Electroreflectance of thin-film solar cells: Simulation and experiment

Electromodulated reflectance (ER) is a standard characterization method to determine critical points such as the band gap in the band structure of semiconductors. These critical points show up as spectrally narrow features in ER and are typically evaluated using Aspnes's third-derivative functional form. ER spectra of stratified semiconductor systems such as thin-film solar cells, however, are significantly distorted by optical interference due to their layered structure. Furthermore, strong built-in electric fields result in a deviation from the typically assumed low-field conditions. We present here simulations of ER spectra from stratified systems based on transfer matrices using the Franz-Keldysh theory in its general form. For realistic thin-film solar cell conditions, distortions of ER line shapes due to the above-mentioned interferences and strong electric fields appear in the simulations. Furthermore, the results show good agreement with measured ER spectra of a structurally well-characterized $\mathrm{Cu}(\mathrm{In},\mathrm{Ga}){\mathrm{Se}}_2$ (CIGS) solar cell. Our analysis points out the restrictions on the determination of energetic position and number of critical points from ER spectra of stratified systems.

Figure 1

Basic layer stack of a CIGS thin-film solar cell.

Figure 2

Simulated field distribution within the SCR of the solar cell with (red) and without (blue) reverse bias of $-2\text{V}$. The electric field decays almost linearly over a large portion of the SCR justifying the use of the Schottky approximation in the optical simulation.

Figure 3

Simulated ER spectrum (blue) and TDFF fit (red) for a single CIGS interface [inset of (a)] and a single contributing optical transition. In (a) modulation occurs from zero field within the low-field limit while in (b) the low-field limit is exceeded. A TDFF fit can estimate the band gap in good agreement even though in (b) the FKOs cannot be described by a TDFF. In (c) an intrinsic field with realistic values for the electro-optic energy is implemented. In this case the simulated data deviates from the TDFF line shape and the fit parameter for $E_{\text{g,sim}}$ differs from the input parameter by 19 mV.

Figure 4

Simulated $\mathrm{\Delta }R/R,R$, and $\mathrm{\Delta }R$ signal for a CIGS half-space with low doping concentration and a ZnO window layer of varying thickness [see inset in (a)]. For a thickness of (a) $d_{\text{ZnO,1}}=225$ nm and (b) $d_{\text{ZnO,2}}=325$ nm the interference minimum in $R$ lies energetically far away from the band gap. $\mathrm{\Delta }R/R$ and $\mathrm{\Delta }R$ both show a TDFF-like line shape and differ only in their phase parameter. For a thickness of (c) $d_{\text{ZnO,3}}=425$ nm the interference minimum in $R$ lies energetically close to the band gap. $\mathrm{\Delta }R/R$ and $\mathrm{\Delta }R$ both show strong deviations from the TDFF line shape.

Figure 5

Simulated $\mathrm{\Delta }R/R,R$, and $\mathrm{\Delta }R$ signal for a CIGS layer on a Mo half-space (see inset). Interferences appear in $R$ below the band gap. Oscillations with the same periodicity can be seen in $\mathrm{\Delta }R$ and $\mathrm{\Delta }R/R$. These extend into the energetic region of the oscillator line shape and distort the signal around the band gap.

Figure 6

Measured (a) $R$ and (b) $\mathrm{\Delta }R/R$ signal of a CIGS solar cell and manual fit of the data by TMM. In (b) blue circles and black squares represent data measured by an InGaAs or Si photodiode, respectively. The simulation reproduces the positions of minima and maxima as well as the oscillator phase accurately.

Figure 7

Comparison of ER and EQE data of the CIGS solar cell from Fig. 6. There is an offset between the data sets for better visibility. The EQE curve slowly decays below the band gap indicating the existence of tail states. The maximum of the first derivative of the EQE curve gives a band gap value of $E_{\text{g,EQE}}=1.171$ eV lying closely below the value $E_{\text{g,sim,3}}=1.180$ eV determined by the manual fit of ER data in Fig. 6.