Determination of carrier lifetime in thermally evaporated In2S3 thin films by light induced transient grating technique

In2S3 thin films were deposited onto soda lime glass substrates using thermal evaporation technique at a constant substrate temperature of 300 °C and the films were annealed in a sulfur ambient at 250 °C and 300 °C for 1 h. Light induced transient grating (LITG) technique was used to determine the carrier lifetime in In2S3 thin films. The determined carrier lifetime values for different excitation energy densities, I0 = 0.06–1.64 mJ/cm2 decreased from 206 to 18 ps and 150 to 14 ps for the films annealed at 250 °C and 300 °C respectively. Further, the bimolecular, Auger recombination coefficients and diffusion coefficient were determined in the films. The observed bimolecular carrier recombination origin was explained by interface and Auger recombination processes.


Introduction
Cu(In,Ga)Se 2 (CIGSe) and CdTe-based solar cells have reached high conversion efficiencies of 22.6% and 22.1% using CdS as a buffer layer [1,2] and are currently commercialized. But, the large scale production of these solar cells using CdS is environmentally unsafe to handle because of the toxicity of cadmium. Therefore, alternate materials are of much interest now that can successfully replace CdS. In this context, In 2 S 3 is a potential alternative material, because of its wide energy band gap (2.0-3.3 eV), n-type conductivity, non-toxic and photoconductive nature [3][4][5][6]. Recently, Spiering et al. [7] reported a record solar cell efficiency of 18.2% using evaporated In 2 S 3 thin film as a buffer layer for Cu(In,Ga)Se 2 -based thin film solar cells.
Charge carrier lifetime is one of the important parameters that significantly influence the performance of optoelectronic devices. Determination of carrier lifetime and carrier diffusion length of the material is highly essential before fabrication of any device. Generally, carrier lifetime is sensitive to impurities or defects that are present in the material. In direct band gap semiconductors, the lifetime of charge carriers is of the order of nanoseconds to microseconds, depending upon the excess carrier concentration and defect properties. The measurement of carrier lifetime is based on the dynamics of excess photo-generated charge carriers. Various techniques such as time-resolved photoluminescence spectroscopy (TRPL) [8], transient absorption spectroscopy (TAS) [9][10][11], time-resolved terahertz spectroscopy (TRTS) [12], time-resolved microwave conductivity (TRMC) [13][14][15], steady-state photo-carrier grating (SSPG) [16] and light-induced transient grating (LITG) [17][18][19] have been used to measure the carrier dynamics in semiconductors. To the best of our knowledge, there are no such reports on the use of LITG technique to find the carrier lifetime and determine recombination mechanisms in In 2 S 3 layers. Therefore, picosecond LITG technique was employed to measure the carrier lifetime (τ) and diffusion coefficient (D) in In 2 S 3 thin films for the first time in the present work and the results are discussed.

Experimental
In 2 S 3 films of ~ 500 nm thickness were produced by thermal evaporation technique using 5 N pure In 2 S 3 powder obtained from Sigma Aldrich company. The layers were formed on soda lime glass substrates at a temperature of 300 °C, followed by annealing in sulfur atmosphere at 250 °C and 300 °C for 1 h. The detailed deposition conditions of the films were reported elsewhere [20]. LITG is an optical pump-probe technique used to measure the photo induced τ and D parameters. In this technique, a Nd:YLF laser pump beam of 351 nm wavelength (hν > bandgap energy, E g of the sample) was split into two laser pulses (pulse duration of 10 ps) that interfere at the sample. As a result, a periodically modulated excess carrier density N(x) was generated. The latter acts as a transient diffraction grating in the sample. In order to monitor the carrier dynamics, an optically delayed probe beam of 1053 nm wavelength was incident upon the sample. This probe beam gets transmitted through the sample and diffracted at the transient grating as shown in Fig. 1.
The carrier density distribution is described as, where ∆N = αI 0 /2 hν (α is absorption coefficient, I 0 is the excitation energy density) and Λ is the transient grating period given by Λ = λ/2sin(θ/2), where λ = 351 nm that is the wavelength of the pump beam and θ = 19.8°, which is the angle between two pump beams respectively for Λ = 3.2 μm. The LITG diffraction efficiency (η) is defined as the ratio of diffracted beam intensity (I D ) to transmitted beam intensity (I T ) and is measured as a function of delay time between pump and probe pulses. Figure 2 shows the schematic representation of light-induced transient grating setup. The rate of diffusive grating erasure depends on Λ, while recombination rate does not, which allows to distinguish these two processes. The ambipolar τ and D parameters can be determined from LITG transients recorded for few different Λ, according to a relation: 1/τ G = 1/τ + 4π 2 D/Λ 2 . Diffraction efficiency is described by a relation, DE ~ exp(-2t/τ G ). Figure 3a and b show the LITG diffraction efficiency decay curves for In 2 S 3 layers annealed at 250 °C and 300 °C for different grating periods, 0.73 μm, 1.6 μm and 3.2 μm. These plots provided the decay curves with different decay rates. While Fig. 3c and d show the decay curves of In 2 S 3 layers for a grating period of 3.2 μm with different excitation energy densities (I 0 ) that varied in the range of 0.06-1.64 mJ/cm 2 . The obtained decay patterns are non-exponential due to injection conditions. From these plots, the τ and D parameters can be directly obtained by fitting the decay pattern by exponents.

Results and discussion
The determined carrier lifetime values for different excitation energy densities, I 0 = 0.06-1.64 mJ/cm 2 decreased from 206 to 18 ps and 150 to 14 ps for the films annealed at 250 °C and 300 °C respectively. Here, the decrease in carrier lifetime with increase of excitation energy density might be due to bimolecular, Auger or surface/interface recombination processes that occur in these films. Bondarenko et al. [21] also observed a similar decrease of carrier lifetime with  increase of excitation energy density for bismuth oxysulfide semiconductor films prepared by chemical bath deposition. Figure 4 shows the variation of D with different excitation, from which, a low D value of 0.2-0.5 ± 0.1 cm 2 /s was obtained due to cumulative effect of large hole mass [22] and carrier transport blocking by grain boundaries. Here, the observed increase of diffusivity with excitation can be related to carrier degeneracy. Figure 5 shows the variation of carrier lifetime with excitation energy density of In 2 S 3 films. As the highest excitation lifetime becomes comparable to the duration of response function of measurement system (see Fig. 3 d) (exp(−t 2 /2σ 2 ), where σ = 6 ps), therefore deconvolution of the decay initial part was performed with Erf function [23], DE(t) ~ exp[(σ 2 -2tτ e )/(2τ e 2 )] × [1 + Erf{(tτ e -σ 2 )/(2 1/2 στ e )}], τ G = 2τ e , where τ e is the exponential fit lifetime to the DE decay. The carrier lifetimes of the films were fitted well with bimolecular law, where the long term lifetime (τ G ) in the kinetic tails for the films annealed at 250 °C is 330 ps and is 240 ps for the layers annealed at 300 °C. The bimolecular fit was done for In 2 S 3 films by the following relation (2), where the coefficient b value (0.027 and 0.032 cm 2 ps −1 mJ −1 for films annealed at 250 °C and 300 °C, respectively) can be directly obtained from the slope of the linear plot of τ −1 versus I 0 (not shown). Auger recombination) in In 2 S 3 films. In general, the indepth photogenerated carrier concentration (∆N) is proportional to the excitation fluence when absorption depth (1/α) is smaller than film thickness [24] Here, α is absorption coeffcient at 351 nm wavelength of pump beam, which was determined from conventional optical absorption spectroscopy and its values are 1.1 × 10 5 cm −1 and 0.9 × 10 5 cm −1 for the films annealed at 250 °C and 300 °C, respectively. The obtained ∆N values varied in the range, 5.8 × 10 18   The recombination rate is one of the limiting parameters of solar cell efficiency and depends on many parameters such as charge carrier mobility, carrier density and doping levels. The recombination rate (1/τ) is proportional to the carrier concentration which is expressed as where A, B and C describe the coefficients of linear, bimolecular (radiative) and Auger recombinations respectively. When C term is neglected in relation (4), the bimolecular coefficient, B (= 2bhν/α) values were determined as ~ 3.3 × 10 −10 cm 3 /s and 3.2 × 10 −10 cm 3 /s for films annealed at T a = 250 °C and 300 °C, respectively. Such values are similar to radiative recombination coefficient evaluated for different direct bandgap semiconductors, where values of 10 −8 -10 −11 cm 3 /s are typical [25]. However, we observe only very weak photoluminescence (quantum efficiency was below 1% as checked by integrating sphere), therefore the determined B should reflect nonradiative processes.
Generally, trap-assisted recombination on the outer sides of any semiconductor sample is one of the current transport mechanisms that can influence the perfomance of the device, particularly the solar cells. As the layers grown in this work are rather thick (~ 500 nm) and diffusion coefficient is small (D = 0.2-0.5 cm 2 /s), its prominence can be neglected. However, interface recombination at grain boundaries is the common recombination path that is observed in polycrystalline thin films [26][27][28]. The Coulomb potential by defect charges at the grain boundaries of In 2 S 3 films can be described by free carrier screening, which is mainly due to interface recombination. This interface recombination velocity (S int ) can be evaluated by the following relation [29], where, S 0 we fitted as 0.8 cm/s and 2.5 cm/s; n 0 is the equilibrium doping density, 3.6 × 10 11 cm −3 and 17.5 × 10 11 cm −3 in In 2 S 3 films annealed at 250 °C and 300 °C respectively. The equilibrium doping density of the films was estimated from the carrier mobility, 16 cm 2 /Vs and 4 cm 2 /Vs for films annealed at 250 °C and 300 °C [30] and respective resistivity of these samples are 1.06 × 10 6 Ω•cm and 0.89 × 10 6 Ω•cm, determined using Ohmic contacts. The fitted S int values (relation 5) in the LITG experiment increased from 3.1 × 10 5 to 16.3 × 10 5 cm/s and 1.2 × 10 5 to 6.7 × 10 5 cm/s with increase of ∆N in the layers. Anita Warrier et al. [31] determined similar values, which varied in the range, 5 × 10 3 -11 × 10 3 cm/s in β-In 2 S 3 films by using photothermal beam deflection technique. The interface related recombination lifetime (τ i ) is described by the following equation [32,33], where r eff is the average grain radius taken as 20 nm [20] and the D is taken to be > 0.2 cm 2 /s. By setting these values in Eq. (6), the second term equals to < 4 ps, which indicates rather fast carrier transport to grain boundaries and thus first interface term should be limiting the recombination process.
The evaluated values of τ i varied in the range, 40-300 ps for the layers annealed at 250 °C and 300 °C. The recombination lifetime in In 2 S 3 films at high carrier densities is controlled by Auger recombination and its coefficient C can be determined by fitting the lifetime excitation dependence with the following relation including bulk, interface and Auger recombination terms [33,34], The obtained C values are 0.8 × 10 −30 cm 6 /s and 1.5 × 10 −30 cm 6 /s and bulk lifetime (τ bulk ) values are 2000 ps and 1000 ps in the grains of In 2 S 3 films annealed at 250 °C and 300 °C, respectively. The latter values are much larger than the interface recombination lifetime on grain boundaries. The Auger recombination rate decreased with increase of carrier density due to the Coulomb interaction [33,35].

Conclusion
In 2 S 3 thin films were thermally evaporated at 300 °C followed by annealing at 250 °C and 300 °C in sulfur ambient. The non-destructive light induced transient grating technique is used to determine the carrier lifetime in In 2 S 3 films at different excitation energy densities. The films annealed at 250 °C showed better carrier lifetime values compared to those annealed at 300 °C. These values decreased with increase of excitation energy density and varied from 206 ps to 25 ps. The decrease of lifetime with the raise of excitation density is explained by recombination at the grain interfaces described by nonradiative bimolecular recombination, consisting of interface and Auger recombination processes. For films annealed at 250 °C, the evaluated bimolecular recombination coefficient is ~ 3 × 10 −10 cm 3 /s and the Auger recombination coefficient is 0.8 × 10 −30 cm 6 /s.