Etalon-induced baseline drift and correction in atom flux sensors based on atomic absorption spectroscopy

Atomic absorption (AA) spectroscopy is a widely used analytical procedure in the food, water, and medical industries for the quantitative determination of trace elements due to its high specificity and selectivity.^1–3 Optical flux sensors based on AA principles have also been employed to monitor atom fluxes during thin film deposition processes, such as physical vapor deposition (PVD) and molecular beam epitaxy (MBE).^4–14 By passing a light beam matched to the absorption energy of the element of interest through the atom beam within the deposition chamber, one can detect the intensity attenuation resulting from resonant atomic absorption. The attenuation is proportional to the atom density within the irradiated volume and can be used to calibrate the atom flux and determine the precise deposition rate. Compared to other commonly used flux or thickness detection methods, such as the quartz crystal microbalance (QCM) and ellipsometer, AA-based atom flux sensors are elemental specific and have the advantage of no components internal to the vacuum system. AA is thus in principle of particular interest for deposition of complex oxide or alloy materials, such as LaCrO₃ or copper indium gallium selenide (CIGS) solar cells, where precise stoichiometry control is required.^4,15,16

However, AA-based sensors currently in use rarely provide sufficiently accurate detection and control, in part because of baseline drift and background interference. Instabilities in the device components (e.g., light sources, detectors, optics, etc.) can result in non-negligible baseline drift over time. Furthermore, unintentional coating of the optical viewports can attenuate the light intensity along the optical path. Moreover, slight optical misalignment or motion in optical guides and/or fiber optic cables can produce spurious changes in light intensity. A double beam approach, sometimes combined with a broadband light source or diode laser for background correction, can increase the baseline stability to a certain extent. However, the ultimate performance is limited by the fact that the light source used for correction is different than that which generates the analytical resonant absorption line, thereby introducing an independent set of instabilities. In order to address these issues, we have developed a self-corrected method for baseline drift removal suitable for use with a single light source. Using a high-resolution spectrometer and a two-dimensional charge coupled device (CCD) detector in a double-beam configuration, we employed either a non-resonant line or a resonant line with low cross section from the same hollow cathode lamp (HCL) as the reference for nearly perfect background correction and baseline drift removal, which has been described in detail elsewhere.¹⁷ 

Almost all baseline correction methods in AA flux sensing are based on the assumption that the baseline drift is independent of wavelength. In this paper, we identify a subtle, previously unexplored source of baseline drift which is highly wavelength dependent, making it immune to all existing correction methods, including our self-corrected scheme.¹⁷ The instability is caused by a temperature-dependent etalon effect,¹⁸ in which thermal contraction/expansion of the optical viewports resulting from changes in radiant heating results in modified interference conditions for directly transmitted and doubly reflected light beams, thereby modulating the detected light intensity. Although etalon-induced interferences have been known about and dealt with in infrared spectroscopy and other laser based measurements,^19–22 their connection to AA based atom flux sensing has not been previously made.

Yet, considering that many thin film deposition systems employ resistive heating or electron beam heating, the thermal load on the AA viewports can be enough to change their temperatures and this effect must be addressed. Here we show that a few degrees of temperature variation in fused silica viewports can induce up to ∼1.5% variation in transmitted light intensity, which in turn significantly degrades the ultimate sensitivity of the AA sensor. If not compensated for, this etalon effect will not only cause long-term baseline drift as a result of lab air temperature variations and thermal load from the heat sources, but will also directly affect the signal response and reproducibility during flux measurements.

A schematic of an AA flux sensor coupled to a deposition system is shown in Fig. 1(a). To detect an atom beam flux, the incident light originating from the corresponding HCL is directed through the deposition chamber via two viewports on opposite sides of the chamber. Fused silica windows are preferred because they have high and roughly constant transmittance across a broad UV-visible light region. The temperature-dependent etalon effect is often negligible compared to other sources of baseline drift, but becomes more of a problem when the heat load on the viewports is high and/or when the source shutter is cycled. In order to get the highest signal response from the AA flux sensor in our most recently constructed MBE system, and be able to monitor and adjust each beam flux separately, a pair of AA viewports was mounted very close to each effusion cell. Close proximity to the atom source is important because the atom density is inversely proportional to the square of the distance from the source, and typical atom densities are low to begin with during MBE deposition. In this configuration, the thermal load from the source coupled with cycling of the source shutter can introduce measureable baseline drifts. These can result from optical misalignment, changes in transmission coefficient, and the etalon effect. By correcting for sources of baseline drift that are independent of wavelength,¹⁷ our self-corrected double-beam design allows the etalon induced baseline drift to be isolated and investigated.

The mechanism for the etalon effect is shown schematically in Fig. 1(b). By passing the light beam through a fused silica window, at least a portion of the doubly-reflected beam mixes and interferes with the direct transmitted beam. If the thickness of the viewport changes due to thermal effects by an amount comparable to the wavelength of the light, the phase of the doubly-reflected light will change, resulting in a change in interference condition with the directly transmitted beam at the detector. The total phase difference between the directly transmitted and doubly reflected beams is given by¹⁸ 

where λ is the wavelength of the light, n is the refractive index, l is the thickness of the window, and $θ′$ is the angle between the light traveling direction inside the viewport and the surface normal. Constructive interference is expected when δ = 2mπ, where m is an integer. The heat load from the metal evaporation sources and the substrate heater shown in Fig. 1(a) can cause temperature changes on the viewport, which can change the spacing between the two reflecting surfaces and, thus the value of δ according to Eq. 1. Also, if the beam is off normal by some angle, only a portion of the doubly reflected beam will be detected (solid red in Fig. 1(b)), whereas trajectories represented by the dotted red line will not be detected. In contrast, if the incident beam is normal to the window surface, the doubly reflected beam will have the same path as the transmitted beam, leading to the strongest intensity modulation. Setting δ = 2π, $θ′$ = 0, n = 1.458 for fused silica, and λ = 400 nm in Eq. (1), a constructive-destructive-constructive interference cycle is expected whenever the window thickness is changed by 137 nm. For the mini CF viewports used in this study, the thickness of the fused silica is 1 mm and the view area diameter is ∼16 mm. Free standing fused silica has a very low linear thermal expansion coefficient of 0.55 × 10⁻⁶/ °C and would require a temperature increase of ∼250 °C for a 1 mm thick window to expand by 137 nm. However, the fused silica window is mounted on a 304 stainless steel CF flange, which has a thermal expansion coefficient ∼30 times larger (17.3 × 10⁻⁶/ °C). It should be noted that the fused silica has a slightly larger specific heat capacity (0.7 J/g °C vs. 0.5 J/g °C) but much smaller thermal conductivity (1.38 W/mK vs. 16.2 W/mK) compared with 304 stainless steel. Thus, the temperature change for the stainless frame occurs more rapidly than that for the fused silica window. The fused silica disk will become thinner as a result of being put in tension by the expanding stainless steel frame. In a simplified model, assuming volume conservation in the fused silica during thermal expansion of the stainless steel, we can write

where r and l are the radius and thickness of the fused silica viewport at the lower temperature, α is the thermal expansion coefficient of stainless steel enforced by the welding, and ΔT is the temperature increase. The reduced thickness after thermal shock can be approximated by l' = l(1 − 2αΔT).²³ We estimate that the 1 mm thick fused silica will become thinner by 137 nm for every ∼4 °C increase in temperature as a result of the stress response to the expanding stainless steel flange (effective thermal expansion coefficient (−2 × 17.3 × 10⁻⁶/ °C), with the negative sign meaning contraction). This effect can be magnified on viewports of other sizes that use a thicker window.

As mentioned above, it is desirable to locate the AA beam as close to the atom beam source as possible. In our MBE system, a pair of AA viewports has been positioned 65 mm above each effusion cell opening as shown in Fig. 2(a). A mechanical shutter, 20 mm below the AA viewports, is installed to block the atom beam, during which time a zero baseline can be re-established. In this design, the two viewports are spaced 100 mm apart. Because of the close proximity to the heated effusion cell, a temperature increase on the viewport is inevitable when the effusion cell temperature is taken above 800 °C, even with active water cooling of the nipple to which the cell is bolted. Fig. 2(b) shows the absorption change during the cooling of a Ti effusion cell from 1590 °C to 300 °C at 30 °C/min starting at ∼500 s. We use absorption (defined as $100%*( Iin−Iout)/Iin)$ instead of absorbance to directly express the light intensity change. During the cooling process, the shutter was closed to block the atom beam, so that the absorption signal should remain at zero. However, different absorption modulations are clearly observed for three adjacent Ti emission lines (λ = 399.8 nm, 398.9 nm, and 398.2 nm) from the same HCL. The amplitudes for all three intensity modulations change by up to 1.5%, and the modulation frequency decreases as the cell temperature goes down. The actual change in viewport temperature during this cool down was 12.3 °C (29.6 °C to 17.3 °C), as measured by a thermocouple, and this change was not linear with time. It should be noted that the reflection coefficient per window for fused silica materials is ∼0.08 in this wavelength range, meaning that the intensity modulation for doubly reflected light can be up to ∼1.3% (2*0.08*0.08*100%). The slightly larger observed absorption modulation (1.5%) is most likely due to the presence of multiple etalons, e.g., two surfaces on the inlet viewport, two surfaces on the outlet viewport, and any pair of surfaces involving both viewports. The etalon effect between the two viewports should be much smaller than that generated within each viewport as the two viewports are not as parallel as the two reflective surfaces associated with each viewport. The observation of three full oscillations over the 12.3 °C temperature change is in good agreement with our estimation from Eq. (2) (∼4 °C/oscillation).

It is clear that spurious signals due to the etalon effect need to be removed in order to achieve a stable baseline and maximize accuracy and sensitivity. In Fig. 1(b), we show that a smaller beam size and slightly tilted optical alignment with respect to the viewport normal can at least partially eliminate the incorporation of multiple reflected light beams into the transmitted beam. The effectiveness of this approach depends on the size of the beam, the thickness of the viewports, and the optical path length within the vacuum chamber. We demonstrate the effectiveness of this approach using the cooling of a Ti effusion cell from 1700 °C to 300 °C at 50 °C/min with the light beam tilted 4° off normal. The results are shown in Fig. 2(c). This extent of tilting not only reduces the etalon effect coming from two sides of the same window (Fig. 1(b)), but also reduces the effect from the cavity in between the two viewports (inset of Fig. 2(c)). Tilting 4° results in the peak-to-peak intensity modulation being reduced from ∼1.0–1.5% to ∼0.5%. More oscillations with shorter periods are observed compared with the 1590 °C cooling curve (Fig. 2(b)) as a result of higher thermal load on the viewports at 1700 °C and a higher cooling rate of 50 °C/min.

Another comparison was performed to evaluate the effectiveness of optical path tilting during deposition, as shown schematically in Figs. 3(a) and 3(b). The AA sensor performance was evaluated using a La cell temperature of 1680 °C, which corresponds to 0.04 Å/s deposition rate at the sample position as calibrated by a QCM. The absorption signal responses for configurations Figs. 3(a) and 3(b) are shown in Figs. 3(c) and 3(d), respectively. The cell shutter was opened and closed several times. Comparing Figs. 3(c) and 3(d), it is evident that the tilted configuration (Figs. 3(b) and 3(d)) results in improved baseline stability and better consistency over multiple cycles. In Fig. 3(c), the average absorption is 1.76% and the standard deviation measured over random 150 data points with the shutter open is 0.06. Yet, the etalon-driven modulation is clearly visible, as seen in the inset. Additionally, the absorption measured in the region marked by the dashed red line is not well fit to a flat line, as expected for stable operation of the sensor; linear regression yields abs = (5 × 10⁻⁴)t + 1.7239 and R²= 0.1766. In contrast, the tilted configuration yields an average absorption of 1.61% with a much smaller standard deviation, 0.03. The absorption region marked by the dotted red line in Fig. 3(d) can be very well fit by a nearly flat line described by abs = (1 × 10⁻⁵)t + 1.6143, with R²= 0.0003. Moreover, the etalon modulation is now reduced to nearly the same magnitude as the noise, as seen in the inset. In order to completely remove the etalon effect, the tilt angle (θ′) should be larger than $sin−1(d/2l)$⁠, where d is the diameter of the beam, and l is the optical viewport thickness.²³ It is evident that in our configuration with d = 6 mm and l = 1 mm, it is impossible to completely eliminate the etalon interference simply by tilting the beam.

We have considered other possible ways of correcting for the etalon effect. First, it might seem that the self-correction method described in Ref. 17 could be used provided the oscillations of the strong absorbing and weakly- or non-absorbing lines are in phase. For example, it appears based on the data shown in Figs. 2(b) and 2(c) that the 398.9 nm line could be used to completely correct the 398.2 nm line, but not the 399.8 nm line, because 398.9 nm and 399.9 nm are almost completely out of phase. However, we have found that the phase differences in the oscillations observed for different closely spaced emission lines change from run to run. Therefore, this approach would not work unless the phase differences are measured as part of each run. A second approach is the use of viewports with anti-reflective coatings. However, based on our tests, broadband anti-reflective coatings display unsatisfactory performance, probably because of erratic changes in optical properties with temperature due to material inhomogeneities. The third possibility is to use wedged viewports, which have been adopted to remove similar etalon effects in laser-based spectrometers.^19–21 Unfortunately, ultra-high vacuum (UHV) compatible wedged viewports are not commercially available at this time.

Finally, we comment on the etalon effect in relationship to the data presented in Ref. 17, which were taken with the probe light beam at normal incident to the viewport. Because of the extraordinarily high AA cross section for the 357.9 nm line of Cr, the absorption values were much higher than those recorded here for Ti and La, despite comparable deposition rates (12.1% in Fig. 2 and 20.6% in Fig. 3, corresponding to the displayed absorbance values of 0.056 and 0.10, respectively). The associated signal-to-noise ratios were thus at least 10 times higher, resulting in the etalon modulations approaching the noise level and being nearly negligible. If we had tilted the probe light off normal, the etalon effect would likely have become negligible. As it is, the different behavior observed for lines A1, A2, A3, and A4 in Fig. 2 of Ref. 17 immediately after opening the shutter at ∼17 min is most likely due to the etalon effect, rather than a thermal shutter transient, as suggested in Ref. 17.

In summary, we have investigated the effect of temperature changes on the accuracy of AA-based atom beam flux measurements. Intensity modulations due to interference between the directly transmitted and multiply reflected beams due to the etalon effect are non-negligible (up to 1.5%) and can occur when the temperature change of the viewports is as little as a few degrees. The etalon interferences become evident when the heat load is high and is exacerbated when the atom beam shutter is cycled. However, etalon effects can also appear in systems that do not generate high thermal load (e.g., III/V and II/VI MBE chambers), if the temperature variation in the laboratory exceeds a few degrees during day-to-day operations. Our results show that tilting the incident beam off normal can at least partially remove this effect, resulting in much more accurate measurement. Should they become commercially available, the use of UHV compatible wedged fused silica viewports may completely eliminate the etalon effect.

This research was supported by the U.S. Department of Energy (DOE), Office of Environmental and Biological Research under a Major Item of Equipment grant for the development of a state-of-the-art oxide MBE system, and the Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award 10122. The work was performed at the W. R. Wiley Environmental Molecular Sciences Laboratory, a DOE User Facility sponsored by the Office of Biological and Environmental Research. The authors would like to thank Hongfei Wang, Tim Droubay, and Tiffany Kaspar for many insightful discussions.