Dynamic kirigami structures for integrated solar tracking

Abstract

Optical tracking is often combined with conventional flat panel solar cells to maximize electrical power generation over the course of a day. However, conventional trackers are complex and often require costly and cumbersome structural components to support system weight. Here we use kirigami (the art of paper cutting) to realize novel solar cells where tracking is integral to the structure at the substrate level. Specifically, an elegant cut pattern is made in thin-film gallium arsenide solar cells, which are then stretched to produce an array of tilted surface elements which can be controlled to within ±1°. We analyze the combined optical and mechanical properties of the tracking system, and demonstrate a mechanically robust system with optical tracking efficiencies matching conventional trackers. This design suggests a pathway towards enabling new applications for solar tracking, as well as inspiring a broader range of optoelectronic and mechanical devices.

Figure 1. Optical coupling efficiency and novel kirigami trackers.

(a) Coupling efficiency (η_C) versus source angle (φ) for a planar solar panel. The panel projected area decreases with the cosφ. (b) A kirigami tracking structure that, upon stretching, simultaneously changes the angle of the elements comprising the sheet. By incorporating thin-film solar cells into this structure, it may be used as a low-profile alternative to conventional single-axis solar tracking. (c) The direction of feature tilt (that is, clockwise or counter-clockwise with respect to the original plane) is controlled by lifting or lowering one end of the sheet (step 1) before the straining process (step 2).

Figure 2. Kirigami cut geometry and geometric system response.

(a) Response of a Kapton kirigami structure to stretching in the axial direction (ɛ_A) is accompanied by a decrease in sample width (ɛ_T) and a change in feature angle (θ). Also shown are the geometric parameters that define the kirigami structure, namely the cut length (L_C) and spacing between cuts in the transverse (x) and axial (y) directions, which can be expressed in terms of the dimensionless parameters, R₁ and R₂. (b) Schematics of four kirigami structures, where R₁=R₂=3, 5, 10 and 20, along with their corresponding units cells. (c) ɛ_T and θ versus ɛ_A for several kirigami structures where R₁=R₂=3, 5, 10 and 20 (b). Theoretical predictions per equations (1) and (2) are shown by solid lines, while the closed symbols represent experimental data from a 50 μm-thick Kapton sample of the appropriate geometry. While larger R₁ and R₂ enable increased axial strains and correspondingly larger transverse strains, the change in feature angle is independent of cut geometry.

Figure 3. Optimization of tracking process to maximize coupling efficiency.

(a) Coupling efficiency (η_C) versus source angle (φ) for two systems with different extent of tracking (θ*). Inset: Feature angle (θ) versus φ. Non-optimized tracking (closed symbols) close to the geometric maximum (θ_MAX, point 1) results in a sharp decrease in sample width that decreases optical coupling efficiency. Instead, coupling efficiency is optimized (open symbols) by a tradeoff between sample narrowing, self-shadowing, and cosine losses (c.f. equation (4) in text) corresponding instead to an optimal angle (point 2). Simulated system response is shown for R₁=R₂=5, and is compared to a conventional non-tracking panel. (b) Coupling efficiency, η_C integrated over a range of tracking angle (from φ=0 to φ=θ*) and normalized to conventional planar cell performance. For a given kirigami structure, optimal performance is obtained by tracking the source at normal incidence to θ* corresponding to the maximum of each curve. For comparison, tracking to θ_MAX versus tracking to the optimal θ* is shown as solid and open symbols, respectively.

Figure 4. Tracking performance for GaAs kirigami trackers.

(a) Integrated thin-film, crystalline GaAs solar cells, mounted by cold weld bonding on a Kapton carrier substrate, as used for testing. Here, L_C=15 mm, x=5 mm and y=5 mm (R₁=R₂=3). (b) Normalized solar cell short circuit current density J_SC(φ)/J_SC(φ=0) for two samples, where R₁=R₂=3 and R₁=R₂=5 (closed symbols). Also shown are the simulated data for coupling efficiency (η_C) obtained from equation (4) (solid lines, open symbols). The agreement between experimental and simulated results suggests that η_C is a direct measure of optical coupling, and that performance may be optimized by increasing R₁ and R₂. (c) Output electrical power density incident on the solar cell versus time of day for several kirigami cut structures, stationary panel and single-axis tracking systems in Phoenix, AZ (33.45° N, 112.07° W) during the summer solstice. Inset: Integration of the curves yields the associated energy densities, where kirigami-enabled tracking systems are capable of near single-axis performance.