Hammerhead, an ultrahigh resolution ePix camera for wavelength-dispersive spectrometers

TL;DR

This paper introduces a novel high-resolution ePix camera with rectangular 'strixel' sensors for wavelength-dispersive spectrometers, achieving ultrahigh spatial and energy resolution with low noise and simplified integration.

Contribution

The paper presents a new sensor design using high aspect ratio pixels and redistribution techniques, enabling ultrahigh resolution in WDS without redesigning ASICs.

Findings

Achieved ~1 μm position resolution in the dispersion direction.

Demonstrated low noise performance (43 e$^-$, 180 eV rms).

Enabled precise photon counting and subpixel position reconstruction.

Abstract

Wavelength-dispersive spectrometers (WDS) are often used in synchrotron and FEL applications where high energy resolution (in the order of eV) is important. Increasing WDS energy resolution requires increasing spatial resolution of the detectors in the dispersion direction. The common approaches with strip detectors or small pixel detectors are not ideal. We present a novel approach, with a sensor using rectangular pixels with a high aspect ratio (between strips and pixels, further called "strixels"), and strixel redistribution to match the square pixel arrays of typical ASICs while avoiding the considerable effort of redesigning ASICs. This results in a sensor area of 17.4 mm x 77 mm, with a fine pitch of 25 $\mu$m in the horizontal direction resulting in 3072 columns and 176 rows. The sensors use ePix100 readout ASICs, leveraging their low noise (43 e$^-$, or 180 eV rms). We present results obtained with a Hammerhead ePix100 camera, showing that the small pitch (25 $\mu$m) in the dispersion direction maximizes performance for both high and low photon occupancies, resulting in optimal WDS energy resolution. The low noise level at high photon occupancy allows precise photon counting, while at low occupancy, both the energy and the subpixel position can be reconstructed for every photon, allowing an ultrahigh resolution (in the order of 1 $\mu$m) in the dispersion direction and rejection of scattered beam and harmonics. Using strixel sensors with redistribution and flip-chip bonding to standard ePix readout ASICs results in ultrahigh position resolution ($\sim$1 $\mu$m) and low noise in WDS applications, leveraging the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development complexity through sharing the ASIC, hardware, software and DAQ development with existing versions of ePix cameras.

Figures

Equations

$$V\ge V_D=\frac{q_{e}N{d}^2}{2\epsilon }$$

$$x_1=\frac{\epsilon {\mu }_n{\rho }_{n}V}{d}-\frac{d}{2},x_2=x_1+d.$$

$$t_{d}(\xi)=\frac{x_{2}-\xi}{v_{s}}+\frac{\ln\big{(}\frac{x_{2}}{\xi}\big{)}}{b}$$

$$\sigma (\xi )=\sqrt{2D{t}_d(\xi )}.$$

$$I(\xi )=I_0{e}^{-\mu (\xi -x_1)}=I_0{e}^{-\mu (\xi -x_2+d)}$$

$$\bar{\sigma}^{2}=\frac{\int_{x_{2}-d}^{x_{2}}\sigma^{2}(\xi)p(\xi)d\xi}{\int_{x_{2}-d}^{x_{2}}p(\xi)d\xi}=\frac{2D\mu}{1-e^{-\mu d}}\int_{x_{2}-d}^{x_{2}}\bigg{[}\frac{x_{2}-\xi}{v_{s}}+\frac{\ln\big{(}\frac{x_{2}}{\xi}\big{)}}{b}\bigg{]}e^{-\mu(\xi-x_{2}+d)}d\xi$$

$${\bar{\sigma }}^2=-\frac{1}{\mu v_s}\frac{e^{-\mu d}+\mu d-1}{e^{-\mu d}-1}+\frac{1}{b}\frac{e^{\mu x_2}[Ei(\mu x_1)-Ei(\mu x_2)]+e^{\mu d}\ln (\frac{x_2}{x_1})}{e^{\mu d}-1}$$

$$Ei(x)=-{\int }_{-x}^{\infty }\frac{e^{-t}}{t}dt$$

Full text

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in AIP Conf. Proc. 2054, 060037 (2019) and may be found at https://doi.org/10.1063/1.5084668 .

1 INTRODUCTION

Wavelength-dispersive spectrometers (WDS) are often used in synchrotron and FEL applications where high energy resolution (in the order of eV) is important [1, 2]. Increasing WDS energy resolution requires increasing spatial resolution of the detectors in the dispersion direction. One approach to increase the resolution is to use small pixel sizes (e.g., $25\text{\times}25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ [3]), however, the small ASIC size and complex charge sharing are challenging [4].

Another approach to increase the resolution while maintaining the advantages of pixel detectors over strip detectors (high counting rates, 2D position sensitivity) is to design rectangular pixels with a high aspect ratio (between strips and pixels, further called “strixels”). Developing new readout ASICs with rectangular pixels is complex. However, existing readout ASICs for hybrid pixel detectors can be easily matched with novel sensors with rectangular strixels where the strixel contacts are redistributed to match the square pixel arrays of typical ASICs.

The Hammerhead camera uses two novel strixel sensors, developed at SLAC, with a total of $176\text{\times}3072$ strixels of $100\text{\times}25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ redistributed to match regular $50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ ASIC pixel arrays. Each sensor is flip-chip bonded to two ePix100 readout ASICs [5, 6], leveraging their high resolution ($50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$) and low noise performance ($180\text{\,}\mathrm{eV}$ rms or $43\text{\,}\mathrm{e^{-}}$ equivalent noise charge, ENC).

We present results obtained with a Hammerhead ePix100 camera, showing that the small pitch ($25\text{\,}\mathrm{\SIUnitSymbolMicro m}$) in the dispersion direction maximizes both the subpixel resolution and the energy resolution of charge summing, while yielding good results at high photon occupancies. The low noise level at high photon occupancy allows precise photon counting, while at low occupancy, both the energy and the subpixel position can be reconstructed for every photon, allowing an ultrahigh resolution (in the order of $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$) in the dispersion direction and rejection of scattered beam and harmonics.

Using strixel sensors with redistribution and flip-chip bonding to standard ePix readout ASICs results in ultrahigh position resolution (\sim$$1\text{\,}\mathrm{\SIUnitSymbolMicro m}) and low noise in WDS applications, leveraging the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development complexity through sharing the ASIC, hardware, software and DAQ development with other versions of ePix cameras [7].

2 MATERIALS AND METHODS

2.1 High Resolution Sensor

We developed a novel spectroscopic sensor with high aspect ratio pixels (further called “strixels”), redistributing the contacts of the $100\text{\times}25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ strixels to a regular grid of $50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of flip-chip bonding pads and matching the existing ePix100 readout ASICs [5]; details show in Fig. 1.

Each sensor has a size of $17.6\text{\times}39.2\text{\,}\mathrm{mm}$, with a strixel size of $100\text{\times}25\text{\,}\mathrm{\SIUnitSymbolMicro m}$, resulting in $176$ rows and $1536$ columns with a high position resolution along the horizontal axis. Each sensor is flip-chip bonded to two ePix100 ASICs [5], which have a low noise ($43\text{\,}\mathrm{e^{-}}$ equivalent noise charge, or $180\text{\,}\mathrm{eV}$ rms) and high signal to noise ratio [8].

The strixel sensors presented here use typical n-type silicon with a thickness of $500\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and a resistivity of \rho=$$10\text{\,}\mathrm{k\SIUnitSymbolOhm}\text{\,}\mathrm{cm}; other versions are easy to develop. The development of the novel sensor was far less labor intensive than an alternative development of read-out sensors and ASICs with a matching rectangular shape.

2.2 Hammerhead ePix100 Camera

Two sensors are assembled side-by-side in a typical Hammerhead ePix100 module, as shown in Fig. 2 (a). This results in a module with a sensor area of $17.6\text{\times}77\text{\,}\mathrm{mm}$ and $3072$ columns with a width of $25\text{\,}\mathrm{\SIUnitSymbolMicro m}$.

The Hammerhead ePix100 cameras are built around ePix100 hybrid pixel detector modules using the ePix camera platform [7, 9], sharing development of the electronics, mechanical, thermal, vacuum and communication with all other cameras in the family.

2.3 Experimental Setup and Data Processing

We used an 55Fe radioactive source, yielding mainly Mn K\textalpha at $5.9\text{\,}\mathrm{keV}$ and a small amount of Mn K\textbeta at $6.5\text{\,}\mathrm{keV}$. The source was placed $4\text{\,}\mathrm{cm}$ from the sensors to illuminate the entire area of the two sensors. For each data set, $16\,384$ frames were acquired. The raw data was subsequently processed (dark subtraction, common mode correction, gain correction, droplet reconstruction, subpixel resolution, histogrammed).

All processing was performed with Tensorflow algorithms, taking advantage of recent advances in machine learning (software, GPU support) and yielding 1-2 orders of magnitude faster processing with much simplified code (for details see [10]). This approach enables real time processing of the raw data stream, reducing it to sparse photons and their subpixel resolution (at low photon occupancy), or photon counting data (at high photon occupancy), which can be orders of magnitude more compact than the raw data of integrating detectors.

Note that a gain correction is only useful when extracting the energy dispersive spectrum or subpixel resolution; for photon counting at low occupancy, an average gain is sufficient (as the pixel gain variation is limited to a few percent and has an insignificant effect on photon counting).

3 RESULTS

3.1 High Resolution Imaging and WDS Resolution

The fine horizontal pitch of $25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of the Hammerhead ePix100 camera results in a high resolution of $25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (obviously) in the horizontal, i.e., energy dispersive direction, for signals with high photon occupancy. An example of imaging with high horizontal resolution is shown in Fig. 1(a); the displayed height-to-width ratio corresponds to the physical sensor size; note however the fine pitch in the horizontal direction, corresponding to pixels of $100\text{\times}25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (height x width). The corresponding high resolution spectrum is depicted in Fig. 1(b).

3.2 Energy Dispersive Resolution

The relatively small pixel size ($25\text{\,}\mathrm{\SIUnitSymbolMicro m}$) in the horizontal direction results in a relatively large amount of charge sharing between neighboring pixels in the horizontal direction. In the vertical direction, charge sharing is minimized by the large vertical pixel size (of $100\text{\,}\mathrm{\SIUnitSymbolMicro m}$). Because charge sharing is mostly due to the horizontal charge sharing, both the energy dispersive spectrum and the subpixel resolution can be calculated with high accuracy.

The energy dispersive spectrum results are shown in Fig. 4; the thick red line indicates the raw spectrum and the thick black line shows the result of charge summing (which rectifies the effect of charge sharing). Panel (a) shows the results at a typical bias voltage of $200\text{\,}\mathrm{V}$, while panel (b) shows the results with intentionally maximized charge sharing. Note that in both cases, charge summing rectifies the position of the photon peak at $83$ ADU.

The thin lines indicate the contributions of individual photons with charge cloud sizes of $1$, $2$ and $3$ pixels. At $200\text{\,}\mathrm{V}$, $81\text{\,}\mathrm{\char 37\relax}$ of photons are detected in $2$ pixel clusters and $17\text{\,}\mathrm{\char 37\relax}$ in $1$ pixel clusters. At $100\text{\,}\mathrm{V}$, $71\text{\,}\mathrm{\char 37\relax}$ of photons are detected in $2$ pixel clusters and $26\text{\,}\mathrm{\char 37\relax}$ in $3$ pixel clusters.

3.3 Subpixel resolution at low photon occupancy

This results at a typical bias voltage of $200\text{\,}\mathrm{V}$ in a high subpixel accuracy for horizontal detection further than $5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ from the center of the nearest pixel, and no subpixel accuracy within $2.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of the pixel center; in practice, the subpixel position resolution is limited to $5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in this case, see Fig. 5(a).

The average charge cloud size depends on the photon energy, sensor characteristics (thickness, resistivity), and bias voltage (for a discussion, see next subsection); decreasing the bias voltage to $100\text{\,}\mathrm{V}$ results in larger photon clouds, Fig. 4(b), resulting in turn in a high position resolution in the order of $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ everywhere, including photons detected near the center of the pixels.

Successful measurements with ultrahigh subpixel resolution (in the order of $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$) require optimization of the bias voltage for the photon energy, and a calibration of the relation between centroid positions and corresponding photon positions (using either measurement statistics, see Fig. 6, or theoretical considerations, see next subsection).

3.4 Size of Photon Charge Clouds

Sensors in hybrid pixel detectors are typically reverse-biased p-n junctions; after photon detection and conversion to electron-hole charge clouds, the charge drift can be described by the partial differential equations describing charge drift, diffusion and recombination [11]. We derive from first principles the factors that influence the size of the charge clouds, which in turn are important for optimizing detector parameters for subpixel resolution.

For a fully depleted sensor, the bias voltage $V$ must be higher than minimum voltage for full sensor depletion $V_{D}$:

[TABLE]

which for the sensor described in this paper is \sim$$85\text{\,}\mathrm{V} (calculations and measurements in good agreement). Using the convention in [11], with coordinate $x$ denoting the depth of the sensor measured from the origin of real or virtual transition from fully depleted to undepleted region, the front and back planes of the fully depleted sensors are at

[TABLE]

The charge drift time from photon detection depth $\xi\in(x_{1},x_{2})$ to position $x_{2}$ is

[TABLE]

leading to a lateral charge cloud size due to thermal diffusion

[TABLE]

which is a function of sensor bias $V$ and actual photon detection depth in the sensor $\xi$. The distribution of photon detection depths follows the typical exponential decay function

[TABLE]

where $\mu$ is the linear attenuation coefficient in the sensor (Si) corresponding to the photon energy $E$. Using this distribution allows calculating an average cloud size as a quadratic weighted average of the cloud sizes for all possible detection depths, weighted by their probabilities:

[TABLE]

[TABLE]

where $Ei$ is the exponential integral:

[TABLE]

The average charge cloud size depends thus on the bias voltage $V$ and photon energy $E$ as shown in Eq. 7.

4 CONCLUSIONS

Strixel sensors with redistribution leverage the advances in 2D hybrid pixel detector development, reusing existing pixel readout ASICs with minimal effort and enabling high horizontal resolutions for wave dispersive spectrometer applications. Strixel sensors maintain all advantages of 2D pixel detectors (high counting rate, 2D position sensitive) and enable a high position accuracy of $25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in all conditions.

By using subpixel resolution at low photon occupancies, an ultrahigh horizontal position resolution of $5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ with default sensor bias of $100\text{\,}\mathrm{V}$, and $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ with bias optimization. The high subpixel resolution is enabled by the high signal to noise ratio operation of the ePix100 cameras.

The Hammerhead ePix100 cameras leverage the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development complexity through sharing the ASIC, hardware, software and DAQ development with other versions of ePix cameras.

Using strixel sensors with high aspect ratio pixels results in a fine pitch in the energy dispersive direction. By redistributing the flip-chip bonding pads to match the square grid of existing ASICs we obtain a low noise and ultrahigh position resolution ($25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ at high photon occupancy and $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ at low photon occupancy) in WDS applications, leveraging the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development effort through sharing the ASIC, hardware, software and DAQ development with other versions of ePix cameras [12]. Versions for other readout ASICs with different pixel pitches are easy to develop.

5 ACKNOWLEDGMENTS

Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Publication number SLAC-PUB-17276.