1.

Introduction

Fifteen to 20 years ago, developments in the semiconductor industry enabled the earlier generations of uncooled focal plane array (FPAs) and cameras with small format, 160 by 120 and then 320 by 240 array sizes with large pixels, generally in the neighborhood of $50\times 50{\mu \text{m}}^2$. The detector material was usually vanadium oxide (VOx), alpha-silicon (a-Si) or ferroelectrics. The wave band over which the optics and detectors of a camera were generally designed to receive and respond to radiation that is approximately $7.5\pm \mathrm{.0.5}\mu {\text{m}}^2$ to $13\pm 1\mu {\text{m}}^2$. The user community, mainly the military at that time, specified camera operational requirements, which were typically around a 50-mK noise equivalent temperature difference (NETD), a frame rate of 30 Hz, and commensurate time constants for applications such as a thermal weapons sight or helmet-mounted goggles. The sensitivity of the detectors was far from the fundamental limits and thus drove the need for optics with an $F$/number near 1.0 to obtain the desired NETD. The modulation transfer function (MTF) of the system was almost never dominated by the MTF of the optics. Over the years, the semiconductor industry has made advances with ever smaller design rules, enabling the uncooled camera manufacturers to further push their designs and performance. Pixel sizes have been reduced from 50 to $\sim 25\mu \text{m}$, then to 17 μm, and today uncooled camera manufacturers are looking into developing FPAs with pixels in the range of 10 to 13 μm while also increasing the resolution of the arrays to a nominal $1\mathrm{K}\times 1\mathrm{K}$ format.^1,2 The user-desired operational specifications generally require a 35- to 50-mK NETD and a 10- to 12-ms time constant with a frame rate of 30 or 60 Hz. A nominal $F$/1 optic is still required to obtain this sensitivity. There is also interest in further shortening the time constant to 5 ms or less while maintaining good NETD performance for higher speed motion applications. This raises a number of considerations, practical and theoretical, related to the benefits of making uncooled detector pixels much smaller than 17 μm. This paper explores some of those considerations.

2.

System MTF Constraints

The overall system MTF consists of a number of contributors including optics, detector (size, shape, fill factor, etc), electronics, motion blur, display, eye, vibration, and atmosphere. For this analysis, the concept of the system MTF is reduced to the sensor side of the system and comprised of the optics and the detector to identify the theoretical limits of an uncooled system. The other components are necessary to translate the theoretical system to a practical system. Here we consider only circular optics and square detectors. Changing these shapes does not change the argument; it merely slightly shifts it. The exception is a system with a highly obscured aperture³ that can have a substantial change in the shape of an MTF curve. For a circular aperture, the optics diffraction MTF curve is described by the following equation, where ${\rho }_c$ is the optics cutoff frequency described by ${\rho }_c=1/\lambda F$. Here $\lambda$ is the wavelength and $F$ is the $F$/number.

The detector MTF for a square pixel is below where $a$ is the instantaneous field of view (IFOV) and $a=d/f$. Here $d$ is the pixel width, f is the focal length, and $u$ is the spatial frequency.

The “system” MTF as described by just the optics and detector is then the multiplication of the optics MTF and the detector MTF.

The ideal detector MTF is dependent solely on the detector size, while the diffraction optics MTF is dependent on the $F$/number and the wavelength. These dependencies are why the relationship between the optics and detector is often described by the ratio $F\lambda /d$. This figure of merit can then be used to describe the regions where a system is described as diffraction limited and where the system is considered detector limited, as done by Driggers.⁴ If we consider the optics cutoff frequency (${\rho }_c$), the detector cutoff frequency ($u_c=1/d$), and the Nyquist frequency [$1/(2u_c)$], three different optics MTF curves can be calculated to identify these regions of interest. Setting the optics cutoff to have zero MTF at the Nyquist frequency results in an $F\lambda d=2$. Setting the diffraction based optics blur to equal the detector pixel size results in an $F\lambda d=0.41$. These two curves generate the regions of the system that are described as “optics limited” and “detector limited.” Driggers also describes a transition region between these two curves.⁴ This transition region can be further split by setting the optics cutoff frequency to equal the detector cutoff frequency, resulting in an $F\lambda d=1.0$. The region that lies between the diffraction limited and this curve can be further described as being “optics dominated,” while the region between this curve and the detector limited curve can be described as being “detector dominated.” In the optics-dominated region, changes to the optics have a greater impact on the system MTF than the detector. Likewise for the detector dominated region. These curves are described in Fig. 1 for the optics and detector MTF and in Fig. 2 for the “system” MTF.

Fig. 1

Optics modulation transfer function (MTF) and detector MTF curves for various $F\lambda /d$ conditions describing the different regions within the design space. Spatial frequencies are normalized to the detector cutoff.

Fig. 2

System MTF curves further illustrating the different regions within the design space for various $F\lambda /d$ conditions. Spatial frequencies are normalized to the detector cutoff.

It is educational to look at the results of the $F\lambda /d$ relationships in the terms of diffraction spot sizes, and relate them to the size of the pixel. Using the Rayleigh spot size formula, $B_{\mathrm{lur}}=2.44*\lambda *F$, when $F\lambda d=0.41$, the spot size equals the size of the pixel. When $F\lambda d=1.0$, the spot size equals 2.44 times the size of the pixel, and likewise, when $F\lambda d=2.0$, the spot size equals 4.88 times the size of the pixel. The relationship for these values and other pixel sizes (historic and potential future) are described in Table 1.

Table 1

Calculations for F/number, spatial frequencies, and spot sizes for various Fλ/d conditions and pixel sizes. F/#≥1.0 for practical optics.

Table 1 and Figs. 1 and 2 highlight a few very key points for trying to determine what the smallest practical reasonable size is for a an uncooled FPA. The motivation for decreasing the pixel size is to enable smaller, lighter optics for a given FOV if NETD remains constant. The optics volume is reduced in terms of focal length and diameter, which translates to reduced size and weight. However, going to smaller pixel sizes increases the $F\lambda /d$ value for any given $F$/number. If we design the system to the absolute resolution limit ($F\lambda d=2$), then the smallest pixel for a 10-μm center wavelength would be 5 μm based on $F$/1.0 optics.

In uncooled systems, sensitivity often drives the designs more than resolution, driving the $F$/number to values between 1 and 1.4. Since sensitivity is inversely proportional to $F^2$, uncooled pixel technology has to continually become more sensitive in order to maintain a reasonable $F$/number. Assuming a fundamental limitation in the sensitivity of a pixel, there will become a point at which our spot sizes will become too large to provide a reasonable sensitivity for the FPA. Historically, most systems have been designed to have a resulting optics blur (to include aberrations) of less than 2.5 pixels ($\sim F\lambda /d<1.0$). This is of course very dependent on the application and range requirements. Figure 3 illustrates the diffraction MTF curve of a lens for a 12-μm pixel at $F$/1.2 as compared to modeled optics designs from larger pixels. In this case, the IFOV remained constant by scaling the focal length and aperture with the pixel size (thus a single detector MTF for the three systems when observed in object space). The aberrated MTF curves for the 25 and 17-μm pixel designs still remain above the diffraction limit for the 12-μm optics with the same IFOV and $F$/number (including aberrations and tolerances). If an equivalent performance is desired from a smaller pixel, a similar MTF is required. In this case, a 12-μm pixel would require the equivalent of diffraction limited MTF curve at $F$/1.2, or roughly the equivalent of performance associated with $F\lambda d=1.0$ to maintain the same performance. Since this is the transition point to the optics-dominated region, any further degradation to the optics via aberrations or tolerances has a more significant impact to the system performance, making the optics more of a challenge as the pixel size shrinks. In this case, a 12-μm pixel with optics at $f$/1.2 would be required to have zero degradation from the diffraction limit to maintain the same performance as the larger pixel systems. In order to obtain the advantage of small pixels, the fabricated optics is required to be closer to the diffraction limit. Selecting pixel sizes that enable systems to be designed outside of the optics-dominated region allow for more leniencies on the optics design and tolerance.

Fig. 3

Optics and detector MTF curves for 12-, 17-, and 25-μm pixel systems showing the aberrated curves from the larger pixels falling slightly higher than the $F\lambda d=1.0$ condition for the 12-μm pixel system.

Current uncooled systems are generally designed at $F\lambda /d\le 1.0$. While the $F\lambda d=2.0$ MTF curve is useful to generate the spatial resolution limits based on diffraction, many applications are not solely limited by resolution, and require an $F\lambda d=1.0$. This is useful knowledge in determining the practical limit in pixel size. Assuming that optics faster than $f$/1.0 are not very practical, it is easy to see from Table 1 that 10 μm may be the most practical minimum pixel size to select. Systems that can benefit from an MTF curve at $F\lambda d=2.0$ (resulting in smaller optics) can still be designed via a slower $F$/number up to $f$/2.0. Systems that required more MTF (such as $F\lambda d=1.0$) are still feasible. If 5 μm was selected as a practical minimum pixel, the flexibility to design the system at anything other than $F\lambda d=2.0$ is gone. This would significantly limit the performance capability for a number of applications for uncooled systems. This flexibility is crucial in determining the practical limitations of the pixel size.

3.

Limiting Factors for Performance of Small Pixel Microbolometers

The small pixel microbolometer development started with the $\sim 25\text{-}\mu \text{m}$ pixel (circa 2001)⁵ that provided a multi layer structure that separated the thermal isolation from the optical fill factor for improved sensitivity. Continued improvements in photolithography and transitioning from projection aligners to 150 mm steppers with line width resolution improving from 2 µm to 0.5 µm (2004–2010) have been sufficient for fabricating the current detector products. Detector designs in the 10- to 13-μm range will require deep ultraviolet (UV) photolithography with line widths $<0.25\mu \text{m}$ (2012 to 2014). The combination of uncooled detector designs and processes have allowed significant advancements in performance improvements and yields; Hence, uncooled has become the technology of choice for low-cost, high-performance systems with reduced size, weight, and power (SWaP). The latest improvement is the transition from 150-mm in-house wafer production facilities to commercial CMOS/MEMS (class1) foundries⁶ with low defect, high yield, and 200-mm high-volume wafer capability. Figure 4 is an example SEM of foundry-processed bolometer with leg widths of $<\mathrm{0.0.2}\mu \text{m}$ for single-level and multi-level designs.^7–9

Fig. 4

SEMs of 17-μm bolometer pixels with fine line geometry for (a) single- and (b) multiple-level pixel designs.

There is, however, a significant design and process challenge for microbolometer designs $<17\mu \text{m}$. Specifically, with as much as a $15\times$ to $25\times$ reduction in pixel area from the initial 50-μm designs, there is a proportional increase in NETD (Sec. 4) unless significant design changes are made for pixels in the range of 12 μm (a notional design for illustration), and even more so for 5-μm pixels. This design requires a significant decrease in thermal conductance, such as decreasing leg width and thickness or an increase in leg length to maintain sensitivity while thinning the bridge for lower mass to reduce or maintain a reasonable time constant. Figure 5 shows actual SEMs for bolometer pixels of 50-, 25-, and 17-μm designs with approximate area scaling added for a notional 12-μm design. This figure clearly demonstrates the area challenges when the pixel size is reduced from 50 μm to notionally 12 μm and the importance of having a fine-line photolithography capability to make the desired changes stated above.

Fig. 5

Significant design and process challenges exist when a bolometer structure is reduced from 50 μm to a notional 12-μm design.

4.

Design Considerations and Practical Limits

The theory below provides a roadmap of design considerations and tradeoffs that need to be addressed for all bolometer pixel designs especially as the pixel area is decreased. The basic equation for a typical VOx detector and its NETD is given as^10–12

The temperature fluctuation term $\mathrm{\Delta }{T}_{\mathrm{TF}}$ represents the noise remaining when all the terms under the radical are small compared to one. It represents the noise due to the exchange of heat between the detector and its surroundings through the thermal conductance of the legs suspending the detector over the substrate and also the radiation conductance of the detector with its surroundings, including the scene seen through the lens. Due to a combination of cost and practical limitations of the lithography tools available to manufacture suspended structures, the thermal conductance of the legs is presently much larger than the radiation conductance for smaller pixels at this time. Thus, we are still far from the fundamental limits of performance at which typically cooled detectors operate.

It is not practical to make all of the noise terms fully negligible compared to the temperature fluctuation noise. In practice, the second term representing the electrical Johnson noise contribution of the detector often requires a considerable electric bias pulse be applied. Many designs target this term to be about one or equal to the temperature fluctuation noise. For typical TCR values of 2.5%, the bias-induced temperature change on the detector would need to exceed 10°C. However, for bias-induced temperature changes at this level and larger, the simple approximations for NETD begin to break down.¹⁰ The third term represents $1/f$ noise of the detector, which increases as the detectors become smaller. To the extent it becomes a problem, materials research work becomes necessary to figure out how to lower the $1/f$ noise factor constant ($\chi$), since it depends on volume and material properties. This term, along with additional downstream noise introduced by the readout electronics, is generally thought not to exceed the total noise by more than twice the temperature fluctuation noise.

Further design constraints are a 10-ms second time constant for an approximate match for a 30-Hz (or 60-Hz) video frame rate, and maintaining a sensitivity of $\sim 35\mathrm{mK}$ as we reduce the pixel size. With the total noise set at about two times the temperature fluctuation noise and all the other parameters now known, the problem reduces to the value of thermal conductance needed once the detector size is selected.

The design relations indicate that as the pixel gets smaller, the conductance must go down. This is because as the detector area decreases resulting in less signal power, the thermal conductance must decrease to maintain the same response. But as the pixel gets smaller, absent a change in design rules allowing legs with smaller cross sectional area, the legs get shorter and the thermal conductance increases. In the past, some designs made the legs longer by folding them underneath the pixel as the size went from 50 to 17 μm (Fig. 4). This allowed the legs to be thinner and/or narrower by separating the thermal isolation from the optical fill-factor. Reducing the pixel size from 17 to $\sim 10\mu \text{m}$ and assuming the same total noise as twice the temperature fluctuation value, and maintaining the absorption efficiency and time constant, requires that the thermal conductance go from values near ${10}^{-8}\mathrm{W}/\mathrm{K}$ to ${0.3\times 10}^{-8}\mathrm{W}/\mathrm{K}$. While there is no theoretical physics reason that stands in the way, other than some potential $1/f$ noise issues, the practical problem is whether a bolometer manufacturer possesses or has access to lithography tools at an acceptable cost to manufacture the bridges and legs to achieve such thermal isolation and accompanying thermal mass, and also to make denser read-out integrated circuits (ROIC). Often, the first resort is to push or stretch the capabilities of existing tools used to make a previous generation of detectors for making smaller designs, but that is usually at the cost of lower yields. Whether that is acceptable depends on the importance and benefits of the smaller design together with any savings of lower materials costs. Therefore the use of CMOS/MEMS (class1) commercial foundries is one way to take advantage of a huge process capability.

While there are reasons, as explained above, for not making uncooled pixel smaller than between 5 and 10 μm, depending on the particulars for long-wave infrared (LWIR) applications, there is room to make the detector more sensitive for several reasons. The first is that it allows a trade against $F$/number and Blur to maintain the system NETD (i.e., smaller optics). Second, it can be traded for shorter time constants while maintaining system NETD.

5.

Approaching the Performance Limit

We can obtain a basic qualitative idea of the limit in performance subject to and in the context of some simplifying approximations, including absence of bias effects. We note that $G$ is actually the sum of the thermal conductance of the legs $G_l$ and $g_r$ where $g_r$ is the radiation conduction that remains when the legs hypothetically disappear. The radiation conductance arises from the first term of the expansion of Wien’s law for radiating bodies. That is:

By explicitly writing the thermal conductance as the sum of leg and the radiation conductance and with slight rearrangement, we can write where $N_i$ denotes noise terms other than temperature fluctuation:

Whereas we may desire to make $G_l$ tend toward zero leaving only the radiation conductance to boost signal and reduce NETD, we also desire to keep the thermal time constant fixed to maintain the frame rate or information rate for the camera. The thermal time constant is

Thus we see that reducing the thermal conductance requires reducing the thermal mass. We note that reducing the thermal mass tends to increase the total temperature fluctuation exchange noise and reaches the maximum when $G_l$ becomes zero. Replacing $C_{\mathrm{th}}$ in the first radical we obtain:

In this simple description, the NETD can be reduced by taking $G_l\to 0$ or reducing the noise terms $N_1$, $N_2$ etc. or both. Reducing $G_l$ to zero we obtain

We reach the ideal NETD when all noise sources are small except for the temperature fluctuation noise so that only the term 1 remains in the sum of noises. We obtain

This last approximation may stretch the limits of the initial assumption that the bias power and its contributions are negligible.^10–12

Assuming an 8- to 12-μm band, 100% efficiency, 300 K, 10-μm detectors, and $\varsigma$ to be somewhere around $1/3$, $F=1$ and 10 ms time constant, we obtain an NETD $\sim 1.5\mathrm{mK}$. The radiation conductance is approximately ${0.0044\times 10}^{-8}\mathrm{W}/\mathrm{K}$. To achieve that, we would need to have the detector levitate over the substrate and have a warm shield and substrate that does not interact with the detector. If we may assume a reflecting warm-shield that contributes about the same as the radiation conductance through the lens and 70% absorption efficiency, some leg conductance near the radiation limit to allow for electrical connections and three equal parts noise added to temperature fluctuation noise, we may get into the neighborhood of 7 or 8 mK. While state-of-the-art equipment exists to contemplate an attempt to make detectors with the required thermal conductance and accompanying thin bridges to maintain usable time constants, the demand for detectors approaching the radiation limit and the cost to realize such a device is not currently considered for uncooled products.

6.

Summary and Conclusions

The trades between System MTF and smaller pixels allowing smaller die suggests that pixels sizes may be reduced to between 5 and 10 μm for uncooled LWIR applications. The benefits of doing so are smaller optics, smaller die and systems, and less weight and power assuming that performance metrics are maintained. In addition, smaller pixels provide more FPAs per wafer (lower cost/die) or permit larger formats at a reasonable cost. This may require better optics designs, since at such smaller pixels the optics MTF may become a limiting factor. It also requires uncooled detectors that have significant better sensitivity due to loss in signal as the size decreases, and will require better photolithography tools to manufacture the thin bridges and legs required to maintain sensitivity. This is mainly related to access or availability of such tools at a reasonable cost. Additionally, there is still considerable improvement possible as present uncooled bolometer detectors are still far from the fundamental limits of performance. Flexibility in system design suggests that pixel sizes smaller than 10 μm may be the practical limit for a focal plane that would be used for all applications.