Influence of Germanium Substitution on the DC Electrical Properties and Energy Density of States in Pb_50−xGe_xTe₅₀ Ternary Chalcogenide Alloys

1 Introduction

Chalcogenide materials containing one or more elements from Groups IV to VI (elements such as tellurium (Te), selenium (Se), sulfur (S), or polonium (Po)) have recently received considerable attention due to their unusual properties, including anharmonic effects, poor lattice thermal conductivity, unparalleled thermoelectric performance [1,2], complex band structures, high chemical power coefficient, chemical stability, and low toxicity [3,4]. Some of these compounds exhibit paraelectricity, ferroelectricity, and superconductivity [5,6,7].

Chalcogenide materials have garnered significant interest across various industrial sectors due to their versatile properties. However, once materials with the desired properties are obtained and tailored to specific uses, significant progress is expected. Although these materials will enable many new applications, not all of their properties can be derived directly from binary materials or manufactured raw components. Therefore, combining two or more elements to form an alloy is the most common and simplest way to modify their properties [8].

The alloys of tellurium based on Germanium have a large stoichiometric deviation of the tellurium element. The primary non-chemical defects are divalent ionic vacancies of metals. Due to such a stoichiometric deviation, GeTe always portrays sp-type conductivity. Doping of GeTe with electrochemical impurities of donor type is required to decrease the concentration of holes and attain the best thermoelectric characteristics. When GeTe is dissolved in Bi2Te3, it serves as a donor. Better performance in thermoelectric should be achieved with (Pb, Sn)1−xGe2Te alloys [9,10].

Such alloys may be engineered to have better electronic properties, and have lower lattice thermal conductivity than SnTe, PbTe and GeTe. Moreover, these alloys are able to reduce the phase transition temperature to lower than operating temperature of the thermoelectric device to enhance stability [11]. Partial replacement of lead with germanium was selected to: (i) tune the energy band gap (ii) capability to control energy band gap, (iii) implementation of directed average lattice defects in the system and (iv) improvement in conduction process.

Studying the composition dependence of these alloys is crucial, as it allows researchers to precisely map the solubility limits and identify the exact stoichiometric ratios that yield optimal carrier mobility and minimal thermal conductivity for device integration. It makes Pb50−xGexTe50 alloys even more valuable in high-end applications, as the adjustment of both electrical and structural properties can be precisely done. The study of the effects of germanium on electrical conductance and energy density inter Pb50−xGexTe50 alloys may be artificially chosen perhaps because germanium doping can greatly change the conduction behavior and electronic structure in materials. One can vary, by adding germanium to the alloy matrix, properties such as density of states and transport of charge carriers that can be studied [12], which are important in order to investigate the characteristics of a semiconductor material. The specific electronic properties of the Ge can produce an effect on energy band gap and interferes with distribution of both well-localized and extended energy state (one of the most important factors that control the electrical conducting capabilities) [13].

Hence this study is intended to investigate systematically the effect of lead (Pb) replacement by germanium (Ge) on the DC electrical properties and the energy densities of states in ternary Pb50−xGexTe50 alloys. By preparing the compositions with different germanium concentrations (x = 5, 10, 15, and 20 at. %) and studying their temperature-dependent conductivities (for the range 290–475 K) in order to provide information on the conduction mechanism. The significance of this work is to understand how doping by Ge can be used in order to tailor the energy band gap, induce controlled defects and heavily modify its electronic structure. Finally, this work investigates the scope for control over both electrical and structural properties of such chalcogenide alloys for high application-centred, advanced semiconductor and optoelectronic devices.

2 Experimental Details

The ternary mixture of Pb50−xGexTe50 was produced through melting point technique. Pb50−xGexTe50 alloys containing germanium concentrations of 5, 10, 15 and 20 were produced using high-purity lead, tellurium and germanium powders, 99.999 percent pure. The raw materials were weighed according to their atomic mass percentages of the elements and the concentration of the elements used in the alloy in order to achieve uniform proportions. The process of mechanical grinding was conducted using a planetary ball mill (Model PM 100, RETSCH, Germany) for 50 min was conducted using a mechanical vibrator” or “ball mill in 50 min. Each sample was finely crushed and pressed into pellets under a pressure of 5 t/cm2 using a standard hydraulic press (Specac Atlas 15T, UK). The samples were put in separate capsules that were vacuumed at 10−3 bar and then sealed. The method was employed to maintain quality of the end alloy, avoid contamination and have a perfect control over the levels of activation. The capsules were put in an electric furnace and the samples heated to 1100°C in five hours. Following heat treatment, Following heat treatment, the sealed vacuumed quartz capsules were rapidly quenched in air. The material remained strictly sealed inside the vacuumed environment (10−3 bar) during the entire cooling process to completely prevent ambient exposure, oxidation, and the formation of oxygen vacancies. The ingots were pressed into fine and pressed them with a hydraulic press in 6 t per square centimeter. The samples were shaped into 1.5 cm diameter discs and 3 mm in thickness. The crushed samples were put back in the furnace at 200°C with 2 h of time until they cooled to room temperature. The samples were cooled and then ready to analysis. This meticulousness allowed even distribution of germanium in the Pb50−xGexTe50 matrix allowing to characterize the impact of germanium on the conduction mechanisms and the structural properties. Measurements of electrical resistivity that are dependent on temperature [14,15].

Surface morphology analysis was performed to study the structural properties of the sample surfaces. The electrical resistivity is measured by clamping the sample between two copper electrodes using a special designed holder and then the sample should be put in an electric furnace as seen in Fig. 1. A Keithley-type electrometer (Model 2400 Source Meter, Keithley Instruments, USA) is connected to measure the voltage and current passing via the sample and give proper readings. To have an accurate temperature reading, the furnace temperature is steadily raised in 10 K steps until it attains a temperature of 475 K. Current and voltage are recorded at every temperature step and electrical resistivity and conductivity of the sample is determined versus temperature. This arrangement guarantees that the data of conductivity analysis is accurate. The estimated instrumental error for electrical resistivity measurements was within ±3%, and temperature control accuracy was ±1 K.

Figure 1: A schematic diagram of the electrical resistivity measurement apparatus.

3 Results and Discussion

The surface morphology of the prepared Pb50−xGexTe50 alloys was probed to determine the structural evolution caused by the substitution of germanium probed by scanning electron microscopy (SEM; JEOL JSM-IT500, Japan). Fig. 2 shows the changes in microstructures as a function of the compositional spectrum. The micrographs reveal a amorphous structure characterized by granular agglomeration and glassy matrix formations. As seen in Fig. 2a for the low-concentration specimen (x = 5), the surface is relatively porous, made up of smaller and fairly irregularly shaped grains, which are indicative of a stochastic chalcogenide matrix. As the germanium fraction increases to x = 10 (Fig. 2b) and x = 15 (Fig. 2c), there is a strong change in the appearance of the surface topology: the density of voids decreases significantly, and a qualitative tendency toward the refinement of grains and an increase in inter-granular connection is observed. For the highest concentration at x = 20 (Fig. 2d), this matrix densification is highly pronounced. This densification is critical, as it likely facilitates charge transport processes by reducing the scattering centres related to the structural disorder. These enhancements in the grain packing and attenuated porosity on the SEM images are consistent with the later electrical performance measurements that support the speculation that Ge-doping is an effective suppressor of structural randomness and improves conduction pathways.

Figure 2: Scanning Electron Microscopy (SEM) micrographs exhibiting the surface morphology and microstructural evolution of Pb_50−xGe_xTe₅₀ ternary alloys with different Germanium concentrations at: (a) x = 5, (b) x = 10, (c) x = 15, and (d) x = 20.

The DC resistance and conductivity of four samples of a Pb50−xGexTe50 ternary alloy at the concentrations of germanium x = 5, 10, 15, and 20, as a function of temperature, were investigated in the temperature range 290–475 K. The experiment data was well captured in this temperature range using the thermally activated process model.

All alloys exhibit semiconductor behavior, i.e., their conductivity increases with increasing temperature, as shown in the thermal conductivity curves. This indicates that the higher the germanium concentration in the alloy, the higher the electrical conductivity. This indicates that the electrical conductivity of the Pb50−xGexTe50 system increases as the germanium concentration increases. It is also noted that there is a difference or variation in the behavior of the curves with different temperature ranges, depending on the conductivity patterns at different temperature ranges. Conduction may be due to electrons bouncing between energy levels near the Fermi level, which occurs at low temperatures, or jumping between distant levels at medium and high temperatures. These results are consistent with the Mott and Davis model, which assumed that continuous electrical conduction in random semiconductors (random chalcogenides) has three conduction mechanisms (at different temperatures: low, medium, and high) according to the following relationship [16,17]. σ=σ01e−ΔE1kβT+σ02e−ΔE2kβT+σ03e−ΔE3kβT(1) where σ 01 , σ 02 , and σ 03 are the pre-exponential factors, Δ E 1 , Δ E 2 , and Δ E 3 are the activation energies for DC conduction, T is absolute temperature and k β is Boltzmann’s constant.

With increasing germanium concentrations, the electrical conductivity of Pb50−xGexTe50 alloys increased significantly (x = 5, 10, 15, 20). All alloys exhibited semiconducting behavior, with conductivity growing considerably with temperature, according to the data. Three distinct conduction regions were identified by the relationship between conductivity and temperature: low, intermediate, and high temperatures [18]. Electrical conduction between localized states near the Fermi level determines conductivity in the low-temperature range. Electrical conduction in the intermediate-temperature region dominated conduction at low temperatures, which was influenced by the high density of band-tail states resulting from germanium doping. The transfer of charge carriers between extended states increased electrical conductivity at high temperatures, while germanium increased the activation energy required for these changes. The germanium doping also decreased the width of the energy tail (ΔE), which improved the hopping distances (R) and the Atomic distance (a) [19]. As shown in Table 1 and Table 2.

By calculating the logarithm of both sides of Eq. (1), the relationship between ln logarithm σdc and 1000/T can be plotted, identifying three distinct regions with different slopes. These regions show the dominance of distinct conduction mechanisms in specific temperature ranges. These slopes correspond to the three terms in Eq. (1), which represent different conduction modes [20]. Three distinct regions can be seen in the plot of the relationship between logarithm σdc and 1000/T when examining ternary alloy samples of Pb50−xGexTe50 graphically with Germanium concentrations x = 0, 5, 10, 15, and 20, as shown in Fig. 3.

Figure 3: ln σ d c as a function of (1000/T) for Pb_50−xGexTe₅₀ ternary alloy samples with Germanium concentrations x = 5, 10, 15, and 20.

The curves generated by three linear parts by each of the four samples were plotted in the graph of Fig. 3 (representing the relationship between the logarithm of the conductivity and 100). At low temperature (290–340 K), the original conduction zone does not need much energy to allow the electrons to hop between Fermi levels. Second conduction is electron hopping between the tail of the density of states by mechanisms involving localized states in the intermediate temperature range between 340 and 390 K and finally conductors are accessed by transition to the third conduction region at high temperatures between 390 and 475 K where transitions between extended states of the conduction band and the valence band occurs. It is possible to observe three distinct linear regions of the lnsigma dc variation vs. 1000/T per alloy sample. The steepnesses of these lines are computed to obtain the two activation energies ΔE1, ΔE2 and ΔE3 at every temperature interval. Also, using the extrapolation of each line to the intercept with the y-axis, the pre-exponential terms σ01, σ02, and σ03 can be obtained. The factors before the exponential are determined by values at which each of the lines crosses the y-axis, which are lnN00N with N being 1, 2 or 3. Energies of activation and pre-exponential factors of each of the samples in each of the three temperature ranges were determined and have been tabulated in Table 1.

The high-temperature semiconductor region is considered to be the first one, which is located between 390 K and 475 K. This value is the initial term of Eq. (1). At this high temperature regime, the carrier density is equal to the intrinsic carrier density. The conductivity in this region is based on two key factors; sample temperature and lattice vibrations. The more the temperature is raised, the greater the number of free carriers in the material and the higher the conductivity of the material. The lattice vibrations however bring about phonon which interacts with the electrons, which results in the electron-phonon interactions. These interactions can decelerate the movement of electrons and take more energy to be activated. Consequently, the activation energy in the first region is significantly higher [21]. The latter section of the curves describes the intermediate range of temperature between 340 and 390 K. This area is semiconducting in nature. In this range, the carrier and intrinsic carrier density are equal. The DC resistance in this region varies with the concentration, mean free path, and carrier mobility. This variation is due to the small crystal size and poor crystallinity. Conductivity decreases due to surface defects, dislocations, and structural distortions, which cause randomization in the crystal structure, leading to the emergence of levels within the energy gap at the tails of the conduction and valence bands, according to previous studies. The low-temperature range, extending from 290 to 340 K, is described as the third limit of the curves. The ionization of impurity atoms affects the conductivity of this region. Due to the thermally assisted movement of carriers between localized states at the Fermi level, conduction occurs at low temperatures between localized levels close to the Fermi level [21]. There is a distinct drop in the pre-exponential factor (σ02) for the x = 20 sample compared to the x = 10 and x = 15 compositions. This variation highlights that the optimal enhancement of transport parameters is bounded between x = 10 and x = 15, beyond which excessive Ge addition alters carrier mobility.

The density of extended states in the conduction and valence bands and the density of localized states in the tails of the energy bands and near the Fermi level within the energy gap were calculated using Eqs. (2)–(4) below given in, after substituting the pre-exponential factor ( σ 01 , σ 02 , and σ 03 ), for each sample parameters in Table 1, the electron charge ( e ), the phonon frequency ( ν p h ) set at 1013 s−1 [22], and the hopping distance ( R ) which is given by Eq. (5) [16,17]. Table 2 shows the calculations for all Pb50−xGexTe50 ternary alloy samples with Germanium concentrations x = 0, 5, 10, 15, and 20.

In chalcogenide glasses, especially those in which the group VI elements are present in large fraction, the valence band is made up of the lone pair electrons [22]. The first work on the effect of additives on the properties of V-VI alloys was by Kastner, who observed that the additives modify the tail width in the valence band. In particular, valence electrons that are located close to the more electropositive atoms have greater energies than the valence electrons located close to the more electronegative atoms [23]. Also, the alteration of the tail of the conduction band is due to the variation in the bond type in the alloy [24]. It is not always symmetrical that the band is broadened and it could lead to changes in the conduction band edge [18]. It, in its turn, affects the densities of localized states N(Eloc), extended states N(Eext), and states close to the Fermi level N(EF) [15]. These are manifested in the findings reported in Table 2 and Fig. 4 indicating the effects of the alloy composition on the electronic properties by changing state densities and band structure.

Figure 4: Densities of states as a function of Germanium concentrations for Pb_50−xGe_xTe₅₀ alloy samples with x = 5, 10, 15, and 20.

It is noted from Table 2 that all values of the extended and localized densities of states in the tails and near the Fermi level were significantly affected by the partial substitution of tellurium by germanium, as both the conduction and valence bands were affected by changes in the atomic sizes of the substituent elements [24]. This is because in chalcogenide glasses, the valence band consists of lone pair electrons [22,25]. The influence of additives on the properties of V-VI alloys was first discussed by Kastner, who observed that width of the valence band tail is influenced by the additives. Particularly the valence electrons that are located near electronegative atoms are found to be higher in energy than those near less electronegative atoms. In addition, changes in the conduction band tail result from differences in the types of bonds within the alloy [25,26]. The band width is not necessarily uniform and this can result in the shifts on the conduction band edge [25,26,27]. This further influences the densities of localized states N(Eloc), extended states N(Eext) and states near Fermi density N(EF) [28]. The latter are manifested in the findings which are provided in Table 2 and indicate how the alloy mixture influences the electronic properties by affecting the band structure and state densities.

Replacement of part of terylium by germanium has a strong impact on the energy density by altering the band structure, decreasing the band gap, and creating regulated defects. This adjustment customizes the densities of energy in the extended, localized and Fermi states. Parameters like tail width (ΔE) and hopping distance (R), interlayer spacing and other parameters associated with conductivity show significant variation with enhanced electronic properties and energy storage capabilities. In general, germanium doping increases electrical conductivity and energy densities of alloys studied and thus, they are promising candidates in the development of future semiconductor and optoelectronic devices [28,29]. The tails become narrower with an increase in concentration of germanium in Pb50−xGexTe50 alloys leading to a decrease in the randomness of the crystal structure as illustrated in Fig. 5 indicating the dependence of the width of the tails of the energy bands on the concentration of germanium.

Figure 5: Width of the tails (∆E) as a function of Germanium concentrations for Pb_50−xGe_xTe₅₀ alloy samples with x = 5, 10, 15, and 20.

Germanium doping significantly influences the electrical conductivity and energy density states of alloys by altering the electronic structure and conduction pathways. Germanium substitution decreases the energy gap, increases the density of extended states, and localizes them closer to the Fermi level, thereby improving the mobility of charge carriers. The exponential rise in electrical conductivity with temperature can be attributed to the rearrangement of alloy atoms and the reduction of structural randomness, aligning with the hopping mechanism in both localized and extended states within the conduction band.

The systematic enhancement in DC electrical conductivity observed for compositions up to x = 15 is attributed to the structural modification of the PbTe lattice, where the substitution of Pb atoms with smaller Ge atoms likely increases the local disorder and the density of localized states near the Fermi level (N(EF)). This modification facilitates carrier hopping and supports the premise that controlled doping optimizes electronic transport by tuning the band structure, as observed in recent investigations into chalcogenide alloys [30]. However, the distinct reduction in conductivity and the pre-exponential factor at x = 20 suggests that the Ge concentration has exceeded the solubility limit within the matrix. As explicitly demonstrated in Table 1, there is a sharp drop in the pre-exponential factor (σ01) for the x = 20 sample, which falls drastically from 5.1 × 10−3 (Ω·cm)−1 at x = 15 down to 1.4 × 10−6 (Ω·cm)−1 at x = 20. This severe decline provides clear evidence of a disruption in the conduction pathways. At this high concentration, it is hypothesized that the system approaches its solubility limit, potentially leading to local structural inhomogeneities or Ge-rich clustering as suggested in similar systems, which could act as scattering centers for charge carriers, creating structural inhomogeneities that act as scattering centers for charge carriers. This behavior does not support the continuity of the enhanced hopping mechanism observed at lower concentrations but instead aligns with the mechanism where excessive defect density and secondary phase precipitates drastically reduce carrier mobility and degrade overall transport properties [30].

The current results about the enhancement of the DC conductivity and the simultaneous structural upgrading with the rise of the Germanium content is in agreement with the latest trends that have been reported in similar chalcogenide systems. Germanium replacement increases the density of extended states, but suppresses structural disorder, which is consistent with our findings of reduced porosity and increased inter-granular connectivity in PbGeTe alloys [26]. The improvement in electrical performance caused by defect engineering through the Germanium doping is also in line with the findings of Zhao et al. (2025), who established that the addition of Germanium to the chalcogenide matrix is an effective way of tuning the electronic structure and enhancing charge-transport efficiency [31].

It is important to emphasize that the demarcation into low, intermediate, and high-temperature zones refers strictly to distinct electronic transport regimes governed by different activation mechanisms within the framework of the Mott and Davis model, rather than thermodynamic phase transitions.

4 Conclusion

This investigation into the DC electrical properties of Pb50−xGexTe50 ternary chalcogenide alloys successfully demonstrates that substituting lead with germanium significantly enhances the material’s electrical performance. The study confirmed that all alloy compositions exhibit characteristic semiconducting behavior, with electrical conductivity increasing as a function of temperature over the 290–475 K range. A key finding is the direct relationship between germanium concentration and electrical conductivity; as more germanium was added, the conductivity of the alloys systematically increased. Analysis of the temperature-dependent conductivity, guided by the Mott and Davis model, revealed three distinct conduction mechanisms operating in different temperature regions: carrier hopping between localized states near the Fermi level at low temperatures, hopping between band-tail states at intermediate temperatures, and transitions in extended states at high temperatures. Specifically, at high temperatures, the activation energy varied from 0.203 eV (x = 5) to 0.281 eV (x = 15), while the density of extended states increased from 2.655 × 1019 to 1.69 × 1021 eV−1 cm−3. The addition of germanium was found to fundamentally alter the electronic structure by increasing the density of states while simultaneously narrowing the band tail width, indicating a reduction in the material’s structural randomness. These findings underscore the efficacy of germanium doping as a method to precisely tune the electronic properties of these alloys, establishing them as highly promising candidates for the development of advanced semiconductor and optoelectronic devices.