EFFECT OF THE DIFFUSION OF COPPER ATOMS IN POLYCRYSTALLINE CdTe FILMS DOPED WITH Pb ATOMS †

The process of diffusion of labeled copper Cu


INTRODUCTION
In recent years, significant progress has been made in the technology of manufacturing thin-film solar cells based on A B semiconductor compounds [1][2][3][4].Unfortunately, Cu S − CdS(ZnCdS) and Cu S − CdTe thin-film solar cells tend to change their parameters during operation.The degradation of such solar cells is mainly associated with a change in the heterojunction interface and shunting of the base thin CdS(ZnCdS) and CdTe layers due to the high diffusion rate of copper atoms.
In [5], a hypothetical model was proposed -associations of doped Cu atoms with ionized acceptors of non-vacancy origin, leading to a sharp decrease in the diffusion rate in cadmium telluride films.
However, the microparameters of these local acceptor centers are not specified, their nature is not disclosed, it is only indicated that at the annealing temperature the Fermi level should be above the level of acceptor centers A of nonvacancy origin.This condition allows acceptor centers A to be in a charged state and form an associate (complex) with interstitial ions of copper atoms of the Cu A type.
The development of a controlled reproducible technology for producing thin-film solar cells and their modules using layers of honey sulfide and telluride is mainly associated with the search for and determination of impurities that could localize copper atoms in the space of crystal lattices of cadmium sulfide and telluride by forming stable complexes.
Since Ge, Sn, and Pb impurities are located at the sites of the cadmium sublattice in cadmium telluride crystals, they can, in principle, play the role of ionized acceptor centers leading to the formation of associates with doped copper atoms.Among these impurities, Pb atoms have a certain advantage.Pb is highly soluble in CdTe, secondly, Pb can be doped at relatively low temperatures (773÷973 K), thirdly, Pb in CdTe gives a "shallower" level than impurities of Sn and Ge atoms.
The aim of the authors is to study the diffusion of labeled copper atoms in p-CdTe large-block films with different contents of Pb atoms in the temperature range 573÷723K.

MATERIALS AND METHODS
The distribution profiles of the concentration of labeled 64 Cu atoms in polycrystalline p-CdTe films in the temperature range 573÷723 K are shown in Fig. 1.

EEJP. 3 (2023)
Sharifa B. Utamuradova, et al.The study showed that the concentration distributions of copper atoms over the thickness of the p-CdTe film in this temperature range are described by the function erfc (Fig. 2).
The initial p-CdTe films were synthesized by the gas transport method in a quasi-closed volume in a flow of purified hydrogen [7].Pb atoms were introduced into a growing p-CdTe film during synthesis from a molybdenum substrate, which had a lead layer with a thickness of d = 2 mm deposited by magnetron ion sputtering on the surface of molybdenum [8].Pb atoms were introduced into the growing p-CdTe film in the course of synthesis from a molybdenum substrate.The content of Pb impurities was controlled by the neutron activation method [9].The thickness of the grown p-CdTe<Pb> films is 100÷120 μm, the working area S ≥ 1 cm 2 .In such films, grains (crystallites) are oriented in the direction of growth, and their dimensions are not less than the film thickness.The diffusion volume was ≡ 9 cm 3 .The radioactive isotope 64 Cu was used as a diffusant.The sample weight in the ampoule was 2 mg, which corresponded to a diffusant vapor pressure of 0,15÷0,2 atm.Diffusion annealing was carried out in electric furnaces for 4 h, the temperature was maintained with an accuracy of ±3 K.
The composition of the p-CdTe<Pb> film samples obtained was monitored using a Jeol JSM-6380LV scanning electron microscope equipped with an IN-CAx-sight X-ray spectral microanalysis of the elemental composition.X-ray analysis of p-CdTe<Pb> films was carried out on a DR0N-4-07 diffractometer with a step of 0.01° and exposure at a point of 15 s (Fig. 1).The results of the indexing of the fingerprint comparison of the obtained results with a set of reference X-ray patterns (ASTM) made it possible to determine the composition of the p-CdTe<Pb> films.film composition, as predominantly homogeneous, cubic modification.
In samples, as a result of lead doping in all types of samples, the mobility µ decreases deeper into the thickness and the value of resistivity ρ increases.Table 1 shows the parameters of mobility µ and resistivity ρ of doped CdTe layers during layer-by-layer removal of film thickness d at room temperature.The distribution profile of the concentration of labeled 64 Cu atoms in polycrystalline p-CdTe films with a columnar grain structure was recorded using the activation analysis method [9], the CdTe layers doped with 64 Cu isotopes were removed by chemical etching with Br:C 2 H 2 OH (1:5) bromomethyl.The activity of the removed layers was measured on a gamma spectrometer for 1 h.

RESULTS AND DISCUSSION
The distribution profiles of the concentration of labeled 64 Cu atoms in p-CdTe polycrystalline films in the temperature range 573÷723 K are shown in Fig. 2.
The study showed that the concentration distributions of copper atoms over the depth of the p-CdTe film in this temperature range are described by the erfc function (Fig. 3).In this case, the concentration and diffusion coefficient of copper atoms on temperature are described by an exponential dependence (Fig. 4) and the following analytical expressions An analysis of the obtained results shows that the pre-exponential tallow factor D 0 and the diffusion activation energy Q correspond to the formula obtained in [10]: where T . is the melting point of the material; P -dimensionless coefficient depending on the geometry of the unit cell of the crystal and the diffusion mechanism; a is the period of the crystal lattice; ν -Debye frequency; ΔG -Gibbs free energy of activation at a temperature equal to T melt .
Substituting the experimental value of the pre-exponential factor D 0 = 6.7•10 -9 cm 2 •s -1 and Т melt (CdTe) = 1315 K into (5), we find Q = 0.5 eV.The value of Q calculated in this way satisfactorily agrees with the value determined directly from the experiment, which confirms the correctness of expression (3) in the calculation of the diffusion parameters of labeled copper atoms in large-block p-CdTe<Pb> films.
The low values of the effective diffusion coefficient of copper atoms D(T) = 2,7•10 -13 ÷1.8•10 -12 cm 2 •s -1 in the temperature range 573÷723 K show that Cu diffuses in p-CdTe polycrystalline films by a complex mechanism.The most probable is diffusion with association [12].This is also supported by the small value of А = 9.6•10 -11 cm 2 •s -1 in expression (3).It shows that the associate between the ions of Cu and Pb atoms is stable even at the melting temperature of cadmium telluride.
Assuming that the Pb acceptors are located in the cation sublattice, and the interstitial Cu atoms occupy tetrahedral interstices in equilibrium, we obtain the shortest distance between ions r = 2,8 Å.Assuming that only the Coulomb interaction contributes to the enthalpy of the associate, we estimate ΔН by the formula [13]: ΔН = e 2 /4πξξ0 = 0.50 eV, where ξ = 10.3 is the low-frequency (static) permittivity of cadmium telluride.
The associate enthalpy value Cu Pb ΔH = 0.50 eV coincides with the diffusion activation energy Q = 0.49 eV of Cu atoms in p-CdTe<Pb> coarse films.This result shows that all diffusing Cu atoms are completely bound in complexes with ionized Pb acceptor centers since N(Pb )≥Cu .Therefore, the activation energy Q of diffusion of copper atoms is almost entirely determined by the binding energy of the Cu Pb .associate.In this case, the rate of diffusion of interstitial copper ions depends on the probability of decay of the associate, and the diffusion process itself consists of the stages of decay and formation of Cu Pb .The electronic structure of the ionized Pb .acceptor center probably plays an important role in the formation of such an associate.This, probably, explains the sharp difference between the diffusion coefficient of copper atoms D(T=160°С)≅10 -8 cm 2 •s -1 and the value of the pre-exponential factor D 0 = 1.4 cm 2 •s -1 obtained in [14,15], from our data.
The difference in the values of D(T) and D 0 is most likely due to the thermodynamic state of the system, the associate.Probably, in [16] an associate Cu Á, is formed, in which the atomic energy of atoms is high, therefore, in the process of diffusion, when atoms pass into activated states, the change in entropy is large.Since D 0 is related to the entropy ΔS by the following relationship [17].
then a noticeable change in ΔS leads to large values of D 0 .
In the case of the formation of the Cu Pb associate, the system is apparently in a more stable position, closer to the equilibrium state.In such a material, diffusible Cu atoms rapidly dissolve; are mixed, and without much effort form associates of the Cu Pb type, which is facilitated by the Coulomb interaction between the Cu and Pb ions.In this process, the change in the vibrational entropy can be neglected; therefore, the value of D 0 is small, which is observed in the experiment (see (6)).
Let us now consider the influence of the Pb content in p-CdTe on the diffusion parameters of Cu atoms.Pb concentration in films is within N = 10 18 ÷ 10 20 cm -3 .Studies have established the dependence of the diffusion coefficient of Cu atoms in p-CdTe on the concentration N , which is clearly manifested at N ≤10 19 cm -3 .For example, when the Pb concentration changes by two orders of magnitude, i.e., from 10 20 to 10 18 cm -3 , the diffusion coefficient increases from 2•10 -13 to 1,8•10 -9 cm 2 •s -1 , almost by four orders of magnitude, at 573 K.Moreover, the increase in DT is mainly provided by increasing D 0 , since the activation energy of diffusion of copper atoms in this case changes insignificantly, only by 0,07÷0,08 eV, and becomes Q = 0,55÷0,56 eV.
The presented experimental results confirm the correctness of the proposed model of diffusion of Cu atoms, i.e., diffusion mechanism with the association Cu Pb .Indeed, at concentrations N ≤5•10 18 cm -3 in p-CdTe films, extra Cu atoms appear that are not bound in complexes, which begin to diffuse through other channels, among which dissociative diffusion is most likely, since free vacancies of cadmium atoms V Cd are formed.
Recombination parameters were determined on p-CdTe<Pb> samples with different Pb content: diffusion length L p , minority carrier lifetime τ p , and surface recombination rate S.
To measure L P in CdTe, a heterostructure with an upper optical window from a wide-gap semiconductor CdS was formed by vacuum deposition in a quasi-closed volume with an area of 1 cm 2 according to the technology described in [18].The front contact, from the side of which illumination is provided, is made of indium deposited in a vacuum of ~10 -5 Torr in the form of a comb.In this case, the width of the contact strip was 0.8 mm, and the distance between the strips was ~2 mm.The back contact was a molybdenum substrate.The deposited indium contact on CdS was connected to the heterojunction in the blocking direction.
L p was measured by the diffusion method described in [19], as well as by the method [20], including the measurement of the photocurrent depending on the absorption depth α -i at a constant intensity F in the region of the intrinsic absorption spectrum.Both methods give almost identical results.
At high concentrations of Pb (N = 5•10 19 ÷10 20 cm -3 ) in p-CdTe<Pb>, the electron diffusion length reaches its maximum value, ≌60 µm.With a decrease in N Pb , the value of L p also decreases at N Pb = 10 18 cm -3 , L p ≌14 µm.
From the short-wavelength region of the photocurrent spectrum I ph (hv) (hv≥2 eV), the surface recombination rate S was determined for holes at the p-n junction boundary adjacent to the CdS wide-gap filter.The results show that S depends on the Pb content in CdTe, and it increases with an increase in the Pb content, and S≌10 5 cm•s -1 is maximum at N Pb = 5•10 19 cm -3 .Further, as N Pb increases to 10 20 cm -3 , the surface recombination rate remains constant.Note that S for holes has the lowest value of ≌ 7•10 3 cm•s -1 in the absence of impurities of Pb atoms in the samples under study.
The lifetime τ p of minority current carriers was also determined on p-CdTe<Pb> samples by the phase difference method.At the same time, a certain correlation between τ p and N Pb was revealed.It has been established that τn reaches its maximum value ≌ 2•10 -6 s at N Pb ≌10 20 cm -3 , and at N Pb ≌10 18 cm -3 τ p =10 -7 s.
Thus, the presence of Pb atoms in large-block p-CdTe films leads to the formation of recombination centers with sharply different electron and hole capture cross sections, the ratio of which is directly dependent on the N Pb concentration.These results do not contradict the data obtained in [21].
The diffusion and recombination parameters of control samples of large-block p-CdTe films with ρ ≌ 10 3 -10 4 Ω•cm, in which there are no Pb atoms, have also been studied.The control p-CdTe films and the p-CdTe<Pb> films were synthesized in identical technological modes, the only difference being that the control p-CdTe films were grown on mica substrates, while the p-CdTe<Pb> films were grown on substrates with an impurity of Pb atoms, of which, during the synthesis, Pb atoms were doped into growing films.
As for the recombination parameters, they are low in p-CdTe control samples and correspond to the literature data, for example, L p = 0,5÷0,6 mkm and τ p = 10 -8 ÷ 5•10 -9 s coincides with the results [20].CONCLUSIONS Thus, by introducing impurities of Pb atoms, it is possible, firstly, to control the diffusion rate of copper Cu atoms in p-CdTe films, this opens up wide opportunities for using thin-film solar cells with Cu 2 Te-CdTe and Cu 2 S-CdS (ZnCdS) structures in terrestrial conditions.Secondly, the possibility of controlling the charge states of recombination centers in large-block p-CdTe films by introducing atomic impurities.Pb makes it possible to obtain semiconductor base materials with desired properties, i.e., given values of the microparameters Ln and τn, which is extremely important in materials science, for the microelectronic and semiconductor industries, especially for the creation of thin-film solar cells.

Figure 2 .Figure 3 .
Figure 2. The distribution profiles of the concentration of labeled 64 Cu atoms in p-CdTe polycrystalline films Figure 3. Calculated curves of the concentration distribution of impurity atoms over the thickness of the films at the constructed time t=4 h depending on the diffusion coefficient

Figure 4 .
Figure 4. Temperature dependences of the concentration of doped impurity atoms (a), and the diffusion coefficient (b)The numerical value of the coefficient А is determined by the impurity diffusion mechanism, А = 9.6•10 -11 cm 2 •s -1 during the diffusion of copper atoms in large-block p-CdTe films.Approximately for semiconductor materials, according to[11],

Table 1 .
Electrophysical parameters of p-CdTe<Pb> films at a temperature of 300K