Suns-V OC characteristics of high performance kesterite solar cells
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J un Suns-V OC characteristics of high performance kesterite solar cells Oki Gunawan, ∗ Tayfun Gokmen, ∗ and David B. Mitzi IBM T. J. Watson Research Center, PO Box 218, Yorktown Heights, NY 10598 USA (Dated: June 11, 2014)Low open circuit voltage ( V OC ) has been recognized as the number one problem in the current generationof Cu ZnSn(Se,S) (CZTSSe) solar cells. We report high light intensity and low temperature Suns- V OC mea-surement in high performance CZTSSe devices. The Suns- V OC curves exhibit bending at high light intensity,which points to several prospective V OC limiting mechanisms that could impact the V OC , even at 1 sun forlower performing samples. These V OC limiting mechanisms include low bulk conductivity (because of lowhole density or low mobility), bulk or interface defects including tail states, and a non-ohmic back contact forlow carrier density CZTSSe. The non-ohmic back contact problem can be detected by Suns- V OC measurementswith different monochromatic illumination. These limiting factors may also contribute to an artificially lower J SC - V OC diode ideality factor. I. INTRODUCTION
Kesterite Cu nSn(Se,S) (CZTSSe) devices are emergingas a promising thin-film solar cell technology, given sig-nificantly improving power conversion efficiencies [1–3] –currently as high as 12.6%–and predominant use of moreabundant and less toxic elements. This technology, if success-fully developed to reach power conversion efficiency (PCE)beyond 18%, has the potential to replace the existing thin filmsolar technologies, such as Cu(In,Ga)(S,Se) (CIGSSe) andCdTe, which have issues with elemental abundance and tox-icity. Despite the promising recent progress in performance,open-circuit voltage, V OC , remains as the number one prob-lem in this technology [4, 5]. Specifically, CZTSSe suffersfrom large V OC deficit i.e. the difference between the bandgap E g and the open circuit voltage: V OC,def = E g /q − V OC ,where q is the electron charge. The record CZTSSe devicewith 12.6% power conversion efficiency (PCE) has V OC =0 . V ( E g = 1 . eV and V OC,def = 0 . V), which cor-responds to only 57.8% of the maximum V OC allowed by theShockely-Quisser (SQ) limit [6]. In contrast, a record CIGSSedevice with PCE of 20.8% [7] has V OC of . V ( E g ∼ . eV and V OC,def = 0 . V), corresponding to 81.3% of themaximum V OC according to the SQ limit.Prior studies have discussed several possible factors con-tributing to the V OC deficit problem in CZTSSe such as inter-face recombination [5], low minority carrier lifetime [5, 8] andelectrostatic potential fluctuations and tail states [9]. In thisstudy we present another aspect of V OC limitation in CZTSSe,as revealed by high intensity and low temperature Suns- V OC measurements. II. EXPERIMENTAL
To perform a high intensity Suns- V OC measurement we uti-lize the Sinton Suns- V OC Illumination Voltage Tester withsome modifications [10] as shown in the inset in Figure 1.The basic system comes with a set of neutral density filters(NDF) at the outlet of the flash lamp. We remove these fil-ters to increase the light intensity from ∼ sun to ∼ sun maximum. We then apply neutral density filters (NDF2)( × attenuation) on top of the photodetector that monitorsthe light intensity to avoid saturation. Small probe testers areused to probe the two terminals of the solar cell to measurethe V OC . The flash light lasts for about ms and the lightintensity and the V OC are recorded concurrently, as the lightdecays quickly from ∼ sun to . sun. An example ofthe transient plot is shown in supplementary material (SM)Figure S1(b). The measurement can be repeated with a smallshunt resistance ( R sh = 1 Ω ) across the device-under-test tomeasure the J SC . Therefore, by combining Suns- V OC andSuns- J SC the J SC - V OC plot can be obtained (see SM A andFig. S2 for detail). Note that in most devices studied, espe-cially at low light intensity ( < sun), J SC is proportionalto the light (sun) intensity – thus a description in terms ofSuns- V OC or J SC - V OC characteristics is identical and theyare used interchangeably in this report. We also performeda wavelength-dependent Suns- V OC measurement by repeat-ing the Suns- V OC curves with different color bandpass filters.This approach provides some depth sensitivity to the electricalmeasurements, as will be described later.In the second part of the study, we developed a simple Sun- FIG. 1. High intensity Suns- V OC setup using a modified Sinton tool(inset) for a high performance CZTSSe “Z1”, CIGSSe “G1” andmono-crystalline silicon “S1” solar cell. Solid circle : The Suns- V OC reversal point where the ideality factor drops to zero. Right panel :The ideality factor n S as a function of light intensity. No Device Type
Eff F F V OC J SC E g V OC,def [ Cu ][ Zn ]+[ Sn ] p µ (%) (%) (mV) (mA/cm ) (eV) mV (/cm ) (cm /Vs)1 G1 CIGSSe . . . . .
17 569 . n.a. ∼ × . . . . .
12 512 . n.a. – –3 Z1 CZTSSe . . . . .
13 636 . ∼ . ∼ × . . . . . .
13 670 . ∼ . – –5 ZA CZTSSe . . . . .
13 648 . . ± . . × . . . . . .
13 649 . . ± . . × . . . . . .
10 683 . . ± . . × . TABLE I. Device parameters of solar cells used in this study under simulated AM1.5G illumination. Sample ZA, ZB and ZC are CZTSSedevices with varying Cu composition (and carrier density). V OC,def is the V OC deficit ( E g /qV OC ), p and µ are the Hall carrier density andmobility of the absorber layer measured on separate identical film. V OC (or J SC - V OC ) measurement integrated to a standard ex-isting solar simulator (Newport-Oriel, W, × beamsize) to facilitate immediate comparison of the light J - V and J SC - V OC curves (See SM B for details). A common methodin performing Suns- V OC measurement is to use discrete neu-tral density filters to obtain different light attenuations (see.e.g. Ref. [11]); however this technique yields insufficient dataresolution to accurately calculate the ideality factor. To solvethis issue we developed a custom-made large area continu-ous neutral density (CND) filter, configured in a radial shape(see SM B) to achieve continuous light attenuation from to ∼ − sun. This filter is made using a common overheadprojector transparency printed with a radial grayscale patternby ink-jet printing [12]. The filter is driven by a stepper motorbox to achieve a smooth, slow rotation that allows the J SC and V OC data to be recorded at varying intensities with fineresolution. III. RESULTS
High intensity Suns- V OC measurements were performed ona high performance CZTSSe cell (Z1), in comparison withanalogous CIGSSe (G1) and silicon solar cells (S1) (Fig. 1).The detailed characteristics of these solar cells are presentedin Table I. We can calculate the ideality factors from the Suns- V OC (or equivalently J SC - V OC ) curves using the relationship J SC = J exp( V OC /n S V T ) and by assuming that the shortcircuit current J SC is proportional to the light intensity, i.e. J SC = SJ L , where S is the sun concentration factor (in unitof suns) and J L is the photocurrent at sun. The idealityfactor n S can be calculated as: n S = [ V T d ln J SC /dV OC ] − = [ V T d ln S/dV OC ] − , (1)where V T = k B T /q , K B is the Boltzmann constant and T isthe device temperature. The ideality factors of the Suns- V OC curves are shown in the right-hand side plot of Fig. 1. Theideality factor tends to drop at higher light intensity for allcells, partly because of the Auger recombination effect thatbecomes more dominant at high carrier density [13]. We observe that the silicon (S1) and CIGSSe cells (G1)exhibit normal Suns- V OC curves that monotonically increasewith higher light intensity. In contrast, the CZTSSe cell Z1shows a Suns- V OC curve that saturates at high sun inten-sity. Furthermore, beyond a certain point (indicated by a solidcircle) the Suns- V OC curve bends slightly backward. Cor-respondingly, the CZTSSe ideality factor derived from thiscurve ( n S ) becomes anomalously low and turns negative atvery high sun intensity (Fig. 1 right panel). Some CZTSSesamples show more severe backward bending as will be dis-cussed in Fig. 6. This behavior suggests some mechanismthat limits the V OC . We have also repeated this measurementfor CZTSSe with various band gaps (with low carrier density < /cm ) and observe similar bending behavior in all de-vices, as shown in SM Fig. S3.A similar observation can also be made at low light in-tensity Suns- V OC ( < sun) at low temperature from thetemperature dependent study of the J SC - V OC curves for theCIGSSe and CZTSSe cells as shown in Figure 2. We use J SC - V OC measurement using the rotating CND filter as shown inFig. 2(a) inset, this time focusing on the lower light inten-sity regime. The J SC - V OC curves look normal (monotonic)for the CIGSSe cell at all temperatures and also normal forthe CZTSSe at high temperature ( ∼ K). However, at lowtemperature ( < K) the CZTSSe J SC - V OC curves exhibitbending behavior, very similar to what has been observed atambient temperature under high sun intensity (Fig. 1). Fig2(c) shows that at a constant 1 sun intensity, the V OC increasesat lower T ; however, as has been reported earlier [2, 5], dueto the Suns- V OC bending behavior, the V OC drops at lowesttemperatures for CZTSSe ( T <
K).Another important set of information is obtained in a studyof CZTSSe with varying [Cu]/([Zn]+[Sn]) ratio. Higher Cu-content leads to higher majority carrier (hole) density [14, 15].Fig. 3(a) shows that the high intensity J SC - V OC bending onlyoccurs for the sample with the lowest carrier density (ZA).Similarly, this behavior is also confirmed in low temperaturemeasurement [Fig. 3(b)], i.e. only sample ZA shows a V OC - T curve that bends within the lowest temperature range ( T <
K).
FIG. 2. Temperature dependence of the J SC - V OC curves ( − to sun) for: (a) CIGS; Inset : The Continuous Neutral Density filter used totake the J SC - V OC data with standard sun solar simulator; (b) CZTSSe; and (c) V OC vs. temperature plot for both compounds. IV. DISCUSSION
With respect to the possible origins of the observed Suns- V OC bending or pinning behavior in CZTSSe, we can differ-entiate two kinds of behaviors: first is “pinning” where the V OC gets saturated beyond some light intensity and secondis “bending” where the Suns- V OC curve bends backwards, asfor the CZTSSe data in Fig. 1. Three factors can account forthese pinning or bending behaviors as detailed below: A. Conductivity
The first possible issue is low bulk conductivity, due to lowcarrier density or low majority carrier mobility. In order togive insight into this mechanism we perform device simula-tions using the wxAMPS program [16, 17]. In Figure 4(a) weshow the Suns- V OC simulation results for a baseline CIGSmodel [18] at three different hole mobility values. As the mo-bility value is reduced from to cm /Vs the Suns- V OC pinning behavior starts to develop; the effect becomes evenmore pronounced once the hole mobility is further dropped to . cm /Vs.The physics of the observed behavior can be understood asfollows. In a normal solar cell, the photo-generated electron-hole pairs in the depletion/junction region are separated bythe built-in electric field (electrons are swept to the front andholes are swept to the back of the device) and therefore con-tribute to the J SC . Because of the need for current continu-ity, in the short circuit condition this photo-generated current( J SC ) in the depletion region is maintained by majority carri-ers both at the front and the back of the device. At the backof the device majority carriers are holes and therefore it is thehole current, J p , that can be considered to maintain the photo-generated current at any given Sun intensity. The hole currentat the back can simply be written as J p = qpµ p E where q is the unit charge, p is the hole (carrier) concentration, µ p isthe hole mobility and E is the electric field at the back of thedevice. For the device with a hole mobility of cm /Vs,the necessary electric field at the back would be only . V/ µ m, even at suns, and therefore this field does not no- ticeably affect the band bending throughout the device [Fig4(b)]. However, for the device with a very low mobility (e.g., . cm /Vs), the necessary electric field at the back is . V/ µ m in order to maintained the J SC at Suns. Since thisis a relatively large electric field, the band diagram completelychanges throughout the device [Fig 4(c)] and the band bend-ing mostly happens at the back of the device (giving rise toa voltage drop in the back region). The bending within thejunction region is mostly screened due to the increase in holeconcentration in the junction region because of the failure ofthe hole extraction from this region. Clearly this is an unde-sirable situation that reduces J SC compared to the ideal caseand also results in the pinning of the V OC because of the volt-age drop in the back region. Even under V OC condition [Fig.4(c), right panel], there is still a significant band bending atthe back that reduces the V OC due to significant hole currentto cancel off the electron current.Using this analysis we can also estimate the light intensitywhere the V OC pinning starts to occur. We set a maximumhole current ( J max p ) that the back of the device can accommo-date without substantially disturbing the band banding in thedevice, which we estimate at E max ∼ . V/ µ m. Also, theshort circuit current would be the product of the light inten-sity, S , and J SC at sun ( J L ). Therefore, using the equation J p = qpµ p E and by equating these two currents, one couldsolve for the value of S when the device starts to show a sig-nificant signature of V OC pinning: J max p = qpµ p E max = J L S . (2)We note that this simple equation is reasonably accurate topredict the Sun intensity where V OC starts to get pinned andthe results are in good agreement with our simulation resultsshown in Figure 4(a). For example, in Fig. 4(a) we have J L = 33 mA/cm for the baseline device ( µ p = 25 cm /Vs).Using Eq. 2, we can estimate that the pinning should hap-pen at approximately S = 100 and suns for the deviceswith µ p = 1 and . cm /Vs respectively. Equation (2) alsoimplies that the V OC pinning issue can be resolved (i.e., thebending pushed to higher Sun intensities) if the hole concen-tration and hole mobility product (bulk conductivity) is in-creased. FIG. 3. (a) High in-tensity J SC - V OC measure-ment (up to suns) forCZTSSe samples with in-creasing [ Cu ] / ([ Zn ] + [ Sn ]) ratio or carrier density ( p )(see inset). (b) V OC vs. tem-perature profile for the Cu-poor and Cu-rich devices. To assess the bulk conductivity, Van-der Pauw and Hallmeasurements were carried out on a set of high performanceCZTSSe films, yielding carrier densities in the range of to /cm (depending on [Cu]/([Zn]+[Sn]) content) whilereference high performance CIGSSe films yield carrier den-sity of ∼ × /cm as shown in Table I [19]. However, theCZTSSe mobility is notably lower, µ p ∼ (0 . ± . cm /Vs,compared to CIGSSe, µ p ∼ (4 ± . cm /Vs. For a baselineCZTSSe device with low carrier density ∼ /cm (e.g.sample Z1), this translates to lower bulk conductivity and as aresult CZTSSe devices tend to suffer from higher series resis-tance and lower FF [2, 3, 20]. Thus, as further highlightedin the modeling results shown in Fig 4(a), it is reasonablethat CZTSSe devices, especially those with low hole density( < /cm ), more readily develop the Suns- V OC pinningdue to its lower mobility.This V OC limiting mechanism is also consistent with theexperimental data obtained from CZTSSe solar cells with in-creasing carrier density due to higher [Cu]/([Zn]+[Sn]) ra-tio. Fig. 3 shows a set of CZTSSe devices with increasing[Cu]/([Zn]+[Sn]) ratio, which corresponds to higher carrierdensity p . We observe that the Suns- V OC pinning disappearsas p increases with the mobility remaining roughly constant(Table I). This behavior is also confirmed in low T measure-ment, as shown in Fig. 3(b); the higher carrier density sample(ZC) does not show V OC - T pinning anymore at low tempera-ture, at least down to ∼ K. Nevertheless, as our simulationin Fig. 4 shows, even for higher performance samples with alower range of carrier density, this V OC limitation mechanismshould be effectively benign at 1 sun (less than mV re-duction), as long as carrier density and mobility remain above ∼ /cm and µ h ∼ . cm /Vs, respectively (correspond-ing to a bulk conductivity of . S/m).
B. Bulk or interface defects and tail states
Bulk and interface defects, including tail states introduceextra states in the band gap that could pin the Fermi level,thereby leading to Suns- V OC saturation. In a solar cell, the V OC can be calculated from the separation of the electron( E F n at the front contact) and hole ( E F p at the back con- tact) quasi Fermi levels: V OC = E F n − E F p [see Fig. 4(b)].For a typical p -type solar absorber, the hole Fermi level ismainly determined by the free hole concentration and doesnot change with light illumination, as long as the excess car-rier concentration does not exceed the free hole concentration.In contrast, the position of the electron Fermi level, E F n , isdetermined by the balance between generation ( G ) and recom-bination ( R ) rate. With light illumination, E F n increases andstabilizes once the generation rate (which is proportional tolight intensity) and recombination rate are equal. Most gener-ally this condition can be represented by: G ( S ) = R = Z ∞
11 + exp[( E − E F n ) /k B T ] g ( E ) τ ( E, n ) dE , (3)where g ( E ) is the density of states in the conduction bandincluding both extended and localized states (such as statesthat might arise from tails states or defect states) and τ ( E, n ) is the minority carrier lifetime that might depend on energyand excess carrier concentration. In the simplified case, where τ ( E, n ) is just a constant, the above equation can be reducedto: G = R = R ∞ g ( E ) / (1 + exp[( E − E F n ) /k B T ]) dE/τ =∆ n/τ . In this simplified form and assuming density ofstates (DOS) for a clean semiconductor ( g ( E ) ∝ √ E − E c ) ,one could arrive at the familiar relationship where ∆ n ∝ exp( E F n /k B T ) and hence we obtain a V OC that increasesmonotonically with the sun intensity with ideality factor n S =1 (see detailed derivation in SM C).However for a disordered material, g ( E ) will have statesbelow the band gap (e.g. in the form of tail states [9]). Inaddition, the minority carrier lifetime will become energy de-pendent, with lifetime being smaller for higher energy statessince higher energy states are more delocalized. Indeed, life-times that are factor of different have been observed forCZTSSe solar cells at low temperatures, as recombinationchanges from extended to localized states [9, 21, 22]. In-terestingly, lifetime would also depend on the excess carrierconcentration, where the shorter lifetimes would be observedfor higher carrier concentrations. This is also consistent withexperimental observation of increasing lifetimes that is re-ported for CZTSSe solar cells as the time-resolved photolu-minescence (TRPL) signal decays [3, 20]. The dependence FIG. 4. (a) Suns- V OC simulation study of devices with varying hole mobility. (b), (c) Band diagrams at J SC (left column) and V OC (rightcolumn) for the (baseline) high mobility and low mobility device (at sun). of lifetime on carrier concentration can be understood in thecontext of electrostatic potential fluctuations [21, 22] or Augerrecombination [23]. We note that the increased rate of Augerrecombination in the presence of tail states and electrostaticpotential fluctuations has been theoretically discussed in asRef. [23]. Therefore, once all of these contributions are takeninto account, the Suns- V OC pinning behavior that we observein CZTSSe could also be due to the high density of bulk de-fects that result in band-tail states and electrostatic potentialfluctuations. Basically, since DOS increases with increasingenergy and also higher energy states are more effective forrecombination due to reduction in lifetime, E F n (and hence V OC ) does not need to increase as much to satisfy the gener-ation rate, thereby giving rise to V OC pinning behavior. Thesame pinning behavior could also be the result of interfacedefects (arising from lattice mismatch and dangling bonds in FIG. 5. Suns- V OC simulation of the impact of defect state in theabsorber: S1 (baseline device) and S2 (device with deep defect at . eV below conduction band with density × /cm ). heterojunction) as discussed by Ref. [24]. In CIGSSe, theFermi level pinning problem at the interface has been asso-ciated with interface defects such as donor-like anion (S,Se)vacancies [25] or with Cu/Cd exchange [26].To illustrate this Suns- V OC pinning effect due to the pres-ence of an electronic defect we perform a Suns- V OC simu-lation using the baseline CIGSSe model [18] (device “S1”)with parameters η = 16 . %, FF = 79 . %, V OC = 0 . V, J SC = 33 . mA/cm . We create a “defected device”model “S2” by introducing a deep defect at E C - . V, where E C is the conduction band edge, with a high defect density N d = 2 × /cm . Device S2 yields solar cell parame-ters with notable reduction in V OC : η = 10 . %, FF = 61 . %, V OC = 469 V, J SC = 35 . mA/cm . The result of thesimulation is shown in Fig. 5, with the “defected device” S2clearly exhibiting Suns- V OC pinning. C. Non-ohmic back contact
While the two factors discussed above can explain the Suns- V OC pinning behavior, they cannot reproduce the bending be-havior (i.e., measurements for which the V OC actually getssmaller with increasing light intensity) as found experimen-tally for some samples. We consider two factors that can ac-count for this feature. One possible cause is a heating effectunder high light intensity, as higher temperature will lead tolower V OC [e.g. see Fig. 2(c)]. The heating could be non-negligible at very high light intensity ( > sun) given thatall the absorbed light energy has to be converted to heat some-where in the device for the open circuit condition. Althoughheating may not be enough to give bending behavior alone,once combined with the pinning due to any of the two factorsdiscussed above, it could contribute to mild backward bendingbehavior (and negative ideality factors). However, the heatingeffect is not considered as the intrinsic V OC limiting factorand at sun this heating effect is expected to be negligible for FIG. 6. Device char-acteristics of a CZTSSedevice Z2 with a sus-pected back contact prob-lem: (a) J - V character-istics; (b) Monochromatic J SC - V OC test, using vari-ous band pass filters. Thelong wavelength light in-duces a more severe bend-ing or lower V OC for thesame J SC . the duration of the flash light < ms. This is evident fromthe fact that in some samples [e.g. high carrier density sampleZC, Fig. 3(a)] the bending or pinning behavior is absent.Nevertheless, in some mediocre CZTSSe devices, partic-ularly those with very poor Fill Factor (FF), we observe se-vere backward bending behavior in the Suns- V OC curve evenat relatively low light intensity ( < sun). An example isshown for device CZTSSe Z2 in Fig. 6. In this kind of de-vice, the cause of the backward bending may be attributed toa non-ohmic back contact. This issue has been well studiedin silicon solar cells [27] using Suns- V OC measurement of upto suns and has also been suspected to be the problemin an earlier generation of CZTSSe [2, 28]. Green [29] sug-gested a model consisting of a primary diode that representsthe main photovoltaic (PV) junction and an opposing parasiticback contact (BC) diode in parallel with a back contact shuntresistance R BC , as shown in Fig. 7(a) inset. This resistance isnecessary for the whole device to operate at forward bias (oth-erwise an ideal back contact diode will block all forward biascurrent). When the back contact shunt resistance R BC is suf-ficiently high, appreciable photovoltage or V OC could developacross the BC junction producing an opposing voltage to thefront junction. Physically, this back contact junction couldarise at the CZTSSe/Mo(S,Se) interface or Mo(S,Se) /Mointerface – unfortunately we do not know the detailed elec-trical characteristics of the Mo(S,Se) layer since it is burieddeep within the absorber layer. However this model is suf-ficient to describe the Suns- V OC behavior qualitatively (Fig.7).Using this model we can attempt a fit to experimental datato gain more insight, as discussed in more detail in SM D.Our device can be modeled as a standard solar cell junction“PV” and a parasitic back contact junction “BC” shunted by aresistance R BC as shown in Fig. 7(a). The model has five in-dependent parameters: J L A , n A , J L B /J B , n B and JR BC ,where J L is the 1 sun J SC , J is the dark reverse satura-tion current, n is the ideality factor, and subscript A and Brefers to the “PV” and “BC” diode, respectively. Figure 7(a)presents the individual contributions of the PV and BC diode.The main PV diode produces ideal increasing voltage with thelight intensity and the BC diode produces small but increasingnegative voltage that reduce the total V OC . Based on the pa- rameters extracted, we can estimate the negative V OC contri-bution of the back contact at sun, which yields the relativelysmall value, V OCB = 13 mV. Note, however, that the modelabove does not take into account other factors that contributeto the Suns- V OC pinning or bending as described previously,such as a low conductivity effect, a bulk and interface defecteffect and a prospective Auger recombination process (thatdominates at very high intensity). We also find that the darkreverse saturation current J B of the BC diode (relative to thephotocurrent J L ) is much larger than that of the primary diode( J A ) indicating a very leaky junction. This is expected forsuch a junction that is originally intended to serve as an ohmiccontact. Furthermore, the simulations [Fig. 7(b,c)] show thata lower reverse saturation current ( J B ) (more Schottky-like)and higher shunt resistance ( R BC ) (less ohmic) back contactwill lead to more severe Suns- V OC bending.Further evidence of the non-ohmic back contact problemcan be obtained by performing Suns- V OC measurement withdifferent color or band pass filters ( to nm) on thesuspected device with very low FF (CZTSSe Z2, Fig. 6).The low FF is mainly due to the large series resistance, asapparent from the significant difference between the light J - V and shifted J SC - V OC curve (also called pseudo J - V curve)[Fig. 6(a)]. Based on this back contact model we expect that,by shining a longer wavelength light, the photo-absorption atthe back contact junction and thus the (negative) photovoltagewill increase, thereby reducing the overall V OC . Indeed thisis what we observe in Fig. 6(b). The J SC - V OC curves withlonger wavelength illumination bend earlier and yield lower V OC for a given J SC value.Finally, the back contact model can also provide a justifica-tion for the low temperature J SC - V OC and V OC vs. T behav-ior in Fig. 2. We observe that the J SC - V OC reversal points[solid dot in Fig. 2(b)] become visible below 1 sun and shiftto lower light intensity at lower temperature ( T <
K). Re-gardless of the kind of junction (either p - n or Schottky), lowertemperature results in lower dark current J and increase inthe back contact photovoltage since V OC ∼ ln( J L /J ) . As aresult, the J SC - V OC reversal points occur at lower light inten-sity in the lower temperature J SC - V OC curves. This effect issimulated in Fig. 7(b), where lower dark current J leads tomore severe Suns- V OC bending. The back contact issue could FIG. 7. (a) Circuit simulation to decompose the V OC contributions of the primary (PV) diode and the back contact (BC) diode from theexperimental data. Inset : The circuit model that includes a back contact diode and shunt resistance R BC . (b) The effect of increasing BC darkcurrent J B . Solid dot : Suns- V OC reversal point where n S = 0 . (c) The effect of increasing R BC . also contribute to the J SC - V OC behavior of devices with dif-ferent absorber conductivity, as discussed in Fig. 3. Semi-conductors with very low carrier density tend to yield worseohmic contacts and thus should yield more significant Suns- V OC bending, as observed in the device with the lowest carrierdensity (ZA). D. Ideality factor difference
The V OC reduction due to all different Suns- V OC pinningmechanisms can be estimated by drawing an asymptotic Sun- V OC line for the ideal “PV diode,” as shown in Fig. 7(a), andby noting the difference in V OC at sun between this lineand the experimental data. Although the reduction in V OC at sun is negligible (only ∼ mV ) for a champion levelCZTSSe solar cell [Fig. 1(a)], this reduction can be moresevere ( ∼ mV) for mediocre devices [as shown in Fig.7(a)]. The three factors discussed above are all likely presentto varying degrees in our current portfolio of CZTSSe solarcells and therefore contribute to the Suns- V OC pinning andbending phenomena. While it is difficult to decompose thecontributions of each factor separately, we attempt to analyzethis bending problem more quantitatively in order to investi-gate its impact on the V OC deficit at sun.Figure 8 presents a plot of V OC,def of our CZTSSe de-vices as a function of bandgap. The CZTSSe samples showvarying degrees of Suns- V OC pinning/bending behavior at sun. Using similar analysis to that presented in Fig. 7, wecan estimate the expected V OC if the pinning behavior wereabsent (indicated as V ′ OC , which is higher than the original V OC , thereby corresponding to lower V OC deficit as denotedby open circles in Fig. 8). Evidently, at sun the Suns- V OC pinning/bending behavior has little impact on V OC deficit forthe top performance samples ( E g ∼ . eV). Note that, incomparison with similar band gap CIGS devices and with thetargeted V OC,def of < mV, we can conclude that the ob-served Suns- V OC bending/pinning effect does not account for the majority of the V OC deficit encountered in the CZTSSe-based devices (i.e., > mV).One can also compare the ideality factor extracted from theSuns- V OC and the usual light J - V curves. As shown in Fig. 1,the Suns- V OC bending behavior in CZTSSe artificially lowersthe ideality factor n S extracted from this data. We can thendefine a new parameter ∆ n LS , which is the difference of theideality factors: ∆ n LS = n L − n S , (4)where n S is the Suns- V OC or J SC - V OC ideality factor at sun, extracted from the asymptotic slope at sun (see SMC); and n L is the light J - V ideality factor (at sun) derived FIG. 8. V OC deficit in CZTSSe and CIGSSe as a function of bandgap(solid circles). At sun the effect of Suns- V OC pinning/bending onthe V OC reduction (open circles) is relatively small, especially forthe champion level device ( E g ∼ . eV). Inset : Schematic illus-tration of a pinning/bending Suns- V OC curve. Solid (open) circleis the original V OC (estimated V ′ OC if the pinning/bending effect isabsence). FIG. 9. (a) Light J - V and”pseudo J - V ” curves (the J SC - V OC curve offset by J SC ). Inset : The efficiencyand ideality factors extractedfrom LJV curves ( n L ) and J SC - V OC curves ( n S ). (b) V OC deficit vs. ideality fac-tor difference n L − n S (solidcircles) and n L − n ′ S (hollowcircles) (see text). from the following standard diode equation: J = J exp[( V − JR S ) /n L V T −
1] +
V G S − J L , where R S is the series re-sistance, G S is the shunt conductance in the device and J L isthe photogenerated current. We employ Sites’ method to ex-tract the four diode parameters—i.e., J , n L , R S and G S asdescribed in [30] and [31].An example of the ideality factor comparison of a CIGSSeand CZTSSe cell is presented in Fig. 9(a). We performthe Suns- V OC measurement using the rotating CND filter ap-proach (SM B) in the same sitting right after light J - V mea-surement (The J SC - V OC curves are shifted down by J SC at sun for convenient comparison with light J - V curves [10]).The ideality factor n S is extracted at the highest J sC point thatcorresponds to sun intensity using Eq. 1. In Fig. 9(a) weobserve that the ideality factors n L and n S of the high perfor-mance CIGS cell are the same. In contrast, the CZTSSe Suns- V OC ideality factor ( n S ) is smaller than the light J - V idealityfactor ( n L ). We repeated this study in a collection of high per-formance CZTSSe and CIGSSe cells (with η ∼ − . %and spanning the full range of CZTSSe bandgaps, . − . eV) and investigated V OC deficit vs. bandgap and ∆ n LS asshown in Figures 8 and 9. We also present the data points ofour recent 12.6 % champion CZTSSe [3] in Fig. 9(b) (shownas a star). As expected, it has nearly the lowest V OC deficitand the lowest ∆ n LS ( ∼ . ), very close to the CIGSSecluster. This suggests that the ∆ n LS parameter can serve asanother device quality indicator for thin film solar cells.As discussed before, for mediocre devices the Suns- V OC bending can be significant even under sun condition andtherefore this bending can artificially reduce n s , giving riseto a large ∆ n LS . However, using similar analysis to that pre-sented in Fig. 8, we can define n ′ S , which is the Suns- V OC or J J SC - V OC ideality factor at light intensities below sunwhere the pinning issue is absent. Interestingly, even afterthese corrections the difference n L - n ′ S for the CZTSSe solarcell is still significant as illustrated in Figure 9(b). These ar-guments suggest that the difference between n L - n ′ S derivesfrom mechanisms beyond those discussed in this manuscript,therefore requiring further investigation. V. SUMMARY
In summary, we have presented high intensity and temper-ature dependent Suns- V OC (or J SC - V OC ) measurements in acollection of high performance CZTSSe and CIGSSe cells.Unlike CIGSSe and silicon solar cells, many high perfor-mance CZTSSe cells (with typically low carrier density andlow [Cu]/([Zn]+[Sn]) exhibit Suns- V OC bending at high lightintensity ( ∼ sun) at room temperature or even below sun at low temperature ( < K). We discriminate two kindsof Suns- V OC behavior. The first is “pinning” whereby the V OC gets saturated beyond some light intensity, which maybe attributed to two factors: low bulk conductivity (mainly tolow mobility) and the presence of bulk and interface defectstates (including tail states) that could pin the Fermi level inCZTSSe. The second behavior is “bending,” where the Suns- V OC curve bends backwards at higher light intensity. This ef-fect is attributed mainly to a non-ohmic back contact – whichis prevalent in CZTSSe with low carrier density (althoughheating effects do have the potential to contribute for inten-sities > suns). We have also demonstrated a technique todetect the non-ohmic back contact by performing Suns- V OC measurement employing different color band pass filters.The Suns- V OC pinning/bending symptom generally disap-pears for cells with higher carrier density due to increased bulkconductivity and better ohmic contact. However, these highcarrier density samples ( p > /cm ) have not historicallybeen the devices with the highest performance. Also, the re-duction in V OC at sun due to the pinning/bending behaviordoes not account for the majority of the observed large V OC deficit for current-generation high-performance CZTSSe so-lar cells. Therefore, even in cells where there is no Suns- V OC bending, there is still substantial V OC deficit. We believe thatthis large V OC deficit is mostly accounted for by the band edgetail states in the CZTSSe material [9]. We also observe thatthe difference in the Suns- V OC and Light J - V ideality factors( ∆ n LS ) grows with larger V OC deficit, suggesting that thisparameter could serve as another indicator for device quality.The techniques described here (high intensity Suns- V OC mea-surement, non-ohmic back contact detection and ideality fac-tors comparison) are currently employed in our developmentof high performance CZTSSe devices to monitor and mitigatethe V OC deficit issues, and can also be applied to other emerg-ing solar cell technologies. ACKNOWLEDGEMENT
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