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Room-temperature single-photon detector based on single nanowire Wenjin Luo, Qianchun Weng, Mingsheng Long, Peng Wang, Fan Gong, Hehai Fang, Man Luo, Wenjuan Wang, Zhen Wang, Dingshan Zheng, Weida Hu, Xiaoshuang Chen, and Wei Lu Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b01795 • Publication Date (Web): 22 Aug 2018 Downloaded from http://pubs.acs.org on August 23, 2018

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Room-temperature single-photon detector based on single nanowire Wenjin Luo#,†,‡,§, Qianchun Weng#,†,§, Mingsheng Long†,§, Peng Wang†,§, Fan Gong†, Hehai Fang†,§, Man Luo†,§, Wenjuan Wang†,§, Zhen Wang†,§, Dingshan Zheng†, Weida Hu*,†,‡,§, Xiaoshuang Chen†,§, Wei Lu*,†,§ †

State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics,

Chinese Academy of Sciences, Shanghai 200083, China. ‡

Synergetic Innovation Center of Quantum Information and Quantum Physics,

University of Science and Technology of China, Hefei 230026, China. §

University of Chinese Academy of Sciences, Beijing 100049, China.

#

These authors contributed equally to this work.

*

Corresponding authors: W. H. (email: [email protected]); W. L. (e-mail:

[email protected]).

ABSTRACT: Single-photon detectors that can resolve photon number play a key role in advanced quantum information technologies. Despite significant progress in improving conventional photon-counting detectors and developing novel device concepts, single-photon detectors that are capable of distinguishing incident photon numbers at room temperature are still very limited. Here, we demonstrate a room-temperature photon-number-resolving detector by integrating a field-effect transistor configuration with core/shell-like nanowires. The shell serves as a photo-sensitive gate, shielding negative back-gated voltage, and leads to a persistent photocurrent. At room temperature, our detector is demonstrated to identify 1, 2, and 3 photon-number states with a confidence of more than 82%. The detection efficiency is determined to be 23% and the dark count rate is 1.87×10-3 Hz. Importantly, benefiting from the anisotropic nature of one-dimensional nanowires, the detector shows an intrinsic photon-polarization selection, which distinguishes itself from existing intensity single-photon detectors. The unique performance for the single-photon detectors based on single nanowire demonstrated the great potential for future single-photon detection applications.

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KEYWORDS:

single-photon

detectors,

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photon-number-resolving

capability,

room-temperature operation, polarization sensitivity

For decades, single-photon detectors (SPDs) have drawn tremendous attention in the fields of quantum information and quantum communications technology1-3. Many kinds of SPDs such as avalanche photodiodes (APDs)4-6, photomultiplier tubes (PMTs)7,8,

superconducting

nanowire

single-photon

detectors

(SNSPDs)9-11,

transition-edge sensors (TESs)12,13, visible light photon counters (VLPCs)14,15, frequency up-conversion16,17 and quantum dot based single photon detectors (QD-SPDs)18,19 have been widely studied. SPDs have been developed for more than 20 years and are commercially available today. However, they still have some limitations that can be improved, such as the ability for room temperature operation, photon-number-resolving capability, high detection efficiency, low dark count rate, ease of fabrication and operational convenience. For example, the APD SPDs need to operate in the high operating voltage Geiger mode as in PMT SPDs. Furthermore, except for APDs and PMTs, most SPDs need to work in cryogenic temperatures of several

Kelvins.

Though

TESs

and

SNSPDs

are

capable

of

efficient

photon-number-resolving detection and have been routinely applied in the quantum key distribution field, the required operating temperature of a few tenths Kelvins is too low for a wide range of applications. Moreover, early efforts in the fabrication process of SPDs based on epitaxial semiconductors added complexity due to epitaxial crystal growth requirements and the need to mitigate material contamination and impurity

doping.

In

communications,

for

many

protocols,

the

photon-number-resolving functionality is so crucial that few SPDs, such as partial APD, PMT and VLPC, TES, QD-SPD can be implemented. However, the QD SPDs, including

quantum

dot-field-effect

transistor

SPD18,20,

quantum

dot-resonant-tunneling diode SPD19 and quantum dot-single-electron transistor SPD21, have many advantages, such as room-temperature detection, nonvolatile memory, high theoretical quantum efficiency, low dark count rate and low operating voltage. In addition, QD SPDs have the potential to identify spin photons, which will play an 2


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important role in the quantum memory and repeater technologies. Very recently, two different photodetection mechanisms using both the positive and negative photoresponse of nanowires (NWs) have been discovered22-25. Except for the photoconductive effect of positive photoresponse, the surface states of NWs can also lead to positive or negative photoresponse by the photogating effect, and act as optically addressable floating gates analogous to quantum dots (QDs) in previous work18. Many papers have reported superior performance in low-dimensional photodetection at room temperature26-32 with devices enhanced by the photogating effect. For instance, the responsivity and gain can reach 107 A/W and 108 electrons per photon for QDs-based phototransistors33. However, to the best of our knowledge, most reported photodetectors based on photogating effects are focused primarily on the performance of responsivity and detectivity and little success has been made in the operation of single-photon detection. Previously, some results show that epitaxial semiconductors have a certain response to photons, but the impressive performance was achieved at extremely low temperatures of 4 K18. In this work, we propose a novel approach for the development of photon-number-discriminating,

room-temperature,

easily

manufactured

and

cost-effective SPDs by appropriately integrating field-effect transistors (FETs) with a cadmium

sulfide

(CdS)

semiconductor.

Specifically,

we

demonstrate

that

semiconductor NWs with a core/shell-like structure can be used as active elements for the detectors based on the photogating effect. Our technique exploits a photogating effect which is formed after the photogenerated holes are trapped by the shell (photogating layer) and alleviates the scattering effect from negative back-gated voltages to the core. As a result, a current increase of 0.5 nA was achieved in the experiment. In addition, our detector shows excellent performance with the photon-number resolutions at a low bias voltage of Vds = 0.1V and Vbg = -3V at room temperature. Furthermore, the one-dimensional anisotropic nature of a nanowire can directly identify the polarization of incident photons, which plays an important role in quantum key distribution34 and polarimetric imaging systems35. Specifically, monolithically integrated SPD devices with on-chip photon-number resolving 3


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capability

and

photon-polarization

sensitivity

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to

directly

measure

the

polarization-encoded quantum state of qubits are critical in the quantum key distribution field. Here, we demonstrate the physical principles that govern the operation of the photogating effect dominated SPD through experiments and numerical calculations, and show the great potential of the device with easily fabricated techniques. Figure 1a shows the sketch of the back gate, core/shell-like NW and FET configuration. The upper panel of Figure 1a shows a three-dimensional schematic view of the NW FET and an illustration of a single core/shell-like NW, in which the core is a CdS single crystal and the shell is the self-assembled photogating layer (PGL). The bottom plot shows the three-dimensional schematic front view of the FET. In this work, by controlling the source temperature and the pressure in the growth chamber using a conventional chemical vapor deposition (CVD) method, we enabled the growth of core/shell-like NWs with perfect single crystal cores and highly defective shells (see Methods). To intuitively observe the core/shell structure of the CdS NW, we obtained transmission electron microscopy images of a typical CdS NW (see Supporting Information Figure S1). The result shows that the NW contains a well-crystallized core with neatly arranged lattice structure and a defective shell with an uneven surface (native oxide layer), regard as the self-assembled PGL. The core of NW has also been examined by high-resolution transmission electron microscopy (see Supporting Information Figure S2), which clearly indicates the core is a perfect CdS single crystal. The basic electrical characteristics of an as-fabricated device were measured and a scanning electron microscopy image was obtained (see Supporting Information Figure S3). Besides, the passivation experiments have been done (see Supporting Information Figure S4). To clearly understand the positive contributions of photogating effects to the photocurrent, the working principle schematics are shown in Figure 1 b,c. A negative bias is applied to the back gate, which effectively suppresses the channel current and reduces the dark noise. When photons reach the NW core, photo-excited electrons and holes are separated by the internal electric field. The holes are directed towards the 4


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PGL in which there are abundant randomly distributed trapping centers to capture and maintain photogenerated holes for minutes to hours (Figure 1b), while electrons remain in the core. Trapped by the PGL, positively charged holes screen the internal gate field, enhancing electron concentration in the core through capacitive coupling (Figure 1c) and a macroscopic increase of Ids could be easily monitored. In other words, the core acts as a resistance, determining the dark current associated with its diameter and channel length, while the shell, acting as the photogating layer, can form a gate-like voltage to modulate the carrier density of the core of the nanowire when the incident photons illuminate the device. And this structure is similar to a Bipolar Junction Transistor (BJT). The effective change in the channel current, under the small-signal limit, is caused by the trapping of populated N photogenerated holes in the PGL. It can be written18,36 by

△I = g eW Nη εA ds

m

(1)

where e is the elementary charge, W is the thickness of SiO2, ε is the dielectric constant of SiO2, A is the active area and η is the correction factor of our device model (see Supporting Information Figure S5). Therefore, the PGL charged even by a single trapped hole can lead to a dramatic change in the channel current. In addition, the transconductance gm related to this process has a key role in determining the photon sensitivity of the device. Moreover, according to equation (1), △Ids is proportional to N, so N can be provided by the direct measure of current response. To investigate detector detectability, we illuminated the device with an attenuated light-emitting diode (LED) having a center wavelength of 457nm. The photons emitted from the LED had no specific polarization. Quantized current changes under weak illumination are monitored in the time-trace of current, labeled with 1-photon detection, 2-photon detection and 1-photo-hole neutralization as shown in Figure 2 (the collecting data rate is 0.6s and more cases can be seen in see Supporting Information Figure S6). The increased quantized current signals are 0.33 nA, 0.48 nA, 0.52 nA, 0.62 nA, 0.73 nA, 0.99 nA and 1.2 nA. According to equation (1), a net 5


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photocurrent of 0.5 nA excited by a single photon and 1nA by two photons can be calculated, when gm is 7.26×10-8 A/V, W is 100nm, A is 0.0785µm2, ε(SiO2) is 3.9×8.85×10-12 F/m, e is 1.6×10-19 C and η is 1.16. On the other hand, among the data of quantized increased currents, 0.5 nA current results dominate while 0.99 nA or 1.2 nA results appear approximately twice as frequently as 0.5 nA results, which fit the calculated data quite well. Note that there are two quantized current drops with the values of -0.4 and -0.55 nA respectively, as shown in Figure 2. This is because the photo-excited holes captured by the PGL have a large probability to escape when the devices are working at room temperature, leading to the photo-holes neutralization. To obtain the time-trace of current, the power of the LED is attenuated to five different low levels which illuminate the device without specific polarization (Figure 2). This process is repeated many times, then we individually construct five histograms of the measured time-trace of current. The left column of Figure 3 shows , five histograms with the mean number of detected photons per illumination, which is labelled on each panel (see method). As discussed above, we have known that △Ids = 0.5nA × N. In Figure 3, grey vertical lines represent current changes caused by the detection of N = 0, 1, 2 and 3 photons. To take into account the detector response, every photon-number peak is fitted by Gaussian distributions (red dashed curves). Green curves are the superposition of Gaussian functions and fit quite well with the experimental data. In the absence of light, there is only a single high peak which is associated with noise and the detection of zero photons. The spread in the distribution should be ascribed to the current fluctuations induced by electrical noise. By comparison, when the detector is weakly illuminated, additional distinct peaks are observed in the data, clearly showing that the distinct peak centers are approximately 0.5 nA, associated with the detection of 1 photon. But since the peak of zero photons is too high to observe the rest of the details clearly, we translate the ordinate to the bottom (see the right column of Figure 3). Apart from the second figure labelled with = 0.44 (to be discussed below), the remaining graphs reveal that the peak centers are around 1nA, associated with the detection of 2 photons. Moreover, these figures point out that the peak of N = -1 is consistent with the de-trapping of holes, as 6


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described in Figure 2. Additionally, the peak altitude of N = -1 decreases relative to . Due to the increase in the incident photon that of N = 1 along with the increase of numbers, the increase in the number of the photogenerated holes captured will cover the escaping holes, that is, the observable probability of quantized current drop decreases. Despite this, it does not prevent the device from detecting a single photon. As an added bonus, it should be noted that the last graph shows a distinct peak center at around 1.5 nA, which shows that the detector has the capability of detecting 3 photons at room temperature. An

ideal

detector

should

have

a

perfect

figure

of

merit

of

photon-number-resolving with 100% probability of accuracy. In practice, however, detectors suffer uncertainty that leads to ambiguity in the determination of N. A proper solution assigning decision regions for the current changes related to different photon number states is necessary. The solution has two operational steps. In the first step, we use the points where preceding and succeeding Gaussian functions intersect to define the boundary of the decision regions. In the next step, we use the ratio of the area of the corresponding Gaussian function over total area of all Gaussian functions in the decision region, to evaluate the accuracy probability for each number state. In Table 1 we list the estimated probability of correctly determining the photon number states = 1.46. The 82% confidence of N = 1 is not using defined decision regions for high, which is attributed to the fact that the peak with zero photons is too high, resulting in the right shift of the point where the zero-photon Gaussian function and the single-photon Gaussian functions intersect. One of the data previously mentioned in Figure 2, the 0.33 nA current result, is assumed to be caused by a single photon-excited hole, in relation to the decision region ranging from 0.35 nA to 0.79 nA. The detection efficiency and dark count rate are important parameters for SPDs. Figure 3 shows a dark count rate of 1.87×10-3 Hz under no illumination. Figure 4a demonstrates the relation of the dark count rate to photon flux based on the results shown in Figure 3. It is found that the detection efficiency is 23%. The devices also demonstrate the possibility of photon-number-resolving capability. In addition, the 7


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photoresponse spectrum of the devices has been measured (see Supporting Information Figure S7). In order to further describe the existence of the PGL and its effect on the photoresponse, we studied the time-resolved photoresponse of the device. = Figure 4b demonstrates the time-resolved photoresponse of the device with 0.72 photons/s at Vds = 0.1V. At t = 0, Vbg = 0, Ids is the initial dark current. After 100 seconds, we changed Vbg to -3V, and the carrier concentration in the channel was modulated to a low level and Ids stabilized at around 11nA. After 180 seconds, we turned on the LED so that several photons arrived at the device. Over time, as shown in Figure 2, a phenomenon of several quantized current changes was observed. During the long time of illumination, the device can detect the photon numbers from one to a large number (several mW), which is attributed to its significant defective shell which can capture many photogenerated holes. With this wide linear dynamic range, it has an important application in photon imaging. The detector response speed between adjacent illumination levels is approximately 4 ms (see Supporting Information Figure S7). The LED was turned off at the time of t = 580s and there was no rise of Ids. After an additional 100s, Ids instantly came back to dark current as Vbg = 0V. However, the dark current at this moment is slightly greater than the initial one, the difference being 10nA (refer to the inset in the Figure 4b) which is also consistent with the result discussed in see Supporting Information Figure S8. Furthermore, additional evidence can clarify the existence of PGL. We applied a positive voltage to the back gate and successfully released the holes captured by the PGL, which is reported as “electrical reset” 18,37,38 previously. Further work was done to characterize the working mechanism of our device. We changed the gm to obtain various △Ids by applying different voltages to the back gate. The relation of the gm versus Vbg, (see Supporting Information Figure S9), is extracted from the Ids-Vbg characteristics (see Supporting Information Figure S3b). The statistical histograms wherein the device was operated at three different back-gated voltages are displayed in Supporting Information Figure S10. △Ids of 0.12 nA induced by a single photon is observed as Vbg = -3.5V. Similarly, the characteristic currents of 0.55 nA and 0.57 nA are obtained at Vbg = -2.6V and -2V, 8


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respectively. By combining the previous measurement of △Ids (0.5 nA) at Vbg = -3V, it is shown in Figure 4c (red curve, where the additional point of 0.4 nA can also be seen) that △Ids increases as Vbg decreases. On the other hand, different △Ids are obtained for various gm according to equation (1), which is consistent with the experimental values (see Supporting Information Table S1). Figure 4c shows the best working region (grey area) of our device by evaluating the signal-to-noise ratios (△Ids/In). This is a trade-off between transconductance and noise. The signal-to-noise ratio is a key parameter to evaluate the sensitivity of a detector. However, for the conventional photodetector, achieving single photon detection is very difficult without a gain mechanism even though a single photon can be absorbed successfully. In this work, the nanowire device can detect a single photon due to its high amplification mechanism with the help of the photogating effect. The smaller △Ids of 0.4 nA shown = 0.44 can be explained as follows. The total current in Figure 3 labelled with = 0.44 under the weakest illumination, level changed from 11 nA to 16 nA for with total current which resulted in a smaller gm compared to that of the other three level from 11 nA-40 nA, leading to smaller △Ids. The detailed theoretical calculations are consistent with experimental results and can be found in Supporting Information Table S1. Another of the required priorities in precise single-photon detection operating in a complex environment is achieved by directly providing the polarization information of incident photons. Currently, the SPDs can detect the intensity of incident photons without polarization states. An additional polarization analyzer must be used to identify the polarization state in polarization-dependent detection applications, such as in quantum communication filed, where many protocols based on qubits are defined by the polarization of photons. Direct measurement of the polarization-encoded quantum state using single-photon detectors with photon-number resolving capability and

photon-polarization

sensitivity

on

a

chip

is

highly

important.

The

one-dimensional nanowires have a large variation in the dielectric constant of the surrounding media and a cylindrical, strongly confining potential for both electrons and holes, which accounted for the polarization response39-43. To verify the 9


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polarization-sensitive characteristics of our device, a counts ratio was performed using an attenuated polarized light to illuminate the device. Figure 5a displays a schematic overview of the polarization anisotropy measurement setup. A linear polarizer was used to polarize the detected light. By rotating the half-wave plate (HWP), the polarization direction can be adjusted to specific directions and the attenuator was used to ensure that there are only a few photons arriving at the detector. Figure 5b shows the count rate of the device as a function of linear polarization. The measured count rates follow a dependence (cos2θ) on the polarization angle (θ) and are minimal when the direction of polarization is perpendicular to the nanowires (defined as 90° polarization). Quantitative analysis of the results shows that polarization contrast of the count rates of 50% can be obtained, and is reproducible. This polarization ratio is comparable to a value of 0.56 recently observed with crossed-nanowire devices43. The lower polarization contrast is likely related to the interference of the dielectric contrast of the shell39 or the finite diameter of nanowires43. With additional optical elements to enhance polarization sensitivity, a much greater polarization contrast is expected. In conclusion, for the first time, we demonstrated a nanowire single-photon detector with the photon-number-discriminating capability at room temperature, in which the shell of nanowires has a crucial role as optically addressable floating gates. Well-defined Gaussian peaks in histograms of the detector response correspond to the discrete photon numbers and a confidence of more than 82% have been achieved. A detection efficiency of 23% and a dark count rate of 1.87×10-3 Hz are also demonstrated. By applying different back-gated voltages, the optimal working state can be obtained. Importantly, as a one-dimensional nanowire detector, our device shows the characteristics of polarization sensitivity. The experimental and theoretical studies are both investigated for the operating mechanism of the photogating effect dominated SPD and are in good compliance with each other. Future studies will include improving transconductance by combining a ferroelectric polymer, embedding the channel material in a resonant cavity, selecting proper band gap material to correspond to telecommunications wavelengths and fabricating a 10


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star-shaped nanowire device to promote polarization sensitivity. The new phenomenon and related characters of single material integration room-temperature SPDs will pave a way to enable novel easily-manufactured, cost-effective, broad-spectrum,

room-temperature

polarization-sensitivity

SPDs

with

photon-number-resolving functionality.

Methods Nanowire Growth. CdS nanowires in this study were synthesized by the CVD method. In the upstream of the carrier gas stream zone of a quartz tube, CdS powders were placed on a ceramic boat. A silicon substrate was placed in the downstream. Prior to the preparation of a silicon substrate, a 1 nm thick Au catalyst was deposited using the thermal evaporation technique. After the tube pressure was pumped down to 1 × 10−3 mbar, a constant flow of mixture gas (argon/hydrogen = 100:20, 50 sccm) was introduced into the tube. The evaporated precursors, by heating CdS powder to 700 °C, were carried to the silicon substrate zone and this process was maintained for 50 min at 100 mbar. Finally, the system was cooled down to room temperature naturally. In the scenario, the formation of the core/shell nanowires may be attributed to two most likely factors: first, the temperature of precursors is relatively high up to 700 °C. Thus, enough source vapors were provided to create catalytic supersaturation and the excess source vapor will induce non-uniformly on the NW surface to produce the defected shell. And second, the high growth pressure, 100 mbar, induces a shorter mean-free path of the precursor vapor, thereby forming the defects on the NW surface. Detectors Fabrication and Measurements. The CdS nanowires were transferred mechanically onto the p+-Si/SiO2 (100 nm) substrate. The source and drain electrodes were defined by electron-beam lithography (JEOL 6510 with the NPGS) technique, metallization, and lift-off processes. The metal electrodes (Cr/Au, 15 nm/65 nm) were deposited by the thermal evaporation technique. Then, the detector was placed in a

11


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finely screened metal box to shield it from external stray light and electromagnetic interference. An attenuated LED with a center wavelength of 457 nm illuminated the device at room temperature. The voltage of Vds was supplied by the Keithley 6430 that simultaneously recorded the real-time current, while Vbg was supplied by the Keithley 2400. The LED source calibration. In order to estimate the mean number of incident photons, we measured the photon intensities using a Si detector (S130C, THORLABS). The minimum light intensity that the SPDs can detect is beyond the detection range of the Si detector used. Therefore, we extrapolated from the collected data and made assumptions as described in the supplemental information to obtain the results reported in this paper. The data analysis process includes: 1) the LI curve linearity of the LED in the low current regime, 2) the area ratio of our devices and Si detector, 3) the spectral bandwidth of the LED, 4) and assumptions described in Supporting Information Figure S11. For the case of the mean photon number of 1.46, the intensity detected by the Si detector is 0.9 nW (2.07×109 photons/second). The mean photon number is computed to be 1.46 when combined with the area ratio of 7.057×10-10. Other cases can be deduced based on extrapolation and the assumptions that are found in Supporting Information Figure S11. In addition, we used a commercial single photon detector (H10682-210, Hamamatsu Photonics) to calibrate the LED source, and the results are consistent with the previous values (see Supporting Information Figure S12).

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Acknowledgments The authors thank James Torley from the University of Colorado at Colorado Springs for critical reading of the manuscript. This work was supported in part by the National Natural Science Foundation of China (Grant No. 61725505, 11734016 and 61521005), Key Research Project of Frontier Science of Chinese Academy of Sciences (Grant No. QYZDB-SSW-JSC031), Royal Society-Newton Advanced Fellowship (Grant No. NA170214) and CAS Interdisciplinary Innovation Team.

Author contribution W. H. and W. L. proposed and supervised the research. W.J. L. fabricated the SPDs and performed the measurements. D. Z. and Z. W. did the growth of the nanowires. W.J. L., Q. W., W. H. and W. L. performed data analysis and interpretation. W.J. L. and Q. W. co-wrote the paper, and all authors contributed to the discussion and preparation of the manuscript.

Supporting Information Available Supplementary figures including the SEM, TEM, HR-TEM images, SAED pattern 14


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and EDX spectrum of single CdS nanowire, mathematical derivation of Equation (1), reproducible time-trace of current measurements, photoresponse spectrum range and response time, additional optoelectronic and electrical measurements, comparison between calculated △Ids and experimental △Ids, calibration of the LED source by a Si commercial detector and PMT single-photon detector, respectively.

Competing financial interests The authors declare no competing financial interests.

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Figures

Figure 1. Diagram of a photogating effect dominated single-photon detector. a, Schematic of the single nanowire SPD, in which a single CdS nanowire is deposited onto a Si/SiO2 structure. b, The process of an electron-hole pairs induced by a single photon. The hole (h+) is excited into the photogating layer and remains trapped. Electron (e-) remains in the nanowire core. c, The process of photogating effect dominated photodetection. A photogating effect was induced by the trapped hole in the photogating layer.

Figure 2. Time-resolved of current measurements at room temperature.

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Time-trace of Ids during the time the device was exposed to 0.73 photons per second. The measurements were performed with Vds = 0.1 V and Vbg = -3 V at room temperature.

Figure 3. Histograms of binned of photon-number discrimination. The mean number of photons under five different illumination levels is labelled on each panel. The measurements were performed with Vds = 0.1 V and Vbg = -3 V at room temperature. The total number of data for each measurement is 25,631, 29,227, 32,786, 14,706 and 20,444 individually.

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Table 1. Probabilities of correctly determining the number of detected photons for a = 1.46. given attenuated illumination source for

Percent correct

Photon number

Decision region

0

△I ≤ 0.35 nA

98

1

0.35 nA

Room-Temperature Single-Photon Detector Based ... - ACS Publications

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