The performance of an optical thin-film interference filter can be influenced by the change of ambient temperature. The peak or cut-off wavelength will shift and the pass-band shape and peak transmission will deteriorate due to the effects of varying temperatures. In particular, when the filter is used in light-wave communication systems or spaceborne remote sensing instruments, optical thin-film interference filter performance degeneration due to temperature changes is not acceptable. It becomes difficult to sustain the functional performance of non-dispersive narrow-band interference filters for precision spectroradiometric measurements from space [1]. It is not practical to add an auxiliary temperature control to a narrow-band filter in order to maintain its stable optical performance in spaceborne remote sensing systems.

There are two factors that cause the instability of the performance of a thin-film interference filter accompanied by the change of temperature: one is the temperature-induced variations in the indices of refraction of layers; another is the variations in the physical thicknesses of layers. Since the bulk temperature coefficients of linear expansion are an order of magnitude smaller than the temperature coefficients of refractive index for substances employed for interference filters, it may be speculated that the shift of wavelength should be ascribed to the variations of temperature coefficients of indices of layers [2].

By classical design, Optical interference filters typically consist of multiple homogeneous layers of two materials with low and high refractive indices, n_L and n_H. As far as the infrared interference filters employed in the spaceborne remote sensing systems are concerned, as a rule, the materials are lead telluride (PbTe) for high-index layers, and either zinc sulphide (ZnS) or zinc selenide (ZnSe) for low-index layers [3,4]. All materials are fully transparent over the infrared. The negative temperature coefficient is usual with filters having PbTe as one of the layer materials. This negative coefficient in PbTe is especially useful as it tends to compensate for the positive coefficient in ZnS or ZnSe.

Interestingly, although PbTe itself is not ferroelectric, the addition of even 0.05% Ge to PbTe induces the structural transition at the transition temperature T_c, which is a strongly nonlinear function of Ge concentration x, rising from 0 to 230 K from x=0.005 to 0.10 [5,6]. Moreover, the phase transition occurs at room temperature when x=0.18. Our previous investigations [7] revealed that there exists a maximum of refractive index in evaporated Pb_1-xGe_xTe thin films corresponding to the structural phase transition, which reflects an increase of lattice polarizability.

Since the temperature coefficient of refractive index of Pb_1-xGe_xTe layer is a function of temperature and Ge concentration, at the designated low-temperature, it can be tunable from negative to positive by varying x, and the specific composition may be use as the high-index layers in the thin-film interference filters. It is very possible to utilize the intrinsic property in the fabrication of shift-free infrared filters. An attempt has been presented in our previous paper [8] to fabricate a simple infrared narrow-band filter, in which Pb_1-xGe_xTe was substituted for PbTe. It was found that the low-temperature stability is obviously improved: in the temperature range of 80-300 K, the shift of peak wavelength with temperature is reduced from 0.48 nm.K^-1 to 0.23 nm K^-1; furthermore, the peak transmittance of filter fabricated with Pb_1-xGe_xTe is ~3 % over that fabricated with PbTe. In this letter, we report a new advance in our investigation.

The single crystal ingots of Pb_1-xGe_xTe, which have a range of Ge concentration x from 0.08 to 0.75, were grown in our crystal-growth laboratory using a modified Bridgman method. The ingots were then crushed into small pieces and used as source bulk alloys for evaporation of thin films. The thin films were prepared by conventional thermal evaporation with a background vacuum 2.0 × 10^-3 Pa. The silicon wafers polished on both sides, with a diameter of 10 mm and a thickness of 0.8 mm, were used as substrates. The substrate temperatures varying in the range from 100 to 300 °C were monitored. The thicknesses of the thin film were 2.0 μm and the errors are less than 2%. The optical transmission spectra of thin films were measured in the spectral range of 2.5-25 μm using a Perkin Elmer Spectrum GX Fourier-transform infrared spectrometer (FTIR) with a resolution of 8 cm^-1 at normal incidence.

Since the component elements in an multi-component alloy system will evaporate at a different rate, which causes changes in compositions of thin films relative to the initial bulk alloys, it is in great necessity to measure directly the compositions in evaporated Pb_1-xGe_xTe thin films. The compositions of thin films were analyzed using energy-dispersive X-ray analysis (EDAX) with a sensitivity limit for element detection of 0.1 wt.% in a Hitachi S-520 scanning electron microscope. The determination of element concentrations of lead, germanium and tellurium was performed by the analysis of the Pb M_α, Ge K_α, and Te L_α lines, respectively. Taking the uncertainties originating from inhomogeneity in thin films into account, for each sample measurements were repeated randomly at three different points on the surface of thin films, then the average of all counts for each element was taken as the standard intensity for that element. It is shown that Te concentration deviates from the stoichiometry in the form of either Te-rich character or Te-deficient one, together with a reduced Ge concentration x compared with initial bulk alloy. Therefore, the corresponding chemical compositions of evaporated Pb_1-xGe_xTe thin films should be expressed by the formula (Pb_1-xGe_x)_1-yTe_y.

Subsequently, Pb_1-xGe_xTe initial bulk alloy with appropriate Ge concentration x was selected to fabricate the thin-film narrow-band filters under the optimized processing condition. The design of filters is a simple 8-layer Fabry-Perot type, that is, one half-wave layer immersed in quarter wave layers is deposited on a germanium substrate of index 4.0 without rear surface antireflection, as follows:

where L and H represent, respectively, quarter-wave layers of ZnSe and (Pb_1-xGe_x)_1-yTe_y and the underlining signifies a spacer. The spectral characteristics of fabricated narrow-band filters were measured in the temperature range of 85-300 K using a bath cryostat (Oxford, DN1704). The measurements were reproducible, and no indication of hysteresis effect was observed.

The measured characteristics accompanied by the change of temperature for a filter fabricated with initial bulk alloy Pb_0.79Ge_0.21Te, from which the evaporated layer has the corresponding chemical composition (Pb_0.8584Ge_0.1416)_0.4575Te_0.5425, are shown in Fig. 1(a). The enlargement of the pass-band designed with peak wavelength of 11.30 μm is presented in Fig. 1(b). A comparison was made for the values of peak wavelength and peak transmittance versus temperature is given in the Fig. 2.

It can be found that when temperature varies in the range of 150-300 K, the peak wavelength of pass-band shifts linearly towards longer wavelengths with decreasing temperature, similar to the results obtained by Seeley and his colleagues using PbTe for high-index layer [3] and ours using Pb_0.94Ge_0.06Te (the deviation of Te concentration from the stoichiometry is small enough to be overlooked) for high-index layer [8]. The changes in peak transmittance with temperature also resemble results reported in the investigation initiated by Seeley as well as those obtained in our previous study. However, when temperature is below 150 K, the situation is entirely different: peak wavelength can shift back and the peak transmittance can recover from the deterioration. It is revealed that the temperature of 150 K is the critical point for the narrow-band filter, at which the temperature coefficient of filter is exactly zero. It is also implied that the temperature-induced variations in refractive index of (Pb_1-xGe_x)_1-yTe_y layers are compensated for by changes of refractive index induced in ZnSe layers and germanium substrate. Depending on the design of the filter and especially on the number of (Pb_1-xGe_x)_1-yTe_y layers, the critical temperature for the narrow-band filter is a function of composition of (Pb_1-xGe_x)_1-yTe_y layers, in particular, Ge concentration x (the exact limits of y depend on x).

 

Fig. 1. (a) Low-temperature spectral characteristics of the filter with (Pb_0.8584Ge_0.1416)_0.4575Te_0.5425 layers; (b) Enlargement of low-temperature spectral characteristics of pass-band with peak wavelength of 11.30 μm

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Fig. 2. Comparison of peak wavelength and peak transmittance versus temperature

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It is also shown that due to the existence of critical temperature for the narrow-band filter, variation of the temperature from 300 to 85 K results in a change of peak wavelength from 11.28668 μm to 11.29944 μm. Therefore, the shift of peak wavelength with temperature will be 0.05935 nm.K^-1. Compared with our previous result [8], a significant progress has been achieved. It can be inferred that, if further improvements on the control of the composition of (Pb_1-xGe_x)_1-yTe_y layers can be carried out, furthermore, a initial bulk alloy with more appropriate Ge concentration x can be selected, a critical temperature slightly greater than 150 K will be reached for the designed narrow-band filter. In this way, when temperature varies from 300 to 85 K, the shift of peak wavelength towards shorter wavelength below the critical temperature will balance that towards longer wavelength above the point, consequently, an absolute shift-free infrared narrow-band filter will be fabricated.