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Solar Energy Conversion and the Shockley-Queisser Model, a Guide for the Perplexed

Jean-Francois Guillemoles, Thomas Kirchartz, David Cahen, Uwe Rau

arXiv:1903.11954v1physics.app-phcond-mat.mtrl-sci

TL;DR

The Shockley–Queisser model is highly idealized, and its relation to real solar cells can be misunderstood. This paper connects the model to real devices and defines figures of merit for assessing how closely they approach its assumptions. It reports maximum efficiencies of 30% under a 5800 K black-body spectrum and 33% for the terrestrial spectrum, each at an optimum band gap.

  • Problem

    The SQ model is highly idealized, and its connection to real solar cells and what it means to be “close” require clarification.

    Source: Introduction · p. 1

  • Method

    The paper connects the SQ model to real solar cells and defines figures of merit for assessing proximity to its assumptions.

    Source: Introduction · pp. 1–2

  • Results

    30% maximum efficiency for a 5800 K black-body solar spectrum and 33% for the terrestrial spectrum, each at an optimum band gap.

    Source: Description of SQ-model and its… · p. 4

  • Takeaways & Limitations

    The guide provides guidelines for effective use of the SQ model when relating it to real solar cells.

    Source: Introduction · pp. 1–2

    Optimizing devices with respect to only one figure of merit cannot be associated with the SQ model.

    Source: Consequences · p. 8

Abstract

from arXiv · show

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.

Introduction

The paper clarifies how the idealized Shockley–Queisser model relates to real solar cells and what it means for them to be “close” to the model. It defines measurable figures of merit to quantify those differences and guide effective use of the model.

Introduction

  • The paper examines claims of “exceeding or approaching the SQ-limit” [6,7] and clarifies what “close” means for real-world solar cells.It proposes experimentally measurable figures of merit to quantify how real cells differ from the ideal model and guide its use.Source: Introduction · pp. 1–2

Description of SQ-model and its assumptions

  • The SQ model describes photovoltaic action in three stages: photon absorption creates an electron–hole pair, the pair relaxes thermally, and carriers are extracted or recombine radiatively.The passages identify these as optical, thermal, and electronic stages.Source: Description of SQ-model and its… · pp. 2–3
  • A pn junction is used to illustrate carrier separation, but it is not a necessary requirement for an efficient solar cell [8,11].Source: Description of SQ-model and its… · p. 3
  • The model defines those stages through five assumptions, idealizing optical absorption, carrier relaxation, radiative recombination, and selective, resistance-free contacts.For example, absorptivity is a step function: zero below the band gap and one above it.Source: Description of SQ-model and its… · pp. 3–4
  • 30% for a 5800 K black-body spectrum (33% for the terrestrial spectrum) is the maximum efficiency at an optimum band gap.The model’s output power is maximized by choosing a voltage that minimizes the combined emission and isothermal-dissipation losses.Source: Description of SQ-model and its… · p. 4

Accounting for losses in real, single absorber solar cells

This section examines how optical, thermal, and electrical losses in real single-absorber cells relax the Shockley–Queisser assumptions and affect photocurrent, recombination, operating temperature, and the current–voltage curve. It uses figures of merit to account for departures from the ideal and identify technology strengths and weaknesses, while noting that all figures of merit cannot be brought close to unity simultaneously.

Accounting for losses in real, single absorber solar cells

  • No real cell has step-function absorptivity, and the authors propose the derivative of external photovoltaic quantum efficiency with respect to photon energy to define the photovoltaic band gap.Band tails, disorder, charge-transfer states, and finite thickness or absorption coefficients complicate the SQ band-gap definition.Source: Accounting for losses in real, single… · p. 5
  • Violating optical assumptions 1–2 reduces JSC; FSC exceeds 90% for top laboratory cells of commercial types, while Fem ranges from ≈0.1–0.5 in GaAs or c-Si to ≪10^-3 in amorphous or organic cells.The best c-Si FSC is 95%.Source: Accounting for losses in real, single… · p. 6
  • FSC has an approximately linear effect on solar-cell efficiency: a 10% FSC loss implies a little more than 10% efficiency loss; a 90% Fem loss entails ≈60 mV VOC loss, i.e., <10% if VOC > 600 mV.Source: Accounting for losses in real, single… · p. 6
  • Elevated operating temperature exponentially increases recombination losses and primarily reduces VOC; outdoor module annual energy yield falls by 2–10%, depending on technology and location.The second-order effects are on other parameters.Source: Accounting for losses in real, single… · p. 6
  • Except for record GaAs cells, recombination losses in solar cells are entirely dominated by non-radiative recombination; a change generally implies an increase in losses by orders of magnitude and a corresponding decrease in open-circuit voltage.Source: Accounting for losses in real, single… · p. 7
  • Resistive elements change the JV curve while hardly affecting JSC and VOC, but reduce FF below FF0 and lower efficiency; FFrs exceeds 97% in record Si and GaAs cells.FFrs ranges above 90% for polycrystalline thin-film cells to near 85% for polymer-based devices.Source: Accounting for losses in real, single… · p. 7

Consequences

  • The four figures of merit assess departures associated with four SQ assumptions at Tcell = 300 K; the ideal is approached when all are near unity.This goes beyond comparing JSC, VOC, and FF with SQ references; measurements should be made on complete devices, since optimizing one figure of merit can worsen others.Source: Consequences · pp. 7–8
  • Trade-offs prevent all FoMs from being close to unity at the same time, so their simultaneous optimization requires understanding those trade-offs.Source: Consequences · p. 8
  • Standard illuminated current-voltage and quantum-efficiency measurements provide some FoMs for calculating ηreal/η0 via Eq. (5), but Qe and Fem require device luminescence analysis.Source: Consequences · p. 8
  • Even an incomplete set of loss-term FoMs can reveal different technologies’ strengths and weaknesses against the SQ reference case.The presentation provides a precise reference to the SQ case.Source: Consequences · p. 8

A. OPTICAL (1-10 fs) - Loss of photons that are not absorbed

The optical assumption sets absorber absorptivity to 0 below the bandgap and 1 at the bandgap, defining the loss of photons that are not absorbed.

A. OPTICAL (1-10 fs) - Loss of photons that are not absorbed

B. THERMAL (0.1-10 ps)

- Loss of excess kinetic energy · C. ELECTRONIC (0.1-1000 ns)

The Shockley–Queisser model assumes electron–hole recombination occurs only radiatively, through emission of radiation.

C. ELECTRONIC (0.1-1000 ns)

- Loss by emission of photons

The model assumes no Ohmic losses and perfectly selective contacts.

Loss by emission of photons

- Isothermal dissipation loss during carrier collection

During charge collection, carriers undergo further thermalization in the semiconductor and contacts, contributing to isothermal dissipation losses. At maximum power, these losses are depicted alongside recombination losses as reductions in solar-cell output.

- Isothermal dissipation loss during carrier collection

  • The maximum output power is Pmax = (JV)max and is usually factorized as JSC × VOC × FF, with FF depending on VOC and parameters such as resistive losses and nid.The efficiency is defined relative to input power Psun.Source: - Isothermal dissipation loss during… · p. 11
  • Charge collection entails further thermalization within the semiconductor and contacts after carriers are photogenerated.The energy-band schematic presents absorption, local thermalization after photogeneration, and charge collection as the three conversion steps.Source: Figure 1 · p. 12
  • At the maximum power point, the photon-flux diagram depicts isothermal dissipation losses alongside recombination losses; relaxing assumptions 1+2, 4, and 5 reduces maximum output power.The diagram represents the losses as areas and compares current-voltage curves as specified assumptions are relaxed.Source: - Isothermal dissipation loss during… · p. 11, Figure 2 · p. 13
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