NREL Quantum Simulation for Perovskite Solar Cell Efficiency Optimization

The Problem

Perovskite solar cells have advanced from 3.8% efficiency in 2009 to over 25% in certified single-junction devices, the fastest efficiency improvement of any photovoltaic technology in history. The absorber layer has an ABX3 crystal structure: a lead-halide framework (PbI3 or PbBr3) with an organic or inorganic cation at the A-site (methylammonium MA, formamidinium FA, or cesium Cs). This structural flexibility allows bandgap tuning from 1.2 to 2.3 eV by compositional engineering, making perovskites attractive for both single-junction and tandem cell architectures.

The efficiency ceiling for current perovskite cells is set by non-radiative recombination at point defects: iodine vacancies, lead interstitials, and grain boundary trap states capture photoexcited carriers before they reach the electrodes. The Shockley-Read-Hall recombination rate at these traps depends on the defect capture cross-section, a quantum mechanical quantity determined by the overlap between the defect wavefunction and the band-edge states. Classical GW-BSE calculations (the state-of-the-art method for excited states in semiconductors) can compute these quantities but scale as O(N^4) with system size, making screening of compositional variants computationally expensive on classical hardware.

Perovskite Electronic Structure and Quantum Encoding

The A-site substitution in mixed FA-MA-Cs perovskites modifies the tolerance factor and octahedral tilting of the PbI6 cage, which in turn shifts the valence band edge character (predominantly Pb 6s and I 5p hybridization) and modifies defect capture cross-sections. NREL’s quantum simulation focused on iodine vacancy (VI) defects in FA0.85MA0.10Cs0.05PbI3, computing the exciton binding energy and the defect-to-band transition matrix element that determines the non-radiative capture rate.

The active space for the quantum calculation was defined by the defect-localized states within the bandgap: for a VI defect in the perovskite lattice, the relevant active space includes 4 electrons in 4 orbitals (Pb 6s contribution and the three I 5p neighbors), mapping to 8 qubits under Jordan-Wigner encoding. Qiskit Nature’s PySCFDriver was used with an embedded cluster model of the VI defect site. A second calculation targeting the exciton binding energy used the singlet-triplet gap of the Pb-I cluster as a proxy for the bright/dark exciton splitting relevant to radiative efficiency.

from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import JordanWignerMapper, ParityMapper
from qiskit_nature.second_q.circuit.library import UCCSD, HartreeFock
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_algorithms.minimum_eigensolvers import VQE
from qiskit_algorithms.optimizers import L_BFGS_B
from qiskit_aer.primitives import Estimator
import numpy as np

# VI defect cluster: Pb atom with 5 I neighbors (one vacancy site)
# Approximates the local coordination after iodine removal
vi_defect_geometry = """
Pb   0.000  0.000  0.000
I    3.175  0.000  0.000
I   -3.175  0.000  0.000
I    0.000  3.175  0.000
I    0.000 -3.175  0.000
I    0.000  0.000  3.175
"""
# Note: vacancy is at 0,0,-3.175 -- no atom placed there

driver = PySCFDriver(
    atom=vi_defect_geometry,
    basis="def2-SVP",
    charge=0,
    spin=0
)
problem = driver.run()
problem.num_particles = (2, 2)       # 4 electrons: 2 alpha, 2 beta
problem.num_spatial_orbitals = 4     # 4 orbitals -> 8 qubits JW

mapper = JordanWignerMapper()
qubit_op = mapper.map(problem.hamiltonian.second_q_op())
print(f"VI defect qubit count: {qubit_op.num_qubits}")   # 8

hf_state = HartreeFock(
    num_spatial_orbitals=4,
    num_particles=(2, 2),
    qubit_mapper=mapper
)
ansatz = UCCSD(
    num_spatial_orbitals=4,
    num_particles=(2, 2),
    qubit_mapper=mapper,
    initial_state=hf_state
)

Quantum Dynamics for Carrier Lifetime

Beyond the ground state energy calculation, NREL used Qiskit’s quantum dynamics module to simulate the time evolution of a photoexcited carrier wavepacket near the VI defect state. The Hamiltonian was encoded as a qubit operator and evolved using the Suzuki-Trotter decomposition. The decay of the carrier population from band-edge states into the defect trap was tracked as a function of time, giving a simulated carrier lifetime that could be compared against time-resolved photoluminescence (TRPL) measurements on synthesized perovskite films.

from qiskit_algorithms import TimeEvolutionProblem
from qiskit_algorithms.time_evolvers import TrotterQRTE
from qiskit.circuit.library import PauliEvolutionGate
import numpy as np

# Simulate carrier decay at VI defect over 1 ns equivalent timescale
# Hamiltonian includes band-edge state, defect state, and coupling term
# H = E_band |band><band| + E_defect |defect><defect| + V_coupling (sigma_x coupling)

E_band = 0.0     # eV, reference
E_defect = -0.45  # eV below band edge (trap depth from VQE)
V_coupling = 0.03  # eV, electron-phonon mediated coupling

# Encode as 2-level system in qubit basis for dynamics demo
from qiskit.quantum_info import SparsePauliOp
H_dynamics = SparsePauliOp.from_list([
    ("Z", (E_band - E_defect) / 2),
    ("X", V_coupling)
])

dt = 0.1e-12   # 0.1 ps timestep
n_steps = 100  # 10 ps total

populations = []
for step in range(n_steps):
    t = step * dt
    # Trotter evolution: exp(-i H dt)
    # Analytic result for 2-level: population oscillates and decays
    omega = np.sqrt((E_band - E_defect)**2 + 4 * V_coupling**2) / 2
    p_band = np.cos(omega * t * 1e12)**2  # simplified; real calc on QPU
    populations.append(p_band)

carrier_lifetime_ps = np.trapz(populations, dx=dt * 1e12)
print(f"Simulated carrier lifetime: {carrier_lifetime_ps:.1f} ps")

GW-BSE Comparison and Efficiency Validation

The classical GW-BSE calculation (using VASP with the GW0 approximation and Bethe-Salpeter equation for excited states) predicted a VI defect capture cross-section of 1.2 x 10^-14 cm^2 for the FA-MA reference composition. This corresponded to a carrier lifetime of approximately 400 ns in a high-quality film, consistent with TRPL measurements showing 300 to 500 ns lifetimes in champion cells.

For the Cs-substituted variant (FA0.75MA0.10Cs0.15PbI3), GW-BSE predicted only a minor change: capture cross-section of 1.1 x 10^-14 cm^2. The quantum simulation gave a substantially different result: the Cs substitution modified the Pb-I bond length distribution in a way that reduced the defect-band coupling matrix element by a factor of 2.1, predicting a capture cross-section of 5.7 x 10^-15 cm^2 and a corresponding carrier lifetime near 900 ns. The difference between methods traced to the way Cs modifies local lattice dynamics, a polaronic effect that GW-BSE at fixed geometry misses.

NREL fabricated Cs-substituted test cells and measured efficiency via certified I-V measurements under AM1.5G illumination. The baseline FA-MA cells achieved 18.3% efficiency. The Cs-substituted variant achieved 21.1%, a 2.8 percentage point absolute improvement driven primarily by improved open-circuit voltage (Voc), consistent with the predicted reduction in non-radiative recombination. The quantum simulation correctly identified the magnitude and direction of the improvement where GW-BSE predicted a negligible effect.

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