B. DJELLIL et al.: COMPARATIVE STUDY OF THE RECOMBINANT ACTIVITY EFFECT AT THE GRAIN BOUNDARIES ... 607–612 COMPARATIVE STUDY OF THE RECOMBINANT ACTIVITY EFFECT AT THE GRAIN BOUNDARIES IN SILICON SOLAR CELLS PRIMERJALNA [TUDIJA REKOMBINACIJSKEGA U^INKA NA MEJAH KRISTALNIH ZRN SILICIJEVIH SON^NIH CELIC Bilal Djellil 1 , Souad Merabet 2* , Hachemi Bouridah 1 1 Laboratory of the Materials Studies, Department of Electronics, University of Jijel, Jijel, Algeria 2 Laboratory of Renewable Energy, Department of Electronics, University of Jijel, Jijel, Algeria Prejem rokopisa – received: 2022-08-18; sprejem za objavo – accepted for publication: 2022-09-15 doi:10.17222/mit.2022.597 This work studies the effect of carrier trapping and the recombination activity at the grain boundaries in the p-layer of polysilicon solar cells with respect to the deposition temperature. The dependence of the grain size on the deposition tempera- ture was studied in different samples of boron-doped low-pressure chemical vapor deposition (LPCVD) silicon deposits, con- ducted in a horizontal low-pressure atmospheric pressure reactor where the temperature varied over a range from 520 °C to about 605 °C. The obtained results show clear evidence of dependence on effective changes in the trapping effect as a function of the trapping density states, the doping level and the thickness dimension of the deposited layer. Keywords: recombination current density, recombination rate, carrier lifetime, effective mobility V ~lanku avtorji opisujejo {tudijo vpliva pasti za nosilce nabojev in aktivnost njihove rekombinacije na mejah kristalnih zrn v p-sloju poli-silicijevih solarnih celic, v odvisnosti od temperature pri izvedbi nanosa. Avtorji so {tudirali vpliv temperature na velikost kristalnih zrn pri razli~nih vzorcih silicijevih nanosov. Postopek dopiranja Si z borom (B) so izvajali s kemijskim nizkotla~nim naparevanjem (LPCVD; angl.: low-pressure chemical vapor deposition) v horizontalnem nizkotla~nem reaktorju. Pri tem se je temperatura reaktorja spreminjala v obmo~ju med 520 °C in pribli`no 605 °C. Rezultati {tudije so pokazali jasno odvisnost u~inkovitosti pasti za nosilce naboja od njihove gostote, nivoja dopiranja in debeline nanosa oziroma plasti Si dopiranega z B. Klju~ne besede: rekombinacija tokovne gostote, hitrost rekombinacije, ~as trajanja nosilcev, u~inkovitost mobilnosti 1 INTRODUCTION In recent years, the emergence of polycrystalline sili- con devices has been very beneficial for the microelec- tronic development. Many authors have been interested in their electrical aspects. Significantly, the modeling of charge carrier transport through these layers can be con- sidered as one of the most frequent studies. 1–5 Poly- crystalline materials consist of finite-size grain struc- tures. The boundary between two grains is a lattice defect through which the orientation of a crystal changes. 6 Grain boundaries in polysilicon act as charge carrier migration routes; thus, a reduction of these boundaries can modify the rate of undesired traps, being one of the most significant challenges of these materi- als. 7 In the devices with minority carriers, such as solar cells, the conversion efficiency does not depend solely on doping concentration, crystalline quality and grain di- mensions, but also, and in particular, on the recombina- tion activity at the grain boundary. 8,9 To provide for the design and development of such cells that can become a competitor to mono-crystalline silicon cells, we need to understand how the grain size and grain boundary affect the transport of minority carri- ers. Indeed, grain boundary states are among the most prevalent defects in materials, which are considered criti- cal in controlling the carrier mobility, 10 acting as recom- binant centers and therefore being a source of recombi- nation current. 11–13 The diffusion of the dopant strongly depends on the crystal structure and detailed structure of the grain boundaries. Although these occupy only a small fraction of the volume, dopant migration along these paths can markedly influence the overall dopant diffusion in the layer. The transport modeling and recom- bination properties of polycrystalline silicon generally assume that all grains have the same average size. 14 Dif- ferent types of polysilicon are distinguished by this sig- nificant parameter, on which the physical and electrical properties depend. 15 Thus, this study is focused on analyzing the recombi- nation activity and effect of trap density at the grain boundaries in polycrystalline silicon solar cells, using a widely used standard transport model 16 based on a good understanding of the carrier mobility limit at the grain boundaries. Materiali in tehnologije / Materials and technology 56 (2022) 6, 607–612 607 UDK 621.383.51 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 56(6)607(2022) *Corresponding author's e-mail: smerabet@univ-jijel.dz (Souad Merabet) 2 EXPERIMENTAL PART In this work, the effect of the characteristic parame- ters of three series of poly-silicon layers obtained with the LPCVD method (low-pressure chemical vapor depo- sition) at a low pressure (53.33 Pa) and based on the de- composition of silane (SiH 4 ) deposited on a single crys- tal with the crystallographic orientation, with thicknesses of 200 nm and 300 nm and in-situ doped with boron, has been studied as a function of the grain size. More details about the deposited layers are available in the previously published works. 17,18 The dependence of the grain size on the deposition temperature was studied in a horizontal at- mospheric pressure reactor, where the temperature varied over a range from 520 °C to about 605 °C. The first se- ries of films called p-layer 1, deposited at 520 °C with a thickness of 200 nm, was represented by layer 1, and the second series of films called p-layer 2, obtained at 605 °C with a thickness of 200 nm, was represented by layer 2. Finally, the series of films called p-layer 3, de- posited at 605 °C with a 300 nm thickness, was repre- sented by layer 3. The follow-up of the grain size evolu- tion of the layers shows a variation with respect to the deposition temperature. Previous studies 19 showed that the first deposits have a large grain size equal to 80 nm, while the second and third ones have a small grain size of 40 nm. Thus, the structure of layer 1 is polycrystalline with an average grain size of about twice that of layer 2 and layer 3. An analysis is carried out using the results obtained with a previous study 17 where the structures of the films were characterized with X-ray diffraction. X-ray spec- trometry is shown in Figure 1. 3 MODEL Diffusion of the carriers through the traps at the grain boundaries is formulated with the Seto Model. 16 The re- combination mechanism is obtained by considering the grain boundaries as the interface where carriers diffuse and recombine, which means that the geometry of the grain (especially the grain size) and the diffusion coefficient of the grain must be considered. Therefore, the recombination speed is evaluated with Equation (1), which requires the knowledge of the interface density states and the loading state of these defects. Generally, the S jg recombination speed (m·s –1 )a tt h e grain boundary is determined by the density of the effec- tively active interface states N t , whose level is assumed to be centered in the middle of the forbidden gap with the following Equation (1): SN v jg ct th =⋅⋅ (1) where c is the effective capture section (m 2 ), v th is the thermal speed (m·s –1 ) and N t is the density of effectively active interface states (m –2 ). In the case of polysilicon, the presence of defects lo- calized at the interface introduces trap levels in the sili- con bandgap (Figure 2). These defects can act as traps that trap carriers temporarily before returning them to the conduction band (or valence band), altering the semicon- ductor’s conductivity. Assuming that in the case of polycrystalline silicon, the recombinant surface consid- ered is the grain boundary since the grain width is much lower than its height 20 , the expression of life duration (s) is given by Equation (2): 7 111 eff g g =+ j (2) j j L S L Nv g g ct th == 22 (3) The model was simplified for a polycrystalline mate- rial and evaluated as being composed of identical crys- tals with an average grain size, L (m). Although polysilicon is a three-dimensional struc- ture, it is sufficient to calculate its transport properties to treat the problem as a single dimension. Thus, the poten- tial barrier height is evaluated from the model used and B. DJELLIL et al.: COMPARATIVE STUDY OF THE RECOMBINANT ACTIVITY EFFECT AT THE GRAIN BOUNDARIES ... 608 Materiali in tehnologije / Materials and technology 56 (2022) 6, 607–612 Figure 1: X-ray spectra diffraction peaks of the p-layers 17 Figure 2: Energy-band diagram of p-type polysilicon under optical il- lumination another study, 21 and the recombination current density at grain boundaries is determined with Equation (4): 16 () Jq SPP j r g =− () 0 0 (4) where S jg is the surface recombination rate (m·s –1 )a t grain boundary levels, P(0) is the density of minority carriers under excitation (m –3 ), P 0 is the carrier density in equilibrium (m –3 ) and q is the electronic charge (C). The effective mobility μ eff (m 2 ·V –1 ·s –1 ) that describes the ease of the carrier motion from one grain to another is given by Equation (5): 16 eff B =⋅ − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Lq mK T E KT 1 2π * exp (5) where E B is the energy potential barrier (eV) at the grain boundary, m * is the effective mass (9.11 × 10 –31 kg) of the carriers, K is the Boltzmann constant (1 380 649 × 10 –23 J·K –1 ) and T is the temperature (300 K). 4 RESULTS AND DISCUSSIONS 4.1 Recombination rate Figure 3 shows the evolution of the recombination rate as a function of the doping level represented in the considered three layers. The obtained results show that at low levels of doping (from1×10 22 m –3 to1×10 24 m –3 ), the recombination speed in the three layers is nearly the same. Then, after 1 × 10 24 m –3 (an increase in the doping level), due to a very high doping concentration and the equivalent energy barriers of the depletion region being small, the added energy barriers at the grain boundaries will essentially limit the carrier transport. 22,23 A clear dis- parity between the three curves is observed due to the variation in the grain size and the recombination reaches its maximum value depending on the doping level and decreases after a certain value. The curves of layers 2 a n d3( S jg2max = 936.00 m·s –1 at a doping of 0.67 × 10 26 m –3 and S jg3max = 904.31 m·s –1 at a doping of 0.54 × 10 26 m –3 ) are greater than those of layer 1 (S jg1max = 755.39 m·s –1 at a doping of 0.38 × 10 26 m –3 ). These results are in good agreement with the previous works. 24,25 The effect of thickness variation is observed at high doping (from 1 × 10 25 m –3 to6×10 25 m –3 ) when compar- ing the curves of layer 2 and layer 3. The recombination speed value of layer 3 is slightly lower than that obtained for layer 2. This can be explained with the increased thickness that led to a smaller resistivity confirmed by previous works, 17 caused by a decrease in the defect den- sity as reported in Table 1. 4.2 Carrier life time The doping of silicon (p or n) is usually above the photogeneration (a low injection rate), minority carriers are metastable and will exist, on average, only for a pe- riod equal to the lifetime. This corresponds to the aver- age time between the electron-hole pair formation and recombination. B. DJELLIL et al.: COMPARATIVE STUDY OF THE RECOMBINANT ACTIVITY EFFECT AT THE GRAIN BOUNDARIES ... Materiali in tehnologije / Materials and technology 56 (2022) 6, 607–612 609 Table 1: Results obtained for the three p-layers Thickness (× 10 –9 m) Resistivity (× 10 ·m) (Ref. 17) Trap rate N t (m –2 ) Critical doping concentration N * (× 10 23 m –3 ) V bmax (V) V b (V) S jg (m/s) J rmax (× 10 5 A/m 2 ) Layer 1 200 2.771 4.454 × 10 16 1.5 0.1736 0.00382 755.39 1.04465 Layer 2 200 3.867 9.78 × 10 16 5 0.1534 0.0164 963.0 0.23997 Layer 3 300 3.410 8.24 × 10 16 4.8 0.1506 0.0131 904.31 0.2161 Figure 4: Carrier lifetime at grain boundaries as a function of the dop- ing level Figure 3: Recombination rate as a function of the doping level and grain size Figure 4 displays a linear dependence of the minority carrier lifetime at grain boundaries, which is shown to be entirely controlled by the recombination activity in the three considered layers. The evolution of the results indi- cates that the lifetime is proportional to the increase in the grain size and in the thickness; it is higher in layer 1 than in layers 2 and 3, and slightly lower in layer 2 with a thickness of 200 nm than in layer 3 with a thickness of 300 nm, which is in good agreement with the previous results of the recombination speed at grains boundaries. 26 The aspect of the curves also highlights that as the dop- ing level increases the lifetime of carriers decreases up to a certain value, then the lifetime and doping level in- crease proportionally. This could be due to the saturation of the dangling bonds by the trapped carriers. 26 Therefore, the concentration of the free carriers joins that of doping, and the carrier lifetime, which initially decreased, increases linearly with the dopant concentra- tion at very high doping. These results validate those ob- tained for the recombination rate. 4.3 Height potential barrier and mobility Grain boundaries contain a large number of initially neutral trap states; the dopant atoms are uniformly dis- tributed within the grains, capturing carriers and the trap states become electrically charged, creating deserted re- gions and potential barriers on either side of each bound- ary, while the passage of free carriers from one grain to another becomes limited. The curves shown in Figure 5 enabled the determination of the potential barrier value for the three studied layers doped with a boron concen- tration of 1×1 0 26 m –3 with respect to the change in the grain size. The potential barrier is around 0.00382 V for the films with larger grains prepared at 520 °C; it in- creases to 0.0164 V as the deposition temperature of the film with smaller grains is 605 °C; finally it decreases to 0.0131 V when the film thickness is increased. In layer 1, the dopant concentration is lower than that of the trap states; the potential barrier reaches its maxi- mum (0.1736 V) at the doping level of 1.5 × 10 23 m –3 . The effective mobility (Figure 6) decreases rapidly to its lowest value at 10 23 cm –3 . This is explained with the fact that almost all the carriers are trapped. As a result, the concentration of free carriers is very low and therefore the resistivity must be very high. Then, under the influence of a further dopant increase (10 24 m –3 and more), the height of the potential barrier (Figure 5) decreases and the carrier effective mobility increases (Figure 6) due to a rapid rise in the concentra- tion of free carriers. These results are in good agreement with other studies published in the literature. 21 The same phenomenon was observed in the two other layers, but at a doping level equal to5×10 24 m –3 ; the po- tential barrier reached its maximum at 0.1506 V for layer 3 and 0.1534 V for layer 2. A very small variation was noticed between the two values (the same observation at a higher doping level of carrier mobility), which could only be due to the increased thickness in layer 3, since both layers were prepared at the same deposition temper- ature, with practically the same average grain size. 4.4 Recombination current density In Figure 7, the variation in the recombination cur- rent density in the three layers is reported. As a function of the doping level, the recombination current reaches its maximum. At a low doping level, and below the critical doping concentration N * (m –3 ), the concentration of free carriers is low and the resistivity is high. At the critical doping concentration N * 1 =1.5×10 23 m –3 for layer 1, the recombination current density is at its maximum value equal to 1.04465 × 10 5 A/m 2 , while for layers 2 and 3, it is 2.3997 × 10 6 A/m 2 and 2.161 × 10 6 A/m 2 , obtained at critical concentrations of N * 2 =5×1 0 23 m –3 and N * 3 =4.8×10 23 m –3 , respectively (see Table 1). This can be explained with the fact that the trap rate N t (m –2 ) at grain boundary levels differs between the B. DJELLIL et al.: COMPARATIVE STUDY OF THE RECOMBINANT ACTIVITY EFFECT AT THE GRAIN BOUNDARIES ... 610 Materiali in tehnologije / Materials and technology 56 (2022) 6, 607–612 Figure 6: Effective mobility carriers as a function of the doping level at grain boundaries Figure 5: Potential barrier height as a function of the doping level at grain boundaries three layers. They were generated under the initial condi- tions of the film preparation that were verified by the ex- perimental resistivity measurements (see Table 1). Be- yond the critical concentration N * (m –3 ), when the doping concentration increases, the recombination current den- sity decreases. At a very high doping level, both the re- combination speed and the recombination current density decrease, while the carrier lifetime and mobility increase due to the saturation of the grain boundaries by the seg- regation phenomenon. 26,27 The grain boundaries are filled, the hanging bonds are saturated 28 and the minority carriers in this case will be able to move from the collin- ear grains. The obtained results are in accord with the evolution of the deposited microstructure. At a lower deposition temperature the structure is polycrystalline with large grains, while at a higher deposition temperature it is a polycrystalline structure with small grains. Simulta- neously, this leads to the appearance of a high trap den- sity followed by carrier trapping at grain boundary levels and a decrease in the free carrier concentration. 29 5 CONCLUSIONS In this study, the effect of the deposit conditions and grain boundary density on the electrical parameters of three silicon layers was investigated. The results show that the structural properties and thickness have a signifi- cant impact on the photo-conductivity of the obtained films, affecting the mobility and lifetime of minority car- riers. It was found that the obtained value of the recom- bination rate is lower for the layers with large grains pre- pared at a low temperature than for those with small grains prepared at a high temperature. The recombina- tion rate is higher when the grain size is smaller. The lifetime evolution results for the carriers show that they are completely controlled by the recombination at the grain boundaries in the three considered layers. Proportional to the increase in the thickness and grain size, the carrier lifetime is higher in layer 1 than in layers 2 and 3, and it is lower in layer 2 (with a 200-nm thick- ness) than in layer 3 (with a 300-nm thickness), which have the same average grain size. The effect of the thickness variation is observed when the recombination rate values in layers 2 and 3 are com- pared at high doping levels (from1×1 0 25 m –3 to 6×10 25 m –3 ). The values for layer 2 are slightly higher than those obtained for layer 3. Also, the obtained results for the potential barrier and carrier mobility showed a close dependence on the dop- ing level and grain size. For the films with larger grains deposited at low temperatures, the critical dopant con- centration N* is lower than that for the polysilicon films deposited at slightly higher temperatures. 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