Design Guidelines for Plasmon-Enhanced CsSn$_x$Ge$_{1-x}$I$_3$ Perovskite LEDs: A DFT-Informed FDTD Study

TL;DR

This work addresses the challenge of achieving efficient light extraction from lead-free CsSn$_x$Ge$_{1-x}$I$_3$ PeLEDs by marrying composition-specific optical data with plasmonic enhancement. A DFTDTD framework is developed, where density functional theory yields wavelength-dependent $n(comega)$ and $k(comega)$ for $x=0,0.25,0.5,0.75,1$, which are then used in finite-difference time-domain simulations of an ITO/Spiro-OMeTAD/CsSn$_x$Ge$_{1-x}$I$_3$/ZnO/Ag device incorporating Au/SiO$_2$ coreshell nanorods. The study reports Purcell enhancements up to about $12\times$, light-extraction efficiencies up to $25\%$, and spectral overlaps approaching $96\%$, with CsSn$_{0.5}$Ge$_{0.5}$I$_3$ identified as the optimal compromise between extraction, emission-rate enhancement ($\sim5.3\times$), and oxidation stability for wearable/flexible applications; CsSn$_{0.25}$Ge$_{0.75}$I$_3$ is recommended where maximizing spontaneous emission rate is priority. These findings provide a quantitative, design-driven route to balance radiative rate, outcoupling, and material stability in lead-free NIR PeLEDs, enabling practical deployment in flexible and wearable optoelectronics.

Abstract

CsSn$_x$Ge$_{1-x}$I$_3$ as lead-free perovskites are promising for next generation NIR emitting perovskite LEDs due to their tunable bandgaps and stability. However, they suffer from poor light extraction efficiency, and accurate composition-specific optical data for these materials remain scarce. This study presents a DFT-FDTD framework to optimize light extraction via compositional tuning and plasmonic enhancement. First, DFT calculations were performed to obtain composition-specific complex refractive index and extinction coefficient values for $x = 0, 0.25, 0.5, 0.75$, and $1$. Results show bandgap increased from 1.331 eV for CsSnI$_3$ to 1.927 eV for CsGeI$_3$ with increasing Ge content, while refractive index ranges from 2.2 to 2.6 across compositions. These optical constants were then used as inputs for FDTD simulations of a PeLED structure with optimized Au/SiO$_2$ core-shell nanorods for plasmonic enhancement. A 12.1-fold Purcell enhancement was achieved for CsSn$_{0.25}$Ge$_{0.75}$I$_3$, while light extraction efficiency reached 25% for CsSn$_{0.5}$Ge$_{0.5}$I$_3$. LEE enhancement of 36% was obtained for CsSnI$_3$, and spectral overlap between emitter and plasmon resonance reached 96% for Sn-rich compositions. Design guidelines indicate CsSn$_{0.5}$Ge$_{0.5}$I$_3$ offers optimal balance of extraction efficiency (25%), Purcell enhancement (5.3$\times$), spectral overlap (93%), and oxidation stability for wearable and flexible optoelectronic applications, while CsSn$_{0.25}$Ge$_{0.75}$I$_3$ is recommended for applications prioritizing spontaneous emission rate.

Figures (17)

• Figure 1: Computational workflow for FDTD simulation of plasmonic CsSn$_x$Ge$_{1-x}$I$_3$-based PeLEDs. Device setup incorporates DFT-derived optical constants for the perovskite layer alongside literature data for other materials. FDTD simulations employ refined meshing near critical interfaces and integrate Au/SiO$_2$ NRs at the ZnO/perovskite boundary. Performance analysis yields near-field and far-field distributions, Purcell factors, light extraction efficiency, and spectral overlap metrics, enabling composition-dependent device optimization.
• Figure 2: (a) Layered device architecture of the CsSn$_x$Ge$_{1-x}$I$_3$-based PeLED, illustrating the anode/HTL/perovskite/ETL/cathode stack and the upward light-emission direction. (b) Energy-band diagram of the ITO/Spiro-OMeTAD/CsSn$_x$Ge$_{1-x}$I$_3$/ZnO/Ag structure, showing hole injection from ITO into Spiro-OMeTAD, electron injection from Ag into ZnO, and carrier recombination within the perovskite layer.
• Figure 3: Schematic illustration of the CsSn$_x$Ge$_{1-x}$I$_3$-based PeLED structure incorporating a plasmonic Au/SiO$_2$ nanorod. The device stack (ITO/Spiro-OMeTAD/CsSn$_x$Ge$_{1-x}$I$_3$/ZnO/Ag) includes a dipole emitter positioned near the embedded Au/SiO$_2$ core--shell nanorod to enable plasmon--emitter coupling. The nanorod geometry is defined by the Au core length ($l$) and radius ($r$), surrounded by a SiO$_2$ shell.
• Figure 4: Different doping arrangement of CsSn$_x$Ge$_{1-x}$I$_3$. (a) $x=1$, (b) $x=0.75$, (c) $x=0.5$, (d) $x=0.25$ and (e) $x=0$. Green, grey, brown, and violet indicate Ge, Sn, I, and Cs, respectively.
• Figure 5: Optical properties of CsSn$_x$Ge$_{1-x}$I$_3$. (a) Refractive index and (b) extinction coefficient for various compositions of $x$.