltier heat absorbe at the s is release on crossing the junction, this effect can strongly affect quantitative evaluation of localize shunting phenomena. Seconly, the cell eges appear brighter than the rest of the cell at low cell current (aroun maximum power point voltage). At higher currents, the contrast becomes inverse an the eges get less intense than the cell area. A correct moel must escribe this contrast reversal appropriately. To buil such a moel, the eltier coefficients were measure on test structures of the thin film material (section ). Since the current istribution in a cell is not homogenous a circuit moel of the cell was evelope (for the Spice circuit simulator, section 3.). The results of the electrical simulation were then translate into a map of heat generation (local power issipation an eltier heat). Convolution of this heat generation map with the thermal point sprea function gives the temperature moulation signal measure in DLIT (section 3.3). Finally, comparison of the measure ata to the calculate DLIT signal allows meaningful conclusions about cell parameters (section 4). 1.1 CSG moule layout Before a etaile escription of the measurements an simulations, a few wors about the CSG thin film moule structure are inicate. Each moule consists of 6 mm broa stripes of 1.5 µm thick silicon on glass, separate by 5 µm wie grooves. These stripes are the iniviual cells. The light enters the silicon through the glass superstrate sie. From the glass sie, it is an n -p-p structure. The cells are interconnecte by.5 mm wie aluminum pas that span two cells each an are arrange in an interigitate pattern (see Figure 1). Each pa has a number of holes reaching to the n layer in the upper cell or connecting the p layer in the lower cell, respectively. In the moules use in this stuy, each pa ha 14 n an 14 p holes. For etails about this ing scheme an its benefits, see [3]. Figure 1: CSG moule layout with three silicon cell stripes an corresponing interconnectors. Only 4 of 14 holes per pa are rawn. MEASUREMENT OF THE ELTIER COEFFI- CIENT.1 Basics In a recent contribution we escribe how to measure the eltier coefficient of semiconuctor material thermographically [4]. The basic argument is as follows: In the case of silicon on glass the -45 signal S from the lock-in process is irectly proportional to the heating ensity Q (blurre with the point sprea function). In a purely resistive sample uner isothermal conitions Joule (S J ) an eltier (S ) heating signal (corresponing to the heating terms Q J, Q ) in every point are even or o functions of the bias, respectively. Therefore, aing an subtracting signals obtaine at positive (S ) an negative bias (S - ) gives separate images proportional to Joule an eltier heating contributions: J S = ( S S ) / (1) S = ( S S ) / 5
4th European hotovoltaic Solar Energy Conference, 1-5 September 9, Hamburg, Germany For a homogenous current flow, straightforwar calculations give an expression for the eltier coefficient Π that oes not epen on the ratio of heating ensity an signal (hence no calibration is neee): A B S x S x A B Π = U = U, () B B J J S x S x A A where A an B are the (metallic) s, where the current enters an leaves the semiconuctor. U is the voltage applie between them (A positive). The integration has to be extene a istance over the actual s in orer to collect the whole signal blurre by the point sprea function of the system.. eltier coefficients in CSG CSG Solar routinely manufactures series resistance test structures which iffer from the regular structure (see Figure 1) only by that every hole is either imple (to p ) or crater (to n ). In such a structure the current never crosses any p-n junction throughout the moule. These structures are thus purely resistive an the proceure for measuring the eltier coefficient Π outline above can be applie. The resistive test structure use here is part of the same batch as the actual moule that is moele. Typical images are shown in Figure. Note that at every pa there is a homogenous current flow to the left an to the right such that the signals uner each pa are twice as high as suppose for (). The raius in () is about. mm. Figure : Measure signals S, S - an corresponing Joule S J an eltier S contributions calculate from (1) in the p region of the CSG resistive test structure. Contact pa locations are marke with soli lines. The eltier coefficient Π is foun to be (9±5) mv for the p region an (9±5) mv for the n region (U= mv for p, U=1 mv for n, at approximately short circuit current equivalent). The physical meaning an origin of these values is etaile in [4]. Following the proceures outline in [4] opant concentrations of 3 4 1 19 cm an 1 19 cm for n an p, respectively, are estimate. 3 Halving the voltages gives the same results for the eltier coefficients, which confirms the symmetries use to erive ()..3 Applicability check for CSG The approach of section.1/. requires isothermal conitions over the sample surface. In the case of thin film cells on a thick glass substrate, these cannot be impose by an external temperature control. However, it can be shown that () is still vali by calculating an upper boun to the aitional thermoelectric heating terms not consiere above. This upper boun is calculate below. In the lock-in process, the temperature at every point can be escribe by an oscillating contribution an a spatially varying mean temperature T ( = T T (. Only the oscillating contribution is etecte in the lock-in measurement. The stationary temperature inhomogeneities T ( occur only because no temperature control can be applie for a (thermally thick) substrate an give rise to aitional thermoelectric contributions. T ( can be calculate by solving the stationary heat conuction equation, assuming only half the heating power Q, since in the lock-in process the current is flowing only half of the time (κ heat conuctivity): κ T = Q /. (3) It is known that both the highly ope p an n layers have eltier coefficients less than 1 mv [4]. The Joule heating sheet resistance is fairly homogenous, an it nee not be consiere here. The temperature profile of a isk of homogenous eltier heating (isregaring for the time being any further effects) can be calculate by solving (3) numerically an is shown in Figure 3. It was assume that each hole carries the same current as in an actual moule uner short circuit conitions ( ma/cm or 5µA per hole). mean temperature offset (mk) 18 16 14 1 1 8 6 4 area uner 5 1 15 5 3 istance from center (µm) Figure 3: Mean temperature inhomogeneity T aroun a hole (heating), assuming a eltier coefficient of 1 mv an a current of 5 µa. The systematic errors cause by this temperature istribution are ue to aitional thermoelectric effects. In that case the heating power Q [the source term of the oscillatory part of the heat conuction equation (4)] is [5]: 51
4th European hotovoltaic Solar Energy Conference, 1-5 September 9, Hamburg, Germany Figure 4: Spice moel for a 1 mm wie portion of a CSG cell. In the first line, the n region (blue) is connecte to the next cell of the moule by 14 holes (below). In the secon line, 14 holes (above) the p region (re) to the previous cell. The elementary ioes, istribute accoring to the location of the holes, are interconnecte by the sheet resistivity in the p an n layers. Q( = ρ( j( j( T α( r, T ) j( T j( τ ( T ( α( r, T ) (, where τ is the Thomson coefficient, an the temperature epenence of α is taken to be explicit. lease note the Thomson relations τ = T α / T an Π = αt. The first j two terms ρ (Joule heating) an jt α = j Π (isothermal eltier heat transport) are the ones alreay iscusse in section.1. In the test structure the Joule heating term is equally strong in the whole structure: ρj = 1 Ω/sq (33 µ A/6mm) = 3 W/m The eltier term only appears irectly uner the s as oes the thir term ( α is a step function at the metal-semiconuctor interface) I 66 µ A/14 Tα = 3 K (.1V / 3 K) A π (7 µ m) = 36 W/m I 66 µ A/14 T α = mk (.1V / 3 K) A π (7 µ m) =. mw/m The fourth term, the Thomson effect, is strongest at the highest temperature graient which is at the hole s circumference. 66 µ A/14 jτ T =. mv/k 4 K/m π (7 µ m) =.86 W/m Thus, both aitional terms appearing since the surface temperature cannot be force to a constant value (i.e. T ( ) ), are small compare to the terms consiere r in section.1. Hence, equation () can be use to etermine the eltier coefficient. 3 SIMULATION ROCEDURE 3.1 Overview A single cell consisting of a perioic arrangement of pas was ivie into ioes an resistors suitable for calculations with Spice (Spice version 9.). The Spice simulation output file was then parse for the iniviual ioes an resistors whose heat issipation an eltier type heat transport are copie into a map of the local heating ensity Q, that can have negative values because of the eltier effect. This map can then be convolute with the appropriate point sprea function (SF) to give the simulate LIT images that can be compare to the experimental images. Realistic values for the ioe saturation currents are extracte by ajusting the moel parameters to the ata at high an low currents. 3. Spice moel The area uner each hole is moele by one ioe an these ioes are interconnecte by resistors corresponing to the sheet resistivity (Ω/sq) of the p an n regions, respectively. Aitionally, two area ioes have been introuce to the regions without holes near the cell eges in orer to better assess series resistance losses there. Lock-in thermograms of CSG moules show a pronounce signal at the laser cut lines (grooves) between the cells. This signal is not ohmic an was moele as an extra ioe with elevate saturation current. The moel components for a small part of a single cell are shown in Figure 4. For every ioe in the Figure, a n=1 ioe an a n= recombination ioe are assume. For comparison with experiment a region of the moule without any shunts was use so that no parallel resistors ha to be introuce in the moel. The effects of shunting in a CSG moule are escribe elsewhere [3]. The result of the Spice simulation is a set of currents I an voltages U for every simulate resistor an ioe of which the corresponing areas A in the image plane are known. The current information can be use to raw a map of the eltier power istribution which is given by Q = ( jπ). This is easy to evaluate at the holes because there Π is just a step function between the (negligibly small) eltier coefficient of the aluminum an the silicon p or n layers, respectively. With the known current through the resistors the eltier heat ensity is given by Al to p n : to Al : Q Q = = ( I / A ) ( Π p ), ( I / A ) Π. Both contributions are negative uner forwar bias. Due to the low iffusion length in a thin film cell, minority carriers cannot move appreciably in the image plane an the actual shape of the eltier coefficient across the p-n junction is insignificant. Therefore it hols that the overall eltier heat contribution is just: p to n : n ( I / A ) ( Π ) Q =. p Π n This contribution is always positive an cancels the cooling from the s. Note that the energy-conserving 5
4th European hotovoltaic Solar Energy Conference, 1-5 September 9, Hamburg, Germany eltier heat transport has no effect on the performance of the moule, but has to be consiere when evaluating lock-in thermograms. The map of power issipation Q = j E can be rawn in a straightforwar manner from the currentvoltage information for each element of the Spice simulation output, Q J = IU / A. 3.3 Convolution with the point sprea function (SF) Trying to convolve the power maps Q J, Q, Q J Q generate through the Spice simulation we note that both the moel of heat wave propagation through a thermally thin an a thermally thick meium [1] are not vali for the silicon on glass structure. Instea, both the heat propagation through the 1.5 µm thick silicon layer an through the thick glass superstrate have to be taken into account. The problem is thus that of solving the threeimensional heat conuction equation 1 T T = Q (4) D t with the bounary conition of two-imensional heat flow in the silicon layer on the surface κ T 1 T T =, (5) z D t κ f f where an are the three an two-imensional Laplace operators, respectively, D enotes the iffusivity an κ the heat conuctivity. The inex f is use for film quantities. An analytical solution to these equations is possible an will be etaile in an upcoming publication [6]. The solution for the present case in comparison with the limiting cases of heat wave propagation through thermally thin an thick meia is shown in Figure 5. 3..5. Limit of conuction only through glass (thermally thick), -45 signal Limit of conuction only through silicon (thermally thin), -9 signal Conuction through both glass an silicon, -45 signal J Unfortunately, there is a problem with the convolution at the grooves that separate the iniviual cells from each other, since at those lines the (highly heat conuctive) silicon film is interrupte an the bounary conition (5) no longer hols. Here, we ecie to avoi this ifficulty by assuming perioic continuation of the power istribution over the grooves in the simulation an proviing an approximately perioic continuation in the experiment through the neighboring cells in the moule. In this way the heat flux across the groove is minimize. 4 FIT ROCEDURE AND RESULTS Realistic values for the cell parameters can be extracte by comparing images (Figure 6) an linescans (Figure 7) from experiment an simulation. Both simulate an experimental images can be scale in mw/m² with only the known overall current/voltage values, i.e. an arbitrary scaling factor is not necessary. Figure 6: Maps of heating power ensity from experiment (left) an simulation (right) at low, meium an high voltages for the values cite in Table I. The maximum power point was at approx. 4 mv. Note the contrast reversal between grooves an area for low an high currents. K/mW 1.5 1. 3.5....4.6.8 1. 1. 1.4 1.6 1.8. os. (mm) ower (mw/m²) 1 Figure 5: oint sprea functions for the case of silicon on glass in comparison with the limiting cases of heat wave propagation through thermally thin an thick meia (maximum intensity single phase signal, -9 for thermally thick, -45 for the other cases) 4 6 osition (mm) Figure 7: Horizontal linescans of experimental (soli lines) an simulate thermograms (ashe lines) average across 1 cell pas (5 mm). Voltages range from 35 mv (black) to 65 mv (blue) in steps of 5 mv. The geometry parameters (number of holes, pa with, etc.) are easily accessible an their error is negligible. The eltier coefficient was etermine on a test structure in the same sample batch (see section.) an was assume to be the same for the moule. Both the 53
4th European hotovoltaic Solar Energy Conference, 1-5 September 9, Hamburg, Germany hole an sheet resistances use in the simulation were measure on another full moule of the same batch. This measurement coul not be one on the same moule since it involves cutting the pas. At the center of the cell the effect of the grooves is low an the area-average eltier effects cancel as they o in a stanar solar cell. Therefore, with the signal Q=UI in the center of the cell, the area current ensities J 1, J an the sum of the resistances coul be etermine. The ratio of p to n sheet resistance can be etermine by looking at the linescans perpenicular to the pas. As can be seen in Figure 6, the lower series resistance in the n region causes more heat to be issipate below the p type s. Finally, the groove ioes can be ajuste via the asymmetry of the linescans in Figure 7. The left groove raws significantly more current than the right one as can be seen in the 35 mv part of Figure 6, where the current flows ominantly from the left holes (eltier cooling at the s) to the left cell ege. (These ifferences in the currents through the inner an outer holes get less pronounce at higher voltages. Therefore the assumption of equal currents through every hole in the estimation of thermoelectric effects in section.3 is also vali for moules.) Unfortunately, the ratio of current rawn by the left cell ege to that rawn by the right cell ege can only be etermine very inaccurately because the groove signals of neighboring cells cannot be istinguishe, it is between.1 an.1. Here a ratio of about.5 was assume. Accoringly, the absolute values of the line groove currents J 1, J given in A per cm groove length, are only known to their orer of magnitue. The parameters of this (manual) best fit simulation are shown in Table I. Values in italic were not varie as they are known from other moules (eltier coefficients an hole resistances) or are simple geometry parameters. Table I: Simulation parameters p hole resistance n hole resistance p sheet resistance n sheet resistance Value ± (approx.) 49 Ω 5 % (iff. moule) 154 Ω 5 % (iff. moule) 1.8 kω 1 % 1.1 kω 1 % area J 1 7.4 1 11 A/cm 1 % area J 11 9.7 1 A/cm 1 % left groove J 1 4.75 1 A/cm (see text) left groove J 7 7.6 1 A/cm (see text) right groove J 1 1.5 1 A/cm (see text) right groove J 8 4. 1 A/cm (see text) p eltier coefficient 9 mv 5 % (test struct.) n eltier coefficient 9 mv 5 % (test struct.) holes per pa 14 pa with.5 mm istance groove-groove 6 mm ist. between holes.36 mm hole raius 7 µm Note that the holes are always coler than their environment because of the eltier cooling there (in spite of their resistances, Figure 6). In the cell center the cooling at the s an the heating at the ioes is less than half a millimeter (one pa with) separate which results in only a slight oscillation in the linescans. At the eges the istance of the outer holes to the cell grooves is much longer an the contrast between eltier cooling at the holes an heating at the ioes is plainly visible (Figure 7). Figure 8 shows a comparison of the I-V characteristics of the whole experimental eight cell mini-moule to the I-V characteristics of the simulate cell resulting from the values of Table I. Both curves are normalize to a 1 mm long portion of a cell, no further correction factors were applie. 9 Current (A/mm) 1-3 1-4 1-5 1-6 1-7..1..3.4.5.6 Voltage (V) Figure 8: Experimental (soli lines) an simulate (ashe lines) current-voltage characteristic normalize to 1 mm length of a (6 mm wie) cell stripe. 5 CONCLUSION AND OUTLOOK In this contribution we showe how to fully unerstan the behavior of a CSG structure in DLIT over a wie voltage range. A strong eltier contribution is observe an inclue in the thermal simulation, since n an p holes are resolve. A shunt-free region was moele in Spice, the results were mappe in an image of local power issipation an convolute with the point sprea function of a highly heat conuctive layer on a glass substrate. Ege (groove) an area ioe properties were separately observe an coul be quantifie through a fit of the simulations to the experimental ata. Direct I- V curve measurement woul only give a mixture of both effects. The strength of this groove shunting is ifferent for both eges of the cell (with a ratio between.1 an.1, here). Therefore it woul be esirable to resolve the contributions from both sies of a groove separately which coul be one by ing one cell of the moule separately. This ha not been one here in orer to minimize the effect of isturbing heat wave reflections at the grooves an will be ealt with in a future publication. 54
4th European hotovoltaic Solar Energy Conference, 1-5 September 9, Hamburg, Germany ACKNOWLEDGMENT This work was supporte by the BMBF project SiThinSolar (contract no. 3I67). The samples were kinly provie by CSG Solar AG, Thalheim. REFERENCES [1] O. Breitenstein, M. Langenkamp, Lock-in Thermography, Springer (3) [] M. A. Green,.A. Basore, N. Chang, D. Clugston, R. Egan, R. Evans, D. Hogg, S. Jarnason, M. Keevers,. Lasswell, J. O'Sullivan, U. Schubert, A. Turner, S.R. Wenham, T. Young, Solar Energy 77 (4) 857 [3] O. Breitenstein, R. Gupta, J. Schneier, Journal of Applie hysics 1 (7) 4511/1-8 [4] H. Straube, J.-M. Wagner, O. Breitenstein, Applie hysics Letters 95 (9) 517 [5] G. S. Nolas, J. Sharp, H. J. Golsmi, Thermoelectrics, Springer (1) [6] H. Straube, J.-M. Wagner, O. Breitenstein (to be publishe) 55