Transition Metal Dichalcogenides Multijunction Solar Cells Toward the Multicolor Limit

TL;DR

This work extends the Shockley–Queisser detailed-balance framework to unlimited, split-spectrum, multi-terminal van der Waals/two-dimensional semiconductor stacks, focusing on transition metal dichalcogenides within a practical $E_g$ window of $[1.0,2.1]$ eV. Using dynamic programming, reciprocity-based photon-flow analysis, and thickness-aware absorptance models that include excitonic TMD absorption, the authors quantify how a realistic bandgap window imposes a plateau in efficiency (about $63.4 ext{ exttt{ extpercent}}$) beyond roughly five junctions and identify an experimentally viable $N=5$ ladder $(E_g ext{)} \\approx (2.10,1.78,1.50,1.24,1.00) ext{ eV}$. They show that external radiative efficiency (ERE), emission-channel management, and nanophotonic thickness constraints dominate beyond five junctions, and they provide a conservative nonreciprocal benchmark indicating potential headroom for multijunction stacks. The results yield concrete design rules for transfer-printed vdW/TMD photovoltaics, emphasizing co-optimized bandgap ladders, high ERE across all subcells, controlled luminescent coupling, and realistic thickness/nanophotonic designs to approach multicolor limits. A reproducible computational framework accompanies the insights, enabling systematic exploration of realistic vdW multijunction configurations.

Abstract

Transition metal dichalcogenides (TMDs) and other van der Waals semiconductors enable transfer-printed, lattice-mismatch--free stacking of many photovoltaic junctions (N), motivating a re-examination of multijunction detailed-balance limits under realistic material and optical constraints. Here we develop an unlimited-junction detailed-balance framework for split-spectrum, multi-terminal vdW multijunction solar cells and apply it to a conservative TMD bandgap window (1.0-2.1 eV). Dynamic-programming optimization shows that the accessible bandgap window imposes a large-N efficiency limit: under full concentration, unconstrained ladders approach 84.5% at N=50, whereas the TMD window plateaus near 63.4%. This plateau is set by photons outside the gaps, so radiative quality and optics dominate beyond five junctions for realistic transfer-printed stacks. We identify an experimentally achievable N=5 ladder Eg~(2.10,1.78,1.50,1.24,1.00) eV and map each rung to candidate vdW/TMD absorbers. Using reciprocity and luminescence thermodynamics, we quantify penalties from finite external radiative efficiency, two-sided emission, and luminescent coupling, and we introduce the upward-emitted luminescence power as a computable entropy-loss proxy. Incorporating excitonic absorptance and nanophotonic thickness bounds yields practical thickness and light-management targets for transfer-printed stacks. Finally, inserting an idealized nonreciprocal multijunction model into the reciprocity-optimized ladders provides conservative headroom estimates, consistent with negligible benefit for single junctions but measurable gains for multijunction TMD stacks.

Figures (10)

• Figure 1: Conceptual schematic of a transfer-printed vdW/TMD multijunction solar cell (representative $N=5$ ladder). In a reciprocal stack without intermediate mirrors, external luminescence from an upper junction can exit upward ($\Phi^\uparrow_\mathrm{ext}$) and propagate downward ($\Phi^\downarrow_\mathrm{ext}$), enabling luminescent coupling to lower junctions and opening additional emission channels (entropy/voltage penalty). Intermediate mirrors or angular filters can suppress unwanted emission channels and recover higher radiative voltage.MillerYablonovitch2012Rau2014 An optional nonreciprocal optical layer can, in principle, further reshape emission pathways and access additional thermodynamic headroom in multijunction stacks.FanNonreciprocalMJ2022
• Figure 2: Detailed-balance efficiency versus junction number. (a) 1 sun and (b) full concentration for unconstrained optimal bandgaps and a conservative TMD bandgap window (1.0--2.1 eV), computed for split-spectrum (multi-terminal) multijunctions with one-sided emission and $\mathrm{ERE}=1$. Numerical tables and bandgap ladders are provided in the SI and the accompanying code package.
• Figure 3: Efficiency limit versus accessible bandgap window. Heatmap of the maximum achievable efficiency for a representative high-$N$ case ($N=20$, multi-terminal, $\mathrm{ERE}=1$, full concentration), as a function of the allowed bandgap window $(E_{g,\min},E_{g,\max})$. The conservative TMD window (1.0--2.1 eV) is highlighted.
• Figure 4: Optimal bandgap ladders in the conservative TMD window.$E_{g,i}$ vs subcell index for selected $N$ values (top cell is index 1). The $N=5$ ladder in Eq. \ref{['eq:ladder5']} is highlighted as a representative design.
• Figure 5: Illustrative mapping between target bandgaps and vdW/TMD candidates. Symbols denote representative optical gaps drawn from the vdW/TMD literature (see Supporting Information, Table S3 for notes and sources), and dashed vertical lines denote the representative $N=5$ target ladder (Eq. \ref{['eq:ladder5']}).