3.2. Effects of base angle size on optical reflectance

As depicted in Figure 4 (a), the calculation results were shown as curve (a) in Figure 10 with different base angle size θ (from 30<sup>∘</sup> to 75<sup>∘</sup> ). It is notable that the structure lost light trapping efficiency when θ ≤ 30<sup>∘</sup> , according to the geometric relationship between the incident and reflected light.

The irregular curve can be discussed as follows:

The variation of reflection times changed with the base angle size was obtained after a rigorous geometric calculation: the nth reflection area started occurrence when the base angle θ reached 180n�270 2n�1 ∘ , i.e., <sup>α</sup> <sup>¼</sup> <sup>360</sup> 2n�1 ∘ ; the whole light trapping area became nth reflection area when the base angle θ reached 90<sup>n</sup>�<sup>1</sup> n ∘ , i.e., <sup>α</sup> <sup>¼</sup> <sup>180</sup> n ∘ . Specifically speaking, all the incident lights reflected only one time when θ ≤ 30<sup>∘</sup> , and the reflectance was stable at 33.333%; the 2nd, 3rd, 4th, 5th, 6th reflection area starting occurrence when θ reached 30<sup>∘</sup> , 54<sup>∘</sup> , 64:286<sup>∘</sup> , 70<sup>∘</sup> , 73:636<sup>∘</sup> respectively, and the whole light trapping area became 2nd, 3rd, 4th, 5th, 6th reflection area when θ reached 45<sup>∘</sup> , 60<sup>∘</sup> , 67:5<sup>∘</sup> , 72<sup>∘</sup> , and 75<sup>∘</sup> , respectively. And the weighted reflection γ maintained constants



<sup>β</sup><sup>20</sup> <sup>¼</sup> <sup>R</sup>max<sup>20</sup> <sup>¼</sup> <sup>3</sup>:<sup>69</sup> � <sup>10</sup>�<sup>6</sup>

54 Solar Panels and Photovoltaic Materials

where Ri

i>20, and the weighted reflectance γ can be shown as:

Figure 8. Refractive index for silicon to different wavelength rays.

where Rj is the reflectance of monochromatic ray at j

in formula (11) becomes

Figure 9. Reflectance for different wavelength rays.

, and ζ<sup>i</sup> < 1 (in Eq. (4)), hence the calculations can be ignored when

th reflection.

ζiRi (11)

Rj (12)

<sup>γ</sup> <sup>¼</sup> <sup>X</sup> 20

i¼1

<sup>R</sup><sup>i</sup> <sup>¼</sup> <sup>Y</sup> i

j¼1


Table 2. Calculated result and analysis by different n (<sup>θ</sup> <sup>¼</sup> <sup>55</sup> <sup>∘</sup> ,r ¼ H=10).

Figure 10. Relationship of weighted reflectance and the base angle size.

is 11.111, 3.703, 1.235, 0.411 and 0.137%. In other areas when there existed a variety of reflection areas, the weighted formula of reflectance was shown as in the following:

$$\gamma = aR^t + (1 - a)R^{t+1} = \left(R^t - R^{t+1}\right)a + R^{t+1} \tag{13}$$

incidence respectively. Every arc-length blocked by rays reflection in the arc equals each other, therefore, the number of reflections of ray in arc-shaped groove is positively correlated with the ratio of total arc-length to single arc-length blocked by each reflection. The rays of short wavelength show higher weighted reflectance when incidence and structure parameters are the same, which is similar to the variation trend of refractive index, it means when the other conditions remain the same, silicon shows lower absorption efficiency for shorter wavelength rays. In practical preparation process of arc-shaped micro-structure, reflectance will be higher

Figure 11. Effects of different ratio of r/H and primary incidence on the reflectance of arc-shaped grooves of rays of

Effects of the Novel Micro-Structure on the Reflectance of Photovoltaic Silicon Solar Cell

http://dx.doi.org/10.5772/intechopen.74972

57

different wavelengths. Wavelengths of (a) 400 nm, (b) 600 nm, (c) 800 nm, and (d) 1000 nm.

An algorithm was designed to calculate the weighted reflectance of the light trapping structure. The light trapping mechanism was studied by numerical algorithm with the morphology

as the existence of one reflection area of uncut part.

4. Conclusions

Where a is the proportion of lights projected onto the t th reflection area. With increasing base angle size, a decreased linearly from 0 to 1, t and t + 1 were the reflection times of the two kinds of reflection area which existed in the light trapping area, and R is the reflectance. Obviously it was a linear function, therefore, in each area which existed a variety of reflection areas, γ decreased linearly with the base angle size.

In a word, 60<sup>∘</sup> was chosen as the final structure base angle of the pyramidal structure considering that the reflectance had reached a relatively stable value. In addition, 60<sup>∘</sup> was a suitable value for the tool design.

#### 3.3. Effects of r/H and incidence on the reflectance of arc-shaped grooved light trapping microstructure

Figure 11a, b, c, and d show the variation curve of weighted reflectance for wavelength 400 nm,600 nm,800 nm,1000 nm respectively when primary incidence and value of r=H change. Four graphs show similar variation tendency to each other, the weighted reflectance tends to be the least for all incidence angles when r ¼ H. As the value of r=H increases, for incidence θ<sup>p</sup> ≤ 30� , the weighted reflectance increases monotonously and then tends to be stable, and for θ<sup>p</sup> > 30� , the result decreases first and then increases, and then tends to be stable. When r/H reaches a specific value, rays tend to reflect once in the trap, the weighted reflectance become stable at the value of one reflection reflectance under the condition of their Effects of the Novel Micro-Structure on the Reflectance of Photovoltaic Silicon Solar Cell http://dx.doi.org/10.5772/intechopen.74972 57

Figure 11. Effects of different ratio of r/H and primary incidence on the reflectance of arc-shaped grooves of rays of different wavelengths. Wavelengths of (a) 400 nm, (b) 600 nm, (c) 800 nm, and (d) 1000 nm.

incidence respectively. Every arc-length blocked by rays reflection in the arc equals each other, therefore, the number of reflections of ray in arc-shaped groove is positively correlated with the ratio of total arc-length to single arc-length blocked by each reflection. The rays of short wavelength show higher weighted reflectance when incidence and structure parameters are the same, which is similar to the variation trend of refractive index, it means when the other conditions remain the same, silicon shows lower absorption efficiency for shorter wavelength rays. In practical preparation process of arc-shaped micro-structure, reflectance will be higher as the existence of one reflection area of uncut part.

#### 4. Conclusions

is 11.111, 3.703, 1.235, 0.411 and 0.137%. In other areas when there existed a variety of

angle size, a decreased linearly from 0 to 1, t and t + 1 were the reflection times of the two kinds of reflection area which existed in the light trapping area, and R is the reflectance. Obviously it was a linear function, therefore, in each area which existed a variety of reflection areas, γ

In a word, 60<sup>∘</sup> was chosen as the final structure base angle of the pyramidal structure considering that the reflectance had reached a relatively stable value. In addition, 60<sup>∘</sup> was a suitable

3.3. Effects of r/H and incidence on the reflectance of arc-shaped grooved light trapping

Figure 11a, b, c, and d show the variation curve of weighted reflectance for wavelength 400 nm,600 nm,800 nm,1000 nm respectively when primary incidence and value of r=H change. Four graphs show similar variation tendency to each other, the weighted reflectance tends to be the least for all incidence angles when r ¼ H. As the value of r=H increases, for

stable. When r/H reaches a specific value, rays tend to reflect once in the trap, the weighted reflectance become stable at the value of one reflection reflectance under the condition of their

, the weighted reflectance increases monotonously and then tends to be

, the result decreases first and then increases, and then tends to be

<sup>γ</sup> <sup>¼</sup> aRt <sup>þ</sup> ð Þ <sup>1</sup> � <sup>a</sup> Rtþ<sup>1</sup> <sup>¼</sup> Rt � Rtþ<sup>1</sup> <sup>a</sup> <sup>þ</sup> Rtþ<sup>1</sup> (13)

th reflection area. With increasing base

reflection areas, the weighted formula of reflectance was shown as in the following:

Where a is the proportion of lights projected onto the t

Figure 10. Relationship of weighted reflectance and the base angle size.

decreased linearly with the base angle size.

value for the tool design.

56 Solar Panels and Photovoltaic Materials

microstructure

incidence θ<sup>p</sup> ≤ 30�

stable, and for θ<sup>p</sup> > 30�

An algorithm was designed to calculate the weighted reflectance of the light trapping structure. The light trapping mechanism was studied by numerical algorithm with the morphology of the light trapping structure. The weighted reflectance of pyramidal textured surface was calculated in different conditions, respectively. The optimized parameters of the pyramid texture were proposed and the best incident angle was obtained by analyzing the values. A basis method is provided for future fabrication of pyramidal textured surface by mechanical way. The following conclusions were carried out.

[5] Yu JJ, Zhang JY, Boyd IW. Laser-assisted mechanical texturing of magnetic media.

Effects of the Novel Micro-Structure on the Reflectance of Photovoltaic Silicon Solar Cell

http://dx.doi.org/10.5772/intechopen.74972

59

[6] Li P, Wang Y, Feng GJ, Zheng CD, Zhao L, Zhu JT. Study of silicon micro-structuring using ultra-short laser pulses. Chinese Journal of Lasers. 2006;33(12):1688-1691

[7] Wu DJ, Ma GY, Cao XS, Wang XY, Zhao FL, Guo DM. Analysis of silicon surface profile of pulsed laser bending processing. Chinese Journal of Lasers. 2007;34(11):1589-1593 [8] Winderbaum S, Reinhold O, Yun F. Reactive ion etching (RIE) as a method for texturing polycrystalline silicon solar cells. Solar Energy Materials and Solar Cells. 1997;46(97):239-248

[9] Ruby DS, Zaidi SH, Narayanan S, Damiani BM, Rohatgi A. Rie-texturing of multicrystalline

[10] Chen WH, Lin HH, Hong FCN. Improvement of conversion efficiency of multi-crystalline silicon solar cells using reactive ion etching with surface pre-etching. Thin Solid Films.

[11] Zhao JH, Wang AH, Campbell P, Green MA. A 19.8% efficient honeycomb multicrystalline silicon solar cell with improved light trapping. IEEE Transactions on Electron Devices. 1999;

[12] Webber KJ, Blakers AW, Catchpole KR. The epilift technique for Si solar cells. Applied

[13] Chen YS, Wang HY, Yang SE. Application of light trapping in the crystal silicon cell.

[14] Qiu MB, Huang YH, Liu ZD, Tian ZJ, Wang W. Numerical study on effect of silicon texture structure on reflectance of light. Acta Optica Sinica. 2008;28(12):2394-2399

[15] Yang SY, Ge PQ, Zhang L. The effects of different pyramidal textured silicon surface

[16] Hua X, Zhang Y, Wang H. The effect of texture unit shape on silicon surface on the absorption properties. Solar Energy Materials and Solar Cells. 2010;94(2):258-262

[17] Huo DH, Lin C, Choong ZJ, Pancholi K, Degenaar P. Surface and subsurface characterisation in micro-milling of monocrystalline silicon. The International Journal of Advanced

[18] Choong ZJ, Huo DH, Degenaar P, O'Neill A. Effect of crystallographic orientation and employment of different cutting tools on micro-end-milling of monocrystalline silicon. Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering

[19] Rusnaldy, Ko TJ, Kim HS. Micro-end-milling of single-crystal silicon. International Jour-

[20] Mews M, Leendertz C, Algasinger M, Koynov S, Korte L. Amorphous/crystalline silicon heterojunction solar cells with black silicon texture. Physica Status Solidi RRL: Rapid

Physics A: Materials Science & Processing. 1999;69(2):195-199

parameters on the optical reflectance. Solar Energy. 2016;134:392-398

Lasers & Optoelectronic Progress. 2004;41(5):56-58

Manufacturing Technology. 2015;81(5):1319-1331

nal of Machine Tools and Manufacture. 2007;47(14):2111-2119

Manufacture. 2016;230(9):1756-1764

Research Letters. 2014;8(10):831-835

silicon solar cells. Solar Energy Materials and Solar Cells. 2002;74(s1–4):133-137

2005;597:50-56

46(10):1978-1983

Applied Physics A: Materials Science and Processing. 2001;72(6):687-690

