Source-linked AI summary
Solar Energy Conversion and the Shockley-Queisser Model, a Guide for the Perplexed
Jean-Francois Guillemoles, Thomas Kirchartz, David Cahen, Uwe Rau
TL;DR
The Shockley–Queisser model’s assumptions can misdirect device optimization when treated as independently maximizable targets. The paper defines figures of merit to measure how closely real solar cells approach the model across four dimensions, with ideal proximity requiring all four quantities near unity.
Problem
The Shockley–Queisser model’s assumptions and implications can guide optimization in the wrong direction when one figure of merit is maximized against the others.
Method
The paper defines figures of merit for four dimensions associated with complete devices to quantify proximity to the Shockley–Queisser situation.
Results
30 % maximum efficiency applies to a 5800 K black-body solar spectrum, whereas 33 % applies to the more complex terrestrial spectrum at optimum band gap energy.
Takeaways & Limitations
A solar cell approaches the Shockley–Queisser situation when all four quantities are close to unity, rather than when only one figure of merit is optimized.
Takeaways & Limitations
No real solar cell can fulfill the step-function absorptivity assumption, and optimizing only one figure of merit cannot represent the Shockley–Queisser situation.
Abstract
from arXiv · showhide
The Shockley-Queisser model is a landmark in photovoltaic device analysis by defining an ideal situation as reference for actual solar cells. However, the model and its implications are easily misunderstood. Thus, we present a guide to help understand and avoid misinterpreting it. Focusing on the five assumptions, underlying the model, we define figures of merit to quantify how close real solar cells approach each of these assumptions.
Description of SQ-model and its assumptions
The SQ model describes photovoltaic conversion through five idealizing assumptions spanning optical absorption, thermalization, recombination, and carrier collection. Its ideal reference enables comparison with real cells, whose deviations reduce current, voltage, fill factor, or efficiency.
- Model stages: The model divides photovoltaic operation into optical absorption, thermal relaxation, and electronic extraction or radiative recombination.These stages describe photon absorption, excess-energy loss toward the band edges, and either carrier collection or photon-emitting recombination.
- Optical assumption: Assumption 1 idealizes absorptivity as a step function: photons with E > Eg are absorbed, whereas photons with E < Eg are transmitted.The model therefore treats the band gap as the threshold separating absorption from transparency.
- Optical assumption: Assumption 2 states that each absorbed photon with E > Eg generates precisely one electron-hole pair contributing to JSC.Parasitic absorption and other departures from this ideal reduce the short-circuit current from its SQ value.
- Contact assumption: Assumption 5 idealizes contacts as carrier-selective and resistance-free; violating it, for example through series resistance, lowers FF below FF0 and reduces efficiency.The SQ framework also treats detailed-balance rate constants as applicable in the non-equilibrium operating state.
- Ideal reference and comparison: The ideal model reaches a maximum efficiency of 30% for a 5800 K black-body spectrum and 33% for a more complex terrestrial spectrum at an optimum band gap.Real-cell proximity to the SQ situation is assessed by figures of merit, with the SQ situation approached when all four quantities are close to unity.
A. OPTICAL (1-10 fs) - Loss of photons that are not absorbed
The SQ model assumes a sharp absorptivity threshold at the band gap, one collected electron–hole pair per absorbed photon, and carrier temperature equal to cell and ambient temperature.
- A. OPTICAL (1-10 fs) - Loss of photons that are not absorbed: At Eg, absorptivity switches from 0 to 1.
- A. OPTICAL (1-10 fs) - Loss of photons that are not absorbed: The model assumes exactly one electron-hole pair per absorbed photon, with each pair collected at short circuit.
- A. OPTICAL (1-10 fs) - Loss of photons that are not absorbed: Heat extraction keeps the carrier temperature equal to the cell and ambient temperature.
C. ELECTRONIC (0.1-1000 ns)
The SQ model assumes that electron-hole recombination occurs only radiatively, through emission of radiation.
- C. ELECTRONIC (0.1-1000 ns): Electron-hole recombination is only radiative, meaning it occurs through emission of radiation.
- Loss by emission of photons
The SQ model assumes no Ohmic losses and perfectly selective contacts.
- - Loss by emission of photons: The model assumes no Ohmic losses and perfectly selective contacts.
- Isothermal dissipation loss during carrier collection
The paper quantifies departures from the SQ ideal using figures of merit and equations linking current, voltage, fill factor, and efficiency. These quantities support comparison of real solar cells with SQ reference values and partition efficiency losses.
- Device comparison: Table II applies these figures of merit to record cells using a photovoltaic band gap extracted from solar-cell quantum-efficiency data.FSC and FFreal are readily determined from typically published solar-cell data, whereas separating Qe is less direct.
- SQ equations: The current-voltage relation combines the short-circuit current with diode current, while real-cell deviations alter J0, JSC, Tcell, and potentially nid.The SQ model uses nid = 1; real cells may deviate from this value.
- Voltage losses: VOC decreases from the SQ value when JSC decreases and J0 increases in the transition to a real solar cell.The loss in open-circuit voltage is represented by the product of FSC, Fem, and Qe FoMs.
- Efficiency decomposition: Efficiency is defined as Pmax divided by Psun, with Pmax commonly factorized as JSCVOCFF.The fill factor depends on VOC, resistive losses, and the ideality factor.
- Efficiency comparison: The ratio ηreal/η0 is calculated using four figures of merit, with FSC entering both linearly and logarithmically through VOC.The SQ reference calculations use an AM1.5G spectrum and nid = 1 for FF0.