Recently, in opto- and photoelectronics, considerable attention has been paid to the development of cheap light emitters, photodetectors, ionizing radiation detectors and efficient solar cells with improved optical and photoelectric properties based on solid solutions and heterostructures of cadmium chalcogenides [1] [2] [3] [4] . At the same time, cadmium telluride, which has deep centers with significantly different electron and hole capture cross sections, remains a very attractive object with unique physicochemical properties [5] [6] [7] [8] . In this regard, the study of long-term relaxation of anomalous photovoltage (APV) during dark depolarization of photoelectrets depending on the polarization conditions is of interest when analyzing the mechanisms of formation and destruction of the photoelectret state (PES) without an external field in semiconductor polycrystalline films of CdTe:M [9] [10] [11] [12] . Previously, in [11] , the results of studying the time kinetics of photopolarization of film photoelectrets “without an external field” were presented, and photopolarization curves and polarization isopaacs were analyzed. In this work, we will consider the relaxation processes for APV and PES in CdTe:(Ag, Cu, Cd) and Sb₂Se₃:Se films depending on the method of photopolarization and dark depolarization at different temperatures. It is shown that in the studied polycrystalline films, a two-stage time relaxation of the maximum stationary value of APV of the order of V_APV ≈ (500 - 600) V is detected with characteristic times τ_init ≈ (2 - 3) min and τ^* ≈ (20 - 45) min, and almost 90% - 95% of V_APV disappears within ~(10 - 20) min, and the rest, as photoelectret voltage (PEV), experiences long-term relaxation (~100 - 120 min), which confirms the formation of PEV in activated films.

The studied films from CdTe and Sb₂Se₃ in size 5 × 20 mm² and a thickness of 1.0 - 1.2 μm were produced by thermal evaporation in vacuum 10⁻³ - 10⁻⁴ mm. Hg alloying with appropriate impurities directly during the deposition of semiconductor material at an angle of 40˚ - 50˚ to a glass substrate, heated to 250˚C - 300˚C.

In this case, the impurity materials Ag, Cu, Cd, and Se evaporated from a separate crucible at a rate of 1.8 × 10⁻⁶, 1.3 × 10⁻⁶, 2.9 × 10⁻⁶ and 3.5 × 10⁻⁶ g/cm² s for 4, 10, 6, 8 s, respectively. The evaporation of impurities was carried out for films of cadmium telluride and Sb₂Se₃ no later than 35 minutes and 22 minutes from the initial moment of semiconductor deposition. After deposition of the impurity, the growth of films continued for another 30 - 50 minutes.

Samples of CdTe photoelectret films with Ag, Cu and Cd impurities were obtained at a substrate temperature in the range from 150˚C to 350˚C. Table 1

shows the maximum values of V_APV and V_PEV generated by photoelectret films CdTe:Ag, CdTe:Cu and CdTe:Cd, as well as V_APV by pure CdTe film, depending on the substrate temperature t_s under stationary illumination with a mercury lamp with an intensity of 500 lux. Measurements of V_APV and V_PEV were carried out with an electrostatic voltmeter with sufficient internal resistance at room temperature in atmospheric air. It can be seen that such values of V_APV and V_PEV gradually increase with increasing t_s to 300˚C, and then drop sharply.

The main distinctive technological parameters of obtaining films of triselenite antimony (Sb₂Se₃:Se), which have optimal photoelectric properties, are the following (see Table 2): temperature of selenium evaporation was t_e = 165˚C, degree of vacuum was ~5 × 10⁻⁵ mm Hg, the average deposition time of Sb₂Se₃ was ~50 min, the thickness of both activated and initial films was ~1.5 µm, the deposition angle was ~45˚, the time interval for deposition of impurity material from the beginning of deposition of the semiconductor material was 20 min, the optimal deposition rate of the Sb₂Se₃ film was υ ≤ 0.5 nm/s.

Photopolarization [11] and dark depolarization curves of anomalous (APV) and photoelectret (PEV) voltages were recorded in the dark and in idle mode at room temperature. Figure 1(a) shows the time dependence on a semi-logarithmic scale for doped CdTe:Ag (1, 2, 3) and control CdTe (4) films. Curves 1 and 2 correspond to the relaxation of V_APV in CdTe:Ag films in air and in a vacuum of 10⁻² mm Hg, and Curve 3 represents the relaxation of the photovoltage of the same film in air after incomplete photopolarization (polarization time: 2 - 3 s). Straight line 4 characterizes the progress of V_APV relaxation of the control sample obtained under identical conditions with activated films. From relaxation of Curves 1 – 4, it is clear that the long-term decay time of the APV of the doped CdTe:Ag film (t ≈ 120 min at V_APV = 1 V, and V_APV(t = 0) ≈ 600 V) is significantly longer than the decay time of the undoped cadmium telluride film (t ≈ 20 min at V_АPV = 1 V, and V_АPV(t = 0) ≈ 500 V). So, from the initial sections of Curves 1 - 3, collinear to straight line 4, we determine that τ_M ≈ 3 min. If we take into account the resistance of the films under study R ≈ 10¹² Ohm, we will obtain for their electrical capacity the value C ≈ 200 pF (τ_M = R∙C). Secondly, for a CdTe:Ag film, the stationary value of V_APV ≈ 600 V, regardless of the depolarization method (Curves 1, 2), first relaxes with a characteristic time τ_init ≈ 3 min to a value of

V_APV ≈ 55 V, with almost 90% of V_APV disappearing for ~10 min. Next, long-term

relaxation is detected, and the decay time to the values of V_APV = 1 V for the same CdTe:Ag film in air and in vacuum differed by tens of minutes (120 min of Curve 1 and 90 min of Curve 2 in Figure 1(a)). This is explained by the fact that the value of V_APV of films exposed to air or in an atmosphere of other gases is affected by ions and electrons adsorbed on the surface of the sample.

To separate the “pure” PEV from the APV, the contacts of the photopolarized sample were short-circuited for 2 - 3 s. When the film was again connected to the electrometer, then after ~10 s a stationary V_PEV ≈ 100 - 150 V was established.

Figure 1(b) shows the depolarization curves of “pure” PEV for two samples of activated CdTe:Ag films obtained under the same technological conditions.

From the depolarization curves V_PEV, it is clear that each of them has two characteristic straight sections, just like the curves V_APV(t) in Figure 1(a), for which the depolarization of the photovoltage is described by an exponential dependence:

V P E V = V P E V S Т exp ( − t τ * ) (1)

here, V P E V S Т is the initial value of the stationary PEV (in Figure 1(b) V P E V S Т =

V_PEV (t = 0) ≈ 150 V for the initial section, and for the second section V P E V S Т ≈ 50 V), τ^* is the characteristic lifetime of minority charge carriers at deep impurity levels, the value of which is different for sections of curves with different slopes.

The initial sections (for clarity, dashed straight lines 1', 2' are drawn) of the relaxation curves correspond to a relatively rapid decline in V_PEV (where τ = τ^* ≈ 2 min) and are associated with the presence of not very deep levels of adhesion in the films, leading to the formation of weak PES. Naturally, the second region with long-term relaxation V_PEV (τ = τ^* ≈ 35 min) is due to deeper levels of minority carrier capture centers and the manifestation of significant PES in the CdTe:Ag film.

Figure 2 shows the V_PEV relaxation curves for CdTe (Curve 1), CdTe:Cu (Curve 2), Sb₂Se₃:Se (Curve 3) films after complete photopolarization. As can be seen from the figure, for Curves 1 - 3 the maximum PEV values are V P E V S Т ≈ 70, 60 and 50 V, and the decay times at V_PEV = 1, V are 150, 85 and 60 min, respectively. The region of the relatively rapid decline in V_PEV in all studied samples has a qualitatively identical character and practically does not depend on the exposure Z = L‧t. The second section of the curves, corresponding to the long-term decline in V_PEV, significantly depends on exposure (compare the curves in Figure 1(b) and Figure 2).

The values of τ_init and τ^* were determined from the slope angles of the dark depolarization curves V_PEV as:

τ = t   / l n V P E V S Т V P E V ( t ) . (2)

Figure 3 shows the dependences of the characteristic relaxation times τ_init and τ^* calculated by (2) on the photopolarization time in the case of excitation of the films under study with natural light of intensity L = 8 × 10⁻² W/cm² at room temperature.

As can be seen from the figure, the maximum value of τ^* for the CdTe:Cd, CdTe:Ag, CdTe:Cu and Sb₂Se₃:Se films (Curves 1-4) reached values of 40 - 45, 30 - 35, 25 - 30 and ~24 min, while the value of τ_init(1' - 4') was only 2 - 4 minutes at t > 10 s and did not depend on the photopolarization time. It further turned out

that with decreasing temperature, the value of τ^* increased sharply and was measured in hours, and the value of τ_init weakly depends on temperature. These results once again show a significant difference in the depth of the energy levels of the attachment centers responsible for the rapid (τ_init) and long-term (τ^*) relaxation of the PES in the films under consideration. The experimental value τ allows using the expression [9] :

τ = λ τ ′ = M N υ exp Δ ε M k T ⋅ τ ′ (3)

determine the activation energy of deep levels of adhesion Δε_М, responsible for a particular relaxation of the PES film. Here, τ' is the effective lifetime of the minority carrier at the local level, M is the concentration of deep centers, N_v is the effective density of states in the valence band. From the second linear section of the dependence V_PEV(t) in Figure 1(b), we find the characteristic relaxation time τ = τ* = 35 min.

If we assume that this main section of the PEV relaxation curve is associated with the capture of holes at a deep impurity level, then taking for this level М = 5 × 10¹⁷ cm⁻³, τ' = 10⁻⁷ s and kT = 0.025 eV, we obtain the following value of its depth occurrence:

ε М 2 = ε v + 0.025   э В × ( 40 − 15 × 2.3 + 7.69 ) = ε v + 0.33   э В , (4)

which coincides well with the position of the main impurity level of Ag in CdTe [14] . This value of the activation energy is also confirmed by the results of studies of the temperature dependence τ^*(T) (Figure 4), in which a level of 0.3 ± 0.02 eV appears in the temperature range of 300 - 400 ˚K, and in the temperature range of 200 - 250 ˚K, described by the dependence lnτ^*~T^−1/4 (it is assumed that τ* is determined by electrical conductivity as in a disordered semiconductor of the Mott’s law type, which is observed in highly compensated CdTe)—one small level ε_М1 = ε_v + (0.05 - 0.11) ± 0.02 eV [12] .

The energy levels M1 and M2 discovered here by the method of temporary relaxation of PES are also observed in the temperature dependences of R_fl (T), V_PEV (T), and a level with an activation energy of 0.32 eV was previously observed in the optical spectra of the stationary photoelectret voltage V_PEV(λ) and short-circuit current I_s.c.(λ) of CdTe:Ag films [12] From this we can make the statement that the PES of activated CdTe:Ag films without an external polarizing field is due to deep impurity levels of Ag or its complexes, which is also the case for other studied films CdTe:Cd, CdTe:Cu and Sb₂Se₃:Se.

The experimental relaxation curves of V_PEV allowed us to estimate the effective values of the electrical capacitance of the activated films. The film capacitance (C_fl) was determined from the formula τ^* = R_fl (С_сc + С_fl), where С_сc-circuit capacitance (in our measurements С_сc ≈ 3 pF).

Table 3 shows the values of the electrical capacitance of the APV films of CdTe and Sb₂Se₃, determined by us for control and activated samples, where a

Note that increasing the electrical capacity and power of APV films, as a system of series-connected microphotocells that directly generates high photovoltage, is one of the pressing problems of photoelectronics.

comparison is made with the results of [9] [13] .

The table shows that at room temperature, activated films of CdTe:Cd, CdTe:Cu and Sb₂Se₃:Se have significantly larger (almost two orders of magnitude) capacitances compared to undoped films of cadmium telluride and antimony triselenide. Naturally, such an increase in the capacity of APV-activated films is associated with the possibility of charge accumulation at deep adhesion levels [10] .

In thin photovoltaic films of CdTe:Cd, CdTe:Cu and Sb₂Se₃:Se, a two-stage exponential time relaxation of the initial photovoltage V_АPV ≈ (500 - 600) V was discovered, and ~10% of it experiences long-term relaxation (t~60 - 150 min) due to the formation of PES, due to the fact that deep centers with significantly different electron and hole capture cross sections predominate in photocarrier recombination processes. Analysis of the obtained experimental results allows us to conclude that the probable centers responsible for the PES are impurity complexes consisting of a Cd vacancy and a metal ion (Ag, Cu) in the Cd:(V²⁻M⁺) position. Some parameters of such centers have been determined.

The authors declare no conflicts of interest regarding the publication of this paper.

Nurmatov, O.R., Mamadieva, D.T. and Yuldashev, N.K. (2024) Photoelectric State with Long-Term Relaxation in CdTe:(Ag, Cu, Cd) and Sb₂Se₃:Se Photovoltaic Films. Journal of Applied Mathematics and Physics, 12, 43-51. https://doi.org/10.4236/jamp.2024.121005