Which gap? Measuring voltage loss in organic solar cells

1 / 9 · THE QUESTION

One cell, three voltage losses

A common figure of merit for a solar cell is its voltage loss, ΔV_OC = E_g/q − V_OC. When this report was written, many papers claimed "low" losses between about 0.47 and 0.6 V. But each paper took the optical gap E_g from the spectra in its own way, so the numbers could not be compared directly.

Take the PBDB-T:IEICO-4Cl cell from the report's Table 3, with V_OC = 0.74 V. Read its gap from the onset of the quantum-efficiency (EQE) spectrum and the loss is 0.51 V. Use the two other EQE-based definitions and you get 0.57 V or 0.62 V. The device is the same; only the definition changes.

E_g, V_OC and ΔV_OC values from Table 3; the EQE curve is schematic.

2 / 9 · STEP VERSUS SMEAR

Organic semiconductors have no sharp edge

In the Shockley–Queisser (SQ) limit the absorptance is a step: 1 above the band gap, 0 below it. The gap is then simply the energy of the step. A cell that absorbs must also emit, and its emission is the black-body spectrum multiplied by that step, so it peaks right at the gap.

A real organic blend is disordered and has no clean gap in its density of states. Its absorptance rises gradually. Below the gap there are weak features from charge-transfer (CT) states at the donor–acceptor interface, and because the black-body factor favours low energies, these weak CT features often dominate the emission. Any "gap" for such a material is a practical definition, much like the E₀₄ gap used for amorphous silicon (the energy where the absorption coefficient reaches 10⁴ cm⁻¹).

Schematic, after Fig. 1a,b; log scale.

3 / 9 · THREE LOSSES

Where the definition enters

The report splits the voltage loss into three parts (its Eq. 1):

ΔV_OC = (E_g/q − V_OC^SQ) + (V_OC^SQ − V_OC^rad) + (V_OC^rad − V_OC) = ΔV₁ + ΔV₂ + ΔV₃

V_OC^SQ is the SQ voltage for a step at E_g, so it depends on the chosen gap. V_OC^rad is the voltage the cell would reach if radiative recombination were the only loss. It is calculated from the measured EQE spectrum and needs no gap at all.

So the choice of E_g moves ΔV₁ and ΔV₂. The non-radiative loss ΔV₃ is the same whatever definition you use.

Schematic; level heights illustrative.

4 / 9 · WHAT MOVES

ΔV₁ barely moves, so ΔV₂ takes the change

ΔV₁ is the unavoidable radiative loss of an ideal SQ cell, about 0.2–0.3 V depending on the gap. Plotted against E_g, the curves of E_g/q and V_OC^SQ rise almost in parallel, so ΔV₁ changes very little when the definition changes. The difference almost all goes into ΔV₂.

ΔV₂ comes from the absorption edge not being a step. It has a small part from the lower short-circuit current, ΔV₂^SC, and a larger part, ΔV₂⁰, because emission sits below the gap. In organic cells ΔV₂⁰ is unusually large because of the red-shifted CT states. In newer blends with almost no energy offset, the CT absorption and emission disappear and ΔV₂⁰ shrinks.

Curves computed from the SQ expression (Eq. 2) with AM1.5G at 300 K, after Fig. 3a.

5 / 9 · DEFINITION 1

The onset: popular, but arbitrary

The most common choice is to fit a straight line to the absorption edge and take its intersection with the energy axis. The result depends on which part of the edge you fit, light scattering in spin-coated films blurs the tail, and there is no physical basis for the construction. Blending can also shift the edge: a PIPCP:PC₆₁BM film absorbs about 70 meV further to the red than neat PIPCP.

The onset also gives the smallest gap and hence the smallest losses. For PBDB-T:IEICO-4Cl (Table 1), a neat-film onset of 1.25 eV gives V_OC^SQ ≈ 0.99 V, but the cell's V_OC^rad is ≈ 1.02 V. That makes ΔV₂ negative (−0.03 V): the "ideal" SQ cell would be worse than the real cell's radiative limit. For a voltage-loss analysis, the report concludes, this gap is not helpful at all.

Table 1 values: E_g 1.25, V_OC^SQ 0.99, V_OC^rad 1.02 V; ΔV₁ 0.25, ΔV₂ −0.03, ΔV₃ 0.29, ΔV_OC 0.51 V. Left panel schematic, after Fig. 2a.

6 / 9 · DEFINITION 2

Where absorption meets emission

A physically motivated choice is the 0–0 energy E₀₋₀, the gap between the relaxed ground state and the relaxed lowest excited singlet. Absorption peaks above it and emission below it, each shifted by a relaxation energy:

E_max,abs = E₀₋₀ + λ_abs E_max,fl = E₀₋₀ − λ_fl

When the two spectra are roughly mirror images where they overlap, as for most organic semiconductors, E₀₋₀ is where the normalised absorptance and photoluminescence cross. The method is reproducible and has a clear meaning. Its drawbacks: not every group reports emission spectra, and blending can shift them. For IEICO-4Cl in PTB7-Th the blend absorption edge moves by ≈ 20 meV and the PL by ≈ 10 meV. Table 2 lists neat-film values, for example 1.67 eV for PTB7-Th and 1.33 eV for IEICO-4Cl.

Schematic, after Fig. 1d and 2b.

7 / 9 · DEFINITIONS 3 AND 4

Reading the gap from the solar cell itself

The EQE spectrum of the finished device is easy to measure. Unlike film spectra, it already includes any changes the blend morphology causes. (It does depend slightly on device optics such as layer thickness.) Two definitions use it:

E_g^edge (Vandewal and co-workers): extrapolate the EQE edge and see where it meets the horizontal tangent at the EQE peak. A sharper edge puts it closer to the onset.

E_g^PV (Rau and co-workers): treat the measured EQE as a mix of SQ steps with different gaps. The share of each step is P(E) = dEQE/dE, and E_g^PV is the mean of P(E) between the two energies a and b where P falls to half its maximum. The ½ is arbitrary, but small changes to it hardly matter unless the data are noisy.

Schematic, after Fig. 2c,d.

8 / 9 · 32 CELLS

No trade-off between EQE and voltage loss

The authors collected 32 published cells, with fullerene and non-fullerene acceptors, and recalculated each one's loss with three EQE-based gaps (Table 3). The same cell can look very different: TQ1:PC₇₁BM loses 0.81 V by the onset, 0.94 V by E_g^PV and 1.08 V by E_g^edge.

A 2015 analysis of mostly fullerene cells had suggested that a high peak EQE needs a large voltage loss, a large energy offset to split the excitons. In these 32 cells there is no clear trend with any of the three definitions. Peak EQE can stay high even as ΔV_OC approaches about 0.6 V.

Every point is a Table 3 row (Fig. 6a–c). Blue: fullerene acceptors; red: non-fullerene acceptors and the 6T/rubrene/SubNc/SubPc stack.

9 / 9 · OUTLOOK

Not much below 0.6 V, and about 18%

The onset gap marks where absorption is zero. Efficiency predictions assume a constant EQE above the gap, so the onset is no use for them. With E_g^PV or E_g^edge, no organic cell up to that point lost much less than 0.6 V.

Using a published prediction with EQE fixed at 85% and a fill factor of 75%, these smallest losses correspond to a realistic single-junction efficiency limit of about 17–18%. To reach the efficiencies of inorganic and perovskite cells, the voltage loss itself had to come down. The authors' recommendation: use E_g^PV or E_g^edge, which come straight from the EQE and link the SQ limit to real devices.

Smallest losses per definition from Table 3: onset 0.48 V, E_g^PV 0.53 V, E_g^edge 0.59 V. ≈ 17–18% from Fig. 6d.