## 4 Single Pixel Optimization
### ac Bias
At high bias frequency, the ratio (\(I_{Q}/I_{I}\)) is increased of more than a factor of 2 at low voltage bias. In the two lower graphs, the detectors operates at a high saturation power (\(P_{sat}\sim 10\,\)pW) and similar bias frequency (\(f_{bias}\sim 4\,\)MHz). The two TESs have, respectively, \(R_{N}\simeq 8\,\)m\(\Omega\) and \(R_{N}\simeq 220\,\)m\(\Omega\). The high ohmic, high power detectors show almost negligible Josephson effects even at high bias frequency. There are two ways to fabricate devices with high \(R_{N}\). One is to increase the bilayer sheet resistance \(R_{\square}\), by reducing the thickness of the normal metal film (Au). Despite the good results achieved in squared TESs even after increasing the \(R_{\square}\) from 15 to \(50\,\)m\(\Omega/\square\)[54], this approach is not scalable due to limitation in the fabrication process and, eventually, to the increase of the internal thermal fluctuation noise. A better way to achieve high \(R_{N}\) is to increase the TES aspect ratio, defined as AR = \(L\times W\), with \(L\) and \(W\) the TES length and width, respectively. Higher aspect ratio devices, while increasing \(R_{N}\), offer additional design flexibility to simultaneously reduce the speed of the pixel (by reducing the perimeter) and the TES bias current (at the same saturation power) measured by the SQUID amplifier. Both the effects are beneficial to increase the multiplexing factor, as discussed in Section 5.2. After a few promising results obtained at NASA-GSFC, SRON developed high aspect ratio TES microcalorimeters based on Ti(35 nm)/Au(200 nm) bilayer with a \(R_{\square}=25\,\)m\(\Omega/\square\). In Figure 11, we give an example of the mitigation of the Josephson effects achievable by using high aspect ratio (AR) TESs. From left to right, we show the I-V curves and the \(I_{Q}/I_{I}\) ratio of, respectively, an NASA-GSFC Mo/Au \(75\times 17.5\,\)um\({}^{2}\) (AR = 4:1, \(R_{N}=120\,\)m\(\Omega\)), an SRON Ti/Au \(80\times 20\,\)um\({}^{2}\) (AR = 4:1, \(R_{N}\simeq 100\,\)m\(\Omega\))[22], and an SRON Ti/Au \(80\times 10\,\)um\({}^{2}\) (AR = 8:1, \(R_{N}\simeq 200\,\)m\(\Omega\)). All the devices have a \(P_{sat}\sim 1\)-2 pW, compatible with the X-IFU requirement. The NASA-GSFC device is biased at 3.8 MHz, while for the SRON devices, I-V curves for pixels biased at different frequencies (from 1.5 to 4.4 MHz) are shown. The SRON \(80\times 10\,\)um\({}^{2}\) turns out to be very promising, with a \(I_{Q}/I_{I}<0.025\), at \(f_{bias}\sim 4\,\)MHz, smaller than the other devices biased at the same frequency. Although the weak-link effects are not completely eliminated, these new TES design configuration reduces the size of the oscillatory structures in the transition and allows the access to a wider range of higher signal-to-noise ratio bias points in the transition. We have to experimentally investigate the performance, under ac bias, of many high aspect ratio devices fabricated at SRON with high (\(T_{c}\simeq 110\,\)mK) [120], and low (\(T_{c}\simeq 90\,\)mK) [22]  
Figure 11: TES I–V curves for different X-ray microcalorimeter types and MHz bias frequencies. In the lower graph of each plot the ratio \(I_{Q}/I_{I}\) of the quadrature or Josephson (\(I_{Q}\)) and in-phase \(I_{I}\) current is shown. The data are from the following devices: **(a)** NASA-GSFC Mo/Au \(75\times 17.5\,\)μm\({}^{2}\) (AR = 4:1, \(R_{N}=120\,\)m\(\Omega\)), ac biased at 3.8 MHz, **(b)** SRON Ti/Au \(80\times 20\,\)μm\({}^{2}\) (AR = 4:1, \(R_{N}\simeq 100\,\)m\(\Omega\)) [22], ac biased at 2.4–4.4 MHz and **(c)** SRON Ti/Au \(80\times 10\,\)μm\({}^{2}\) (AR = 8:1, \(R_{N}\simeq 200\,\)m\(\Omega\), ac biased at 1.4–4 MHz) [22]. critical temperature. The energy resolution was shown to scale with \(T_{c}\) as expected. Five different TES designs with low \(T_{c}\) were then further studied.