Shown in figure 3.5 are Scanning Electron Microscope (SEM) pictures of silicon wafers etched in a KOH-IPA solution. The mono-Si-wafers were etched in the experimental array shown in figure 2.12 (chapter 2).
Figure 3.5 a) shows the pyramidal texture of a wafer etched for 25 min. On the surface of the wafer, smaller and larger pyramids are visible. There are also areas not yet covered with pyramids, which is due to the short etching time.
After 30 min of etching time (figure 3.5 b), the whole surface is covered with small pyramids (wide ≈ 10 - 16 µm and height ≈ 7 - 11 µm). This texture reduces the total light reflection of the Si-wafer to approximately 10% in the wavelength of 800 ≤ λ ≤ 1000 nm (see figure 3.6).
In figure 3.5 c), after 35 min of etching time, some pyramids have become larger, and some smaller regions have become free of pyramids, i.e., after 35 min the homogeneity of the pyramidal texture begins to decline, which is also seen in its reflection properties.
In figure 3.5 d), after 40 min of etching time, pyramid size become smaller with respect to the pyramid size observed in fig. 3.5 c. Also, small regions become free of pyramids.
c) 35 min d) 40 min
b) 30 min a) 25 min
Fig. 3.5: Scanning Electron Microscope (SEM) pictures of silicon wafers etched in a KOH solution (120 grams KOH, 300 ml IPA, 6 liters water, 80oC) at different periods of time; 25 min (a), 30 min (b), 35 min (c) and 40 min (d). After 30 min of etching time, the whole surface is covered with small pyramids (wide ≈ 10-16 µm and height ≈ 7-11 µm), this texture reduces the total light reflection of the wafer to approximately 10% (800 ≤ λ ≤ 1000 nm).
Figure 3.6 summarizes reflection measurements of the pyramidal texture shown in figure 3.5. The reflection values of silicon wafers reach a minimum (approximately 10%) after an etching time of 30 min, and longer etching times do not further reduce reflection values.
From figures 3.5 and 3.6, we can infer the importance of etching time in producing a homogenous pyramidal texture with low reflection values. But it is not just etching time that considerably influences the pyramid formation on Si-wafers, but also all components of the etch solution. Therefore, all etching parameters have to be carefully investigated in order to obtain the desired optimal pyramidal texture and thus to reduce the total reflection of silicon wafers. Here it is necessary to mention the importance of IPA for the formation of pyramids. For the absence of IPA in this etch solution also means the absence of pyramids. In other words: high etching rates mean an absence of anisotropy in the etch solution.
In all the SEM pictures of figure 3.5 we see small pyramids. The formation of pyramids on a silicon surface is due to the strong dependence of the etch rate on the crystal orientation (anisotropy). The lowest etch rate is observed with the (111) plane in comparison with the other crystallographic orientations of the crystals; (100) and (110). The reason why the (111) crystal orientation shows the lowest etch rate will be explained now.
Fig. 3.6: Reflection measurements of silicon wafers etched in a KOH solution for different periods of time. After 25 min of etching time, the reflection of the Si-wafer is reduced by approximately 15%. The silicon removal has a value of 24.3 µm (in parentheses). After 30 min of etching time, the reflection of a Si-wafer is reduced to approximately 10% (800 ≤ λ ≤ 1000 nm), the silicon removal is now 25.9 µm. Longer etching times do not further reduce reflection values. However, the silicon removal of Si-wafers continues to progress.
From the crystalline structure of Si, it can be seen that silicon crystal is a face-centered cubic structure with a base of two identical atoms, which are located at the (0,0,0) and (1/4,1/4,1/4) position. This is a diamond structure. Every silicon atom is located at the center of a tetrahedron and is bonded to four other atoms. The difference in surface planes depends on the number of free bonds of silicon atoms.
Si atoms in the (111) crystal plane are bonded to the Si crystal with three other Si atoms, whereby one bond remains free. Atoms of the other crystal planes, like (100) and (110), are bonded to the Si crystal with two Si atoms; therefore, two bonds remain free. Thus, a higher energy demand is required to dissolve Si atoms located on the (111) plane compared with the energy needed to remove Si atoms located on the (100) or (110) planes. The difference in free bonds of the different planes results in the formation of the pyramidal texture on mono-Si-wafers with a (100) orientation.
3.3 Determination of the heights of the pyramids (also referred to as pyramid size)
The pyramids on a mono-Si-wafer are well defined by four (111) planes with a base on the (100) plane. From SEM pictures, the length of the base of the pyramids can be seen and estimated. Such information can then be used to estimate the height of the pyramids (also referred to in the literature as pyramid size). This estimation can easily be made in two dimensions, taking into consideration the following figure 3.7.
Fig. 3.7: Representation of a pyramid on a textured mono-Si-wafer in two dimensions.
Due to the symmetry of the pyramid, it is sufficient to consider half of the pyramid shown in figure 3.7. On the left half of the pyramid, the base is located on the (100) plane, and the left side of the pyramid is limited by the (111) plane. The angle between the (111) and (100) planes corresponds to Ɵ = 54.7o. So, by defining the length of half of the base of the pyramid as 1 µm, the height of the pyramid can be calculated. For this purpose, the tan(Ɵ) function is used, tan(54.7o) = height/1 µm, height = 1 µm*tan(54.7o), height = 1.4 µm, as is shown in figure 3.7. For the length of the side of the pyramid with the (111) plane (l), the cos(Ɵ) function is used, cos(Ɵ)= 1/l. The length of the side l has the value of 1.7 µm.
Also, if the length of the base of a pyramid is known, the height of this pyramid can be calculated as: height = 1.4 µm*(length of the base of the pyramid)/2.
To determine the height of several hundred pyramids, (also referred to in the literature as pyramid size), special programs have been developed. Kuchler et al.
[12: Kuchler 2003] used two REM pictures of textured silicon wafers taken at asymmetrical angles (for example 15o and -15o, symmetrical pictures) and then by using the stereoscopic technique (also known as machine vision) reproduced (simulated) the pyramidal texture. Thus, they were able to determine the pyramid sizes of over 1500 pyramids.
In this work, pyramid size is directly obtained from Atomic Force Microscope (AFM) pictures, see chapter 5.
3.4 Theoretical calculation of light trapping in textured silicon