Showcasing the optical properties of monocrystalline zinc phosphide thin films as an earth-abundant photovoltaic absorber

Zinc phosphide, Zn3P2, is a semiconductor with a high absorption coefficient in the spectral range relevant for single junction photovoltaic applications. It is made of elements abundant in the Earth's crust, opening up a pathway for large deployment of solar cell alternatives to the silicon market. Here we provide a thorough study of the optical properties of single crystalline Zn3P2 thin films grown on (100) InP by molecular beam epitaxy. The films are slightly phosphorus-rich as determined by Rutherford backscattering. We elucidate two main radiative recombination pathways: one transition at approximately 1.52 eV attributed to zone-center band-to-band electronic transitions; and a lower-energy transition observed at 1.3 eV to 1.4 eV attributed to a defect band or band tail related recombination mechanisms. We believe phosphorus interstitials are likely at the origin of this band.

: Rutherford backscattering spectrum acquired with a grazing exit detector at 104° from normally-impinging 2.275 MeV He ++ . Elemental fits of the atoms in the Zn 3 P 2 layer and InP substrate are shown.
Electronic Supplementary Material (ESI) for Materials Advances. This journal is © The Royal Society of Chemistry 2021 Summary of photoluminescence peak properties Figure S2: Peak center positions of the gaussians best fitting the data. For the high-energy peaks (green), at 1 mW. For the low-energy peaks (red) at 30 K and below, extrapolated to 0 mW. For the low-energy peaks (red) at 100 K and above, averaged over the range of measurements. Numerical values indicate the exponent of the I=P k relationship, linking the peak intensity (I) to the laser power (P).
Variability of the photoluminescence spectrum Fitting of the photoluminescence spectra Figure S4: Detailed fitting of the sub-1.36 eV peaks in the spectra acquired at 30 K. The fits were carried out in the range from 1.24-1.25 eV to 1.36 eV with gaussians. No constraints were applied to the peaks besides their number, having a positive area, a baseline at y = 0 and the FWHM of the InP peak near 1.33 eV being constant. Figure S5: Detailed fitting of the sub-1.36 eV peaks in the spectra acquired at 12 K. The fits were carried out in the range from 1.24-1.25 eV to 1.36 eV with gaussians. No constraints were applied to the peaks besides their number, having a positive area and a baseline at y = 0. Figure S6: Best fit parameters (with two or three gaussians) of spectra acquired at 100 K. Data acquired at different positions on the same sample (data not shown).  Optical pump terahertz probe data analysis -calculation of carrier density For the reflection geometry used in the mansucript, the photoinduced change in THz reflected signal, ΔR is measured and referenced to the unphotoexcited THz reflected signal, R, as follows: where E p is the measured reflected THz electric field when the sample is photoexcited and E 0 is the THz electric field measured in equilibrium (i.e. unphotoexcited case). R is therefore the sample reflectivity without photoexcitation and is equal to: where n 0 is the complex frequency-dependent refractive index of the unexcited sample at THz frequencies. This measured signal, , is directly proportional to the effective photoinduced charge Δ carrier density. The number of charge carriers induced by the pump beam is calculated using: Where α is the absorption coefficient and d is the thickness of the thin film. E is the total energy and λ is the wavelength of the photoexcitation beam. is the ratio of free charge-carriers created per photon absorbed and is assumed to be unity ( ), to provide a maximum value for the number of photoinduced = 1 charge carriers.
To calculate the effective photoinduced charge density in the thin film, the overlapping area between the optical pump beam and THz probe beam is also taken account. Both beams are assumed to have 2D Gaussian profiles, so that the effective overlap area is given by: where w pump and w THz are the beam waists of the pump and THz beam respectively. The effective photoinduced charge carrier density is therefore given by: For this analysis, we used a measured value for the absorption coefficient of 1.85 x 10 4 cm -1 calculated from the extinction coefficient in reference 1 . This value is given for a photoexcitation with polarization perpendicular to the c-axis of the thin film, matching our experimental geometry. This value also coincides with other experimental studies 2,3 . Figure S9 shows the decay of the photoinduced charge carrier density as a function of time after photoexcitation.

Optical pump terahertz probe data analysis -calculation of photoconductivity
To convert the transient photoinduced reflected THz signal into photoconductivity, the sample is modelled as a thin film on a thick bulk substrate. All multiple internal reflections of the probing THz pulse can therefore be separated by temporal windowing. The front face of the thin film is optically excited at a central wavelength of 750 nm and the thickness of the thin film is larger than the absorption depth of the material, so that the photoinduced THz response is dominated by the thin film with negligible contribution from the bulk substrate.
ΔE r can be calculated via solving the wave equation, as demonstrated in ref. 4 , so that the measured signal, ΔE r is equal to: where Z 0 is the vacuum impedance, t 1 =2n 1 /(n 0 +n 1 ) is the transmission coefficient of the Zn 3 P 2 thin film and r 2 =(n 0 -n 1 )/(n 0 +n 1 ) is the internal reflection coefficient at the interface between the thin film and InP substrate. For our sample geometry, n 1 is the refractive index of air (n 1 = 1), n 2 is the refractive index of InP (n 2 = 3.2); and n is the refractive index of the Zn 3 P 2 thin film. The value for the refractive index of InP is an average of previously-reported values in the THz frequency range 5 . For the refractive index of Zn 3 P 2 , the static dielectric constant was used (n = ), which is consistent with other previous studies in the 33 THz range 1,2 . The parameter a takes into account the multiple internal refection of the THz probe inside the sample and is equal to: No internal reflections of the THz probe beam were observed within the time-domain waveform, so a = 1. When the photoexcited part is much thinner than the sample thickness, the unexcited part of the sample can be considered as the substrate, so that n 0 = n 2 and r 2 = 0. The formula reduces to: This assumption is also valid for our case of a thin film on a highly conductive substrate when the substrate refractive index is comparable to that of the thin film 6 , as r 2 reduces rendering the second and third terms in equation 6 negligible. As the thin film is excited within the linear regime (see Figure S10), the complex photoconductivity is assumed to follow the Beer-Lambert absorption law as a result of an exponential excitation profile: (9) Where Δσ s is the photoconductivity at the surface of the thin film. Therefore, the measured signal is equal to: The figure below shows the calculated frequency-averaged photoconductivity as a function of time after photoexcitation: Figure S11: Frequency-averaged photoconductivity of the Zn 3 P 2 thin film and the measured ΔR/R signal as a function of time after photoexcitation.
These values coincide with previously-reported values of > 100 S/cm for photoexcitation above 1.55 eV.

Photoconductivity decay within the thin film
As the OPTP spectroscopic measurements were peformed in reflection geometry, the observed photoinduced THz response is dominated by the photoconductivity at the surface of the Zn 3 P 2 thin film.
To illustrate this point, we model the expected photoconductvity from the InP substrate in our experimental configuration. Given the value of absorption coefficient used for the Zn 3 P 2 , we calculate that 22 % of the intensity of photoexcited excitation will reach the InP susbtrate. Taking into account absorption within the InP 5 , this equates to an effective photoinduced carrier density on the order of 1 x 10 15 cm -3 , which is three orders of magnitude lower than the photoinduced carrier density in the Zn 3 P 2 thin film and comparable to the equilibrium carrier concentration of InP.
The photoconductivity was calculated for this carrier density (n = 1 x 10 15 cm -3 ) using a Drude response. The intrinsic carrier concentration was taken as n 0 = 3.79 x 10 15 cm -3 ; the scattering time, τ = 0.21 ps; and the electron effective mass as = 0.08 m e 5 . Figure S11 shows the calculated photoconductivity * response. Figure S12: The calculated photoconductivity spectrum of the InP susbstrate when 22% of the photoexcited light intensity reaches its surface.
The magnitude of the photoconductivity for the InP susbtrate only reaches a maximum of ~1.2 S/cm, which is significantly smaller than the photoconductivity of the Zn 3 P 2 thin film and below the noise floor of our measurement. The measured photoinduced response can therefore be attributed solely to the Zn 3 P 2 thin film.
Using the expression for the Beer-Lambert law, Figure S12 shows the decay of the photoconductivity as a function of distance within the film. Figure S12: Change in photoconductivity as a function of distance within the Zn 3 P 2 thin film and InP susbtrate.
The photoconductivity decays exponentially into the Zn 3 P 2 thin film until it reaches the film thickness. At the film thickness, only 12% of the light intensity is absorbed by the InP substrate, leading to a reduced photoconductivity <1.2 S/cm. We therefore attribute the induced THz response solely due to the Zn 3 P 2 thin film, with the dominant contribution from the surface of the thin film.