Silicon: quantum dot photovoltage triodes

Silicon is widespread in modern electronics, but its electronic bandgap prevents the detection of infrared radiation at wavelengths above 1,100 nanometers, which limits its applications in multiple fields such as night vision, health monitoring and space navigation systems. It is therefore of interest to integrate silicon with infrared-sensitive materials to broaden its detection wavelength. Here we demonstrate a photovoltage triode that can use silicon as the emitter but is also sensitive to infrared spectra owing to the heterointegrated quantum dot light absorber. The photovoltage generated at the quantum dot base region, attracting holes from silicon, leads to high responsivity (exceeding 410 A·W−1 with Vbias of −1.5 V), and a widely self-tunable spectral response. Our device has the maximal specific detectivity (4.73 × 1013 Jones with Vbias of −0.4 V) at 1,550 nm among the infrared sensitized silicon detectors, which opens a new path towards infrared and visible imaging in one chip with silicon technology compatibility.

6) in line 315, the authors claimed the device requires no interface engineering. However, the authors' previous work (https://pubs.acs.org/doi/10.1021/acsami.0c01744) claims that without appropriate Si surface treatment (CHI3), charge transport between Si and quantum dots will be impeded, resulting in negligent EQE at SWIR region, which seems to be contradictory. Can authors address this? 7) Can authors provide a spectral EQE plot? 8) In line 259 and figure 5, how did authors define rise & fall times. Rise time normally is defined as the time for signal to rise from 10% to 90% of the signal value. Based on this, in figure 5, it seems that the response time including the long tail is in ms order, much longer than 50 us claimed in the work.
Reviewer #2: Remarks to the Author: The paper "Silicon:Quantum Dot Photovoltage Triodes" reports about a phototransistor built upon the heterojunction between Silicon and PbS Quantum Dots. The proposed device structure is quite novel, nevertheless other photodetectors exploiting the Si/QD heterostructures have been described in the past years. Even though such a photodetector can be of some interest for the academic community involved in the study of QD-based devices, the paper is not accurate enough and appears speculative especially in the part dedicated to the device's working principle. For these reasons I believe the paper should be rejected. Here I attach a detailed list of the most important issues affecting the paper.
1. Even though the authors refer to the proposed device as a "triode", it seems to me it should be viewed as a classic heterojunction bipolar transistor (HBT), where base and collector are made of PbS QDs, while the emitter is realized in the silicon substrate. The word "triode" is misleading since it is typically employed to describe vacuum-tube amplifiers.
2. The explanation of the device's working principle is unclear. In particular: 2.1 For Vce < 0 the sentence "the p-Si:nCQD heterojunction is not completely turned on and the dark current at this case is weak" is too speculative and unclear. The authors neglect the different electrostatic characteristics of the materials composing the device. Since the authors employed TCAD simulations in the first part of the manuscript, they could have used the same approach to estimate the voltage drop on the two pn junctions at a given Vce bias. More importantly, the photocurrent gain observed in the case of Vce < 0 could be explained by the theory of operation of HBTs. In this case, a simple calculation, accounting for the difference between Si and CQD bandgaps, gives an expected photocurrent gain between 200 and 500 depending on the diffusion length of the electrons in the Si substrate (for this calculation, I used the data reported by the authors in table 1). This result is completely compatible with the measurements reported in the paper. 2.2 For Vce > 0 the sentence "the photoelectrons will be blocked off at the n-CQD:p-CQD junction and a negative photovoltage is produced at the interface, shrinks the depletion region of the n-CQD:p-CQD junction and extract holes from p-CQD to the base region (n-CQD)" is not clear. According to the band diagram of fig. 3b, it is not clear why only the photoelectrons should be blocked at the n-CQD:p-CQD interface. Moreover, the authors assume that holes are transferred from the n-CQD to the p-Si by tunneling, but this assumption is not substantiated by experimental data nor theoretical analysis (i.e. give the low barrier height at the Si:CQD heterojunction also thermal emission phenomena should be considered). Finally, it is not clear why, at Vce > 0, the authors still observe a photocurrent gain > 1. 2.3 The device current shows a non-monotonic behavior for Vce > 0 both in dark and under illumination. The authors discuss this behavior, but their explanation seems speculative. No numerical, experimental, or theoretical analysis are provided to substantiate the authors' assumptions. Also, references are lacking. 2.4 Fig. 4b and the relative discussion are misleading, since it seems that visible photons are absorbed only at the p-Si:n-CQD interface. The sentence "At a positive bias, photo-induced electron-hole pairs will generate at both sides of the reversed heterojunction" is also misleading, since it neglects carrier generation occurring in the forward bias homojunction.
3. The authors claim to have reached very high detectivity values (4.73x10^13 Jones in the SWIR and 2.47x10^13 Jones in the visible), but it is unclear how they evaluated the noise current. First, it seems the authors assume shot noise is the only type of noise affecting the device performance while, in the "Temporal performance and self-tunable spectral response" paragraph, the authors discuss the need to also consider other types of noise in their calculation. In this second case it is not clear how the authors could obtain a detectivity as high as 1.33x10^13 Jones. In fact, when dealing with flicker noise, it is important to consider the integral of the noise current over the whole bandwidth of the device. Looking at the normalization noise current reported in the supplementary information it is clear that the device is strongly affected by flicker noise, but the authors apparently consider only the noise current measured at a single frequency corresponding to the cut-off frequency of the device. In this case, the authors are assuming to couple the device to an ideal bandpass filter, centered at the cut-off frequency. This assumption seems unrealistic and should have been explained in more detail in the manuscript. Moreover, the reported noise data has been measured at very low Vce (-0.1V) while the responsivity is always discussed at higher voltages. Since the flicker noise current may be nonlinearly dependent on the DC current flowing in the device, the noise should be evaluated at the same bias at which the responsivity is measured. My opinion is that the calculated detectivity is way too optimistic and a thorough noise analysis should be conducted before claiming such high detectivity values.
4. The authors claim that "The distinguishable response time between SWIR and visible light excitation endows our PVTRI the self-tunable capability to distinguish SWIR and visible signals in one chip, which is promising in the cutting-edge optoelectronic applications". This assumption should be discussed in more details, since it is not clear how the authors would employ the proposed device in a real-life application in order to distinguish between different wavelengths. What happens if SWIR and visible light reach the device at the same time?
5. Some references are out of context and should be removed.
6. The paper is poorly written and should be thoroughly checked for language inconsistencies.

Response to reviewers:
We would like to thank the reviewers for their highly constructive reviews of our manuscript. In response to these comments and suggestions, we have carried out extensive additional experiments, acquired new data and conducted further analysis, and thus we have substantially enhanced our results and understanding. We have made a thorough revision of our manuscript accordingly and addressed all the concerns made by the reviewers. In the following, we address each of the reviewers' comments in detail.

Point-to-Point Responses
Reviewer #1 (Remarks to the Author): In this work, the authors provide a comprehensive investigation over a triode photodetector based on Si: quantum dot heterojunction. The working mechanism for the photodetector can be controlled using different voltage biases. The photodetector also has a high detectivity and micro-second response time. The work is convincing and meaningful, and I think it will be of interest for the researchers in the field. Here are some minor issues to be addressed before acceptance. Response: We do thank the reviewer for his/her very positive comments on the significance of our work.   (CHI 3 ), charge transport between Si and quantum dots will be impeded, resulting in negligent EQE at SWIR region, which seems to be contradictory. Can authors address this? Response: We thank the reviewer for this comment. The physical mechanism of our PVTRI is totally different from the heterojunction-based photodiode in our previous work (https://pubs.acs.org/doi/10.1021/acsami.0c01744). The valence (or conduction) band offset induced barrier between p-Si:n-CQD (or n-Si:p-CQD) will block holes (or electrons) transferring from CQD to Si, but will not block holes (or electrons) transferring from Si to CQD.
For the p-Si:n-CQD (or n-Si:p-CQD) photodiode, photon-induced carriers are generated in the CQD under 1550 nm illumination. Taking the p-Si:n-CQD photodiode for example, as shown in Fig. R-2(a), photoholes in CQD should overcome the valence band offset induced barrier at the interface to transfer from CQD to Si. As a result, appropriate Si surface treatment should be performed to lower the barrier and enhance EQE.
As for the p-Si:n-CQD:p-CQD PVTRI, its working principle exactly takes advantage of the barrier at the interface. When applying a negative bias at p-CQD with p-Si grounded (V bias < 0 V), the p-Si:n-CQD heterojunction is forward biased while the n-CQD:p-CQD junction is reverse biased. As shown in Fig. R-2(b), holes from p-Si can unimpededly transport to n-CQD and be extracted to p-CQD by the reversed p-CQD:n-CQD junction. The photoelectrons are blocked off at the p-Si and n-CQD heterojunction interface due to the valence band offset induced barrier. The accumulated photoelectrons can produce a negative photovoltage at the interface via the photovoltaic effect (the same effect that produces an open-circuit voltage in solar cells), which is similar to applying a negative voltage to the base (n-CQD). The photovoltage controls the Si:CQD heterojunction electrostatics, shrinks the depletion region of p-Si, and continuously extracts the holes from Si to CQD under 1550 nm illumination. As a result, the claim that the device requires no interface engineering is not in contradiction with our previous work.

Can authors provide a spectral EQE plot?
Response: We thank the reviewer for this suggestion. The spectral EQE plot is as follows and we have added this plot in the Supplementary Information (Supplementary Figure 9).

Fig. R-3. Spectral EQE plot of the PVTRI.
8. In line 259 and Figure 5, how did authors define rise & fall time. Rise time normally is defined as the time for signal to rise from 10% to 90% of the signal value. Based on this, in Figure 5, it seems that the response time including the long tail is in ms order, much longer than 50 us claimed in the work. Response: We thank the reviewer for this comment. There are two ways to define the response time for a conventional photodetector. One is that the response time is defined as the time for signal to rise from 10% to 90% (or fall from 90% to 10%) of the signal value. The other is that the response time is defined as the time for the photocurrent to rise to (1−e −1 )=63% (or fall to e −1 = 37%) of the maximal photocurrent. In this manuscript, we have referred to Sargent's method [Ref. R1] to distinguish the fast-response component and slow-response component (a long tail) of the response time. The fast-response and slow-response components indicate two different physical mechanisms. The I-t curve can be fitted with a biexponential relaxation equation as follows = I + exp(−t/τ ) + exp(−t/τ ) (R1) where I 0 is the steady-state photocurrent, t is the time, A and B are the constants, and τ 1 and τ 2 are the relaxation time constants corresponding to fast-response and slow-response components, respectively [Ref. R2,R3]. The fast-response component is related to the device structure and the slow-response component is related to the defects of the materials (e. g. defect states in the CQD films and interface). The fast-response of rise and fall edges (Fig. 5 of the manuscript) indicates that our proposed device itself can achieve rapid photoresponse, and this is the key point we would like to state. As for the defects-related long tail, it can be reduced by improving the synthesis method of CQDs.
We have added the above explanation and discussion in the manuscript to make it better reasoned.  Express, 23, 28300-28305 (2015).

Reviewer #2 (Remarks to the Author):
The paper "Silicon:Quantum Dot Photovoltage Triodes" reports about a phototransistor built upon the heterojunction between Silicon and PbS Quantum Dots. The proposed device structure is quite novel, nevertheless other photodetectors exploiting the Si/QD heterostructures have been described in the past years. Even though such a photodetector can be of some interest for the academic community involved in the study of QD-based devices, the paper is not accurate enough and appears speculative especially in the part dedicated to the device's working principle. For these reasons I believe the paper should be rejected. Here I attach a detailed list of the most important issues affecting the paper. Response: We do thank the reviewer for his/her recognition of the novelty of the proposed device structure in our work. Although Si/QD heterostructures have been described in the past years, the physical mechanism of our PVTRI is totally different from the reported Si/QD heterostructure-based photodetectors, and we have addressed this question in the response to the Reviewer #1's Comment 6. In addition, we are very sorry for some of the unclear statements which make the reviewer misunderstand several key points of our work. We have carefully studied the reviewer's comments and have made correction which we hope meet with approval. On behalf of my co-authors, we solemnly state that the paper is definitely not speculative.
1. Even though the authors refer to the proposed device as a "triode", it seems to me it should be viewed as a classic heterojunction bipolar transistor (HBT), where base and collector are made of PbS QDs, while the emitter is realized in the silicon substrate. The word "triode" is misleading since it is typically employed to describe vacuum-tube amplifiers. Response: For the silicon-based devices, "triode" is not just to describe vacuum-tube amplifiers. "Phototriode" has been used to describe the photodetector which is configured in the common emitter mode with the base open circuited since 1960s [Ref. R4,R5]. In addition, "Phototriode" has also been to describe other semiconductor (MAPbBr 3 ) n-p-n photodetector [Ref. R6]. There are two reasons why we use "photovoltage triode" rather than HBT to name the proposed device. i.
As for HBT, the emitter and the base materials form the heterojunction and in order to lower the injection deficit, the band gap of the emitter material should be wider than the base one [Ref. R7,R8]. In our proposed p-Si:n-CQD:p-CQD PVTRI, the bias voltage is applied on p-CQD with p-Si grounded. If using p-Si as the emitter, n-CQD as the base and p-CQD as the collector, the device structure is similar to a HBT (left branch of Fig. SR3). However, if using p-CQD as the emitter, n-CQD as the base and p-Si as the collector, as shown in the right branch of Fig. SR3, the device still has very high responsivity and specific detectivity (e.g. R=156 A·W -1 and D * =3.43×10 13 Jones at V bias of 0.4 V). At this case, the emitter (p-CQD) and the base (n-CQD) are both PbS and have the same bandgap. Therefore, HBT is not appropriate to name the proposed device. ii.
The gain mechanism of the proposed device is similar to a phototriode, using the base-collector diode as a photodiode and amplifying the photocurrent of this diode by base potential regulation. It is worthy to mention that the barrier at the interface of p-Si and n-CQD will block the photoinduced electrons transferring from n-CQD to p-Si but will not hamper the hole transferring from p-Si to n-CQD. When applying a negative bias, the blocked photoelectrons at the p-Si and n-CQD heterojunction interface will accumulate and produce a negative photovoltage at the interface via the photovoltaic effect (the same effect that produces an open-circuit voltage in solar cells), which is similar to applying an extra negative voltage to the base (n-CQD). Therefore, we do think"photovoltage triode" is appropriate to name the proposed device.   Soc., 136,3111-3115 (1989).

The explanation of the device's working principle is unclear. In particular: 2.1 For Vce < 0 the sentence "the p-Si:n-CQD heterojunction is not completely turned on and the dark current at this case is weak" is too speculative and unclear. The authors neglect the different electrostatic characteristics of the materials composing the device. Since the authors employed TCAD simulations in the first part of the manuscript, they could have used the same approach to estimate the voltage drop on the two pn junctions at a given Vce bias. More importantly, the photocurrent gain observed in the case of V ce < 0 could be explained by the theory of operation of HBTs. In this case, a simple calculation, accounting for the difference between Si and CQD bandgaps, gives an expected photocurrent gain between 200 and 500 depending on the diffusion length of the electrons in the Si substrate (for this calculation, I used the data reported by the authors in table 1). This result is completely compatible with the measurements reported in the paper.
Response: We are sorry for the speculative and unclear statements and we do thank the reviewer for his/her affirmation of the compatibility between his/her calculation results with our measurements reported in the manuscript. We have modified the statements and added more theoretical explanation in the manuscript and supplementary information.

i. Estimation of the voltage drop on the two p-n junctions at a given V bias
The voltage drop on the two p-n junctions can be estimated from the I-V curves (Fig. R-4). The dynamic resistances of the junctions can be calculated by R=dV/dI. As shown in Fig. R-4a, for the n-CQD:p-Si heterojunction, the dynamic resistance is in the range of 0.06-1.28 kΩcm 2 when the voltage changes from 0 V to -1 V. However, for the p-CQD:n-CQD junction (Fig. R-4b), its dynamic resistance is in the range of 10.83-95.56 kΩcm 2 when the voltage changes from 0 V to -1.5 V, which is one to two orders of magnitude higher than the one of the n-CQD:p-Si heterojunction. Therefore, at V bias < 0 V, the resistance of the heterojunction is at least ten times than the resistance of the homojunction, and the voltage across the heterojunction is at most 0.13 V. Such a low voltage cannot guarantee the n-CQD:p-Si heterojunction turn on with no illumination, so the dark current at this case is weak. The detailed calculation of the dark current will be discussed in the next section. ii. Theoretical calculation of the dark current and gain at V bias < 0 V As for a triode, the small-signal common-base gain is defined as Ignoring the base region recombination current, eq.R-2 can be derived as where is the current density due to the diffusion of the minority carriers (holes) in the base, is the current density due to the diffusion of the minority carriers (electrons) in the emitter. As for a p-n-p triode, , and the reverse-biased saturation current density in the is the minority carrier diffusion coefficients in the emitter/base/collector, / / is the intrinsic carrier concentrations in the emitter/base/collector, / / is the doping concentrations in the emitter/base/collector, and / / is effective minority carrier diffusion lengths in the emitter/base/collector. According to the above equations, can be written as Similarly, the dark current and the photo gain can be written as where η is the external quantum efficiency of the base-collector junction.
As for V bias < 0 V, e. g. V bias = -1.5 V, , , , and Δ can be calculated according to the parameters in Table R The theoretical calculated value of the gain is completely compatible with the measurements reported in the manuscript.  Fig. 3b, it is not clear why only the photoelectrons should be blocked at the n-CQD:p-CQD interface. Moreover, the authors assume that holes are transferred from the n-CQD to the p-Si by tunneling, but this assumption is not substantiated by experimental data nor theoretical analysis (i.e. give the low barrier height at the Si:CQD heterojunction also thermal emission phenomena should be considered). Finally, it is not clear why, at Vce > 0, the authors still observe a photocurrent gain > 1. Response: We do thank the reviewer for his/her suggestion and we do understand that the reviewer wonders about the high photocurrent gain at V bias > 0 V. We will firstly explain the blocking and transferring processes of the photo-induced carriers at the two p-n junctions and then theoretically calculate the gain at V bias > 0 V to show the reason.

i. Blocking and transferring processes of the photo-induced carriers at the two p-n junctions
For V bias > 0 V，p-CQD is the emitter, n-CQD is the base and p-Si is the collector. The p-Si:n-CQD heterojunction is reverse biased while the n-CQD:p-CQD junction is forward biased. Photoelectrons should overcome the built-in potential barrier to transfer from n-CQD to p-CQD, so it is likely that photoelectrons can be blocked at the n-CQD:p-CQD interface at a low V bias . As for photoholes, of cause they can be blocked at the n-CQD:p-Si interface due to the valence band offset induced barrier. However, the electric field at the n-CQD:p-Si interface is enhanced by the reverse biased heterojunction, so photoholes are possible to overcome the barrier by tunneling or thermal emission. The purpose of using Fig. 3b is to show that a low positive V bias , photoelectrons and photoholes can be blocked at the n-CQD:p-CQD and n-CQD:p-Si interfaces, respectively, but photoholes are possible to overcome the barrier due to the enhanced electric field at the n-CQD:p-Si interface by the reverse biased heterojunction. We have modified several statements in this paragraph to make it clearer. ii.
Theoretical calculation of the gain at V bias > 0 V The gain at V bias > 0 V can still be calculated according to eqs. R2-R9. It is worthy to mention that as for bulk materials, the term in eq. R7 is negligible and eq. R7 is simplified to the following expression: If using eq. R10 to calculate the gain, the obtained value will not exceed 1. This may be the reason why the reviewer thinks the gain at V bias > 0 should not exceed 1. However, as for the zero dimensional materials (e. g. QDs), the diffusion coefficient and the diffusion length are significantly different from the bulk materials, and they cannot be reduced for the calculation of .
According to the parameters in Table R The theoretical calculated value of the gain is completely compatible with the measurements reported in the manuscript. Ref. R16 K. Lu, et al. Efficient PbS quantum dot solar cells employing a conventional structure, J. Mater. Chem. A, 5, 23960-23966 (2017).

The device current shows a non-monotonic behavior for Vce > 0 both in dark and under
illumination. The authors discuss this behavior, but their explanation seems speculative. No numerical, experimental, or theoretical analysis are provided to substantiate the authors' assumptions. Also, references are lacking. Response: We thank the reviewer for the constructive suggestions. We have added more analysis and references to further support our explanation in the manuscript. The non-monotonic behavior of the device current detected at V bias > 0 V is due to the large injection effect. The device current density can be expressed by [Ref. R9] = (1 + ) ≈ (R11) where is the photocurrent density generating in the base-collector junction, is the generation rate of excess carriers under illumination, and is the space charge region width of the base-collector junction. At the case of low injection, both W and β will increase with V bias increasing. When V bias exceeds a threshold, the injected minority carrier concentration will rapidly increase, which can be larger than the majority carrier concentration and lead to more sharp increase of than .
According to eq. R3, will decrease at the case of large injection with V bias increasing. This is one reason why shows a non-monotonic behavior for V bias > 0 V. The second reason is that at the case of high injection, the minority carrier in the space charge region of the base cannot be completely depleted, which increases the neutral region width in the base and moves the depletion region edge in the base towards the collector [Ref. R17,R18]. This effect will also reduce β, and lead to the non-monotonic behavior of the device current. In addition, increasing V bias can enhance the electronic field of the Si:CQD heterojunction, and the photoinduced electrons are easier to be extracted. The photoinduced electrons are blocked off at the interface of the n-CQD:p-CQD junction to increase photovoltage initially. However, with V bias increasing, the barrier of the n-CQD:p-CQD junction will be gradually lowered down. More photoelectrons can tunnel across the barrier of the n-CQD:p-CQD junction and reduce the photovoltage, which also results in decrease.
It is worthy to mention that at V bias > 0 V, p-Si acts as the collector and at V bias < 0 V, p-CQD acts as the collector. The doping concentration of p-Si (5e15 cm -3 ) is far below the doping concentration of p-CQD (1e17 cm -3 ) and the thickness of p-Si (520 μm) is much more than the thickness of p-CQD (~40 nm). Therefore, the large injection effect is prominent for V bias > 0 V and at the range of -1.5 V≤V bias ≤1.5 V, the non-monotonic behavior of the device current is only detected at the positive voltages. 2.4 Fig. 4b and the relative discussion are misleading, since it seems that visible photons are absorbed only at the p-Si:n-CQD interface. The sentence "At a positive bias, photo-induced electron-hole pairs will generate at both sides of the reversed heterojunction" is also misleading, since it neglects carrier generation occurring in the forward bias homojunction. Response: We are sorry that the reviewer misunderstands the key point of this paragraph. At a positive bias, of cause photo-induced electron-hole pairs will also generate at the p-CQD:n-CQD homojunction. However, the homojunction is forward biased and the space charge region width (W) narrows with V bias increasing as follows where ε s is the permittivity of CQD, N A and N D are the acceptor and donor concentrations of p-CQD and n-CQD, respectively, and V bi is the built-in potential. The photo-induced electron-hole pairs will recombine soon at this case, and the photocurrent generated at the forward homojunction is negligible compared with the one at the reversed heterojunction. Consequently, we do not consider the carrier generation and recombination occurring in the forward bias homojunction.
In order to prevent misunderstanding, we have modified the statements to make the manuscript more precise. (4.73×10 13 Jones in the SWIR and 2.47×10 13 Jones in the visible), but it is unclear how they evaluated the noise current. First, it seems the authors assume shot noise is the only type of noise affecting the device performance while, in the "Temporal performance and self-tunable spectral response" paragraph, the authors discuss the need to also consider other types of noise in their calculation. In this second case it is not clear how the authors could obtain a detectivity as high as 1.33×10 13 Jones. In fact, when dealing with flicker noise, it is important to consider the integral of the noise current over the whole bandwidth of the device. Looking at the normalization noise current reported in the supplementary information it is clear that the device is strongly affected by flicker noise, but the authors apparently consider only the noise current measured at a single frequency corresponding to the cut-off frequency of the device. In this case, the authors are assuming to couple the device to an ideal bandpass filter, centered at the cut-off frequency. This assumption seems unrealistic and should have been explained in more detail in the manuscript. Moreover, the reported noise data has been measured at very low Vce (-0.1V) while the responsivity is always discussed at higher voltages. Since the flicker noise current may be nonlinearly dependent on the DC current flowing in the device, the noise should be evaluated at the same bias at which the responsivity is measured. My opinion is that the calculated detectivity is way too optimistic and a thorough noise analysis should be conducted before claiming such high detectivity values. Response: We do thank the reviewer's professional comments and suggestions and we are very sorry for the infelicitous phrasing which leads to misunderstanding. We have revised the statement in the "Temporal performance and self-tunable spectral response" paragraph.

The authors claim to have reached very high detectivity values
As the reviewer stated, we did assume the read circuit performance. It is attributed to the high compatibility with Si technology of quantum dots. The detailed explanation of the assumption is as follows.
The specific detectivity of the device is * = ∆ = ∆ = ∆ 2 ( • + ∅ ) • ∆ + where I ntotal is the noise current, = • , M is the gain, F is the excess noise, A is photosensitive element area, ∅ is the background luminous flux, ∆ is the noise bandwidth, I nROIC is the circuit noise current. Generally, the background luminous flux is relatively small, about 10 8 photons/S/cm 2 . For our device area in the manuscript, the current is in the order of sub femto ampere, which can be ignored. Considering the high compatibility with Si technology of quantum dots and the strikingly similar noise figure of our device and the silicon-only device [Supplementary Information in Ref. R1], we assumed that the number of circuit noise electrons stayed below single figures, which can be ignored in the multiplier detector. In these cases, the specific detectivity of the device is * =