Fundamentals of semiconductor electrochemistry

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Light trapping strategies

The generation analysis above is based on Beer-Lambert law with the assumption that the light is absorbed in one pass through solar cell material as shown in Figure 1-11(b). However, the generation rate can be increased if the light is trapped in the cell. So the light management is a fundamental study to improve solar energy conversion efficiency.

Ray optics limit

The surface texturing is widely used for bulk silicon solar cells and can be greatly increased the light absorption[32]. As presented in Figure 1-11(a), when the light at the back side of solar cell sheet is reflected at an angle exceeding the critical angle for total internal reflection, the light returns to the front surface and no fraction leaks out of the cell. Multiple total internal reflections occurring on the both sides of the sheet of solar cell cause an increase in the path length of light passing through the cell, and therefore enhancement in the absorption efficiency.
When the cell geometric size is much larger than wavelength of illuminating light, the antireflection effect follows a theoretic limit first derived by Yablonovitch and Cody[32]. The absorption will be enhanced at most by a factor of 4n2 where n is the film material’s refractive index. For example, based on this theory, silicon solar cells with antireflective layer on both sides can only have the maximum absorption enhanced by 62 times at 590nm wavelength (n=3.96 at 590nm[33]). Since in their theory the geometric details of antireflective layer shape is relatively unimportant, it is quite possible that this light trapping effect contributes to light absorption in solar cells covered by SiNWs array on the front surface.
However when a solar cell’s dimension is on a sub-wavelength scale or comparable to wavelength of incident light, the appropriate theory to describe light propagation is wave optics rather than ray optics, and the ray optic limit of 4n2 can be surpassed. The next will be a short introduction to another strategy of light trapping beyond the limit.

Light trapping in individual nanowire

The matter is composed of discrete electric charges such as electrons and protons. When the incident light encounters an object, the charges in the object will be set in oscillation where the net effect manifests itself as the emission of secondary radiation known as light scattering. The incident light can also be scattered because of its diffraction on randomly distributed defects. In addition to scattering, part of the incident power is absorbed within the object because of the excitation of oscillating dipoles. The absorption is taken into account with the imaginary part of the refractive index. The scattering or absorption of incident light can be analogous to a virtual cross section around the object. As soon as the illuminating light hits this area, the interaction between incident electromagnetic wave and electronic charges occurs. According to Mie theory, the absorption cross section area Cabs is proportional to the absorbed power. Therefore, the absorption in the object can be described by absorption efficiency Qabs that is defined as the ratio of absorption cross section Cabs to the projected area under illumination.
Within the limits of ray optics, i.e. the object size is much larger than the concerned wavelength, for a perfect absorbing black body, its absorption cross section Cabs is equal to the projected area, and therefore the absorption efficiency is 1. For an imperfect absorber, the cross section Cabs is smaller than the projected area and the absorption efficiency is lower than 1. For larger objects, the absorption efficiency is in general resides between 0 and 1. But on the scale of sub-wavelength, absorption efficiency has been evidenced to be larger than 1[34][17,35].
For example, Krogstrup et al presented the experimental measurements on p-i-n GaAs nanowire solar cell[34]. The nanowire structure can be seen in Figure 1-12(a). The photogenerated current can be as high as 180 mA/cm2 and the apparent conversion efficiency was estimated to be 40% beyond Shockley-Queisser limit of 31% for GaAs semiconductor. They attributed the ultrahigh photogenerated current to resonance trapping effect due to the geometry of nanowire on the sub-wavelength scale.
They spatially mapped the photocurrent generated by the p-i-n nanowire solar cell for three different excitation laser wavelengths of 488nm, 676nm and 800nm as can be seen in Figure 1-12 (b) (c) (d), respectively. The results presented in Figure 1-12 (b), (c), and (d) are deconvoluted with the point-spread function of the diffraction-limited laser spot. As seen in Figure 1-12 (b) (c) (d), a photocurrent from an area much larger than the size of the laser spot appears for all three wavelengths of laser. The effective absorption areas for the three cases are about one order of magnitude larger than the physical cross-section of the vertically standing GaAs nanowire with diameter of 425nm, see the SEM image in Figure 1-12(a). The absorption efficiency Qabs is about 8 times higher than is predicted from the Beer-Lambert law. In other words, the single nanowire can collect photons outside its physical body boundaries.
Figure 1-12 Mapping of photocurrent scanning on GaAs nanowire: a, left: The p-i-n radial doping structure of GaAs nanowire by epitaxial growth; right: SEM image of the nanowire solar cell. b-d Scanning photocurrent measurements on the single vertical nanowire device for three different excitation laser wavelengths 488, 676, and 800nm, normalized to the incident photon flux. Adapted from Reference [34].
The effect of enhanced absorption efficiency can be explained with Lorenz-Mie theory. In the article by Cao et al[36] a nanowire was viewed as small scaled microcylinder resonator that can trap light in resonant leaky modes by multiple total internal reflections. The measured absorption spectrum on the single individual germanium nanowire lying on the substrate was in quite good agreement with the predicted spectra according to Mie theory see Figure 1-13. The absorption peaks in measurement were believed to be related to the Leaky-Mode Resonances. They further pointed out that the absorption efficiency was sensitive to diameter and the radiation wavelength.
Individual silicon nanowire was also examined by Brönstrup et al[37] in a experimental and theoretical work. They observed the reflection spectrum of the individual silicon nanowire was well consistent with the predicted scattering effect. They also found that the peak in scattering spectrum was dependent on the diameter, which can also be explained with Mie theory.
In Figure 1-14 , for the wavelength that is smaller than 360nm corresponding to the minimum direct band gap of silicon[38], the absorption efficiency is independent on the diameter of silicon nanowire, because the absorption is caused by the intrinsic absorption due to a higher extinction coefficient. In the case of wavelength larger than 360nm, the silicon is indirect band gap semiconductor, and the absorption efficiency becomes dependent on the geometry of nanowire. And the absorption is enhanced due to the resonance effect in the silicon nanowire. The resonance is restricted to certain wavelength and diameter, so the branched structure of absorption efficiency spectra appears. The branched structure is almost straight as a line, and its slope decreases as diameter increases and wavelength decreases.
For the spectrum of chief interest 380 to 1100nm in silicon solar cells, there is a trend that larger diameter has higher absorption efficiency. In the case of diameter smaller than 120nm and wavelength larger than 700nm, although the absorption efficiency is smaller than 7%, it is enough for silicon nanowires array to absorb the light[37].
Figure 1-14 Mapping of absorption efficiency Qabs for a single Si nanowire with a diameter d = 2nm and 2000nm and λ= 220 and 1120nm for nonpolarized light. Adapted from Reference [37].
On the contrary to the intuition that optical properties of nanostructure are strongly dependent on the shape of structure, simulation results from the article by Brongersma et al[39] showed weak correlation between absorption and cross sectional shape. In their simulation, four shapes of cross section of single nanowire, rectangle circle hexagon and triangle, respectively, are employed with FDTD method. The similar curves of absorption efficiency vs. wavelength suggest the same mode of resonance occurs in amorphous silicon nanowire, see Figure 1-15(b). The authors further point out that there are two field maxima in all the four plots in Figure 1-15(c), similar to the low-ordered mode of resonance. This similarity suggests that the low ordered mode resonances are less sensitive to the morphology.

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Light trapping in nanowires array

Compared with single nanowire, the nanowires array are much more complicated. The reflectance of silicon nanowires array can be very low less than 3% in the range of wavelength from 400nm to 1100nm. Although the mechanisms are still unclear, many experiments and calculations have been made to understand this unusual physical phenomenon.
Garnett et al.[40] measured the enhancement factor of path length when one photon is scattered in nanowires array in a paper published in 2010, where they stated that the ordered silicon nanowires array has the ability to provide a light-trapping enhancement of ~73 times compared with the planar bulk silicon, beyond the ray optics limit for silicon about 31 times with one side of antireflective layer.
Similar to individual nanowire, some simulation results confirm the enhancement of light trapping in silicon nanowires array.
Gang Chen et al. have studied optical properties of periodic silicon nanowires array by simulation with the transfer matrix method (TMM)[41]. In this paper the model of periodic structure, shown in Figure 1-16, is determined by three key parameters: length L, pitch a, and diameter d. The illuminating light is set as normal to the x-y plane.
Compared with thin film with thickness of 2.33 , the nanowires array with the same thickness has higher absorption efficiency in the high photon-energy regime but lower absorption in the low photo-energy regime – see Figure 1-16(b). Longer length favors larger absorption in the range of lower frequency. All the three nanowires array share the same absorption plateau for higher energy photons.

Light management contribution to VOC

The contribution to the enhancement of photogenerated current is clear due to light trapping effect, but for Voc it is still not clear how light management can affect the Voc. Polman and Atwater[35] gave the relationship in the article in the framework of thermodynamics as follows:
( ) [ ( ) ] 1-13
Where q is the electron charge, Eg is the bandgap energy, T and Ts are the temperatures of the solar cell and the sun, kB is Boltzmann’s constant, Ωemit, Ωsun are the solid angles related to photons emission from the solar cell and absorption into the solar cell, n the solar cell refractive index, I is the enhancement factor of light intensity, QE is the quantum efficiency.
The first term on the right side of Equation 1-13 is related to Carnot efficiency as we stated in the section of Shockley-Queisser efficiency limit. The second term in the square brackets includes three entropy-related terms. The first term in them accounts for the loss in Voc due to the solid angle difference between photon absorption and spontaneous emission. While the solar radiation is incident on the cell from the solid angle Ωsun = 6*10-5 steradians, the spontaneous emission in solar cell emits outgoing photons into the solid angle Ωemit up to 4π. The loss in Voc is as large as 315mV.
The second term in the brackets gives the description on how light trapping influences Voc. As we talked above 4n2 is the maximum value that the enhancement of light intensity trapped in a solar cell can achieve, if the cell is considered much larger than the wavelengths of illuminating radiation. However in the case of cell’s dimension on the sub-wavelength or wavelength scale, the local intensity enhancement factor I in cell can exceed the limit substantially[42,43], and therefore the light trapping effect in SiNWs for example will lead to a rise in Voc.
The last term in the brackets describes the reduction in Voc due to the quantum efficiency QE, which is defined as: where Rrad and Rnrad are the rates of radiative and non-radiative recombinations. The quantum efficiency is related to the non-radiative recombination mechanisms such as Auger recombination and RSH recombination due to defects in cell’s body or carrier trapping states on the surface or interface. Obviously the QE can be increased by reducing the non-radiative recombination rates as we will present later in the section of state of the art. An alternative way may be to increase the radiative recombination rate. The light management helps to increase the local density of optical states which in turn causes an increase in radiation recombination rate. The enhanced QE then directly improves Voc.
All the three terms in the brackets are relevant for the light management strategies. SiNWs at least will work on the second term about Voc by increasing the local light intensity in cell. According to Yang’s estimation about path length enhancement factor of 73[40], the Voc of SiNWs solar cell can be increased by 109mV with respect to the case without any enhancement. It is interesting to study the third term about the optical states enhancement in SiNWs, because silicon is an indirect bandgap which causes very low radiation recombination rate, and therefore the increased optical states in SiNWs solar cell might be also very useful to increase Voc further by optimizing its structure.

Table of contents :

1.1. Solar cell principle
1.1.1. Solar spectrum
1.1.2. Theoretic limitation of efficiency
1.1.3. Basics on bulk silicon solar cells
1.2. Light trapping strategies
1.2.1. Ray optics limit
1.2.2. Light trapping in individual nanowire
1.2.3. Light trapping in nanowires array
1.2.4. Light management contribution to Voc
1.3. SiNWs solar cells state of the art
1.3.1. Junction category in geometry
1.3.2. Charge carriers separation and collection in radial junction
1.3.3. Realization of radial junction in nanowire
1.3.4. Passivation on silicon
1.3.5. SiNWs/PEDOT hybrid solar cell
2.1. Introduction to electroless metal-assisted chemical etching
2.1.1. Mechanism of electroless metal-assisted chemical etching (EMACE)
2.1.2. Wafer properties: doping type, doping level, and crystalline orientation
2.1.3. Etching time and temperature
2.1.4. Lithography technique
2.2. Experiment and characterization
2.2.1. Experiment procedures
2.2.2. Characterization methods
2.2.3. Morphology of SiNWs
2.2.4. Concentration of AgNO3
2.3. KOH tapering
2.4. Active area selection
Conclusions
3.1. Introduction to PEDOT
3.1.1. PEDOT structure and its conductivity
3.1.2. Fundamentals of semiconductor electrochemistry
3.1.3. PEDOT electrochemical synthesis
3.1.4. PEDOT electrochemical characterization
3.2. PEDOT electrochemical deposition on SiNWs
3.2.1. Apparatus
3.2.2. PEDOT fabrication
3.2.3. PEDOT redox characterization
Conclusions
4.1. Fabrication
4.2. Analysis on J-V curves
4.1.1. J-V characteristic parameters
4.1.2. Illumination during PEDOT fabrication
4.1.3. Duration of PEDOT deposition
4.1.4. Potential during PEDOT fabrication
4.1.5. Step-wise deposited PEDOT
4.3. Capacitance measurement
4.4. Interface states density
4.5. EQE measurement
Conclusions

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