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Thermoreflectance microscopy is essential in understanding the unpredictable local heating generation that occurs during microelectronic device operation. However, temperature measurements of multi-layered semiconductor devices represent a challenge because the thermoreflectance coefficient is quite small and is dramatically changed by the optical interference inside transparent layers of the device. Therefore, we propose a spectroscopic thermoreflectance microscopy system using a systematic approach for improving the quantitative temperature measurement of multi-layered semiconductor devices. We demonstrate the quantitative measurement of the temperature profile for physical defects on thin-film polycrystalline silicon resistors via thermoreflectance coefficient calibration and effective coefficient κ estimation.
© 2016 Optical Society of America
1. Introduction
One of the largest obstacles in the design of semiconductor devices is the management of heat generation. As modern semiconductor devices demonstrate an increasingly high level of integration, localized heat generation has become a major issue in terms of the loss of performance and reliability [1,2]. Accordingly, non-contact and non-destructive measurements with sub-micron spatial resolution have become more important in analyzing the thermal behavior of the microscale region of interest (ROI) without leading to contamination or disturbance. Several varieties of thermal analysis have been developed in order to understand the thermal distribution and characteristics of these devices, such as scanning thermal microscopy (SThM), liquid crystal thermography (LCT), fluorescence micro-thermography (FMT), infrared thermography (IRT), and thermoreflectance microscopy (TRM) [3–8]. Among these methods, IRT is widely used in the semiconductor industry, though the spatial resolution it offers does not exceed the sub-microscale owing to the diffraction limit for the range of wavelengths (3–10 μm) used in the most sensitive IR cameras. On the other hand, TRM has become a prominent candidate for meeting all the above requirements. TRM employs a contactless and non-invasive temperature mapping based on measuring variations in the sample surface reflectivity in response to a temperature change. In addition, measurements with sub-micron resolution (0.3–0.5 μm) can be easily achieved as a result of the short visible wavelength illumination [9].
However, the thermoreflectance coefficient, which quantifies the relationship between the reflectivity variation and the temperature change, is too small to measure using conventional methods (i.e., on the order of 10−5–10−3 K−1); furthermore, it depends on the sample material, the illuminating wavelength, and the incident angle of an illumination [10]. In particular, the optical interference of the transparent layer (e.g., the passivation layer) in the semiconductor device strongly influences the value of the thermoreflectance coefficient because the material’s reflectivity at certain illuminating wavelengths is unpredictably changed by the optical interference. For these reasons, it is important to identify the illuminating wavelength with the highest thermoreflectance coefficient in order to ensure high sensitivity for the temperature-dependent reflectivity variation (i.e., thermoreflectance) measurement in multi-layered devices. Therefore, the spectral dependence of thermoreflectance coefficient for a device under test (DUT) must be inspected to determine the optimum illumination that can induce a sufficiently large thermoreflectance signal.
There are two approaches for calibrating the thermoreflectance coefficient based on its spectral dependence. In conventional TRM, the thermoreflectance coefficient spectrum is obtained by repeatedly acquiring thermoreflectance images. Each thermoreflectance image is acquired by non-continuous illumination, such as LEDs with different colors [11] or a white light source combined with a linear variable filter [12]. However, this solution is time-consuming, and provides restricted spectral information as well. Consequently, it is not frequently adopted. An alternative approach has been implemented by a modified microscope with dispersive optical components and a thin line-shaped illumination pattern from a white lamp [10]. The dispersive components allow the reflected light from the sample to be spectrally overlaid on a CCD camera. Using this approach, the spectral dependence of the reflectivity for encapsulated devices can be measured by only a single acquisition. However, this approach focuses on measuring the thermoreflectance spectrum and predicting the optimized illuminating wavelength. Accordingly, this system configuration does not permit us to observe the localized heat generation on a DUT with the predicted optimum illumination.
In fact, there is no systematic approach that leads from the calibration of the thermoreflectance coefficient to the quantitative temperature imaging process for multi-layered semiconductor devices. Therefore, in this paper, we propose spectroscopic TRM as a compact, all-in-one system for achieving high-sensitivity thermoreflectance measurements and accurate quantitative temperature imaging. First, we introduce a straightforward way to develop a spectroscopic TRM system in detail. Second, we describe the process of optimizing the thermoreflectance signal by choosing a proper illuminating wavelength, as well as the process of improving the temperature accuracy by selecting the correct thermoreflectance coefficient. Finally, the quantitative temperature profile of the sub-micron localized hot region is demonstrated in order to verify the feasibility of the system.
2. Experimental setup
The experimental setup for the spectroscopic TRM system is presented in Fig. 1(a). To build up the system, we simply combined three main components: a microscope unit (VMU-L, Mitutoyo), a tunable optical filter (VariSpec-VIS, PerkinElmer), and a dispersive spectrometer (ImSpector-V10E, Specim). Then, two CCD cameras, which allowed us to acquire the thermoreflectance spectrum (Clara E, 14 bit, Andor technologies) and the thermoreflectance image (CCD-1300QF, 12 bit, Allied Vision technologies), were attached into the system with an objective lens (20 × , NA 0.4, Mitutoyo) and a white light source (MegaLight 100, Schott Mroitex). The assembly procedure can be performed quickly and easily because the microscope unit has a compact body that provides multiple standard connecting ports forperipheral apparatuses. Each component also easily connects to the standard mount (e.g., C mount). For system control, the data acquisition (DAQ) board (NI PCIe-6353, National Instruments) generates trigger signals for both the camera image acquisition and the device bias modulation, and also performs precise synchronization between the two triggers. The control and image-processing program were implemented by using the LabVIEW programming environment.
Fig. 1 (a) Schematic diagram of the spectroscopic thermoreflectance microscopy (TRM) system. (b) Sample design with a polycrystalline silicon (poly-Si) micro-resistor on a SiO2 layer/Si substrate.
As shown in Fig. 1(b), the sample for a DUT was fabricated using a thin-film polycrystalline silicon (poly-Si) resistor with Cr/Au ohmic contacts on a SiO2 layer/Si substrate. The poly-Si resistor was 0.5 μm thick, 30 μm wide, and 400 μm long; the resistance was 1.15 kΩ. The power supply (2612B SourceMeter, Keithley) provided the bias modulation signal (V = V0 (1 + sin (2πft))) for the DUT. The probe station was used to apply a bias voltage from the power supply to the DUT. Lastly, a Peltier element and a resistive temperature detector (RTD) were employed for feedback temperature control of the DUT.
It is worth noting a few particular attributes of the various components involved in the system described above. In a previous study, thermoreflectance spectra were measured by a thin line-shaped illumination pattern on the sample and dispersive optical components, such as a grating and a glass prism [10]. However, such an illumination pattern is not suitable for the image-based acquisition of the temperature distribution on the whole sample because an illuminating region is restricted to only a portion of the sample. On the other hand, our system accomplishes both spectral measurements and temperature distribution imaging using wide-field illumination. Although the sample was illuminated widely, an entrance slit, which was located in front of the transmission grating inside the dispersive spectrometer, only allowed light from the ROI to enter into the transmission grating. At this stage, the grating spectrally disperses the entering light on the CCD. Therefore, the entrance slit enables us to sequentially measure a spectrum and to image a temperature distribution by using two different cameras in concert with wide-field illumination.
The other key instrument in this setup – the tunable optical filter – can continuously select a desired wavelength from the white light source. This instrument allows us to detect the optimized thermoreflectance signal by choosing the illuminating wavelength according to the spectral information of the thermoreflectance response of each material. It employs electronically controlled liquid-crystal elements that allow it to tune continuously in the visible wavelength range of 400–720 nm with a pass bandwidth (full-width at half maximum (FWHM)) of 10 nm. In general, the transmittance of a randomly polarized beam in a liquid-crystal element is decreased by a factor of two owing to the sensitivity to the polarization state of the input beam. This drawback can be mitigated by increasing the output power of the light source or controlling the exposure time of the camera during image acquisition. In tuning the optical filter, the effects caused by the limitation of a pass bandwidth should be taken into account. For instance, the narrower the pass bandwidth is, the larger the decrease in the illumination power and the probability of interference occurring in a transparent layer will be. Therefore, it is necessary to choose an optical filter with an appropriate pass bandwidth.
3. Thermoreflectance imaging
The effect of temperature modulation on the semiconductor creates the energy-gap shift due to thermal expansion and electron–phonon interaction, which changes the complex dielectric function of the sample [13]. This variation of the complex dielectric function results in the variation of the reflectivity of a surface material [14]. The scheme of thermoreflectance imaging in TRM is based on the measurement of the relative reflectivity variation on the surface of DUTs due to temperature modulation. The value of the relative reflectivity variation in the CCD can be expressed as the ratio between the AC output signal and its DC component [12]:
where R and T are the reflectivity and temperature on the sample surface, respectively, and κ is the thermoreflectance coefficient. Because of the small thermoreflectance coefficient, lock-in measurement is required to increase the signal-to-noise ratio (SNR) of the thermoreflectance (ΔR/R) signal corresponding to the temperature variation (ΔT). For instance, the four-bucket method is an appropriate measuring technique to derive the image ΔR/R(x, y) from a series of images acquired by a CCD camera. As shown in Eq. (2), the normalization in this method is performed via a simple calculation using four different reflection images (I1, I2, I3, I4) that are taken by the camera during the period of the bias modulation (T = 1/f) [15]. The camera works at a frequency of 4f.4. Thermoreflectance coefficient calibration
The thermal characteristics of multi-layered DUTs can be observed by thermoreflectance measurements if we know the coefficient κ. To this end, it is also necessary to find an illuminating wavelength for which the coefficient κ is sufficiently large for high-sensitivity thermoreflectance measurements. Therefore, during thermoreflectance coefficient calibration, the spectrum κ(λ) is obtained in order to calibrate the coefficient κ and to choose the optimal illuminating wavelength.
The spectral dependence of the coefficient κ can be inferred from the reflectivity spectra measured at different temperatures, which is generally given by:
For the thermoreflectance coefficient calibration in the proposed TRM system, the reflectivity spectra (R(λ)) in the range of 400–800 nm were measured by the white light source and the dispersive spectrometer. The spectral information and spatial information of the reflected light from the sample were mapped along the x- and y-axes of the CCD as the temperature was gradually increased. Then, the thermoreflectance spectrum (ΔR/RT(λ)) for each temperature increment (ΔT) was calculated from the measured spectra RT(λ). During the measurement, the temperature of the whole sample was feedback controlled by the Peltier element and the RTD. All measurements at each set temperature were performed at the best focus. Finally, the spectrum κ(λ) was obtained by calculating the ratio between the change in the temperature and the change in the relative reflectivity. The linear variation of ΔR/R was confirmed over the set temperature range. In this manner, we were able to obtain the spectrum κ(λ) and to calibrate the coefficient κ from it, thereby allowing us to choose the exact illuminating wavelength that was required in order to obtain a large thermoreflectance signal.5. Results and discussion
We validated our experimental setup using the semiconductor device shown in Fig. 1(b). Before the thermoreflectance coefficient calibration of the poly-Si microresistor and the Cr/Au contact on the device, the dispersive spectrometer, which has an operating range of 400–1000 nm, was calibrated by well-known line illumination sources, such as Hg and Kr lamps. The spectrum was obtained by a 1392 × 1040 pixel CCD camera (Clara E, Andor technologies) with a spectral resolution of ~0.7 nm.
As an initial procedure for the thermoreflectance coefficient calibration, measurements of the spectra ΔR/R(λ) as a function of the temperature change were performed in order to figure out the spectral dependence of the coefficient κ. The sample was widely illuminated by the white light source through the 20 × (0.4 N.A.) objective lens. The dispersive spectrometer analyzed the spectrum of the light that is confined by the entrance slit around an arrow line, as depicted in Fig. 2(a). The arrow direction coincides the spatial axis direction on the spectrum. Figures 2(b) and 2(c) show a spectral reflection image and normalized reflectivity spectra for both the poly-Si layer and the Cr/Au contact, respectively. The x- and y-axes in the image represent spectral and spatial information, respectively. For the quantitative measurement of the spectrum R(λ), it is necessary to perform a correction of the spectral response of the CCD camera by using a reference reflectivity spectrum. However, during the themoreflectance coefficient calibration, this correction is not required because the spectrum κ(λ) originates from relative change values, such as the spectrum ΔR/R(λ) and each ΔT value.
Fig. 2 (a) Region of interest (ROI, arrow line) on the sample of the thin-film poly-Si microresistor. (b) Spectral reflection image of the poly-Si layer and the Cr/Au contact at the set temperature of 20 °C. (c) Normalized reflectivity spectra of the poly-Si layer and the Cr/Au contact.
At this stage, thermoreflectance spectra given by [RT + ΔT (λ) − RT (λ)] / RT (λ) were calculated from the measured spectral reflection images. Figure 3 presents the spectra ΔR/R(λ) of the poly-Si microresistor and the Cr/Au contact along with ΔT values from 10 °C to 40 °C. As the set temperature in the Peltier controller is increased by 10 °C intervals from the initial temperature T of 20 °C, the reflectivity spectra of individual material for each ΔT were acquired from the mean value for ten horizontal lines around the solid and dashed lines of Fig. 2(b). They abruptly change along with wavelength and exhibit several positive and negative peaks. The positive and negative signs of ΔR/R derive from the reflection and absorption of the light on the material, respectively. As shown in Figs. 3(a) and 3(b), the largest variation appeared at the wavelengths of 516 nm and 614 nm for the Cr/Au contact and the poly-Si microresistor, respectively.
Fig. 3 Thermoreflectance spectra for (a) the poly-Si microresistor and (b) the Cr/Au contact for various temperature variations.
As the next step in the thermoreflectance coefficient calibration, we obtained the spectrum κ(λ) of the poly-Si microresistor, as shown in Fig. 4. Notice that the spectrum κ(λ) in Eq. (3) must be changed in proportion to the spectrum ΔR/R(λ) because the ΔT value of the sample is constant regardless of the illuminating wavelength. Consequently, as shown in Fig. 4, the calculated spectrum κ(λ) (black square) was confirmed by observing the the good agreement with the spectrum ΔR/R(λ) (solid line) obtained at a ΔT value of 20 °C, which was normalized to fit the calculated spectrum κ(λ). The same results were observed for other thermoreflectance spectra.
Fig. 4 Calculated thermoreflectance coefficient spectrum for specific wavelengths (black square), a normalized thermoreflectance spectrum (solid line), and a normalized reflection spectrum (blue circle) at a temperature variation of 20 °C for the poly-Si microresistor.
Furthermore, we confirmed that the spectrum κ(λ) includes the effect of the interference generated on the sample. The sharp changes in the spectrum κ(λ) occur inside two dips in the normalized spectrum R(λ) (blue circle), which result from the interference effect in the poly-Si microresistor. The interference pattern in the normalized spectrum R(λ) is caused by the combination of the reflected rays at the air/poly-Si and poly-Si/SiO2 interfaces in Fig. 1(b). The wavelength difference of ~80 nm between the two dips is almost matched with the optical path length resulting from the thickness of the poly-Si microresistor of ~550 nm [16]. After the thermoreflectance coefficient calibration, a κ value of 4.34 × 10−3 K−1 (−3.58 × 10−4 K−1) and an optimal illuminating wavelength of 614 nm (516 nm) were determined for the poly-Si microresistor (Cr/Au contact).
Improvement of the measurement sensitivity was observed by comparing two images ΔR/R(x, y) measured with the selected illuminations based on the center wavelength of 614 nm and 635 nm in the tunable filter. Red LEDs (λ = 635 nm) are commonly used for thermoreflectance measurements of samples consisting of the poly-Si material [17]. The image I(x, y) and ΔR/R(x, y) of the poly-Si microresistor for each case are shown in Fig. 5. The ΔR/R signal with the optimized illumination of 614 nm is 1.5 times larger than the non-optimized illumination of 635 nm. By using the other CCD camera (CCD-1300QF, Allied Vision technologies) with the four-bucket method, the image ΔR/R(x, y) was obtained after averaging 800 iterations for four different images I1–4 (x, y). During image acquisition, the sample was supplied with bias modulation at f = 2 Hz; the dissipated power was ~0.39 W. The measurement time with the CCD camera’s frame rate of 8 fps was ~400 s.
Fig. 5 Reflection (I) and thermoreflectance (ΔR/R) images of the poly-Si microresistor for the selected illumination at the center wavelength of (a, b) 614 nm and (c, d) 635 nm.
Generally, the quantitative temperature imaging in the TRM system is performed by applying the coefficient κ to the image ΔR/R(x, y) for conversion into the image ΔT(x, y), and subsequently adding the initial temperature of the DUT. However, note that in the spectroscopic TRM system, this procedure could decrease the accuracy of temperature measurements unless the effect of the illumination that is spectrally limited by the pass bandwidth of the tunable filter is considered during the thermoreflectance coefficient calibration. That is because the coefficient κ directly influences the ΔT value, as shown in Eq. (1). Therefore, we identified the correct coefficient by examining the temperature similarity between two different illuminations. Three approaches were carried out as follows. First, the single κ value was taken at the optimal probe wavelength in the spectrum κ(λ). Second, the averaged κ value was estimated by averaging the values in the spectrum κ(λ) that fell within the range of the tunable filter bandwidth. Third, the effective κ value was directly estimated by using the ΔR/R values in the image acquired by the CCD camera (CCD-1300QF) as the optimum illumination reached the sample.
Figure 6 shows each case of the image ΔT(x, y) for the three methods of calculating the coefficient κ. Table 1 summarizes the coefficient κ and the variation ΔT of the poly-Si microresistor for two illumination wavelengths: 614 ± 5 nm and 635 ± 5 nm. When the poly-Si microresistor is heated by the external bias modulation, the variation ΔT extracted by the TRM system should be identical regardless of the probe wavelength, as mentioned before. As shown in Fig. 6 and Table 1, the discrepancy in the ΔT value was largest for the single κ estimation, relatively smaller for the average κ estimation, and smallest for the effective κ estimation, although the temperature variations in the three methods were not equal. Therefore, the effective κ estimation allows us to achieve the highest temperature accuracy for the quantitative temperature imaging. The small difference of the variation ΔT in Figs. 6(c) and 6(f) mainly results from the low temperature resolution, which is due to the insufficient number of iterations as well as the low bit depth of the CCD camera in the system; as a result, this makes the standard deviation of ΔT large [18].
Fig. 6 Temperature variation images of the poly-Si microresistor obtained by three methods: (a, d) single κ value, (b, e) averaged κ value, and (c, f) effective κ value for two illuminations centered at 614 nm (top) and 635 nm (bottom).
Table 1. Summary of Coefficient κ and the Temperature Variation of the Poly-Si Microresistor for Two Illuminations Centered at 614 nm and 635 nm
If one observes the change of κ values for the same illumination wavelength, it becomes evident that the difference between the single and averaged κ values is associated with the location of the filter center wavelength in the spectrum κ(λ), such as the peak and slope. In the optimum illumination case, the averaged κ value was extracted by averaging values around the peak (the center wavelength of 614 nm) in the spectrum κ(λ). Accordingly, this significantly differs from the single κ value. On the other hand, the difference between the averaged and effective κ values results from both the uncertainty of the valid spectral range for the averaged κ estimation and the spectrum disagreement between the two illuminations used to obtain the spectrum ΔR/R(λ) and the image ΔR/R(x, y). During the effective κ estimation, the illumination for the image acquisition was modified by the spectral transmission property of the tunable filter in front of the CCD camera (CCD-1300QF).
In order to demonstrate the improvement of the temperature measurement accuracy of the effective κ estimation, the measured temperature difference between IRT and spectroscopic TRM was investigated in terms of the temperature quantification accuracy. Here, quantitative IR micro thermography was used to measure the precise temperature distribution as a reference [7]. We increased the bias level in the DUT in steps, and the temperatures on the poly-Si microresistor for each bias level were measured using two systems, as shown in Fig. 7. During the measurement with the spectroscopic TRM, the effective κ estimation was applied. The temperatures measured with the two systems are in good agreement with each other. For each κ estimation method, the temperature quantification accuracy was obtained by calculating the ratio between the reference and the measured temperature difference in the case of the dissipated power of ~0.39 W, as summarized in Table 2. The temperature quantification accuracy is highest for the effective κ estimation and higher for the optimal illuminating wavelength than the non-optimal one. We expect that this tendency could be unchanged for high temperature thermoreflectance imaging, although the temperature quantification accuracy would be decreased owing to the unknown behavior of the dependence of the coefficient κ on temperature [19].
Table 2. Summary of the Temperature Quantification Accuracy of the Poly-Si Microresistor for Two Illuminations Centered at 614 nm and 635 nm
The acquisition procedure for the quantitative image T(x, y) in the spectroscopic TRM system can be summarized as follows. For high-sensitivity and accurate temperature measurements, the optimum illumination is determined from the spectrum ΔR/R(λ) instead of the spectrum κ(λ). The image ΔR/R(x, y) acquisition and the effective κ estimation are performed, and then the quantitative temperature image is obtained by the quantitative temperature measuring method. Figure 8 shows the merged quantitative image T(x, y) of two ROIs of the Cr/Au contact and the poly-Si microresistor, respectively. Localized heat generations that exist in the interface between them are also presented. In order to investigate the temperature dependence of the reflectivity on the Cr/Au contact, the DUT was periodically heated by a bias modulation at f = 2 Hz with a dissipated power of ~0.39 W. The bias modulation conditions for the poly-Si microresistor were the same as above. The optimum illuminations centered at 516 nm and 614 nm for the Cr/Au contact and the poly-Si microresisitor, respectively, were determined from the spectrum ΔR/R(λ). Then, the images ΔR/R(x, y) were obtained using two optimum illumination wavelengths through the tunable filter. The coefficients κ for the two materials (e.g., poly-Si: 3.9 × 10−3 K−1, Cr/Au: −3.69 × 10−4 K−1) were obtained by the effective κ estimation. The images ΔT(x, y) can be deduced by dividing the image ΔR/R(x, y) into the estimated coefficient. Lastly, the quantitative images T(x, y) were obtained by applying an initial set temperature (20 °C) using the temperature controller. In addition, we quantitatively measured the horizontal and vertical temperature profiles for the hot spots on the interface. The temperature in the localized hot region is over 70 °C. In a previous study, we have used a scanning electron microscope to confirm that the hot spots originate from physical defects [17]. Sub-micron scale defects were identified in the interface between two materials, which cause local resistance variations due to thickness changes and thereby generate localized hot regions.
Fig. 8 Merged quantitative temperature image for the Cr/Au contact and the poly-Si microresistor, along with temperature profiles of localized hot regions. Each image was obtained using the effective κ values for the optimal illuminating wavelengths of 516 nm and 614 nm.
6. Conclusion
We have introduced an exemplary spectroscopic TRM system that can be used to measure the optimal thermoreflectance signal and the effective coefficient κ for the quantitative temperature distribution of multi-layered semiconductors. In our system, the spectrum ΔR/R(λ), which is obtained using a dispersive spectrometer and wide-field broadband illumination, guides us in selecting the optimal illuminating wavelength for high-sensitivity thermoreflectance measurements. We have demonstrated that each optimum illumination for different materials is able to improve the thermoreflectance measurements. Moreover, the effective coefficient κ allows us to accurately measure the quantitative temperature distribution from the material surface to the localized hot region. These experimental results prove that our system takes advantage of both the wide-field illumination and the optical tunable filter in performing quantitative analysis of the thermal behavior in multi-layered semiconductors, such as themoreflectance and temperature measurements. Therefore, we expect that the developed spectroscopic TRM can function as an all-in-one imaging tool for thermal characterization in various multi-layered semiconductor devices.
Acknowledgments
This work was supported by the Korea Basic Science Institute Grant (D36500) and National Research Council of Science & Technology grant (PBE083 & PBS087).
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