Maximum Efficiencies and Performance-Limiting Factors of Inorganic and Hybrid Perovskite Solar Cells

The Shockley and Queisser limit, a well-known efficiency limit for a solar cell, is based on unrealistic physical assumptions and its maximum limit is seriously overestimated. To understand the power loss mechanisms of record efficiency cells, a more rigorous approach is necessary. We establish a formalism that can accurately predict absolute performance limits of solar cells in conventional thin-film form. In particular, a formulation for a strict evaluation of the saturation current in a nonblackbody solar cell is developed by taking the incident angle, light polarization, and texture effects into account. Based on the established method, we estimate the maximum efficiencies of 13 well-studied solar cell materials [$\mathrm{Ga}\mathrm{As}$, $\mathrm{In}\mathrm{P}$, $\mathrm{Cd}\mathrm{Te}$, $a\text{−}\mathrm{Si}:\mathrm{H}$, ${\mathrm{Cu}\mathrm{In}\mathrm{Se}}_2$, ${\mathrm{Cu}\mathrm{Ga}\mathrm{Se}}_2$, ${\mathrm{Cu}\mathrm{In}\mathrm{Ga}\mathrm{Se}}_2$, ${\mathrm{Cu}}_2{\mathrm{Zn}\mathrm{Sn}\mathrm{Se}}_4$, ${\mathrm{Cu}}_2{\mathrm{Zn}\mathrm{Sn}\mathrm{S}}_4$, ${\mathrm{Cu}}_2\mathrm{Zn}\mathrm{Sn}(\mathrm{S},\mathrm{Se}{)}_4$, ${\mathrm{Cu}}_2{\mathrm{Zn}\mathrm{Ge}\mathrm{Se}}_4$, ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$, $\mathrm{HC}({\mathrm{NH}}_2{)}_2{\mathrm{PbI}}_3$] in a 1-µm-thick physical limit. Our calculation shows that over 30% efficiencies can be achieved for absorber layers with sharp absorption edges ($\mathrm{Ga}\mathrm{As}$, $\mathrm{In}\mathrm{P}$, $\mathrm{Cd}\mathrm{Te}$, ${\mathrm{Cu}\mathrm{In}\mathrm{Ga}\mathrm{Se}}_2$, ${\mathrm{Cu}}_2{\mathrm{Zn}\mathrm{Ge}\mathrm{Se}}_4$). Nevertheless, many record efficiency polycrystalline solar cells, including hybrid perovskites, are limited by open-circuit voltage and fill-factor losses. We show that the maximum conversion efficiencies described here present alternative limits that can predict the power generation of real-world solar cells.

Figure 1

(a) Optical model adopted for the calculation of the SQ limit and (b) optical model assumed for the thin-film QE limit calculation. In (b), a total absorber thickness is assumed to be 1 µm.

Figure 2

Physical model for a thin-film solar cell placed in the cavity surrounded by a blackbody radiator.

Figure 3

(a) EQE calculation and (b) J₀ calculation performed for the $\mathrm{Cd}\mathrm{Te}$ solar cell assuming θ = 0°. In (a), the black line indicates R obtained using the flat optical model (R_flat), whereas the blue line indicates R estimated assuming a textured structure (R_tex). The R_tex is obtained by linearly connecting the minimum R points of R_flat (blue circles). The EQE spectrum is calculated by adopting R_tex. In (b), the EQE spectrum of the $\mathrm{Cd}\mathrm{Te}$ solar cell and the photon density of the blackbody radiation at 300 K (φ_BB) are shown. The approximated J₀ value of the solar cell is derived as the area surrounded by these two spectra.

Figure 4

α spectra of solar cell absorbers. The closed circles indicate the E_g positions of the absorbers. The optical data were taken from Ref. [9], except for $\mathrm{CZTS}\mathrm{Se}$.

Figure 5

EQE spectra calculated from the ARC method assuming the optical model of Fig. 1 using θ = 0°. The closed circles indicate the E_g positions of the absorbers.

Figure 6

Relationship between J₀ values calculated by assuming θ ≠ 0° and θ = 0°. The J₀ values of θ ≠ 0° are evaluated by performing exact spherical integration of Fig. 2 using Eq. (3), whereas the J₀ values of θ = 0° are obtained by using Eq. (4), assuming the normal incidence for the EQE calculation.

Figure 7

Maximum (a) J_SC, (b) V_OC, (c) FF, and (d) conversion efficiency (η) calculated from the thin-film QE and SQ limits. The closed circles show the calculated QE limits for each absorber, whereas the solid line indicates the SQ limit. The yellow regions in (a) and (b) indicate the absorber materials that exhibit strong tail absorption. In (b), the dotted line indicates E_g/q. In (d), the green region indicates the absorber materials that exhibit over 30% efficiencies.

Figure 8

(a) EQE spectra of $\mathrm{Ga}\mathrm{As}$ solar cells calculated from the ARC method by varying the absorber thickness in the optical model of Fig. 1 and (b) thickness dependence of the QE limit obtained for $\mathrm{Ga}\mathrm{As}$ and ${\mathrm{MA}\mathrm{Pb}\mathrm{I}}_3$ solar cells.

Figure 9

(a) Modeling of hypothetical $\mathrm{Ga}\mathrm{As}$ tail absorption by the variation of the Urbach energy (E_U) in a range of 0–100 meV, (b) change of the $\mathrm{Ga}\mathrm{As}$ EQE spectrum with E_U calculated by the ARC method, (c) variation of the QE limit with E_U, and (d) variation of the maximum solar cell parameters with E_U. In (a), the open circles show the experimental α spectrum taken from Ref. [9]. The numerical values of (c),(d) are estimated from the corresponding EQE spectra in (b).

Figure 10

Limiting factors of record efficiency solar cells calculated from the thin-film QE limit. The experimental conversion efficiencies (η_ex) and the maximum efficiencies estimated from the thin-film QE limits $({\eta }_{\mathrm{QE}}^{max})$ are summarized. The difference between ${\eta }_{\mathrm{QE}}^{max}$ and η_ex is further categorized into the efficiency reduction due to the V_OC deficit (Δη^V_OC), J_SC deficit (Δη^J_SC), and FF deficit (Δη^FF).

Figure 11

(a) Conversion efficiency, (b) J_SC, (c) V_OC, and (d) FF obtained from the QE limit calculations and experiment. The parameter values indicated for the QE limit calculations are consistent with Fig. 10. The experimental values of record efficiency solar cells are adopted from Refs. [5, 46, 50, 52, 53, 55, 56].

Figure 12

Ratio of the experimental efficiency (η_ex) and maximum efficiency calculated from the thin-film QE limit $({\eta }_{\mathrm{QE}}^{max})$. The ratio of ${\eta }_{\mathrm{ex}}/{\eta }_{\mathrm{QE}}^{max}$ is shown by the two-dimensional variables of the J_SC ratio $(J_{\mathrm{SC}}/J_{\mathrm{SC}}^{max})$ and the V_OCFF ratio $(V_{\mathrm{OC}}\mathrm{FF}/V_{\mathrm{OC}}^{max}\mathrm{F}{\mathrm{F}}^{max})$ for each record efficiency solar cell.

Figure 13

(a) EQE and R spectra of the experimental $\mathrm{Ga}\mathrm{As}$ cell (open circles) and the simulated result (solid lines) and (b) λ dependent J₀ contribution (J_0,λ) calculated from Eq. (3) (i.e., θ ≠ 0° and R ≠ 0) and Eq. (4) (i.e., θ = 0° and R ≠ 0). The experimental spectra of (a) are taken from Ref. [65]. In (b), the calculation result obtained assuming R = 0 with θ = 0° is also shown.