Results and Discussion

Fig. 3. 10 Measured complex refractive indices of (a) bare Si and 2D Si-nanorod array, and (b) normal and slanted deposited ITO films.

To quantitatively examine the optical characteristics of our ARC, we first measured the refractive index (n) and extinction coefficient () of our samples, as shown in Fig. 3.10.

The wavelength-dependent complex refractive indices of the samples,

( ) ( ) ( )

n   n   i  

, are determined by ellipsometry with a normal-incidence white light source (180W halogen-lamp). In

Fig. 3.10(a), the n value of the bare Si (black

solid-line) gradually decreases with increasing wavelength, exhibiting normal dispersion behavior. In contrast, the n value of the 2D Si-nanorod array (blue solid-line) is relatively stable and has a much smaller value of n=2.08 for most of wavelengths (λ=400−1000nm). The improved stability and reduction of n are caused by the low filling-fraction (f.f.) of the array. Generally, the effective refractive index of the 2D

Si-nanorod array is defined as the average refractive index between the air and the bare Si, weighted by their respective volumes, It can be expressed as follows [3.31]:

2

where nSi and nair denote to the refractive indices of bare Si and the air, respectively. D is the average diameter of the 2D Si-nanorod array, a is the average pitch between rod-to-rod, and πD²

/4a

² is the f.f. Accordingly, the f.f. of the 2D Si-nanorod array derived by Eq. [(3.6)] is f.f.~40%, which is consistent with the previous observation from the SEM image of Ni clusters in

Fig. 3.9(b). More importantly, compared to that

of the bare Si (black dashed-line), the

value of the 2D Si-nanorod array (blue

dashed-line) is remarkably enhanced, especially for the region of visible light (λ=400−700nm). It is well known that  of a material is defined as

 

4

 

/ , and the larger

 would be expected to lead to a larger value of . As a result, the enhanced

absorption of the 2D Si-nanorod array enables high quantum efficiencies for photovoltaic applications. The randomly distributed and non-planar geometry of the 2D Si-nanorod array is mainly responsible for the enhanced absorption coefficient because of it effectively scatters and traps incident photons [3.32]. Similarly, the refractive indices of the normal and slanted ITO films as a function of wavelength are shown in

Fig. 3.10(b). Again, the refractive indices of both samples decrease with wavelength

and exhibit the normal dispersion profile. The refractive index of the normally deposited ITO is higher than that of the slanted ITO. On average, the n values of the normal and slanted ITO films are 1.98 and 1.63, respectively. For the slanted film, that value corresponds to a porosity of ~34.8%, as evaluated by the Bruggemann effective medium approximation [3.33]. The extinction coefficients of both samples, however, are nearly identical and approximately zero, which allows most of the incident solar

Fig. 3. 11 Cross-sectional SEM images of (a) normally deposited (planar-sheet) ITO film, 2D Si-nanorod arrays (b) without, and (c) with the slanted ITO film. The scale bar of 500nm in the top column applies to all images. The variation of (average) refractive index along the z-direction of each image is also presented in the figure.

energy to propagate in a near-lossless fashion inside the film.

Figure 3.11(a) shows the cross-sectional SEM image of the normally deposited

(planar-sheet) ITO film. SEM images of 2D Si-nanorod arrays (b) without and (c) with the slanted ITO film deposited on top are shown in

Fig. 3.11(b) and Fig. 3.11(c),

respectively. The variation of the refractive index along the z-direction of all samples is also plotted in the figure. In Fig.3-11(a), the normally deposited ITO film was chosen as the quarter-wavelength ARC because its refractive index (n=1.98) is approximately

equal to the geometric mean of those of the air and bare Si [3.34], [3.35]. Additionally, ITO films are widely used as the electrode layers of solar cells because of their good electrical conductivity. The thickness of the ITO film was controlled to d=400nm (odd multiples of λ/4n), leading to destructive interference with extremely low reflection at certain incident wavelengths[3.34]. For other incident wavelengths, the reflectivity of the ITO quarter-wavelength ARC is considerably increased, hindering the absorption of solar energy. In comparison to the ITO quarter-wavelength ARC, 2D Si-nanorod array has been suggested as a promising candidate for solar energy harvesting because of its advantageous optical property [3.36]. According to

Fig. 3.11(b), each individual

nanorod is well defined, with diameters between 40 and 90 nm, and each has a constant thickness of d=350 nm. It is well known that a nanorod diameter that is comparable to

or smaller than the incident wavelengths, produces a strong scattering effect and

enhances the absorption of solar energy [3.37]. However, because of the porous

structure (f.f.=40%) of the 2D Si-nanorod array, its effective refractive index (n=2.08) is much smaller than that of the bare Si (n=3.95), which provides a similar functionality to the ITO quarter-wavelength ARC. Therefore, although the nanorod array itself can effectively trap incident photons, a significant amount of solar energy is still reflected and wasted because of the large difference between the refractive index of the air and the 2D Si-nanorod arrays. We recognize the intrinsic antireflection effect of the 2D Si-nanorod array. To further reduce the Fresnel reflection that occurs at its interface with the air, it is necessary to insert an optically transparency ( ~0) intermediate layer (1<n<2.08). Here, we used the slanted ITO film with controllable porosity as the intermediate layer. As shown in

Fig. 3.11(c), the slanted ITO film (d=350nm), which

consists of nearly continuous nanorods with tilt angle of β=40° grown by oblique-angle deposition, has a lower refractive index (n=1.68) than dense ITO (n=1.98) because of

its nano-porous nature. Furthermore, because of the shadowing effect provided by the 2D Si-nanorod arrays, the incident vapor of ITO vapor flow is deposited preferentially on top of the nanorods, and it eventually coalesces altogether. This coalescence forms an optically transparent thin film with a flat surface morphology, as previously discussed with reference to Fig. 3.9(c). In fact, an optically transparent and electrically conductive slanted ITO film with a nearly continuous surface morphology is extremely important for the subsequent fabrication of the electrode pads of solar cells.

The following discussion concerns the optical characteristics of the samples of interest. Figure 3.12(a) plots the measured reflectivity versus the incident wavelength.

The photographs of all samples (with the identical sizes of 2cm×2cm) are also shown as inserts in the figure. Accordingly, the color images of all samples are uniform with reasonable fluctuations, suggesting that our fabrication processes for all samples are stable and reliable. The profile of the measured reflectivity of the bare Si (black solid line) decreases monotonically from R=48.5% to R=31.8% as the incident wavelength increases from λ=400 nm to λ=1000 nm, because of the slight decrease of the refractive index of Si with wavelength. On average, the reflectivity of the bare Si is R=35.4%.

The measured reflectivity is reduced for unmodified Si with the ITO quarter-wavelength ARC. The corresponding profile of the measured reflectivity (red solid line) oscillates decreasingly with respect to that of the bare Si substrate because of the influence of destructive interference of incident light, This film exhibits an average reflectivity of R=18.7%, with an extremely low reflectivity of R<0.5% at incident wavelengths of λ=470nm, λ=640nm, and λ=990 nm. Furthermore, the average reflectivity of the 2D Si-nanorod array decreases to R=13.2% with non-significant oscillation fringes (green solid line). This decrease is primarily caused by the randomly distributed Si-nanorods, which effectively scatter and traps incident photons, thus

Fig. 3. 12 (a) Measured reflectivity as a function of normal-incident wavelength for bare Si without (black solid-line) and with (red solid-line) ITO quarter-wavelength ARC, and for the 2D Si-nanorod arrays without (green solid-line) and with (blue solid-line) the slanted ITO film. Insert: photographs of the fabricated samples with dimensions of 2cm×2cm. (b) Calculated reflectivity as a function of normal-incident wavelength by the Airy formula for all samples. Insert: schematic of solar light emitted into the m-layer stack (c) Calculated absorption, A(θ, λ)=1- R(θ, λ), obtained by the incidence of TM polarized light for all samples.

decreasing their reflection and interference in the materials. Most importantly, by inserting the slanted ITO film as an intermediate layer, the Fresnel reflection at the interface between the air and the 2D Si-nanorod array can be further reduced, and the measured reflectivity and corresponding profile (blue solid line) become stable and independent of the incident wavelengths, especially over the visible light region. As a result, a low reflectivity with average value of R=9.2% is achievable over a broad spectrum. It should be noted that, although the measured reflectivity of the samples is still higher than those ever reported in other studies [3.38], [3.39], the interaction of the

ARC design with the nanostructures accounts for the elimination of the Fresnel reflection, which is of primary concern in the current study.

To study the dependence of the reflectivity of the samples on the incident angle of solar illumination, the measured reflectivity at normal incidence was numerically fitted, and the result is shown in

Fig. 3.12(b). The angular-dependent

reflectivity of the incident wave, R(,

), in the stack with m layers [inset of Fig.

3.12(b)] is expressed by the Airy formula as follow [3.40]:

2 light emitted into the Nth layer. Accordingly, the calculated results shown in Fig. 3.12(b) are in agreement with the measured reflectivity in

Fig. 3.12(a), suggesting that the

consideration of the 2D Si-nanorod array and the slanted ITO film as homogeneous materials with effective refractive indices is indeed feasible, when the propagation of incident waves between the layers is treated numerically.

To gauge the absorption ability of the samples, the calculated absorptions values obtained by

A ( , ) 1     R ( , )  

were plotted in Fig. 3.12(c), in which

R

( , )

 

was determined from the Airy formula for the TM polarized light, and the transmission of the samples is negligible because the thickness of the Si substrate is larger than 500 μm.

Across the incident wavelengths studied here, the peak absorption of bare Si (upper left) is relatively low at normal incidence and increases at steeper incidence angles, until the Brewster angle (θp=75.8^o) is reached. This absorption profile limits the practical applications for photovoltaics. The average absorption of bare Si (θ=0−80^o;

λ=400−700nm) is A=75.85%. With the assistance of the ITO quarter-wavelength ARC

(upper right), the normal-incidence absorption is significantly increased at certain wavelengths at which the destructive interference of incident light occurs, which causes ( , )

A  

to exhibit a band-like profile. However, the enhancement of the overall absorption remains insignificant (A= 85.00%). As expected, the incorporation of 2D Si-nanorod arrays (lower left) can virtually eliminate the angular sensitivity of ( , )

A  

, and increases the normal-incidence absorption, except for incident light in the visible region. On average, the absorption of the 2D Si-nanorod arrays is A= 88.09%. With the addition of the slanted ITO film (lower right), the average absorption of the 2D Si-nanorod arrays is increased to A= 92.70%, and

A

( , )

 

becomes nearly angle-independent over the broadband spectrum.

Fig. 3. 13 (a) Calculated J-V curves using Eq. [(3.13)] for all samples. (b) A plot of Aavg calculations corresponding to each absorption A(θ,λ) shown in Fig. 4 (c), showing the incident solar light and spectrally weighted absorption of each throughout the day.

To calculate the power generation efficiency (η) of the samples, we assume that each absorbed photon with energy larger than the band-gap energy of Si generates an electron-hole pair that reaches the electrical contacts. Therefore, the current density J versus the voltage V is expressed by the sum of the photon-generated current minus the intrinsic current generated by radiative recombination as follow [3.41]:

2 2

where

dI d

/



represents the light intensity incident on the solar cell per unit wavelength (given by the ASTM AM 1.5 solar spectrum [3.42]), ( )

A 

is the absorption calculated by the Airy formula (as mentioned above), Eg is the band-gap energy of Si, kTis the thermal energy at the operating temperature T in Kelvin unit, and n is average refractive index of Si [3.43]. The resulting calculated J-V curves of all samples are shown in Fig.

3.13(a). As depicted, the calculated short-circuit current densities are J

SC

=23.39mA/cm² and JSC =29.19 mA/cm² for the bare Si without and with the ITO quarter-wavelength ARC, respectively. The short- circuit current values of the 2D

Si-nanorod arrays without and with slanted ITO films are JSC =31.20mA/cm² and JSC

=32.81 mA/cm², respectively. Theoretically, the open-circuit voltage (VOC) and the fill factor (FF) of all samples are identical and remain approximately VOC =0.8V and

FF=0.85, respectively. Compared to the bare Si, the enhancement of the power

generation efficiency observed for the other samples is attributable to the enhanced short-circuit current density; i.e., it is attributable to the enhanced absorption according to Eq. [(3.13)]. As a result, a power generation efficiency of η=22.70% is achievable for the 2D Si-nanorod arrays with the slanted ITO film, corresponding to an improvement of approximately 42% with respect to that of the bare Si sample.

Finally, to distinguish the incident solar light and the spectrally weighted absorption of all samples throughout the operating day of a non-tracking solar cell, the overall fraction of the above band-gap photons that our samples would absorb, Aavg, was calculated based on a time-resolved reference spectrum of direct solar insolation in conjunction with the calculated angle- and wavelength-dependent absorption values,

( , )

A  

. The fraction of above band-gap incident photons that would be absorbed from the reference spectrum, Aavg,is given by the following expression [3.44]:

 

normal radiation corresponding to reference spectrum at each hour (t) and wavelength (λ) throughout the day [3.44], [3.45].

Figure 3.13(b) shows the A

avg calculations that correspond to the contour plot of absorption,

A

( , )

 

, shown in

Fig. 3.13(c).

Importantly, compared to that of the bare Si sample, the 2D Si-nanorod arrays with the

slanted ITO films have Aavg = 86.21%, which corresponds to a remarkable enhancement of ~50% and implies the fundamental optical concentration characteristic of the 2D Si-nanorod arrays.

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