Forthcoming infrared event-based sensors will have utility in the space-based surveillance domain where they could potentially perform traditional sensing and tracking functions with significantly enhanced temporal resolution and reduced downstream datalink demands and power consumption. As a first step toward extending event-based sensing technology into the mid-wave infrared, a DC simulation of the conventional event-based sensor unit cell's photoreceptor circuit is performed, and the results are compared with measurements of a printed circuit board implementation of the same circuit to assess what design freedom is available to interface the photoreceptor with a mid-wave infrared photodetector. Detailed analysis of the circuit and measurements provides insight into which fundamental properties of the transistors drive the photoreceptor's dynamic range and demonstrates several characteristics that are relevant to mid-wave infrared sensing. These characteristics include the capability to produce a stable, low voltage bias on the infrared photodetector to maximize sensitivity, and that operating the circuit below room temperature increases the photoreceptor's dynamic range. Measurements show that even the simplest implementation of the photoreceptor circuit exhibits a dynamic range of logarithmic compression of 150 dB at room temperature. However, the dynamic range is ultimately limited by the mid-wave infrared photodetector's dark current activation energy, which is significantly lower than the threshold voltage (energy) of the photoreceptor's feedback transistor and, thus, there is an incentive for the photodetector's dark current to be diffusion-limited.

Conventional frame-based solid state focal plane arrays (FPAs) have dominated the space-based sensing domain since electro-optical digital imaging replaced traditional photographic film cannisters decades ago. While traditional CCD and CMOS image sensing technologies are highly effective at extracting information from data composed of sequential image frames, the nature of this methodology presents issues and constraints. To resolve higher speed temporal information in the scene necessitates the use of higher frame rates and this, in turn, results in correspondingly higher data communication capacity requirements. To use a frame-based camera for target tracking applications, all the frame data must be processed to maintain continuous monitoring of the scene, taxing satellite communication bandwidth and on-board power resources processing what is often highly redundant information. The negative impacts of performing tracking operations within the frame-based imaging paradigm will only continue to rise with increasing spatial and temporal resolution requirements. However, in mission areas where only the dynamic scene information is of interest and/or higher temporal resolution is needed, the inherently compressed data and high dynamic range of an event-based sensor (EBS), a concept introduced by Delbruck and Lichtsteiner in Ref. 1, may better serve this role in an ever-growing and inter-connected sensing network.

The EBS's low latency, high temporal resolution, and sparse data stream are achieved by designing each of the FPA's readout pixels to asynchronously respond to fractional changes in the illumination level. Typical commercial-off-the-shelf EBS cameras use a Si detector element with an adjacent pixel unit cell circuit consisting of three basic stages: (1) photoreceptor, (2) change amplifier, and (3) comparator in order of the signal path.2 In the photoreceptor stage, the current produced in the photodetector (consisting of both photo current and dark current) flows through a MOSFET transistor operating in weak inversion to produce a logarithmically compressed voltage signal at the photoreceptor output.3 In the change amplifier stage, changes in the photoreceptor stage output voltage are amplified around a reference value corresponding to the last light level to trigger an event. This difference voltage, a signal quantifying the relative change in illumination or temporal contrast, enters the third and final comparator stage to be compared to positive and negative contrast threshold values, producing positive or negative events when the signal change exceeds either threshold. In this way, EBS pixels produce data independently of one another, and any given pixel only produces data when the region of the scene that it views is evolving.4 

While interest in using event-based sensors in the space domain is growing, a key technological obstacle to their adoption for many applications is the spectral response of the photodetector material, which thus far is either silicon (1.1 μm cutoff) or InGaAs (1.7 μm cutoff) in all commercially available EBS cameras to date.5–9 To extend the utility of EBS to longer wavelength applications where thermal emission can be detected, the functionality of the standard three-stage EBS pixel unit cell must be analyzed in that context starting with the stage that directly interacts with the photodetector element, the photoreceptor circuit. For example, unlike silicon photodiodes where increasing the reverse bias voltage has only a small effect on the dark current,10 longer wavelength infrared detector dark current can be much more sensitive to bias voltage variations.11 Under low light conditions where detector dark current dominates the photodetector output, instability in detector bias could produce dark current fluctuations, a corresponding variation in voltage at the output of the photoreceptor stage, and potential false or noise events if the circuit is not designed with the characteristics of the photodetector in mind.

Additionally, at room temperature, the dark current density in a mid-wave infrared (MWIR) detector will be substantially larger than that of a Si detector, necessitating its operation at much lower temperatures. Lower temperature operation serves to increase the maximum potential dynamic range of the event-based sensor's photoreceptor (the photoreceptor's range of logarithmic response); however, as shown in the following, the detector's dark current will ultimately set a practical limit to the dynamic range. Understanding the limitations of the EBS pixel design will provide insight into the relevant figures of merit of the circuitry for infrared applications, how the design can be modified to best accommodate requirements, and the fundamental performance limitations in this implementation of the unit cell.

The photoreceptor stage of the EBS unit cell is analyzed for MWIR event-based sensing by evaluating the basic photoreceptor implementation, which provides logarithmic transimpedance compression of the photodetector current and independent tuning of the detector bias, and comparing the photoreceptor's inputs and outputs to the associated parameters of a typical III–V MWIR detector. The basic properties of the MWIR detector relevant to the discussion of the photoreceptor are outlined in Sec. III. The photoreceptor circuit is then evaluated analytically in Sec. IV to derive the fundamental limits of the photoreceptor's dynamic range defined by the boundary conditions of the constituent transistors’ operating regions and gain insight into which transistor properties have the greatest impact on the photoreceptor's dynamic range. The circuit is then simulated as a function of temperature using PSPICE in Sec. V and implemented on a custom Printed Circuit Board (PCB), to compare with the analytical expectations and make associations with the MWIR photodetector's photo current and temperature-dependent dark current levels in Sec. VI. Key results from Secs. IV, V, and VI are further examined in Sec. VII to comment on the MWIR detector's relationship with the photoreceptor.

The MWIR photodetector analyzed in this work is the III-V nBn infrared detector from Ref. 12 with a 5.5 μm cutoff wavelength at 130 K. This detector is selected because it is representative of a highly manufacturable, III–V sensor technology in the MWIR, exhibiting high internal quantum efficiency (∼89%) and dark current density within a factor of 3× of the Rule 07 expectation at 130 K.13 The quantum efficiency and dark current determine the detector's sensitivity, which here yield a shot noise-limited noise-equivalent irradiance (NEI) of 6 × 1010 photons/cm2s for 3 μm photons in the low-irradiance limit12 (assuming a 10 μm pixel pitch and a 10 ms integration time), or equivalently, a shot noise-limited specific detectivity of 5 × 1012 cm Hz1/2 W−1, again for 3 μm photons.

Figure 1 plots the dark current density of this detector as a function of voltage bias at temperatures ranging from 80 to 250 K and is used to identify the detector's optimal operating point. While the detector is diffusion-limited at temperatures >150 K as evidenced by relative insensitivity to reverse bias (i.e., near-zero slope of the curves at negative biases)10 and full bandgap activation energy,12 this detector would be expected to operate at lower temperatures to further suppress dark current and enhance detector sensitivity. At a more typical MWIR detector operating temperature of 130 K (black curve), the diffusion-limited dark current still dominates, but depletion and tunneling dark currents are beginning to manifest and imparting a measurable bias dependence to the dark current. The shot-noise NEI is evaluated as a function of bias at 130 K in the low-light limit and plotted in the inset, which shows that a reverse bias of −0.2 V yields the minimum NEI of 6 × 1010 photons/cm2 s for the 130 K operating point.12 NEI increases with increasing reverse bias as the detector dark current increases.

FIG. 1.

Dark current density shown at temperatures ranging from 80 to 250 K for the 5.5 μm cutoff MWIR nBn photodetector in Ref. 12. At the detector's intended operating temperature of 130 K (black curve), the optimal bias for minimum NEI is indicated by the black dot. The horizontal black dashed line indicates the Rule 07 dark current density expectation for a detector at this temperature and cutoff wavelength. The inset shows NEI at 130 K for 3 μm photons as a function of voltage in the low-irradiance limit, with the optimal detector bias that yields the minimum NEI indicated by the red circle at −0.2 V.

FIG. 1.

Dark current density shown at temperatures ranging from 80 to 250 K for the 5.5 μm cutoff MWIR nBn photodetector in Ref. 12. At the detector's intended operating temperature of 130 K (black curve), the optimal bias for minimum NEI is indicated by the black dot. The horizontal black dashed line indicates the Rule 07 dark current density expectation for a detector at this temperature and cutoff wavelength. The inset shows NEI at 130 K for 3 μm photons as a function of voltage in the low-irradiance limit, with the optimal detector bias that yields the minimum NEI indicated by the red circle at −0.2 V.

Close modal

Further examination of the dark current characteristics in Fig. 1 illustrates the importance of evaluating the photoreceptor circuit for the characteristics of the MWIR photodetector. First, given that the optimal operating point's 2.1 μA/cm2 dark current density is the main driver of the low-irradiance limit NEI, this will effectively set a practical low light limit to the pixel's dynamic range. Second, the differential conductivity σ d, equivalent to the derivative of the curves in Fig. 1, is non-zero at the operating point, again, due to the influence of depletion and tunneling currents. As a result, any small perturbation Δ V in the detector bias will introduce a corresponding fluctuation in the detector current Δ I = σ d Δ V, which could potentially produce excess noise of false events in the low-light limit. This highlights the importance of confirming that the photoreceptor circuit can maintain a stable detector bias condition on the photodetector in the presence of photo current- or noise-induced detector current fluctuations. The impact of these effects will be evaluated in Sec. V.

The fundamental function of the photoreceptor stage in the EBS pixel unit cell is to convert the photodetector current I D E T to a logarithmically compressed voltage, V P R.5  Figure 2(a) shows the common implementation of the photoreceptor stage circuit,4,14 which, for the purpose of this analysis, uses a 1.5 V voltage supply V D F B for the feedback transistor (MFB) branch and an external current source I P R to provide the active load bias for tuning the circuit's operating condition. The transistor MPR, biased with the active load I P R, acts as a common-source amplifier in a feedback loop with MFB, maintaining the voltage on the photodetector V D E T at a voltage independent of the detector current I D E T. With transistor MFB operating in weak inversion, the voltage at its gate V P R is proportional to the logarithm of its drain current I D E T. This logarithmically compressed signal at the output node V P R then serves as input to the change amplifier stage that would follow in the full EBS pixel unit cell.

FIG. 2.

(a) Basic implementation of the photoreceptor stage in an EBS pixel unit cell. When operated with the feedback transistor MFB in weak inversion, the photodetector current I D E T is converted to a logarithmically compressed photovoltage at V P R. (b) Custom PCB implementation of typical three-stage EBS circuit with the photoreceptor stage highlighted in the red box and external sources supplied indicated at the SMA and the D-25 input connections.

FIG. 2.

(a) Basic implementation of the photoreceptor stage in an EBS pixel unit cell. When operated with the feedback transistor MFB in weak inversion, the photodetector current I D E T is converted to a logarithmically compressed photovoltage at V P R. (b) Custom PCB implementation of typical three-stage EBS circuit with the photoreceptor stage highlighted in the red box and external sources supplied indicated at the SMA and the D-25 input connections.

Close modal
This section derives the dynamic range of the photoreceptor for the traditional circuit operating condition where both MFB and MPR operate in weak inversion. For MFB to operate in weak inversion, it must be the case that its gate-source voltage V P R V D E T is less than its threshold voltage V t F B and that its drain-source voltage V D F B V D E T is greater than 3× the thermal voltage k T / q. Similarly, MPR will likewise remain in weak inversion if its gate-source voltage V D E T is less than its threshold voltage V t P R and its drain-source voltage V P R is greater than 3 kT / q.15 These requirements are expressed by Eqs. (1) through (4),
(1)
(2)
(3)
(4)
Under the assumptions in (1)–(4), the circuit in Fig. 2(a) can be solved analytically. The bias current I P R passes through the channel of transistor MPR governed by the weak inversion conduction expression in Eq. (5), which is a function of the transistor's ideality factor n P R and characteristic current I 0 P R, given by Eq. (6). I 0 P R is a function of effective mobility of the channel μ eff P R, gate oxide capacitance C o x P R, the ratio of the channel width to length ( W L ) P R, and the ideality factor n P R. In practice, I 0 P R carries only a minor temperature dependence as the factor of k T 2 is largely offset by the power law −3/2 temperature dependence of the effective mobility due to lattice scattering,15 
(5)
(6)
Rearranging Eq. (5) to solve for V D E T yields Eq. (7),
(7)

The weak inversion condition expressed through the inequality in Eq. (1) dictates that I P R < I 0 P R so that the natural log term in Eq. (7) is a positive quantity. As a result, the detector voltage V D E T is tunable via I P R and temperature to voltage levels below V t P R in this operational regime, as required by the inequality in Eq. (3). The inequality in Eq. (2) can be satisfied with proper selection of V D F B.

To determine the output voltage V P R, it is noted that the photodetector current I D E T flows through the drain-source channel of transistor MFB. In weak inversion, I D E T is related to V P R by Eq. (8), where I 0 F B is the characteristic current of transistor MFB detailed in Eq. (9).
(8)
(9)
Rearranging Eq. (8) to solve for V P R yields Eq. (10), which demonstrates the circuit's logarithmic compression of the photodetector signal I D E T,
(10)
Comparing Eq. (10) with the inequalities in Eqs. (1) and (4) enables definition of the photodetector current conditions over which the circuit operates with logarithmic compression at V P R. Equation (10) indicates that the quantity V P R V D E T < V t F B for I D E T < I 0 F B, which is the condition that satisfies the inequality in Eq. (1). Therefore, the characteristic current I 0 F B of MFB in Eq. (9) is the maximum photodetector current for logarithmic compression, beyond which MFB operates in strong inversion and the response is no longer logarithmic. The inequality in Eq. (4) defines a minimum photodetector current I m i n below which V P R is too low to maintain weak inversion in transistor MPR. Equation (11) thus provides the range of photodetector current in which the circuit operates with logarithmic compression,
(11)
Together, Eqs. (9) and (11) define the maximum dynamic range of logarithmic compression in this photoreceptor configuration, which would be a contributive factor in the EBS camera's overall dynamic range. The factor n F B k T q in Eq. (10) multiplied by the natural log of 10 yields the subthreshold swing of transistor MFB representing the inverse of the change of I D E T with respect to V P R V D E T. For photodetector currents below I 0 F B, the log response can be expected to follow this slope until the photodetector current low-limit I min of Eq. (11) is reached, at which point MFB ceases to conduct and the circuit turns off. Therefore, the reciprocal of the exponential factor in the low-limit ( e q [ V D E T + V t F B ] / n F B k T ) is the maximum potential dynamic range I 0 F B / I min for this photoreceptor configuration, represented in Eq. (12). Given that the photodetector voltage V D E T is small and constrained to establish optimal biasing conditions on the photodetector, the photoreceptor's dynamic range at a given temperature is primarily defined by the quantity q V t F B / n F B k T in Eq. (12),
(12)
The dynamic range expression in Eq. (12) enables the optimization of fundamental transistor properties to maximize the dynamic range. The expression for threshold voltage V t is given in Eq. (13) as a function of the intrinsic carrier concentration n i and bandgap energy E g of Si, the substrate (base) acceptor concentration N A, the built-in potential ψ B in Eq. (14), the base-source voltage V B S, oxide charge density Q o x, and the oxide capacitance C o x,15 
(13)
(14)
The ideality factor n given in Eq. (15) is a function of the depletion capacitance C dep, the oxide capacitance C o x, and the fast surface state capacitance C F S, which are given as a function of fundamental parameters (depletion width W D, built-in potential ψ B, oxide thickness t o x, fast surface state density N F S, which has dimensions cm−2 V−1, and the oxide and silicon permittivity ε o x and ε S i) in Eqs. (16)–(18),
(15)
(16)
(17)
(18)

Given that there are several common factors defining threshold voltage V t and ideality factor n, it is important to optimize the selection of these parameters to maximize dynamic range for the photodetector to be used. For example, Eq. (10) would lead one to believe that dynamic range can be maximized by decreasing the substrate acceptor concentration N A of transistor MFB, as that has the effect of driving its ideality factor n F B toward unity, reducing MFB's subthreshold swing and increasing the degree of logarithmic compression as a result. However, decreasing acceptor concentration also reduces the threshold voltage which increases the minimum current I min by an exponential factor, ultimately reducing the photoreceptor's dynamic range.

Figure 3 plots the maximum and minimum photodetector currents for log response, I 0 F B and I min defined by Eqs. (9) and (11), respectively, as a function of acceptor concentration N A on the horizontal axis for various values of oxide thickness t o x. There is no oxide thickness dependence in I 0 F B (dotted line), as the factor of C o x F B is canceled by the factor ( n F B 1 ) = C dep C o x in Eq. (9). Increasing N A, therefore, increases I 0 F B by increasing the depletion capacitance C dep and reduces the minimum photodetector current I min for all oxide thicknesses (solid curves) by increasing the threshold voltage. For a given oxide thickness, the intersection of the dotted and solid curves identifies the minimum doping level below which the threshold voltage is too low for the circuit to function ( I min > I 0 F B ). Viable designs of the feedback transistor are, therefore, to the right of this intersection, which is shown in the inset plot of Fig. 3.

FIG. 3.

Photodetector current I D E T as a function of substrate doping concentration N A in the feedback transistor MFB, showing the maximum ( I 0 F B, dotted line) and minimum ( I min, solid curves) photodetector currents for log-response photoreceptor circuit operation. The inset shows the region of viable designs as a function of oxide thickness and substrate doping in the feedback transistor.

FIG. 3.

Photodetector current I D E T as a function of substrate doping concentration N A in the feedback transistor MFB, showing the maximum ( I 0 F B, dotted line) and minimum ( I min, solid curves) photodetector currents for log-response photoreceptor circuit operation. The inset shows the region of viable designs as a function of oxide thickness and substrate doping in the feedback transistor.

Close modal

To design this circuit for operation with a particular photodetector element, one would identify the minimum photodetector current expected for the application and pixel size and then select the oxide thickness curve that provides sufficient dynamic range given the signal levels expected in the scene. The transistor geometry parameter W / L can provide some additional flexibility to tune the dynamic range within the geometric constraints of the pixel dimension, as can the substrate bias V B S to further tune the feedback transistor's threshold voltage or account for uncertainty in oxide charge density Q o x.

PSPICE is used for circuit modeling and simulation, with an input netlist of the photoreceptor stage shown in Fig. 2(a). The photodetector is simulated with a current source producing the photodetector current I D E T, which is swept from 1 fA to 1 A to observe the limits of operation inherent to the photoreceptor circuit (that is, independent of the photodetector itself). In practice, the magnitude of I D E T would represent the sum of the detector temperature-dependent dark current and light-level-dependent photo current at the operating bias V D E T. Therefore, the dark current density scaled by the photodetector's pixel size would define a minimum I D E T in the low-light limit and a practical limit to the dynamic range that will be assessed for the MWIR photodetector in Fig. 1. The simulation uses a level three transistor model, which includes the equations needed to account for all transistors’ regions of operation. The minimum conductance global variable G min is decreased to 10−20 Ω −1 to enable accurate simulation of photoreceptor behaviors at low (fA) photo current levels observed in experiment.4,16

The inset to Fig. 4(a) plots the photodetector voltage bias V D E T as a function of the circuit tuning current I P R at 300 K, with the 0.2 V operating point identified in Fig. 1 indicated with the filled dot at I P R = 20 nA (positive 0.2 V because the detector is oriented to apply that voltage in the reverse bias). Maintaining this value of I P R, the main body of Fig. 4(a) indicates that the photodetector voltage bias V D E T is expected to increase by 1.05 V as the temperature is reduced from room temperature to 77 K, which would be compensated by decreasing I P R or selecting another transistor for MPR with a different characteristic current I 0 P R more suitable for the operating condition. Most importantly, Fig. 4 affirms that the detector bias V D E T is insensitive to the magnitude of detector current. The dotted section of the 300 K curve shows that the magnitude of V D E T will increase when I D E T falls below I min, but otherwise V D E T is stable in the functional operational regime indicated by solid curves in Fig. 4(a), which vary by less than 0.05%/decade over several orders of magnitude in I D E T.

FIG. 4.

(a) Simulated photodetector bias voltage V D E T as a function of detector current I D E T and decreasing temperature from 300 to 77 K, for the operating point shown in the inset plot of photodetector bias voltage V D E T as a function of biasing currents I P R at 300 K. (b) Simulated photoreceptor output voltage V P R as a function of detector current I D E T. The tan shaded area shows the change of operation of the feedback transistor MFB from weak inversion to strong inversion. The inset plots the subthreshold swing of the feedback transistor as a function of temperature.

FIG. 4.

(a) Simulated photodetector bias voltage V D E T as a function of detector current I D E T and decreasing temperature from 300 to 77 K, for the operating point shown in the inset plot of photodetector bias voltage V D E T as a function of biasing currents I P R at 300 K. (b) Simulated photoreceptor output voltage V P R as a function of detector current I D E T. The tan shaded area shows the change of operation of the feedback transistor MFB from weak inversion to strong inversion. The inset plots the subthreshold swing of the feedback transistor as a function of temperature.

Close modal

As the properties of MFB play a large role in defining the logarithmic response, Fig. 3 is used as a guide in the selection of this transistor to achieve a suitable dynamic range between I min and I 0 F B. Figure 4(b) plots the output voltage V P R as a function of the photodetector current I D E T from 300 to 77 K. The solid and dotted curve sections parallel those of Fig. 4(a), where the solid curves represent the circuit behavior in the functional operational regime while the dotted curve sections represent the circuit behavior following the violation of the inequality in Eq. (4). Comparing the room temperature result (solid blue curve) in Fig. 4(b) to Eq. (10), the current I D E T obeys the subthreshold regime expectation for nearly 11 orders of magnitude in I D E T, resulting in a dynamic range of 220 dB at room temperature. This value of 220 dB in the photoreceptor is ∼2× the dynamic range reported in the literature for the complete EBS camera system, indicating that the Si EBS camera dynamic range is not limited by the unit cell's photoceptor. However, this may not necessarily be the case in the MWIR and longer.

As V P R V D E T approaches V t F B, I D E T converges on I 0 F B and the conditions for weak inversion in Eq. (1) are violated as MFB transitions into strong inversion, with V P R varying as power law half with increasing I D E T thereafter [shaded region of Fig. 4(b)]. The photoreceptor would be functional in this region, but would not provide logarithmic compression of the photo current, resulting in a photon-flux-dependent contrast threshold response. The transition from strong to weak inversion occurs at the interface of the shaded and unshaded regions and is relatively insensitive to temperature as expected given the competing influences of thermal voltage and effective mobility in Eq. (9). In the regime of log response (unshaded region), the subthreshold swing is evaluated and plotted as a function of temperature in the inset to Fig. 4(b). This shows the higher degree of logarithmic compression offered by lower temperature operation; however, the consequence of increased compression is that greater gain will be required in the change amplifier stage to yield the same degree of contrast sensitivity when incorporated into the full EBS pixel architecture.

The circuit introduced in Fig. 2(a) is fabricated on a PCB with the transistors simulated in Fig. 4 to evaluate the real-world functionality and probe the limitations of the circuit, as well as to facilitate future testing of MWIR photodetectors as prototype event-based sensors. The photoreceptor stage in the PCB, which can be seen in Fig. 2(b), uses a voltage supply V D F B at 1.5 V for the feedback transistor (MFB) branch and two external current sources. The first current source provides the active load bias I P R, as indicated in Fig. 2(a), while the second takes the place of the photodetector element to provide a controlled magnitude of current I D E T for circuit performance validation.

Figure 5 plots the output voltage V P R as a function of the photodetector current I D E T for biasing currents I P R ranging from 2 to 100 μA (circles, solid curves). Over the range of 7 μA < IPR < 100 μA and 1 nA < IDET < 30 mA, the circuit provides log response in V P R with a better-than-expected slope of 150 mV/decade, indicating a non-ideality factor of 2.5 in the feedback transistor ( n F B ). The corresponding range in V D E T is 0.42 V (IPR = 7 μA) to 0.67 V (IPR = 100 μA), and the non-shaded region in the inset of Fig. 5 varies with a slope of 0.104 V per decade change in I P R. Compared to the PSPICE simulation in Fig. 4(a), there is a difference of about 10% in the slope, which was 0.113 V/decade in the simulation, and the two vary in vertical intercept by about 35 mV. These effects can be accounted for to deliver the intended detector bias at V D E T. Most importantly however, V D E T in the PCB card possesses a high degree of insensitivity to changes in I D E T, varying by less than 0.07%/decade change in I D E T. As a result, the PCB card should be capable of effectively performing the event-based sensor unit cell operation over a wide range of experimental conditions and infrared detector configurations.

FIG. 5.

Photoreceptor output voltage V P R as a function of detector current I D E T and biasing current I P R measured in the PCB implementation of the photoreceptor (circles, solid curves). The light shaded curves show the PSPICE simulation results modified to include shunt resistances across MFB and MPR. The tan shaded area shows the change of operation of the feedback transistor MFB from weak inversion to strong inversion. The inset plots the detector biasing voltage V D E T as a function of biasing current I P R at I D E T = 10 nA.

FIG. 5.

Photoreceptor output voltage V P R as a function of detector current I D E T and biasing current I P R measured in the PCB implementation of the photoreceptor (circles, solid curves). The light shaded curves show the PSPICE simulation results modified to include shunt resistances across MFB and MPR. The tan shaded area shows the change of operation of the feedback transistor MFB from weak inversion to strong inversion. The inset plots the detector biasing voltage V D E T as a function of biasing current I P R at I D E T = 10 nA.

Close modal

The circuit's compromised operability for IPR < 7 μA and IDET < 1 nA in Fig. 5 can be explained by the presence of shunt conduction pathways around the two transistors MFB and MPR. The loss of log response at IDET < 1 nA is attributed to a small shunt pathway drawing current on the order of 1 nA around the channel of MFB, which can be simulated by adding a 25 GΩ resistance in parallel to MFB. The light shaded curves in Fig. 5 plot the PSPICE simulation results for IPR = 2, 4, and 7 μA with the circuit modified to include a 25 GΩ shunt across MFB and an on-board measured 250 kΩ shunt across MPR. The 25 GΩ shunt across MFB produces the sharp increase of V P R at IDET ∼ 0.2 nA in the light shaded curves in Fig. 5.

In the analytical derivations in Sec. IV, the current through the drain-source channel of the feedback transistor I F B was assumed to be equal to I D E T; however, in the presence of this shunt pathway, the current is now given by Eq. (19) where I F B is the magnitude of the shunt current around MFB. As V D E T is constant along any given curve (independent of I D E T), so is the drain-source voltage across MFB and the magnitude of I F B (while V D E T is maintained). As the output voltage V P R is generated by the presence of current through the channel of MFB ( I F B ), the current draw from I D E T through the shunt path ( I F B ) results in a rapid decrease in V P R as the magnitude of I D E T falls below 1 nA. The analytical model can account for this by substituting Eq. (19) in place of I D E T in Eq. (10).
(19)
Furthermore, the circuit's compromised operability for I P R < 7 μ A and I D E T > 1 nA in Fig. 5 can be explained by the presence of a second shunt pathway, this time around the photoreceptor amplifier transistor MPR. This shunt is likewise modeled in Fig 5 (light shaded curves) by the inclusion of a resistance RPR = 250 kΩ in parallel with MPR, which was measured on the PCB. In contrast to MFB where the drain-source voltage is constant along any given curve, the drain-source voltage for MPR is V P R and, thus, the resistive shunt's parasitic draw from I P R will be a function of I D E T and proportional to V P R. This is shown in Eq. (20), which expresses the current through the drain-source channel of the MPR transistor ( I P R ) as a function of the total current provided by the current source I P R minus the magnitude of current through the shunt I P R = V P R / R P R. Substituting I P R in Eq. (20) for I P R Eq. (7) shows that V D E T will collapse as I P R approaches I P R as observed in the inset of Fig. 5. Additionally, because the shunt is resistive with current proportional to V P R, the onset of this collapse is a function of I P R and I D E T. For MPR to provide lower detector bias V D E T, the shunt resistance must be increased by using a different discrete transistor with suitable properties or implementing the card in CMOS very-large-scale integration to eliminate the shunt pathways. In any revised implementation of the photoreceptor, Eq. (7) indicates that reducing the threshold voltage V t P R should be a priority to enable access to lower magnitudes of detector voltage V D E T at higher values of I P R,
(20)

Comparing the results when the circuit is fully operational (green to pink curves) in Fig. 5 to Eq. (10), the output voltage V P R remains in the subthreshold regime for over seven orders of magnitude in I D E T before the feedback transistor MFB transitions out of the subthreshold region at a detector current of ∼13 mA. This photocurrent would correspond to a light flux level of ∼1017 photons/s or equivalently an irradiance of ∼1023 photons/cm2 s assuming a 10 μm pixel pitch, a value that far exceeds the irradiance of typical MWIR applications. The >7 orders of magnitude of logarithmic compression results in a dynamic range of ∼150 dB at room temperature, with the capability to increase that range if the circuit were implemented in the configuration of a readout integrated circuit hybridized to the detector at operating temperature, demonstrated in Fig. 4(b). While this value of 150 dB in the photoreceptor is 70 dB lower than the value demonstrated by the simulation, the measured dynamic range is ∼30 dB higher than the reported value in the literature for EBS systems, which may be limited by other components of the unit cell,4 with potential to increase when operating the circuit at lower temperatures. These results indicate that this basic photoreceptor implementation should be effective in enabling testing of single-element testing of mid-wave infrared photodetectors as prototype event-based sensors.

To evaluate how the photoreceptor will perform in MWIR applications, the performance characteristics in Fig. 5 will be assessed for the case where this photoreceptor is coupled to the 5.5 μm cutoff detector material from Ref. 12 with a 10 μm pixel pitch. While the resulting MWIR EBS camera would not be expected to operate at room temperature, evaluating it in this circumstance is insightful. The detector's 1 A/cm2 room temperature dark current density would result in 1 μA of detector current conducting through the feedback transistor. Comparing this to the results in Fig. 5 (green to pink curves), the photoreceptor's potential 150 dB of room temperature dynamic range cannot be obtained with the MWIR detector at room temperature, which is now limited to just 82 dB. This practical dynamic range limit is imposed by the detector's dark current which ensures that measurements will not be limited by the pixel's dynamic range; however, this detector limit is relaxed with decreasing temperature due to the dark current's strong dependence on temperature, as seen in Fig. 1.

While the photoreceptor's minimum current I min decreases with temperature by an exponential factor of q V t F B / n F B k T in Eq. (11), diffusion-limited dark current decreases by a much smaller exponential factor of E g det / k T (where E g det is the bandgap energy of the detector's active region), thereby ensuring that the system remains limited by the detector's dark current. For the MWIR detector and photoreceptor design being examined here, the detector's dark current activation energy of the detector E g det is 250 meV,12 while the corresponding “activation energy” of the pixel elements q V t F B / n F B is 2 eV. At the detector's intended operating temperature of 130 K, the detector's 2.1 μA/cm2 dark current density yields 2 pA of dark current flowing through the feedback transistor. The purple curve in Fig. 4(b) represents the photoreceptor response at 130 K, which shows that under low-light (dark current limited) conditions, the 2 pA dark current level will hold the photoreceptor output at about 2.8 V. Here again the MWIR detector's dark current limits the dynamic range, but a larger value of 240 dB is obtainable at 130 K. If rather than diffusion-limited, the detector dark current was depletion-limited, the exponential factor becomes E g det / 2 k T and subsequently, the dark current would be larger by an exponential factor of E g det / 2 k T, making the dynamic range improvement much less for the specific temperature. For the MWIR EBS, the photoreceptor's dynamic range of log response is fundamentally related to the activation energy of the detector's dark current.

This PCB card and the DC characteristics discussed here will enable future work evaluating mid-wave infrared detectors as prototype event-based sensors. Background activity and contrast threshold are two characterizations that can be conducted by routing the detector current through the PCB card. Alongside a full characterization of the detector element's dark current and photocurrent properties measured in a radiometric dewar, these characterizations will provide insight into how dark current and noise-equivalent irradiance truly impact the EBS pixel's sensitivity, in a way that is difficult to evaluate in a fully integrated EBS camera system where the detector element cannot be separated from the readout unit cell.

In conclusion, the photoreceptor stage of the conventional event-based sensor unit cell is evaluated to assess how it will perform with a mid-wave infrared detector. It is found that the photoreceptor's transistors can be designed to provide the low detector biases required to minimize noise in a mid-wave infrared detector and that the basic photoreceptor circuit exhibits over seven orders of magnitude of logarithmic compression at room temperature corresponding to 150 dB of dynamic range. However, the inherently larger dark current of the mid-wave infrared detector, in comparison with a visible CMOS detector, puts a practical limit on the photoreceptor's dynamic range. This limit is fundamentally related to the detector dark current activation energy that is substantially lower than the limit otherwise imposed by the properties of the photoreceptor's feedback transistor. The basic properties that govern the photoreceptor's operation outlined here will be the key to understanding how dark current and noise-equivalent irradiance affect an EBS pixel's sensitivity in future testing of infrared detector materials as prototype event-based sensors.

The authors acknowledge financial support through research sponsored by the Air Force Research Laboratory, Section 219 Seedling for Disruptive Capabilities funding under Contract No. FA9453-23-2-0002. The present work has benefited from the financial support of the U.S. Department of Defense SMART Fellowship and Space Vehicles Directorate, Air Force Research Lab. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Energy Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-NA0003525. The views expressed in the article do not necessarily represent the views of the U.S. Department of Defense, Department of Energy, or the United States Government. Approved for public release: distribution is unlimited. AFMC PA No. 2023-5795.

The authors have no conflicts to disclose.

Z. M. Alsaad: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Writing – original draft (equal). J. V. Logan: Methodology (supporting); Writing – review & editing (supporting). C. P. Morath: Conceptualization (equal); Investigation (equal); Supervision (lead); Writing – review & editing (equal). P. N. McMahon-Crabtree: Methodology (supporting); Resources (equal); Writing – review & editing (supporting). L. N. Kulesza: Investigation (equal); Methodology (equal). Z. Theis: Investigation (supporting); Methodology (supporting). D. Maestas: Resources (equal); Supervision (equal); Writing – review & editing (equal). R. Graca: Validation (supporting); Writing – review & editing (equal). B. J. McReynolds: Validation (supporting); Writing – review & editing (equal). P. Zarkesh-Ha: Supervision (equal); Writing – review & editing (equal). P. T. Webster: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
T.
Delbruck
and
P.
Lichtsteiner
, “
Fast sensory motor control based on event-based hybrid neuromorphic-procedural system
,” in
2007 IEEE International Symposium on Circuits and Systems
(
IEEE
,
2007
), pp.
845
848
.
2.
C.
Posch
,
T.
Serrano-Gotarredona
,
B.
Linares-Barranco
, and
T.
Delbruck
, “
Retinomorphic event-based vision sensors: Bioinspired cameras with spiking output
,”
Proc. IEEE
102
(
10
),
1470
1484
(
2014
).
3.
M.
Loose
,
K.
Meier
, and
J.
Schemmel
, “
A self-calibrating single-chip CMOS camera with logarithmic response
,”
IEEE J. Solid-State Circuits
36
(
4
),
586
596
(
2001
).
4.
P.
Lichtsteiner
,
C.
Posch
, and
T.
Delbruck
, “
A 128 × 128 120
db 15 s latency asynchronous temporal contrast vision sensor
,”
IEEE J. Solid-State Circuits
43
(
2
),
566
576
(
2008
).
5.
P. N.
McMahon-Crabtree
,
L.
Kulesza
,
B. J.
McReynolds
,
D. S.
O'Keefe
,
A.
Puttur
,
D.
Maestas
,
C. P.
Morath
, and
M. G.
McHarg
, “
Event-based camera refractory period characterization and initial clock drift evaluation
,”
Proc. SPIE
12693
,
126930V
(
2023
).
6.
See https://scdusa-ir.com/ for “SCD-SemiConductor Devices: Event Based SWIR Sensor.”
7.
See https://www.prophesee.ai/ for “Prophesee: Metavision for Machines.”
8.
See https://inivation.com/ for “iniVation Home: Bioinspired Vision for Machines.”
9.
See http://www.insightness.com/ for “Insightness: Sight for Your Device.”
10.
C.-T.
Sah
,
R. N.
Noyce
, and
W.
Shockley
, “
Carrier generation and recombination in P-N junctions and P–N junction characteristics
,”
Proc. IRE
45
(
9
),
1228
1243
(
1957
).
11.
M. A.
Kinch
,
Fundamentals of Infrared Detector Materials
(
SPIE Press
,
Bellingham, WA
,
2007
).
12.
A. T.
Newell
,
J. V.
Logan
,
R. A.
Carrasco
,
Z. M.
Alsaad
,
C. P.
Hains
,
J. M.
Duran
,
G.
Ariyawansa
,
G.
Balakrishnan
,
D.
Maestas
,
C. P.
Morath
,
S. D.
Hawkins
,
A.
Hendrickson
, and
P. T.
Webster
, “
Effects of doping and minority carrier lifetime on mid-wave infrared InGaAs/InAsSb superlattice nBn detector performance
,”
Appl. Phys. Lett.
122
(
17
),
171102
(
2023
).
13.
W.
Tennant
,
D.
Lee
,
M.
Zandian
et al, “
MBE HgCdTe technology: A very general solution to IR detection, described by ‘rule 07,’ a very convenient heuristic
,”
J. Electron. Mater.
37
,
1406
1410
(
2008
).
14.
T.
Delbruck
and
C. A.
Mead
, “
Analog vlsi adaptive logarithmic wide dynamic- range photoreceptor
,”
Proc. IEEE Int. Symp. Circuits Syst.
4
,
339
342
(
1994
).
15.
T. H.
Ning
and
Y.
Taur
,
Fundamentals of Modern VLSI Devices
(
Cambridge University Press
,
2009
).
16.
T.
Delbruck
., “
Lessons learned the hard way
,” in
2020 IEEE International Symposium on Circuits and Systems (ISCAS)
(
IEEE
,
2020
), pp.
1
18
.