Application of CTLM method combining interfacial structure characterization to investigate contact formation of silver paste metallization on crystalline silicon solar cells

Solid State Electronics 142 (2018) 1–7

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Application of CTLM method combining interfacial structure characterization to investigate contact formation of silver paste metallization on crystalline silicon solar cells

T

⁎

Shenghu Xionga, Xiao Yuana, , Hua Tonga,1, Yunxia Yanga, Cui Liua, Xiaojun Yea, Yongsheng Lia, Xianhao Wangb, Lan Luoc a b c

School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China Carle Zeiss (Shanghai) Co. Ltd., Shanghai 200131, China Shanghai Institute of Ceramics, Chinese Academy of Science, Shanghai 200131, China

A R T I C L E I N F O

A B S T R A C T

The review of this paper was arranged by Prof. A. Zaslavsky

Circular transmission line model (CTLM) measurements were applied to study the contact formation mechanism of the silver paste metallization on n-type emitter of crystalline silicon solar cells. The electrical performance parameters ρc ,Rsk , and Lt , which are related to the physical and chemical states of the multiphase materials at the interface, were extracted from the CTLM measurements, and were found to be sensitive to sintering temperature. As the temperature increased from 585 °C to 780 °C, initially the ρc value decreased rapidly, then flattened out and increased slightly. The order of resistivity magnitude was restricted by the SiNx passivation layer in the early sintering stages, and relied on the carrier tunneling probability affected by the precipitated silver crystallites or colloids, emitter doping concentration and molten glass layer. Based on the calculations that the sheet resistance underneath the electrode was reduced form 110 Ω/ □ to 0.186 Ω/ □ , it could be inferred that there was formation of a highly conductive layer of silver crystallites and colloids contained glass on the emitter. The transfer length Lt exhibited a U-shaped variation along with the temperature, reflecting the variation of the interfacial electrical properties. Overall, this article shows that the CTLM method can become a new powerful tool for researchers to meet the challenges of silver paste metallization innovation for manufacturing high-efficiency silicon solar cells.

Keywords: CTLM Specific contact resistance Contact formation Solar cell metallization

1. Introduction Over the past 40 years, screen printing has been widely applied in the silver paste metallization for silicon solar cells owing to its high throughout, low cost, and robust process, and it is expected to be mainstream technology for at least the next ten years [1]. Silver paste, which is composed of silver powder, glass frit, organic vehicles, and other additives determines the cell performance after the sintering process, in which the silver powders fuse to densify, glass frit melts and etches through antireflection coating, and the organic vehicle is burnt out [2]. Using new technologies such as emitter passivation with Al2O3 [3], metal-assisted black silicon texture [4], as well as the application of PERL and PERT [5] to crystalline silicon solar cells, new requirements have been demanded to the use of silver paste for metallization; for example, metallizing at low temperature around 700 °C in 1 min, firing through double-passivation layers of Al2O3 stacked with SiNx, and a

⁎

1

low charge-recombination rate on black silicon texture. The traditional transmission-line model (TLM) methodology has been applied in the metallization characterization owing to its simple use of data to a finished cell for a long time; however, it ignored that the emitter sheet resistance Rsh beneath the silver electrode changed to Rsk after firing, and was affected by the nonuniformity of the emitter sheet resistance, leading to an inaccurate solution of the specific contact resistance and transfer length [6,7]. Nevertheless, in practice, the operation to split a cell into strips, while maintaining its integrity, avoiding junction shunting, or to screen print paste on strips with extremely narrow spaces between finger and the edge of strips, as required by TLM [8] is inconvenient, especially for researchers. A new convenient and sufficiently accurate characterization technique should be established for scientists and designers to meet the new challenges. Several models, such as TLM, circular TLM (CTLM), contact end resistance (CER), and cross-bridge Kelvin resistance (CBKR) have been

Corresponding author. E-mail addresses: [email protected] (X. Yuan), [email protected] (H. Tong). Principal corresponding author.

https://doi.org/10.1016/j.sse.2017.12.012 Received 30 September 2017; Received in revised form 20 December 2017; Accepted 20 December 2017 Available online 21 December 2017 0038-1101/ © 2017 Published by Elsevier Ltd.

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proposed to evaluate the specific contact resistance of metal and semiconductor on planar devices [9,8]. CTLM is a suitable methodology because it does not require isolating the pattern-covered region from the substrate. There are two types of patterns for CTLM: one, designed by Marlow and Das [10], is composed of rings array; another, designed by Reeves [11], is composed of concentric rings. Gregory applied the former pattern into the bus-bars of solar cells to extract contact resistivity and the emitter sheet resistance, and made a comparison with TLM [12]. Making the assumption of Rsh = Rsk was still its disadvantage. The variation of Rsh beneath the electrode was considered in Reeves’ method, leading to an accurate solution in theory [11]. The disadvantage is the complex computations, but it can be overcome with mathematical software tools such as Scilab, Mathematica, and Matlab. According to the theoretical calculation and simulation reported by Chuan Xu [13], the limitation of Reeves’ CTLM is that the ρc should be greater than 10−6 Ω cm2 . Fortunately, the contact resistivity of silicon solar cells falls in this interval. This paper explored the use of the CTLM method to obtain ρc ,Rsk ,Lt systematically for the silver paste metallization contact on silicon solar cells. Its feasibility was discussed in comparison with other relevant publications, and the relationship between electrical properties and interface physics affected by sintering temperature was also discussed. Finally, the contact formation mechanism of silver paste metallization was explored based on the SEM observations.

r2 r1

1

r1 r0

E (r 0) αr 0

(1)

B (r ,r ′)

· ⎡ αr · C (r1,r1′) + 1 1 ⎣ 1

E

1 A (r 1,r 1 ) αr 1 C (r 1,r 1 )

1 A (r 2,r2′ ) · ⎤ αr2′ C (r 2,r2′ ) ⎦

r1 r0

}

F (r1,r1′)

r′ r′ ρc = ⎡R1ln ⎛ 2 ⎞−R2ln ⎛ 1 ⎞ ⎤·r02·Δ ⎢ r 1 ⎝ ⎠ ⎝ r0 ⎠ ⎥ ⎦ ⎣ ⎜

⎟

⎜

(6)

( ). R

r′ R sh ln r 1 2π 0

E

called CER, is defined as the ratio of

the output voltage VE of the middle ring contact to the input current when the output current between the outer two contacts is zero. VE replaces the voltage drop between the metal and emitter [14]. The resistance was calculated using R = V / I , and the direct current I was applied between the inner electrodes or the outer two electrodes. Fig. 1(b) shows the schematic diagrams of the CTLM pattern and measurement circuit. V1 and VE were simultaneously obtained using a voltmeter and potentiometer, respectively. V2 was measured independently using a voltmeter. The radius of the concentric circles r0,r1′,r1,r2′ and r2 should be carefully designed, for they determine the left-hand-side and right-hand side values of Eq. (2), the solutions region of α , and the accuracy of the measurement. The size given by Reeves, r0 = 46.5 μm,r1′ = 1.65 r0,r1 = 2.74 r0,r2′ = 4.34 r0,r2 = 5.45 r0 [11], is suitable in the microelectronic field for samples that are prepared using lithography, while it is not applicable for solar cells because the fine pattern has reached the resolution limit of normal screen-printing paste [15]. Donald et al. [16] reported that the pattern should reduce the difference between the contact resistance and the space resistance, ensuring a comparable contribution to the total resistance in order to reduce the test error, which means fine circles and fine space. However, it is difficult to apply this approach to solar cells because of the resolution limitation. Considering the principle of reducing the electrode internal resistance and the effect of size fluctuations of about 5–10 μm when produced by screen printing, we designed one pattern with r0 = 0.08 cm,r1′ = 0.2 cm,r1 = 0.2154 cm,r2′ = 0.4 cm and r2 = 0.5 cm, where the spaces were 0.12 cm and 0.1846 cm, much greater than the conductive-layer thickness, ensuring the current to only flow between the two contacts when the current was applied between the inner contacts [14]. The diameter of the center contact pad was equal to that of the probe, and the area of the middle contact was equal to that of the center circle pad. The Keithley2602B digital source meter served as the direct current power and voltmeter, and the voltage resolution was 10 μV in the measuring range using the four-probe method. The contact end voltage was measured accurately using a potential difference meter with accuracy of 1 μV . In other words, the resistance resolution of the source meter was 0.0005 Ω when the injected current was set to 20 mA, which

( ′ )−R ln ( ′ ) ⎤⎦/R = {ln ( ′ )·⎡⎣ + ′ · ′′ ⎤⎦−ln ( ′ ) 2

(5)

ρc / Rsk

resistance of the cell

where α 2 = Rsk / ρc . A detailed derivation for solving the differential equation is shown in Ref. [11]. Here, we list the important Eqs. (2)–(5) that are required to obtain α using the finite integration method, and to calculate ρc (contact resistivity), Rsk (sheet resistance beneath the electrode), and Lt (defined as the length from which the voltage drops to e−1 of its value at the beginning of the contact structure [8]). r2 r1

Lt =

where Functions A [r ,x ]-F [r ,x ] are defined as functions of the first and second modified Bessel functions listed in the appendix of Ref. [13]. R1 is the contact resistance between the inner two contacts, and R2 is the resistance between the outer two contacts. Both of them include the contact resistance between the silver electrode and emitter, and are determined mainly by the space between the contacts and the sheet

Fig. 1(a) shows the CTLM structure. According to the TLM theory, when a current is applied between the center circular and either the middle ring or the outer rings, the relation between the voltage and radial position is satisfied by Bessel equation as follows:

⎡R1ln ⎣

(4)

Δ = 2π /[(αr0)2 ·Φ·F (r1,r1′)]

2. Methods

d 2V 1 dV + −α 2V = 0 dx 2 x dX

Rsk = 2πRE / F (r1,r1′)

(2)

⎟

(3)

Fig. 1. CTLM schematic diagrams. (a) CTLM test structure. (b) Cross section of contact with measurement circuit schematic diagram.

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Fig. 2. (a) Test fixture composed of a nickel-plated copper 1.6-mm-diameter probe array, the center contact, the middle and outer separately 1, 6, and 12 probes. (b) Test sample, showing test patterns screen printed in a 4 × 5 array on a 1/4-part polycrystalline silicon solar cell substrate.

the binarization step of the image processing without making contact with the emitter. The mean values of the test pattern size were adopted in solving Eq. (2) in order to reduce the measurement tasks required, which did no notably affect the distribution of solutions. The test var0 = 0.0809 cm,r1′ = 0.2029 cm,r1 = 0.2191 cm,r2′ = 0.4036 cm, lues, and r2 = 0.5008 cm, were slightly greater than the designed ones. The bulk resistivity of the electrode was estimated to be 3 × 10−6 Ω cm according to the resistance of the outer ring that was about 0.022 Ω measured by Kelvin four-terminal method along the diameter direction. For the silver sintering began at about 300 °C [19,20] and may be completed at 570 °C/15 s, the ring resistance had no obvious decline with increasing the temperature. The middle silver ring was divided into six arcual parts by the six probes. From the bottom of the electrode to the probes, the current passed through a short distance of about 1/12 of the middle ring in horizontal direction. In this case, the maximal corresponding resistance was estimated to be 0.88 mΩ. If the actual contact area is 25% of the middle electrode, the contact resistance between the silver electrode and nickel-plated probes would be 0.05 mΩ estimated by (ρ1 + ρ2 )/4a , where ρ1,ρ2 are bulk resistivity of contact materials, a is the radius of contact region [21]. The contribution of these two values to the measurement value of CER is 0.93 mΩ. Table 1 shows the average of R1,R2 , and RE , calculated by measured voltages and rounded to 2–5 decimal places, which were found to be sensitive to the sintering temperature. When the contact resistance was ignored and the emitter sheet resistance was set to 100 Ω/ □,R1 and R2 were close to the theoretical values of 14.7 Ω and 9.6 Ω, respectively, which implies that the measurement method is reasonable. The CER decreased markedly with increasing the temperature, and had difference in the order of magnitude at four critical temperatures of 615 °C, 645 °C, 660 °C, and 690 °C. Because the minimum value measured for CER was 11.5 mΩ, the electrode internal resistance and the contact resistance accounted for 0.93 mΩ, the measurement error of RE was

was sufficient to distinguish the contact resistance from the total resistance theoretically. The measurements were conducted in a darkroom to avoid the effect of photovoltage [17]. In order to reduce the inner resistance influence of silver electrodes, the fixture was composed of an array of 1.6-mm diameter nickel-plated copper probes, a single center contact probe, six middle probes, and the outer 12 probes, ensuring the current to pass through the electrode perpendicular to the substrate direction, as shown in Fig. 2(a). 3. Experimental details A commercial silver paste was screen printed on the 1/4 -part 156 mm ×156 mm polycrystalline solar cell in the test pattern arranged in a 4 × 5 array as one sample, as shown in Fig. 2(b). The phosphorus concentration of the emitter surface was about 1.5× 1020 cm−3 , the depth was about 0.25 μm , and the sheet resistance was about 95 ± 5 Ω/ □ . The sintering process was divided into 15 groups according to the peak temperature from 570 °C to 780 °C with an interval of 15 °C in a rapid infrared annealing furnace. For each group, the temperature was increased to 550 °C within 1 min, and reached a peak in 8 s, and then maintained for 6 s. The treatment of 705 °C group was similar to the standard sintering process of production lines. The paste of about 0.08 g per cell was printed with a 360 mesh 16-μm diameter steel screen. The electrical properties were tested after sintering. Hitachi scanning electron microscopy (SEM) S4800 and Zeiss FIB-SEM were used to observe the morphology and composition distributions of the surface and cross section. An optical microscope was used to obtain the exact radius of the patterns after firing by employing image-processing methods [18]. 4. Results and discussion The bleeding of silver along the edge of the contacts was removed in

Table 1 R1,R2 , and RE values rounded to 2–5 decimal places, as calculated from measured voltages when the current was set to 20 mA. These values decreased markedly as the temperature increased, especially for the CER before 735 °C. Temp.

570 °C

585 °C

600 °C

615 °C

630 °C

645 °C

660 °C

675 °C

R1 (Ω) R2 (Ω) RE (Ω)

134.54 161.38 110.65

114.18 142.47 72.77

93.3 88.43 29.95

44.44 29.27 10.0858

31.95 23.1551 6.1894

20.138 13.3792 0.64349

19.9197 12.5188 0.59529

17.9978 11.0496 0.14967

Temp.

690 °C

705 °C

735 °C

750 °C

765 °C

780 °C

795 °C

R1 (Ω) R2 (Ω) RE (Ω)

17.1684 10.7077 0.02744

16.4539 10.6224 0.01155

16.0077 10.4412 0.01264

16.0218 10.5231 0.01149

15.6576 10.2721 0.01219

15.1103 10.0637 0.01341

15.4791 10.2734 0.02763

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Fig. 3. Box charts of obtained value. (a) Contact resistivity ρc , which decreased rapidly as temperature increased to 705 °C, then flattened out for a wide temperature interval between

10−3 and 10−4 Ω cm2 . (b) Calculated sheet resistance Rsk of the conductive layer beneath the silver electrode with a minimum about 0.186 Ω/ □ . (c) Transfer length Lt , which shows a Ushaped variation with a minimum around 0.035 cm.

of ρc turned to be 10−3 Ω cm2 , and the emitter surface was clean without silver colloids or crystallites, as also shown in Fig. 5(a) and (b). When the temperature increased to 690 °C, a few inverted pyramid silver crystals were embedded into the emitter for 50 nm depth under the glass melt (Figs. 4(c) and 5(c)) due to the redox reaction (Eq. (8)) between Ag and SiO2 [23]:

estimated to be within 10%. The values of ρc ,Rsk , and Lt were obtained by substituting the above measurements into Eqs. (2)–(5), as shown in Fig. 3. Vertical coordinates were used in the logarithmic scale to facilitate the display of all data. 4.1. Relationship between the special contact resistance and phase compositions at the interface

2 Ag 2 O+ Si → 4 Ag + SiO2

x N2 2

cm2 .

Ω As the temperature At this time, the ρc value decreased to further increased, the size and amount of inverted Ag crystal pyramids increased, and the large-sized crystals of greater than 200 nm in both depth and width damaged the emitter. It was estimated by the image binarization method that the silver crystals coverage in the observation field was about 4% at 690 °C and 24% at 780 °C, respectively, as shown in Figs. 4(d) and 5(d). According to Ref. [24], the ρc value decreased as the coverage of Ag crystallites increased form 0 to 15%, because the crystallites provided more tunnel avenues to electrons, as shown in Fig. 5(b)–(d). Meanwhile, the ρc value remained stable in a wide temperature range and increased slightly from 705 °C to 780 °C with an increase in the silver coverage, as illustrated in Fig. 3(a). With the increasing of temperature and silver crystallites numbers, the highly doped emitter region decreased to make the electrons transport models change from field emission (FE) to thermionic field emission (TFE) at the interface between the silver and emitter, and consequently the contact resistivity would increase at least 10 times [25]. The increasing of conduction channels competed with the increasing of micro contact resistance, which affected the measured contact resistivity. The increment in the contact resistivity caused by the glass layer thickness increasing [26] was small, for the glass frit weight content in the new commercial paste was only about 2–3% far less than the old type, as shown in Fig. 4(d). In this sense, it was not the more the better for the precipitation of silver crystallites and its density on the emitter surface to facilitate electrons transfer. Fig. 6 shows the surface images of two samples from group C respectively fired at 660 °C and 780 °C, which were recorded by SEM with accelerating voltages of 1 kV and 15 kV. It is observed from the 1-kV voltage SEM images (Fig. 6(a) and (c)) that there were differently sized

The obtained ρc values of around 3 × 10−4 Ω cm2 are in good agreement with the reported 5.2 × 10−4 Ω cm2 in Ref. [22], and initially, they decreased exponentially as the temperature increased, then flattened out after 705 °C, as shown in Fig. 3(a). According to the magnitude difference in ρc , the sintering process may be divided into four stages, where the ρc subsequently reached 10−1 Ω cm2 at 615°C,10−2 Ω cm2 at around 660 °C,10−3–10−4 Ω cm2 at nearly 690 °C,10−4 Ω cm2 at temperature of greater than 735 °C. The interface between the electrode and emitter was analyzed by SEM for the samples in each stage. The samples were divided into three groups A, B, and C. The group A was handled with a focused-ion beam to form a smooth cross section, the group B was immersed in 5%HF for 5 min to expose emitter surface, and the group C was soaked in 40% nitric acid for 20 min to remove the bulk silver. Fig. 4(a) shows clear boundaries between the silver bulk, glass melt, silicon nitride passivation layers, and silicon emitter of a sample fired at 615 °C, where the magnitude of ρc was 10−1–10−2 Ω cm2 . Small silver colloids were enriched on the Si Nx surface, implying that the Ag dissolved in the fluidized glass in the form of Ag+ ions was reduced into Ag crystallites by SiNx , which continued to grow during the cooling process [23]. The redox reaction equation is as follows:

2 Ag 2 O+ SiNx → 4 Ag + SiO2 +

(8)

10−4

(7)

The SiNx coating gradually disappeared at around 660 °C due to this reaction, as shown in Fig. 4(b). Most of the micron scale silver particles dissolved completely, and the glass melt was attached to the bulk silver and emitter directly. A small amount of nanometer-scale silver colloids precipitated in glass adjacent to the emitter. Meanwhile, the magnitude

Fig. 4. Cross-sectional FIB-SEM images of silver electrode and silicon emitter sintered at different temperatures with partial enlarged details. (a) 615 °C. The interface is composed of four parts: Bulk silver/Glass melt/SiNx/Silicon emitter (marked out with white lines). The inset shows that silver colloids reduced on the surface of SiNx in glass melt (indicated with white circles). (b) 660 °C. The interface is composed of three parts: Bulk silver/Glass melt/Silicon emitter (plotted with white lines). The SiNx disappeared and the amount of silver colloids decreased. (c) 690 °C. Micron-order silver crystallites were precipitated on the emitter surface. (d) 780 °C. Micron-order silver crystallites covered most of the emitter surface beneath the thin glass melt.

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Fig. 5. SEM images of emitter surface beneath the silver electrode, which was etched off by 5% HF solution at different sintering temperatures. (a) 615 °C. The emitter surface was covered partially by SiNx residue without attaching silver precipitation. (b) 660 °C. The emitter surface was clean. (c) 690 °C. Micron sized silver crystallites were precipitated on the emitter surface between two or three adjacent micro-pits account for 4% (estimated by the binarization method) of the area in the observation field, as shown on the right corner. (d) 780 °C. Silver crystallites coverage was about 24%, as shown in the insert.

holes left under the electrode after the pre-located Ag particles, crystallites and colloids were etched with HNO3 . Under 15-kV voltage, the SEM was also used to probe the information about the internal composition of glass layer. As shown in Fig. 6(b) and (d), there were many white dots underneath the glass melt, which indicates that most of the electrons from the emitter couldn’t be transferred to bulk silver directly, but only tunnel through the glass melt with nonuniform thickness. The conductivity of glass melt and the volume fraction of silver colloids or crystallites imbedded in glass melt become two main factors affecting the further reducing of contact resistivity during the third and fourth sintering stages. 4.2. Differences between calculated and measured sheet resistance beneath the silver electrode

Rsk represents the sheet resistance of a layer between the metal and the doped silicon surface, which commonly differs from the original sheet resistance due to the formation of a medium layer, e.g. silicide [27] or sintering reactions [6]. The compositions of interface between the glass frit mixed silver electrode and emitter are so complicated to cause intricate redox-reactions between Ag /Glass frit/Si . As shown in Fig. 3(b), the calculated sheet resistance Rsk decreased nonlinearly to 0.186 Ω/ □ as the temperature increased to 765 °C. According to Eq. (5), Rsk is proportional to RE , and is inversely proportional to function F [r1,r1′]. The about 10% measurement error of RE was brought to Rsk . The about 5% measurement error of the pattern size would also cause a 5% deviation in the Rsk value. Although the value of Rsk was not absolutely accurate, its declined trend was trustworthy. The theoretical calculation of Rsk value was smaller than 7 Ω/ □ by solving the Bessel Eq. (1) under given boundary conditions. In order to determine the region of Rsk included, a 50 mm × 50 mm -sized silver paste pattern was printed on the cell, and sintered at 615 °C, 660 °C, 690 °C, 720 °C, and 795 °C, respectively. Two types of samples were prepared using the same methods for group B and group C. One approach was to remove the surface layer of bulk silver with nitric acid, leaving the glass surface layer covering the emitter, as shown in Fig. 6(a). The other approach was to remove all of the silver

Fig. 7. Box charts of measured sheet resistance beneath the silver electrode for the samples sintered at different temperatures. (a) With glass melt layer. (b) Without glass melt layer.

and glass melt on the emitter but left the silver crystals locating at the emitter, as shown in Fig. 5(c) and (d). For both samples, the sheet resistance values were measured using the four-probe resistance tester, as illustrated in Fig. 7(a) and (b). As shown in Fig. 7(a), when the surface was covered with glass melt, the sheet resistance increased from 120 Ω/ □ to 200 Ω/ □ as the temperature increased from 615 °C to 795 °C. In contrast, when the glass

Fig. 6. SEM images taken separately under accelerating voltages of 1-kV and 15-kV for the emitter surface covered with glass melt. (a) 1-kV image for the sample sintered at 690 °C, showing many small holes on the glass melt surface due to the removal of the silver particles, crystallites and colloids. (b) 15-kV back-scattered-electron image for the sample sintered at 690 °C, showing silver crystallites that were precipitated on the emitter under the glass melt. (c) 1-kV image for the sample sintered at 780 °C, showing silver crystallites (marked by white circles) that were precipitated on the emitter surface under the glass melt. (d) 15-kV back-scattered-electron image for the sample sintered at 780 °C, showing a large number of silver crystals beneath the glass melt.

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5. Conclusion

melt was removed by HF , the sheet resistance increased from 190 Ω/ □ to 240 Ω/ □ , as shown in Fig. 7(b). This increment in the emitter sheet resistance was related to the corrosion of the emitter by the glass melt. The main compositions of glass frit generally used in front silver paste include PbO-TeO2 -B2 O3-SiO2 [28] or Bi2 O3 -TeO2 -B2 O3 -SiO2 [29]. The redox reductions related to the silver paste contact formation in a sintering process in air, are described as below [23,30]:

2 PbO + Si → 2 Pb + SiO2

Pb +

1 O2 → PbO 2

Ag 2 O+ Pb → 2 Ag + PbO

The CTLM method was used to investigate the contact-formation mechanism on the emitter of crystalline silicon solar cells, and we obtained ρc ,Rsk , and Lt . According to the variation of ρc , the sintering processes could be divided into four stages, where SiNx and glass melt dominated the variation of ρc in the initial and final stages. Increasing the precipitation of silver crystallites on the emitter surface is not a better way to reduce contact resistivity, unless there is no obvious damage to the emitter. The sheet resistance underneath the electrode decreased from 110 Ω/ □ to 0.186 Ω/ □ due to the formation of a highly conductive molten glass layer with imbedded silver crystallites or colloids, restricting the further decrease in the contact resistivity. The transfer length Lt assumed a U-shaped variation with the temperature, which reflected the change in the electrical properties of the interface. Although the patterns, fixtures and measurements still have a space for improvement, the values extracted by CTLM can well reflect the morphologies and phases variations controlled by the temperature and compositions, thus it is a good alternative to traditional TLM methods for the research and formula optimization on metallization.

(9)

(10) (11)

Due to these reactions, a SiO2 enriched layer would be formed near the emitter under the glass melt [31]. The measured sheet resistance for the samples with glass layer was lower than the glass removed samples, which implies that the glass melt should be a conductive layer comparable to the emitter. According to the relation of n-type silicon resistivity to doping concentration, the resistivity of emitter surface is about 10−3 –10−4 Ω cm . As the measured sheet resistance for 0.15 μm thickness emitter was about 200 Ω/ □ , the resistivity was estimated to 10−3 Ω cm . These two values were consistent, indicating that the sheet resistance test was reliable. Pfeffer [32] assumed the resistivity of glass should be 100 times bigger than that of silver, and derived that the critical volume fraction should be about 15% with the resistivity of 10−4 Ω cm based on percolation theory. If the volume fraction of silver colloids and crystallites increases simultaneously, the resistivity would decrease to 10−5 Ω cm . In fact, as the calculated sheet resistance is 0.186 Ω/ □ , the resistivity would be just about 10−5 Ω cm if the glass thickness is set to 0.5 μm . From Fig. 6(a) and (c), we found enormous micron and nano holes on the glass melt surface, which were left after the removal of undissolved silver particles or precipitated silver crystallites by HNO3 . This treatment led to higher sheet resistance measured by four-probe resistance tester. The local two dimensional silver particles, colloids and crystallites coverage was estimated by image binarization to be greater than 40% , as shown in the right middle insert in Fig. 6(a). Accordingly, we could infer that the highly conductive layer corresponding to the calculated sheet resistance value Rsk was more likely to consist of the crystallites or colloids embedded glass melt rather than the silicon emitter. The conduction mechanism and its reliable evidence for the silver crystallites or colloids imbedded glass melt need to be studied further.

Acknowledgments This study was supported by the Shanghai Science and Technology Committee Scientific Projects [Number 15dz1200902] and [Number 17dz1201102]. We also thank Hareon Solar Technology Co. Ltd. for providing cell samples and SEM testing. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.sse.2017.12.012. References [1] Giorgio Cellere MZ. Tom Falcon. International technology roadmap for photovoltaic 8th edition 2017; 2017. URL < http://itrpv.net/Reports/Downloads/ > . [2] Haigh AD. Fired through printed contacts on antireflection coated silicon terrestrial solar cell. In: Proc 12th IEEE photovoltaic specialists conf, vol. 12; 1976. p. 360–1. [3] Lu G, Zheng F, Wang J, Shen W. Thin Al2O3 passivated boron emitter of n-type bifacial c-Si solar cells with industrial process. Prog Photovoltaics: Res Appl 2017;25(4):280–90. http://dx.doi.org/10.1002/pip.2859. pIP-15-253.R2. [4] Zhong S, Huang Z, Lin X, Zeng Y, Ma Y, Shen W. High-efficiency nanostructured silicon solar cells on a large scale realized through the suppression of recombination channels. Adv Mater 2015;27(3):555–61. http://dx.doi.org/10.1002/adma. 201401553. [5] Zhao J, Wang A, Green MA. High-efficiency PERL and PERT silicon solar cells on FZ and MCZ substrates. Sol Energy Mater Sol Cells 2001;65(1):429–35. http://dx.doi. org/10.1016/S0927-0248(00)00123-9. pVSEC 11 Part I. [6] Vinod PN. Specific contact resistance measurements of the screen-printed Ag thick film contacts in the silicon solar cells by three-point probe methodology and TLM method. J Mater Sci: Mater Electron 2011;22(9):1248. http://dx.doi.org/10.1007/ s10854-011-0295-z. [7] Guo S, Gregory G, Gabor AM, Schoenfeld WV, Davis KO. Detailed investigation of TLM contact resistance measurements on crystalline silicon solar cells. Sol Energy 2017;151:163–72. http://dx.doi.org/10.1016/j.solener.2017.05.015. [8] Berger H. Models for contacts to planar devices. Solid-State Electron 1972;15(2):145–58. http://dx.doi.org/10.1016/0038-1101(72)90048-2. [9] Schroder DK. Semiconductor material and device characterization. 3rd ed. WileyIEEE Press; 2006. [10] Marlow GS, Das MB. The effects of contact size and non-zero metal resistance on the determination of specific contact resistance. Solid-State Electron 1982;25(2):91–4. http://dx.doi.org/10.1016/0038-1101(82)90036-3. [11] Reeves G. Specific contact resistance using a circular transmission line model. SolidState Electron 1980;23(5):487–90. http://dx.doi.org/10.1016/0038-1101(80) 90086-6. [12] Gregory G, Gabor A, Anselmo A, Janoch R, Yang Z, Davis K. Non-destructive contact resistivity measurements on solar cells using the circular transmission line method. In: Proc IEEE 44th photovoltaic specialist conf (PVSC), Washington (DC, USA); 2017. [13] Xu C, Wang J, Wang M, Jin H, Hao Y, Wen CP. Reeves’s circular transmission line model and its scope of application to extract specific contact resistance. Solid-State Electron 2006;50(5):843–7. http://dx.doi.org/10.1016/j.sse.2006.03.007. [14] Alok D, Baliga BJ, McLarty PK. Low contact resistivity ohmic contacts to 6H-silicon carbide. In: Proc IEEE int electron devices meeting; 1993. p. 691–4. http://dx.doi.

4.3. Variation of the transfer length as the temperature increases

Lt is originally defined as the distance for which the voltage in a planar transmission attenuates to 1/ e at the edge of the contact. Most of the current flows from the semiconductor to the metal within the length of the transfer, or from the metal to the semiconductor. From Eq. (5), Lt is determined by ρc and Rsk . Fig. 3(c) shows that the relation of Lt to the temperatures from 615 °C to 780 °C takes a U-shaped from, which is due to that the ρc and Rsk had inconsistent trends. The ρc was reduced exponentially before 705 °C, but it increased slightly when the temperature further increased. At the temperatures from 585 °C to 765 °C, the Rsk was declined continually, resulting in an increased Lt (Eq. (5)), as the temperature was greater than 705 °C. If the calculated Rsk values were right, there should be no current accumulation effect perpendicular to the fingers on the emitter surface of solar cells excepted the bus-bars, because the minimum average value of Lt was 350 μm . The width of fingers was only about 50 μm far less than Lt , but the bus-bar width was about 1 mm greater than Lt . Therefore, The width of the busbars could be decreased or hollowed-out to reduce the silver consumption as long as the mechanical performance and reliability can be guaranteed. 6

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Shenghu Xiong received the B.S. degree from China University of Geosciences, Wuhan, in 2001, and the M.S. degree in the department of materials science and engineering, Tsinghua University, Perking, China, in 2005. He is currently pursuing the Ph.D. degree in East China University of Science and Technology, Shanghai. His research interests include metallization and new processes of crystalline silicon solar cells.

Xiao Yuan received the B.S. degree from ShanghaiTech University, China, in 1984 and the M.S. degree from East China Normal University, China, in 2000. He is currently a Professor with East China University of Science and Technology. His main research interests include new energy materials and devices related with solar cells.

Hua Tong received the B.S degree from Zhejiang University, China, in 2001, and the PhD degree from Shanghai Institute of Ceramics, Chinese Academy of Science (SICCAS), in 2007. From 2008 to 2012, he worked as a postdoctoral fellow at the National Institute for Materials Science (NIMS), Japan. At present, he is employed as an associate professor by East China University of Science and Technology, China, and his current research concentrates on the metallization technology and relevant materials for crystalline silicon solar cells.

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