Opto-electronic characterization of third-generation solar cells

Figures & data

Figure 1. (a) Device structure of the ‘base’ case used in this study. LUMO and HOMO stand for lowest unoccupied and highest occupied molecular orbitals, respectively. (b) Simulation parameters of the ‘base’ case. Full simulation parameters of all cases are listed in the supplemental information (SI).

Table 1. Definition of 11 cases of solar cells.

Case	Description
Base	This is the standard single-layer device without charge traps or doping. It is 150 nm thick and has Ohmic contacts with low barriers on both sides. All other devices are derived from this base device.
	The detailed set of parameters can be found in the supplemental information (SI).
Extraction barrier	This device features an extraction barrier for electrons. Such a barrier can occur if an oxide layer forms at the electrode. It is modelled by an additional 3 nm thin layer between active material and electron contact with 0.35 eV energy offset. Such oxide formation has for example been shown in P3HT:PCBM solar cells comprising an aluminium electrode [7,10,11].
Non-aligned contact	This device has an injection barrier for electrons of 0.45 eV. This is the case if the workfunction of the metal is too high to match the LUMO level of the active material [12].
Low mobility	The active material has a mobility that is only 10% of the mobility of the base device. Both electron and hole mobilities are reduced, such that the ratio μ e /μ h remains as in the base device. Low mobilities can for example occur due to a unfavourable donor/acceptor morphology in organic solar cells [5].
High Langevin recombination	The active material has a Langevin recombination efficiency that is 10 times larger than for the base device. The Langevin recombination efficiency depends on the material and on the morphology of bulk-heterojunction solar cells [5]. Phase segregation for example can lead to a lower recombination pre-factor [13].
Shallow traps	The active material has an electron trap density of 3⋅10^17 1/cm^3 with a trap-depth of 0.3 eV. In organic solar cells the trap density can depend on material purity [14].
Deep traps	The active material has the same trap density of 3⋅10^17 1/cm^3 like ‘shallow traps’ but with a depth of 0.8 eV. This trap is located in the middle of the band-gap and leads to enhanced Shockley-Read-Hall (SRH) recombination [15].
Low shunt resistance	This device has an Ohmic shunt resistance of 50 kΩ (2.25 kΩ⋅cm^2). Shunt resistances can occur due to non-uniformity of the film, particle contaminations, spikes of the ITO leading to short-circuits, pinholes or others [16]. Shunt resistances can also be non-Ohmic and show SCLC behaviour [17]. For simplicity Ohmic shunting is used here.
High series resistance	The device has an Ohmic series resistance of 350 Ω (15.7 Ω⋅cm^2). A high series resistance can be caused by the low lateral conductivity of the transparent electrode [18].
High bulk doping density	The bulk of the device is p-doped with 1⋅10^17 1/cm^3. Unintentional doping can occur due to impurities that ionize. Very deep traps can have the same effect. Photo-oxidation of single molecules during degradation can also lead to doping [19].
Low charge generation	In this device the photon-to-charge conversion efficiency is reduced to 1/3. The physical origin can be reduced light absorption or hindered exciton dissociation. The latter can be the case if the phase-mixing is too coarse in an organic bulk-heterojunction solar cell [5,20].

Notes: Each case is a set of parameters describing a solar cell with a particular loss mechanism like charge trapping, doping or a shunt resistance. These cases are later used in the simulation of the various experimental techniques. Parameters are described in the SI.

Figure 2. JV-curve simulations for all cases defined in Table 1. (f) The bar-plot shows the fill-factor of all simulated cases. All the described cases impact the fill-factor. It is difficult to identify a specific physical effect if a JV-curve has a low fill-factor.

Figure 3. Dark JV-curve simulations for all cases in Table 1. (f) Dark ideality factors are extracted using Equation (2(2) $$j=j_s·\left(exp\left(\frac{q}{n_{\text{idd}}·k_B·T}·\left(V-R_T·j·S\right)\right)-1\right)+\frac{V-R_T·j·S}{R_p},$$(2) ).

Figure 4. Simulation of the open-circuit voltage dependent on the light intensity for all cases in Table 1. (f) Light ideality factors obtained from the simulation results – an average is used.

Figure 5. Schematic illustration of a photo-CELIV experiment. The linearly increasing voltage extracts charge carriers and leads to a peak (j _max) in current. The charge carrier mobility is calculated using t _max.

Figure 6. Dark-CELIV simulations of all cases in Table 1. The ramp starts at t = 0 with a ramp rate of 171 V/ms. (f) The bar plot shows the extracted charge carrier density.

Figure 7. Photo-CELIV simulations for all cases in Table 1. The light is turned off at t = 0 and the voltage ramp starts at t = 0 with a ramp rate of 100 V/ms. The voltage offset prior the ramp is set such that the current is zero at t < 0. (f) The bar plot shows the charge carrier mobility calculated from the peak position (t _max) using Equation (9(9) $$\mu =\frac{2·d^2}{3·A·t_{\text{max}}^2}·\frac{1}{1+0.36·\frac{\mathrm{\Delta }j}{j_{\text{disp}}}},$$(9) ). The grey lines indicate the electron mobility used as simulation input.

Figure 8. OCVD simulations for all cases in Table 1. The light is turned off at t = 0. The grey line indicates the analytic solution (Equation (11(11) $$V_{\text{ocvd}}\left(t\right)=\frac{E_g}{q}-2·\frac{k_B·T}{q}·ln\left(N_0·\left(\frac{1}{n\left(0\right)}+\beta ·t\right)\right),$$(11) )) assuming homogeneous charge densities and purely bimolecular recombination.

Figure 9. Calculation of the thermal emission of charge carriers from the density of states. (a) The dashed line is the density of states with square-root dependence above the band edge and exponential dependence inside the band. The solid lines represent the charge carrier distributions at different times. The LUMO-level is located at 0 eV, positive energy values reach into the band-gap. (b) Same as in (a) but for a Gaussian DOS. (c) Calculated currents from carrier emission of (a) and (b) including analytical fits according to Equations (14(14) $$j_{\text{te}}\left(t\right)=\frac{1}{{\tau }_{\text{te}}}·q·d·N_t·exp\left(-\frac{t}{{\tau }_{\text{te}}}\right),$$(14) ) and (16(16) $$j_{\text{em}}\left(t\right)=q·d·N_D·k_B·T·{\omega }^{-\frac{k_B·T}{E_0}}·t^{\left(-\frac{k_B·T}{E_0}-1\right)},$$(16) ).

Figure 10. DLTS simulations for all cases in Table 1. The voltage is 0 V for t < 0. At t = 0 the voltage jumps to −5 V. (f) DLTS simulations of case ‘shallow traps’ at different temperatures (solid lines). The dashed lines are exponential fits according to Equation (14(14) $$j_{\text{te}}\left(t\right)=\frac{1}{{\tau }_{\text{te}}}·q·d·N_t·exp\left(-\frac{t}{{\tau }_{\text{te}}}\right),$$(14) ).

Figure 11. Transient photocurrent simulations for all cases in Table 1. At t = 0 the illumination is turned on. At t = 15 μs the illumination is turned off. The applied voltage is 0 V. The current is normalized by the current at 15 μs.

Figure 12. Charge extraction simulations for varied light intensity (and thus V _oc) for all cases defined in Table 1. The current is integrated over time according to Equation (17(17) $$n_{\text{CE}}=\frac{1}{d·q}·\left(\underset{0}{\overset{t_e}{\int }}j\left(t\right)·dt-\left(V_a-V_e\right)·C_{\text{geom}}\right),$$(17) ) to obtain the charge carrier density (the charge on the capacitance is subtracted). The light intensity is varied by five orders of magnitude. The grey-line is the theoretical V _oc for n = p in a zero-dimensional model. (f) Extracted charge carrier density at the highest light intensity. Grey lines represent the effective amount of photogenerated charge at open-circuit obtained from the simulated charge carrier profiles.

Figure 13. Impedance simulations for all cases in Table 1. The capacitance C is calculated according to Equation (20(20) $$C=\frac{1}{\omega }·\text{Im}\left(\frac{1}{Z}\right)$$(20) ). The offset-voltage is 0 and offset-light is turned on. The dashed grey line represents the geometric capacitance.

Figure 14. Capacitance-voltage simulations for all cases in Table 1 without offset illumination. The capacitance C is calculated according to Equation (20(20) $$C=\frac{1}{\omega }·\text{Im}\left(\frac{1}{Z}\right)$$(20) ). The frequency is kept constant at 10 kHz. (f) Voltage where the capacitance reaches a maximum.

Figure 15. IMPS simulations for all cases in Table 1 with low offset light intensity (3.6 mW/cm²). The offset voltage is zero. (f) IMPS transport time-constant calculated according to Equation (26(26) $${\tau }_{\text{tr}}=\frac{1}{2·\pi ·f_{\text{peak}}},$$(26) ).

Figure 16. Measurements of an organic PCDTBT:PC₇₀BM solar cell (black) and drift-diffusion simulation results (red) from a global fit. (a) JV-curve under illumination (L = 72 mW/cm²). (b) dark JV-curve. (c) Open-circuit voltage for varied light intensity. (d) Dark-CELIV (L = 0) and photo-CELIV (L = 72 mW/cm²) with ramp rate 100 V/ms. Light is turned off at t = 0. (f) Open-circuit voltage decay for two light intensities. Light is turned off at t = 0. (g) Transient photocurrent for two light intensities. Light is turned on at t = 0 and turned off at t = 10 μs. (h) Impedance spectroscopy at 10 kHz with varied offset-voltage. (i) Impedance spectroscopy at constant voltage with varied frequency. (j) Intensity-modulated photocurrent spectroscopy (IMPS) with constant offset voltage.

Table 2. Parameters that were used to simulate all experiments in Figure 16.

Parameter	Symbol	Value	Obtained by
Device thickness	d	85 nm	Measured by AFM
Device area	S	0.045 cm^2	–
Series resistance	R S	90 Ω	High frequency range of capacitance-frequency plot
Parallel resistance	R P	160 MΩ	Reverse current of dark JV-curve
Relative permittivity	ε r	4.7	Capacitance level in capacitance-frequency plot and dark-CELIV
LUMO	E LUMO	3.8 eV	–
HOMO	E HOMO	5.37 eV	Fit
Band-gap energy	E g	1.57 eV	–
Workfunction MoO3	Φ A	5.22 eV	Fit
Workfunction Al	Φ C	3.88 eV	Fit
Built-in voltage	V bi	1.34 V	–
Effective density of states	N 0	1.5⋅10^21 cm^−3	Fit
Electron mobility	μ e	1.6⋅10^−3 cm^2/Vs	Fit
Hole mobility	μ h	8⋅10^−4 cm^2/Vs	Fit
Langevin recombination efficiency	η	1.0	Fit
Photon to charge conversion efficiency	η p2c	0.37	Adjusted to match the short-circuit current
Electron trap density	N t	1⋅10^17 cm^−3	Fit
Electron trap depth	E t	0.4 eV	Fit
Electron trap – electron capture rate	c e	1⋅10^−11 cm^3/s	Fit
Electron trap – hole capture rate	c h	3.2⋅10^−10 cm^3/s	Fit

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