Infrared High-Index Coating Materials, PbTe and Pb1−xGexTe: Properties and Applications

3.1. Low-temperature dependence of mid-infrared optical constants of layers of Pb_1−xGe_xTe

Although many investigations, both theoretical and experimental, have been carried out on the mechanism of ferroelectric phase transition of Pb_1−xGe_xTe, the investigation into the optical constants (refractive index n and absorption coefficient k) of the layers of Pb_1−xGe_xTe as a function of temperature remains to be done [33].

In our investigation, a layer of Pb_1−xGe_xTe was deposited on a silicon wafer using molybdenum boat heating the ingot of Pb_1−xGe_xTe (x = 0.12), of which composition was analyzed using proton-induced X-ray emission (PIXE) at the NEC 9SDH-2 pelletron tandem accelerator and can be represented with Pb_0.94Ge_0.06Te. The optical transmission spectra of the layer were measured using a Fourier-transform infrared spectrometer (BIO-RAD, FTS-40) in the range of 4000–400 cm⁻¹ at normal incidence between 80 and 300 K accompanied by using a bath cryostat (Oxford, DN1704). The optical constants of the layer were determined through the fitting of transmission spectra recorded at different temperature using the Lorentz-oscillator model as the dispersion model for the complex frequency dependent dielectric functions.

As a consequence, the temperature dependence of optical constants can be obtained at low-temperature in the spectral range of 2.5–8.5 μm. It can be found that the layer of Pb_1−xGe_xTe has a refractive index with a value of 5.350–6.000 corresponding to different measured temperatures in the spectral range of 4.0–8.5 μm, in which dispersion originated from the Reststrahlen and the absorption edge can be negligible. At room temperature, the layers of Pb_1−xGe_xTe have a value of refractive index approaching to that of layers of PbTe. A conclusion can be drawn that Pb_1−xGe_xTe is also an infrared high-index coating material.

In Figure 4(a), the change of refractive index of the layers of Pb_0.94Ge_0.06Te as a function of both wavelength and temperature was shown. It can be seen that the maximum value of refractive index occurs at 150 K, which can be regarded as the results of increased lattice polarizability that is an indication of the ferroelectric nature of the phase transition. Therefore, a conclusion can be drawn that anomalies in the refractive index, similar to those in the electrical resistivity and specific heat, emerge at the Curie temperature TC of the layers of Pb_0.94Ge_0.06Te. In Figure 4(b), the temperature coefficient of the refractive index, dn/dT, of the layers of Pb_0.94Ge_0.06Te is given, from which one can find that the value of dn/dT is 20.006–0.002 K⁻¹ in the spectral range of 3.0–8.5 μm at all measured temperatures.

An empirical formula for the temperature coefficient of refractive index in the spectral range of 4.0–8.5 μm can be expressed as Eq. (3):

where

AT=−0.05964+0.00156T−1.41679×10−5T2+5.24258×10−8T3−6.76599×10−11T4; BT=247.15385−6.75508T+0.07137T2−3.69672×10−4T3+9.40269×10−7T4−9.37957×10−10T5; CT=156.18266−4.49072T+0.05023T2−2.65423×10−4T3+6.6734×10−7T4−6.44758×10−10T5.

3.2. The stable narrow bandpass interference filters without temperature induced wavelength shift

When the ambient temperature varies, the performance of an optical thin-film interference filter will be also changed, such as the shift of center wavelength and the deterioration of peak transmission [34, 35, 36]. In particular, when a long wavelength infrared narrow bandpass filter is used in the spaceborne remote sensing instruments, the change of its spectral characteristics, which will lead to the difficulty to sustain the precision radiometric measurements from space, is not acceptable [37]. Addition of an auxiliary temperature control to the filters is not practical in order to maintain its stable optical performance in spaceborne remote sensing systems.

There are two factors that cause the shift of wavelength accompanied by the change of ambient temperature. One is the temperature-induced variations in the indices of refraction of the layers, and another is the variations in the physical thicknesses of the layers. Since the bulk temperature coefficients of linear expansion are an order of magnitude smaller than the temperature coefficients of the indices of refraction for substances similar to those usually employed for thin-film interference filters, it may be speculated that the shift of wavelength should be ascribed to the variations of temperature coefficients of the indices of refraction of the layers [38].

As far as the infrared filters employed in the spaceborne remote sensing systems are concerned, the convenient materials used for the low-index layers are either ZnS (2.2) or ZnSe (2.3). Moreover, Seeley et al. [39] modeled the sensitivity of the narrow bandpass filter to the change of temperature, showing that the spacer and the next two adjacent layers are dominant contributors relative to the other layers (and stacks). Therefore, when a negative shift in PbTe resulting from the negative temperature coefficient of refractive index is suitably combined with a positive shift in ZnS (or ZnSe) from its positive coefficient, temperature-invariant compensation becomes possible; namely, to achieve a negligible wavelength shift with temperature.

However, as a matter of fact, the temperature coefficient of refractive index of PbTe cannot exactly compensate for that of ZnS (ZnSe). Therefore, another solution to the problem is to seek a coating material of which the temperature coefficient of refractive index can be tuned.

Since the maximum value of refractive index of layers of Pb_1−xGe_xTe occurs corresponding to the structural phase transition, as a consequence, at the designated low-temperature, the temperature coefficient of refractive index of layers of Pb_1−xGe_xTe can be tuned from negative to positive by varying the Ge composition, that is, the layers of Pb_1−xGe_xTe with the specific composition may be used as the high-index layers in the thin-film interference filters.

Since the component elements in a multicomponent alloy system will evaporate at a different rate, which causes changes in compositions of layers relative to the evaporants, and it is in great necessity to designate directly the compositions in evaporated layers of Pb_1−xGe_xTe. For example, the corresponding stoichiometry of evaporated layers can be expressed by the formula (Pb_1−xGe_x)_1-yTe_y.

In Figure 5, the spectral characteristics of a simple one-cavity Fabry-Perot filter on a Ge substrate was demonstrated in the temperature range of 85–300 K, which was designed with peak wavelength of 11.30 μm and fabricated using ZnSe as the low-index layer. For its high-index layers, the ingots of Pb_1−xGe_xTe (x = 0.21) were used as the evaporants, from which the layers with corresponding stoichiometry of (Pb_0.86Ge_0.14)_0.46Te_0.54 can be obtained using molybdenum boat evaporation. It can be observed that when ambient temperature changes from 300 to 85 K, a shift of peak wavelength of 0.05935 nm K⁻¹ has been achieved for this narrow bandpass interference filter.

3.3. Homogeneity of composition in evaporated layers of Pb_1−xGe_xTe

It is commonly believed that the existence of inhomogeneity of composition in layers of Pb_1−xGe_xTe will have a disadvantageous influence on the performance of thin-film interference filters, because the existence of graded Ge concentration profile in Pb_1−xGe_xTe layers will lead into the coexistence of ferroelectric and paraelectric phases at a fixed temperature associated with phase transition as a function of Ge concentration and temperature [40]. Although Partin [41] observed the Ge concentration profile in the layers of Pb_1−xGe_xTe grown on (100) oriented PbTe single crystal by molecular beam epitaxy from PbTe, GeTe, and Te source ovens, to the author’s best knowledge, it has still not been clarified whether or not a Ge concentration gradient exists in the layers of Pb_1−xGe_xTe evaporated directly from bulk alloys. Therefore, the investigation on compositional depth profile in evaporated layers of Pb_1−xGe_xTe is of a great significance.

In our investigation, the layers were deposited on silicon wafers using molybdenum boat heating the ingots of Pb_1−xGe_xTe, of which compositions were analyzed using energy-dispersive X-ray analysis (EDAX) in a Hitachi S-520 scanning electron microscope. Depth distribution of elements was measured by using a Microlab 301F Scanning Auger Microprobe (SAM) system combined with a discontinuous ion sputtering mode at a base pressure below 8.0 × 10⁻⁸ Pa.

The results from our investigation are not in agreement with those reported by Partin. In Figure 6, a representative compositional depth profile was illustrated for an evaporated layer of Pb_1−xGe_xTe, of which the measured elemental concentrations are 42.92 ± 0.55 for Pb, 54.96 ± 0.90 for Te, and 2.12 ± 0.74 for Ge, respectively. It can be observed that the Ge concentration at the surface is lower than that of the stoichiometry, meanwhile, the Pb concentration was distinctly higher. However, the Ge concentration increases from a Ge-deficient state at near surface to the Ge-rich one at near substrate. At same depth, all concentrations of elements remain balanced, that is, the increase of the Ge concentration must be accompanied with a decrease of the Pb concentration. After removal of the upper layers with a thickness of about 300 nm, the layer of Pb_1−xGe_xTe transforms to the Te-deficient characteristic from the Te-rich one. In addition, a stepwise change of elemental concentrations in the depth profile cannot be detected in the layer.

In fact, the mechanism of evaporating from an alloy is much more complicated than that from a single metal because of the different vapor pressures of their individual components. It is much more possible that Ge partial pressure will change with the increasing of deposition time because Ge is more volatile than other components, Pb and Te, in the Pb_1−xGe_xTe alloy. Thereby, Ge concentration in the evaporants will be gradually depleted and the deposition process will result in a compositional gradient in the layers. As a consequence, the results obtained in the compositional depth profiles in evaporated layers of Pb_1−xGe_xTe can be reasonably explained.

Because it is often problematic to maintain a desired alloy in layers and over larger substrate surfaces, therefore, an empirical procedure may be used to determine how to control the composition of the layers by adjusting the composition of the bulk alloy.

3.4. Compositional dependence of absorption edges in evaporated layers of Pb_1−xGe_xTe and tunable infrared short wavelength cutoff filters

An ideal cutoff filter should have small losses in the transmission region and high attenuation or reflectance in the rejection region over an extended spectral range, which can be carried out depending on interference or absorption [42]. Therefore, a cutoff filter may take a number of different forms, such as interference cutoff filters and thin-film absorption filters.

A thin-film absorption filter usually has very high rejection in the stop region and consists of a layer of material which has an absorption edge at the required wavelength. It is usually short wavelength cutoff in character. A layer of semiconductor that exhibits a very rapid transition from opacity to transparency at the intrinsic absorption edge is a good example to make an excellent thin-film short wavelength cutoff absorption filter. Nevertheless, as far as a layer of a certain semiconductor, such as Ge or PbTe, is concerned, the absorption filter is inflexible in character and the cutoff wavelength cannot be tuned, because of their fundamental optical properties. In order to take advantage of the characteristic of deep rejection of thin-film absorption filters, it will be of great significance to find out a semiconductor material, of which the absorption edge position can be tuned by means of controlling the composition of its layers, to fabricate the absorption filter.

In our investigation, the layers were deposited on silicon wafers using molybdenum boat heating the ingots of Pb_1−xGe_xTe, of which compositions were analyzed using energy-dispersive X-ray analysis (EDAX) in a Hitachi S-520 scanning electron microscope. The optical transmission spectra of the layers were measured in the spectral range of 2.5–25 μm using a Perkin Elmer Spectrum GX Fourier-Transform Infrared Spectrometer with a resolution of 8 cm⁻¹ at normal incidence. The crystallographic structures of the layers were investigated by X-ray-diffraction (XRD) using Cu K_α radiation on a D/max 2550 V diffractometer with an accuracy of 0.02°. The single-phase nature and polycrystalline of the layers were revealed. The composition dependence of positions of the fundamental absorption edges in the evaporated layers of Pb_1−xGe_xTe was explored. The aim is to elucidate that the tunability of the cutoff wavelength in thin-film absorption filters can be reached if the controllability of the composition of constituent layers can be carried out.

It is revealed that for the evaporated layers of Pb_1−xGe_xTe with an identical Te concentration, the absorption edges will shift toward short wavelength with the increase of Ge concentration x in layers, an example was illustrated in Figure 7(a); furthermore, for those with a similar Ge concentration within a small range of deviation, the edges will also shift toward the short wavelength with Te concentration approach to stoichiometry, an example was illustrated in Figure 7(b).

Our investigation indicates that if the controllability of the composition of evaporated layers of Pb_1−xGe_xTe can be carried out, it will be possible to fabricate an infrared single-layer thin-film absorption filter with the short wavelength cutoff at the required wavelength.

3.5. Compositional congruency, correlation and high-pressure polymorphism in electron-beam evaporated layers of Pb_1−xGe_xTe

Currently, evaporation, as a physical vapor deposition process, is still principally used in optical coating industry, because of its simplicity, flexibility and relatively low cost; moreover, the enormous number of existing deposition systems [3]. However, it may be undesirable from a practical viewpoint to evaporate compound semiconductors from a single source because the vapor compositions of compound semiconductors are usually different from their nominal compositions. As a consequence, the stoichiometry of the layers will differ generally from the evaporants [43].

In our investigation, the ingots with different Ge concentrations were chosen and evaporated using the molybdenum boat heating; meanwhile, the ingots with five Ge concentrations, x = 0.10, 0.14, 0.17, 0.20, and 0.22, together with PbTe, were evaporated using electron-beam heating. The stoichiometry of the evaporated layers was determined using the energy-dispersive X-ray analysis from a Horiba EX-220 energy dispersive X-ray microanalyzer (model 6853-H) attached to a Hitachi S-4300 cold field emission scanning electron microscope (FE-SEM) without coating the surfaces.

In Figure 8(a), for the layers of Pb_1−xGe_xTe evaporated using electron beam heating, the change of Ge and Te concentration, that is, y and z, with the increasing of Ge concentration in evaporants, x, was illustrated. Similarly, in order to make a clear comparison, for layers evaporated using molybdenum boat heating, the dependence of y and z on x, was also described in Figure 8(b).

It can be observed that Ge concentration y in layers evaporated using electron beam heating is approaching to Ge concentration x of the ingots. A green line that designates an exact linear relation y = x serves as a guideline for the eye in the figure. In comparison with the compositional dependence presented in Figure 8(b) for the layers evaporated using molybdenum boat heating, therefore, it can be concluded that electron beam evaporation is a more effective congruent-transfer technique to deposit the layers of Pb_1−xGe_xTe directly from the original Pb_1−xGe_xTe evaporants.

Furthermore, with an increasing of Ge concentration, it can be obviously observed that concentration of tellurium z gradually decreases in the layers evaporated using both electron beam and resistance heating. As a consequence, the Te-rich characteristics presented in the layers will shift into the Te-deficient one with the increasing of Ge concentration.

Perhaps, the congruency in the process of evaporation of Pb_1−xGe_xTe using electron beam heating of ingots can be attributed to the “ablation” characteristics of electron beam evaporation and lower thermal conductivity of the PbTe-based alloy. A significant feature of an electron beam evaporator is its ability to concentrate a large amount of power onto a small area of the surface of evaporants, independent of materials being heated. Usually when the evaporants are heated, water cooling is supplied to the crucible to remove the heat which escapes by conduction through the evaporants and liner. In addition, it has been well accepted that PbTe-based alloys constitute a category of materials with excellent thermoelectric figure of merit, zT, because PbTe has a rather lower value of thermal conductivity (2.3 W m⁻¹ K⁻¹) [44]. Therefore, when electron beam is focused on the surface of the ingots of Pb_1−xGe_xTe, the heat is hardly conducted out and a great temperature gradient is established in the ingots accompanied by the water-cooled crucible. As a consequence, due to the absorption of high energy density by only a small fraction of the ingots irradiated by electron beam, the evaporation behaves like “ablation” with a nonequilibrium nature, at which energy absorbed is much higher than that needed for evaporation, namely, vaporization is independent on the vapor pressures of the constituents.

Furthermore, in our investigation, an assumption can also be proposed to explain the compositional correlation observed in the layers of Pb_1−xGe_xTe. It has been well known that the ionic radii of Ge and Pb are 0.73 and 1.2 Å, respectively; therefore, Pb_1−xGe_xTe belongs to a class of alloys in which a substitutional atom has a size significantly smaller than that of the host atom it replaces. In such a “diluted” alloy, the addition of even a very small number of substitutional atoms will lead to a substantial change in their physical properties. For example, although PbTe itself is not ferroelectric, the addition of even 0.05% Ge to PbTe will induce a structural transition [24]. It is obvious that in such a ternary alloy, due to the substitution of Ge ions for Pb ions, two types of nearest-neighbor bonds, Pb—Te and Ge—Te, must be concerned. Thus, if only the strength of a Ge—Te bond is weaker than that of Pb—Te bond, the amount of Te ions which are incorporated into the system of Pb_1−xGe_xTe will decrease with the increasing of Ge concentration in the layers.

Our assumption can be supported from the experimental data of bond energies reported by Rao and Mohan [45]. It is pointed out that Ge—Te has a bond energy of 1.87 eV, whereas Pb—Te has a bond energy of 1.90 eV; therefore, Ge ions cannot “hold” Te ions as tight as Pb ions do. When the more Ge ions are placed on the Pb site, the more Te ions will “escape.” Therefore, the gradual decreasing of Te concentration will make a Te-rich characteristic in layers shift into a Te-deficient one.

In Figure 9, the patterns of XRD analysis were demonstrated for the layers evaporated using electron beam heating the ingots with Ge concentration x = 0.10, 0.14, 0.17, 0.20, and 0.22, respectively. It is worthwhile to note that the results for the layers evaporated from ingots with x = 0.22 have some important features. First of all, a new peak can be found, which corresponds to the strongest (111) reflection of rock salt-type structure of GeTe (space-group oh5) as referred in JCPDS card number 65-0315. Although the intensity is weak, it can be revealed that a secondary phase GeTe emerges in the layers. Furthermore, the strongest reflection is different from that in the layers of Pb_1−xGe_xTe with a high temperature paraelectric phase. A strongest peak is expected to occur at 2θ = 27.58°, which stands for the (200) plane in PbTe and discloses a highly textured with (001) plane parallel to the silicon substrate. However, the strongest reflection can be attributed to a (111) reflection of substrate silicon (space-group oh5) and (104) reflection of a highly symmetric body-centered cubic (bcc) structure Te-V (space-group oh9). In order to make a clear elucidation, the position and intensity of reflections given in the JCPDS cards for rock salt-type PbTe and bcc structure Te-V were also added in Figure 9, respectively. Therefore, it can be concluded that high-pressure phases for GeTe and Te compounds are also presented in evaporated layers of Pb_1−xGe_xTe, which are commonly generated at the higher pressure applying hydrostatic pressure (such as diamond anvil cell) or shock loaded techniques. Perhaps, the transition from the disorder to the order in the system of Pb_1−xGe_xTe, which is responsible for ferroelectric phase transition, induces high pressure polymorphism in evaporated layers. Of course, more evidence is furthermore needed.

3.6. The mechanical properties of evaporated layers of Pb_1−xGe_xTe

As far as the single-crystal of PbTe is concerned, the microhardness is relatively a constant of ∼30 HV for the various carrier concentrations [46, 47]. To the author’s best knowledge, no data is reported on hardness of layer of PbTe. However, a layer of PbTe is so soft that it can be scratched easily. As a consequence, an infrared thin-film interference filters consisting of the layers of PbTe is not robust enough to withstand the damage originated from standard wafer dicing processing, such as “from wafer to chips,” even if more robust low-index materials, like ZnSe or ZnS, are chosen as an outermost layer.

Therefore, as a solution to the problem in integrating of the standard semiconductor process into the mass-production of infrared thin-film interference filters, a new infrared high-index coating material is needed to deposit the more robust high-index layers to withstand the damages in wafer dicing processing. It is necessary to investigate the mechanical properties of evaporated layers of Pb_1−xGe_xTe.

In our investigation, the layers of Pb_1−xGe_xTe were deposited on silicon wafers using electron beam evaporation, of which compositions were analyzed using energy-dispersive X-ray analysis (EDAX) in a Horiba EX-220 energy-dispersive X-ray microanalyzer (model 6853-H) attached to the FE-SEM without coating the surfaces of the layers. Nanoindentation measurements were performed using a Nano Indenter G200 with a three-side pyramidal Berkovich diamond indenter of 50 nm radius under the continuous stiffness measurement (CSM) option. At least 10 indents were performed on each layer with a maximum load of 13 mN, accompanied with a corresponding indentation depth no more than 500 nm. Following the analytic method proposed by Oliver and Pharr [48], the average values and standard deviations of the hardness and Young’s modulus of thin films were extracted from the load–displacement results.

It can be revealed that the layers of Pb_1−xGe_xTe have greater values of hardness and Young’s modulus compared with those of PbTe. For example, from Figure 10(a), it can be found that the hardness of the layer of Pb_0.83Ge_0.17Te is three times as great as that of PbTe; meanwhile, Young’s modulus is twice greater than that of PbTe, as seen in Figure 10(b). Therefore, a conclusion can be drawn that a mechanically robust infrared high-index layer can be obtained using Pb_1−xGe_xTe as evaporation materials.

These mechanical behaviors of layers of Pb_1−xGe_xTe can be linked to the ferroelectric phase transition. Moreover, the strength loss in the layers can be also explained in light of strong localized elastic-strain fields in concentrated solid solutions.