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Abstract
We propose a new mode of operation when using a photodiode to extract a variable optical signal from a constant (ambient) background. The basic idea of this ‘zero-mode’ of operation is to force the photodiode to operate at either zero current or zero voltage. We present possible implementations of this novel approach and provide the corresponding equivalent circuits while also demonstrating experimentally its performance. The gain and bandwidth of the zero-mode photodetector are measured and simulated, and they show highly agreement. The gain compression effect because of the nonlinearity of the forward bias region is also explored. Comparing to the conventional photoconductive photodetector, the zero-mode photodetector is able to obtain higher AC gain and lower noise. With the same component used in the circuit, the measured input referred root mean square noise of zero-mode photodetector is 4.4mV whereas that of the photoconductive mode photodetector is 96.9mV respectively, showing the feasibility of the zero-mode of operation for measuring the small variable light signal under a high power constant background light.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photodiodes are normally reversely biased or unbiased, corresponding to photoconductive and photovoltaic modes of operation, respectively. It is important to note that in both cases, absolute instantaneous power is the result of the measurement. Under some situations, the light signal of interest is on top of a constant ambient (or background) light that does not contain information. This is particularly true in optical sensing systems. For traditional photodiode and transimpedance amplifier operation, the large output DC signal yields a fairly large loss in the voltage swing for the AC signal component, which may make the detector even useless.
The demand of the DC cancellation and AC amplification are from a number of researchers and applications. An important example from our group is typically referred to as optrodes in the context of neural recording [1]. In this approach, compound action potentials are transduced into the optical domain via a liquid-crystal based transduction mechanism [2] on top of a (ideally) constant optical signal and the experimental results are reported [3–5]. Another biomedical application is photoplethysmography that enables non-invasive vitals monitoring, which is intrinsically limited by the extremely small AC/DC ratio. [6] Other applications also include visible light communication (VLC) and light-fidelity (LiFi) [7]. Among them, some detectors are proposed for the typical applications. For example, a low-noise transimpedance amplifier which is able to split AC and DC signals was designed for the detection of "Violin mode" resonances in advanced laser interferometer gravitational wave observatory suspensions. [8]
State-of-the-art works can be categorised as follow: (1) the transimpedance amplifier amplifies both AC and DC part of the signal as a whole, then the output is filtered or AC coupled to the next stage; [8] (2) One branch of the circuit subtracts the DC part of the signal and then the transimpedance amplifier amplifies the AC current, which usually incorporate DC detection circuit such as integral circuit; [9] (3) The DC gain is made much smaller than the AC gain of the transimpedance amplifier in the feedback loop; [10] (4) Differential/balanced detection by two photodetectors that subtract the reference from the received signal. [11] These approaches are implemented on reverse biased photodidoes and the reverse biased photodiodes used in conjunction with transimpedance amplifier are well known as the basic structure on which most of the works are based. This is because that most of applications acquire high frequency signals (>10kHz) and large signals, and the reverse biased photodiode has a much quicker response and good linearity so that the signal can be properly detected. However, in our optrode neural recording system, the signal is much slower (0.1Hz 10kHz) and the signal amplitude is much smaller (around 1mV) leading to a very small AC/DC ratio (< 10%) at the detector. This makes the signal suitable for a slower receiver and small signal approximation. Moreover, the small AC/DC ratio is the biggest essential issue we are facing.
In this paper, we propose a mode of operation of the photodiode that can detect the variable part and to cancel the constant part of the signal. Comparing to the traditional method above, it has simpler structure, works in nonlinear region, and is potentially less noisy because of the less number of components required and the absence of the dark reverse current. The advantage of it also includes self-adaption and larger maximum AC output signal voltage swing. The core idea is to adjust the operating point of the photodiode to either the zero current or zero voltage point depending on the form of the signal, as shown in Fig. 1. By doing so, the constant background is set to zero during the optical-electrical conversion before current-voltage conversion and amplification. The disadvantage is that at these operating point, the capacitance of the photodiode becomes larger so the speed becomes slower and the linearity is worse than the photoconductive mode of operation (reverse biased).
Fig. 1. I-V curves measured from a InGaAs pin photodiode. There is a big difference between the I-V curves of no light (blue curve) and the highest light power (red curve).
There has been previous research into the photodiode properties under $0{\rm V}$ bias, such as the sensitivity under different temperatures [12] and the zero-bias resistance area product. [13–15] Recently, the ultra high speed optical to RF conversion for communications applications has drawn great attention. The unitraveling-carrier photodiode (UTC-PD) is able to operate faster and outputs larger power when the bias voltage is close to zero. [16–19] Besides the UTC-PD, Kopytko’s group proposed modelling theories on the zero biased long wavelength infrared HgCdTe photodiodes. [20,21] Research has also focused on designing photodiodes that consume less or no electrical power and require lower or zero voltage. This has typically been accomplished by increasing the responsivity and the detectivity at the zero bias voltage. [22,23]
Note that zero bias and zero-mode are different. The term ‘zero bias’ in the above literature refers to the bias voltage being close to $0{\rm V}$, and most of the published works focus on improving the characteristics of the photodiode in this region. As such, previous researches are mostly concerned with the photodiode’s design, whereas the zero-mode is a way of forcing photodiodes to work around their zero current or zero voltage operating points and is suitable for most kinds of photodiode. The purpose of the previous zero bias of photodiode is to characterise the device, or to make the best use of the photodiode internal electric field, while the purpose for the zero-mode detector is to extract the variable light signal from a constant background light. Zero bias research focuses more on the photodiode itself whereas zero-mode is more about the circuitry design.
2. Theory
2.1 Implementation
There are a few approaches to implement the zero operating point. Taking the zero current as an example, one can lift the reference voltage of the trans-impedance amplifier or one pin of the photodiode to the positive voltage of the 0 current operating point. It can be done by a well designed DC tracker to form a feedback loop at the input as shown in Fig. 2(a). An even simpler implementation consists in inserting a capacitor that only conducts variable signal: this is shown in Fig. 2(b). Because of the capacitor’s intrinsic nature, the average current (DC) through the transimpedance amplifier is always zero, and the voltage generated by the photodiode is adjusted and kept by the capacitor $C$ at the zero current bias voltage on that certain IV curve. At the same time, the AC current generated by the variable part of the light signal, which varying around the zero current operating point, can go through the transimpedance amplifier via $C$. The circuit looks like a differentiator but it is not, because the input is current rather than voltage. In the forward bias region under a relatively high power injection, the voltage is almost consstant but the current varies according to the light power, so the signal of interested is the current. Moreover, the transimpedance amplifier also looks like an inverting amplifier if taking into account the output impedance of the voltage signal source, but in practice we analyze the current rather than voltage. In what follows, we are going to discuss in depth this latter solution and focus on the zero current mode.
2.2 I-V characteristics of a photodiode
When the incident optical power is low, the I-V curves of a photodiode can be regarded as identical to that of a normal diode but shifted along the I (i.e. current) axis. Under ideal conditions, this shift should be linear with incident power and the shape of I-V curve should remain unchanged. However, in an InGaAs PIN photodiode (part number is not given by manufacturer, Flyin Optronics, China) for example, in addition to this shift, the shape of the I-V curve also depends on the power level as shown in Fig. 1. This deformation has minor effect on the reverse bias region but is crucial for the zero-mode of operation. Although the I-V characteristic is not the theme of the research, the I-V curves of an organic bulk heterojunction photodiode in [12] has the similar behaviour, which confirms the correctness of the I-V curves we got.
Previous research has confirmed such dependencies: for example, copper indium gallium diselenide (CIGS) solar cells’ I-V characteristics depend both on illumination and temperature [24]. Likewise the I-V curves of Schottky diodes have been studied for years [25,26] and further work even focuses on the forward bias I-V characteristics used in the zero-mode detectors [27–29].
Our current work clearly shows the photodiode we are using potentially experiences a number of such effects, these include:
- • High irradiation can lead to a temperature rise which in turn can influence the shape of the I-V curves [30].
- • High irradiation can form a thin layer near the junction where the density of minority carriers become of the order of majority carriers [31].
- • The high injection leading to high carrier profile, which enlarge the diffusion current in the forward direction thus decrease the reverse total current output [32]. This is similar to [33] where it is claimed that the high injection increases the recombination current in the depletion layer and the emitter-base coupling.
- • The Gaussian distribution of the light beam can cause radial current in the direction parallel to the diode surface, which decreases the lateral current in the photodiode that can be detected outside the diode [34].
Accordingly, the I-V curves are generally not linearly shifted and their shapes cannot remain the same.
We measured a set of I-V curves of an InGaAs PIN photodiode with fibre connection (Flyin Optronics, China) under different incident light power (0–25mW) from an Anritsu AS5B125EM50M superluminescent diode diode (SLD), as shown in Fig. 1, and fitted the positive voltage part of the curves for different light powers using the expression:
where $I$ is the current output of the photodiode, $I_S$ is the saturation current, $V$ is the output voltage of the photodiode, $n$ is the ideality factor, $c$ is the slope indicator, $V_T$ is the thermal voltage, $\alpha$ is the power to current conversion efficiency and $P$ is the light power injected.We assume that the dependence of $I_S$ and $V_T$ on $P$ is through the temperature. In its simplest linear form, we can cast the relationship between the diode’s temperature and the incident light power to take the form [39]:
where $T_0$ is the (constant) ambient temperature, $U$ the thermal conductivity between the diode and its environment and $\eta$ is the light to heat conversion efficiency. The I-V expression (1) is different from the commonly used formula [30] by the addition of the correction term $c(P)V$ which disappears in the low power limit $P \rightarrow 0$, in agreement with [30].Figure 3 illustrates the measured values for the saturated current $I_S(P)$, the slope indicator $c(P)$, the conversion efficiency $\alpha P$ and the thermal voltage $nV(P)$. Figure 3 also illustrates in red the fitting of the same quantities in the low incident optical power region which we take as $P < {5}\;\textrm {mW}$ and where we can assume $c = 0$. Within this region, the saturation current $I_S(P)$ shows an exponential dependence while the thermal voltage $V_T(P)$ shows a linear dependence:
where we introduced two fitting parameters $P_1$ and $P_2$. The above approach clearly provides a workable model in the low power limit but breaks down as incident power increases: in the latter case, $c(P)$ increases rapidly and starts to dominate the device behaviour. With the fact that $P$ is a function of time, $t$, for a changing light power signal, we rewrite the formula with time as:Fig. 3. Fitted parameters from Eq. (1) and Fig. 1. Only fit the power below $5mW$ because of the small signal for low power model restriction in the following section.
It is important to notice that usually in communication applications less than 2mW [40] of optical power is used and hence the above model applies.
2.3 Small signal approximation for low light power
For our analysis it is convenient to decompose the time dependent signals into an average value plus a time-dependent component as:
where $\bar {P}$, $\bar {V}$ and $\bar {I}$ represents the time average of the light power, the voltage across the photodiode and the current through the photodiode respectively.If we assume that the system operates in an environment where the average power $\bar P$ is constant (or slowly evolving) and small we can safely assume that the average current $\bar I$ is zero and from Eq. (1), setting $c = 0$, we have:
When we include the junction capacitance, $C_j$, which can be measured or found from the device manual, we obtain the small signal equivalent circuit of Fig. 4. $C_j$ is a power dependent parameter and it is assumed to be constant for a certain bias point. Because the constant part of the signal cannot reach the output since the capacitor $C$ blocks DC and transmit AC, we only focus on the changing part of the signal that is amplified by the trans-impedance amplifier and also assume the operational amplifier has high gain. Then the trans-impedance amplifier amplifies the current and transfers it to voltage signal.
The transfer function can be found to:
This expression indicates that the circuit is a band-pass filter with its lower cut-off frequency depending both on the photodiode capacitance $C_j$ (which is significant in forward bias region) and $C$. Although the output does not have a term corresponding to the constant part of the incident light $\bar P$, it nevertheless determines the values of $C_j$, $R_{d}$, $\alpha '$ and that of the operating point. In the experiments reported below, we used large $C$ so that in the bandwidth estimation, the term $C_j$ in $\omega _c$ can be ignored, however, it is not always the case. Firstly, the capacitance of the forward biased photodiode is much larger than the capacitance under reverse bias. Secondly, $C_j$ varies significantly according to the light power [41].
2.4 Wide light power range photodiode simulation model
In this section, we are going to build up an equivalent circuit model that can precisely and correctly represent the behavior of the photodiode under a full range of irradiation conditions. This model represents the behavior of the photodiode under reverse biased region as most of the other models, but is more precise in the forward bias region.
From Fig. 1 we know that when the light power is high enough, there will be severe saturation in the form of compression towards the second quadrant of the I-V chart. To estimate the behavior of a larger changing signal that occupies a wide range of the light level, we propose an equivalent circuit model that can generally represent the behavior of the photodiode over that full range.
To that effect, we modified the well-know double diode model [42] by inserting two resistors $R_1$ and $R_2$ as shown in Fig. 5. $D_1$ and $D_2$ are two normal diodes where $D_1$ has a smaller knee voltage. $D_1$ represents the recombination in the depletion layer whereas $D_2$ represents the recombination in surface and bulk region [43].
Fig. 5. Full range equivalent circuit of the photodiode working under a wide range of irradiation power.
The current source $I_{ph}=\alpha P$ represents the photocurrent. $V$ is the voltage across the photodiode. When the light power is low and $I_{ph}$ is small, the voltage across $R_2$ is also small, so the circuit reverts to a normal double diode model and it follows an exponential trend like a normal diode. Under this situation, $R_2$ and $R_1$ limit the current through $D_1$, thus under high voltage only $D_2$ is able to conduct high current and there is only an exponential curve similar to that of $D_2$.
When the light power increases, ($I_{ph}$ becomes larger), with the increment of $V$ from negative towards the positive knee voltage (around 0.6V), there are three stages: First, with low $V$, neither $D_1$ nor $D_2$ reach their knee voltage and only conduct small current, thus only $R_3$ is at play. This section of the I-V curve is a straight line with slope of the reciprocal of the shunt resistor $R_3$, which is similar to a normal diode. Second, when $V$ is increased to an intermediate value, because of the existence of large $I_{ph}$, $D_1$ has a large enough voltage to exceed the knee voltage while $D_2$ has a voltage lower then its own knee voltage. So this section of the I-V curve is a line with a sharper slope which is the reciprocal of $(R_1+R_2)\|R_3$. Third, when $V$ is even larger, both $D_1$ and $D_2$ reach their knee voltages, thus this section of the I-V curve looks like the exponential increment part as a normal diode. And when the voltage increase further, the I-V curve becomes a straight line again with a slope of the reciprocal of the resistor network.
In theory, this model can express the three key behaviors: First, the compression gradually increases with the incident light level. Second, the curve has three parts depending on the applied voltage: flat, ramp and exponential behaviour. Third, the curves intersect with each other, which can be explained by this model only when the temperature is taken into account. Indeed, when the light power is high, the temperature of the photodiode increases so that the current increases faster with voltage.
Using parameter values as shown in in Table 1, we can now simulate the I-V curves displayed in Fig. 6. $R_1$, $R_2$, $R_S$ are the resistors shown in Fig. 5, with parameters $K_1$ and $K_2$ confining their values. $I_{S1}$, $I_{S2}$ are the saturation current of the two diode models $D_1$ and $D_2$ respectively, and $N_1$, $N_2$ are their ideality factors. The temperature is set to be proportional to the photocurrent $I_{ph}$ with a factor $\Phi$ and has a baseline of 20 $^{\circ }$. The values of $R_1$ and $R_2$ have to decrease with $V$ to get a good fit, which is probably due to the illumination-induced electron-hole pairs in the depletion region as demonstrated by research work on Au/PVA (Bi-doped)/n-Si photodiode [44].
Table 1. Parameters used for simulating the VI curves.
With this model, we are now able to simulate the zero-mode detection mode by substituting the circuit model in the photodiode in Fig. 2(b) and then simulate by adding the peripheral circuit.
2.5 Discussion
Above we proposed two methods to estimate the output of the zero-mode detection scheme. First, the small signal approximation ($c \rightarrow 0$) which can be used to estimate the performance of the detector such as the amplification gain and bandwidth. Second, a more complete simulation model can be used to reproduce the non-linearity of positive voltage region under high incident light illumination which includes the influence of temperature and power saturation effect. The models are developed for giving a correct estimation and prediction on the zero-mode detector. The well known models cannot be used because the inaccuracy of the model at zero current point can cause significant error.
The small signal approximation can be extended by defining a compression figure $F$ so that in linear region $F=1$ and in non-linear region $F<1$. As we will show, $F$ can be measured in experiments and indicates the density of the I-V curves around the 0 current point. For an set of evenly distributed I-V curves, $F=1$ and for a set of overlaid I-V curves $F=0$. If we assume the gain of the detector to be $G$ in linear region, then the gain for a specific operating point $p$ can be written as $GF_p$ where $F_p$ is the compression figure around $p$. The frequency response in the next section can be a good example.
The zero-mode of operation has a few advantages over the conventional way of implementing the same functionality. We now compare the zero-mode detector with a commonly used detector in its photoconductive mode, which is a reversely biased photodiode with a trans-impedance amplifier followed by a high-pass filter and potentially a second stage amplifier as mentioned in introduction.
The zero-mode detector has a much wider maximum output signal voltage swing than the traditional one with the same gain. The conventional method converts and amplifies both AC and DC parts of the photocurrent to voltage using a trans-impedance amplifier and eliminate the DC part by high-pass filtering. Whereas the zero-mode detector only amplifies the AC part. Assuming that the conversion gain is $G$ and the saturation voltage is $\pm V_{max}$. The maximum output signal voltage swing of the traditional method is: $2(V_{max}-|I_{DC}G|)$, where $I_{DC}$ is the constant part of the photocurrent. However, the useful maximum output signal voltage swing of zero-mode detector is the full range $2V_{max}$. In other words, only the variable part of the light can lead to saturation in the zero-mode. Further, zero-mode detectors require fewer components and a less complex design: a reduced maximum output signal voltage swing as explained above may require a second stage of amplification with the accompanying risk of a variation and oscillation, which need design efforts to avoid.
In addition, zero-mode detector has the potential of better noise performance, which is also confirmed by the experiment. In some situations that requires large total gain so that the photoconductive detector must have two stages of amplification, the second stage amplifies the noise from the first stage and also introduces noise to the output. Because the zero-mode detector can achieve the large gain with only one stage, it avoids the extra noise from the second stage. Except for that, assuming both modes with only one transimpedance amplifier and without the second stage amplification. There are three sources of noise that are likely much reduced in the zero-mode detector compared with the photoconductive mode detector: reverse dark current, power supply interference, and background light shot noise. The first two are caused by the power supply biasing the photodiode. Also, in a zero-mode detector, the photodiode is grounded and there is no dark current amplified by the transimpedance amplifier. Because the DC current is blocked and shot noise is proportional to the photocurrent, the shot noise of the background light is most likely reduced in a zero-mode detector. We are currently investigating this last hypothesis.
3. Experiment
3.1 Experiment setup
We made the experiments to validate the model described above and compare it to the traditional photoconductive mode photodetector. The exerimental setup is shown in Fig. 7. A laser driver (LCD 1015, Thorlabs, US) controlled by a data acquisition system (DAQ) (USB-6361, National Instrument, US) and a superluminescent diode (SLD) (AS5B125EM50M, Anritsu, Japan) constitute the light source used and exhibits and output light power range of 0-0 25mW and wavelength spectrum centered at 1550nm. An InGaAs PIN photodiode (Flyin Optics, China) received the light from the light source via a fibre isolator to protect the light source while the light power is attenuated using an adjustable optical attenuator between the isolator and the photodiode. The same photodiode is switched to working in zero-mode and photoconductive mode respectively for comparison, as shown in Fig. 7 A) and B). The operational amplifier used in the circuits is OPA177GP (Texas Instrument, US). The outputs of the detector circuits are connected to the input of the DAQ.
Fig. 7. Experimental setup. We switched the mode of operation of the photodiode to compare A) zero-mode and B) photoconductive mode.
3.2 Methods
Because the SLD output light power is linearly related to the driving current when above 50mA, we set a current that is above this value and modulate it sinusoidally such that the:
where $I_{dc}$ is a constant current, $V_{mod}$ is the amplitude of the sinusoidal modulating voltage and $150 (\rm {mA/V})$ is the voltage to current conversion factor. Hence, received light power is: where $f$ is the frequency of the modulation. The output voltage of the zero-mode detector is: where $V_{ac}$ is the amplitude of the output voltage and $\theta$ is the phase shift at the output. We define the en-to-end gain as:We examined the performance of zero-mode detector by measuring its frequency response. We recorded the bode plot of using different $R$ and $C$ values. We measured the light power with 0 and $\pm V_{mod}$ driving voltage on light source and the light signal was:
To start with, $C$ was fixed to ${1000}\;\mu \textrm {F}$, and we change $R=[1.27~{\rm M}\Omega , 811~{\rm k}\Omega , 430~{\rm k}\Omega , 391~{\rm k}\Omega , 46.6~{\rm k}\Omega ]$. Then we fixed $R=811~{\rm k}\Omega$ and changed the $C=[1~{\rm \mu} F,10~{\rm \mu} F,100~{\rm \mu} F,1000~{\rm \mu} F]$ respectively.To find how the $F$ changes with the light power, we measured the pass-band gain of the detector in a wide range of light power irradiation as well as the variable light signal by adjusting the optical attenuator. We adjusted the light power from 0 to 10mWand measured the pass-band gain at 130Hz, with $C=1000\rm {\mu F}$ and $R=128{\rm k}\Omega$ . Instead of plotting frequency responses, we extract the light power to output voltage gain of the pass-band and plot the gain with respect to the constant light level.
With the parameters and formulas derived in Section 2.3, we are able to simulate the frequency response of the zero-mode photodetector and compare it with the experimental data. Parameters used in the simulation are shown in Table 2 where we include a term ’$p_0/V_{mod}$’ that links the light power irradiating the photodiode to the modulating voltage at the light source. The $R$ value is fixed to ${811}\;\textrm {k}\Omega$, and the two chosen $C$ values are ${1}\;\mu \textrm {F}$ and ${10}\;\mu \textrm {F}$.
Table 2. Parameters used for simulating the detector frequency response.
In addition, we compare the noise performance of the zero-mode detector to that of a photoconductive mode detector. The components except for the capacitor $C$ used in the two detectors are identical. The photodiode is reversely biased by 10V and both detectors does not have additional filters. The noise power spectrum is measured with a same constant light irradiation, and, for fair comparison, the noise is referred to the gain. The root mean square (RMS) of the input referred noise (IRN) is defined by:
where $RMS(V_{out})$ is the output noise of detecting a constant light and the gain is measured from the superposition of the same constant light with a sinusoidal modulation. With this calculation, we are able to compare the detectors’ sensitivity working with the same light source. In other words, the baseline noise of the detector is referred at the input to be compared.Lastly, we demonstrated the speciality of the zero-mode detector in the following specific case: a 1mW background light modulated by a sine wave of which amplitude is $3\%$ of the background and the data acquisition system has an input range of ${\pm 10}\textrm {V}$. To get an output with the best signal to noise ratio, the gain is maximised by choosing the maximum possible resistance $R$ to reach the output limit.
3.3 Results
The measured bode plots are shown in Fig. 8 and Fig. 9. When $C$ is large enough so that the lower cut-off frequency is below 1Hz, we are not able to see the filtering at low frequencies because of the limit of our experiment platform. However, we can always observe an upper cut-off at around 10kHz to 20kHz, which is limited by the experimental equipment. As expected, the pass-band gain increases with $R$ and bandwidth increases with $C$.
Fig. 8. Frequency responses of the zero-mode detector with five $R$ values. All other configurations are identical. $C=1000\rm {uF}$, $I_{dc}=300{\rm mA}$, $V_{sin}=100{\rm mV}$. The light power follows $P=12.47\mu W+0.83\sin (2\pi ft)\mu W$.
Fig. 9. Frequency responses using different capacitor $C$. All other configurations are identical. $R=811{\rm k}\Omega$, $I_{dc}=300$mA, $V_{sin}=100{\rm mV}$. The light power follows $P=12.47\mu W+0.83\sin (2\pi ft)\mu W$.
Regard the gain at the lowest light level, $\lim _{\bar {P}\to 0} G(\bar {P})$, as the benchmark and define a compression figure
which allows us to plot $F$ in Fig. 10. In this situation, because the variable light signal varies among observations, we measured the power amplitude of the changing part of the light and use the light-voltage gain in the unit of $V/W$. This is not problematic because F factor is the ratio of gains with no unit. The detector configurations are constant during the experiment and the only thing we have changed is the light level. The higher the $\bar {P}$ the smaller the gain is, because under high light level injection, the photodiode reaches nonlinear region and the I-V curves are compressed. Note that the F curve may deform slightly according to the loading effect.Fig. 10. F figure decreases along the constant light power $\bar {P}$. F reflects the relative gain of the detector with respect to that in the linear low light level region. $C=1000\rm {\mu F}$, $R=128{\rm k}\Omega$.
The frequency response predicted by our model is in satisfactory agreement with the experimental one with a slight mismatch on the gain. Figure 11 is drawn with $\alpha =0.964\ \textrm {A/W}$, however, by changing the parameter to 1.1A/W, we can get almost identical curves (not shown) to the experimental curves, which indicates that the error might appear in the measurement of $\alpha$.
Fig. 11. Comparison between the simulated and the measured frequency response. Formulas and parameters are shown in section 2.3. Two values of $C$ are examined and $R=811{\rm k}\Omega$ in both cases. The measured curves are the same as in Fig. 9
The IRN power spectrum density (PSD) of both photoconductive mode and zero-mode photodete shown in Fig. 12. The photoconductive detector has a noise peak at around 10kHz because of the ’gain peaking effect’ [45], apart from this, the noise floor of the photoconductive mode is still larger than the zero-mode throughout the spectrum. The root mean square (RMS) of the input referred noise (IRN) of the zero-mode detector is 4.4mV, whereas that of photoconductive mode detector is 96.9mV. We cannot observe the peaking effect on zero-mode photodetector because the existence of capacitor $C$ and the small resistance $R_d$ under forward bias compensate the first order pole, such that the feedback factor of the transimpedance amplifier has both poles and zeros at both first and second orders.
Fig. 12. Noise comparison between zero-mode and photoconductive mode. Background light level at around $4\ \rm {mW}$ and amplitude of sine wave signal is around $0.9\ \rm {mW}$ for gain measurement.
Note that the experiment circuits only have the strict necessary elements and no further effort to cancel noise for the purpose of exploring the noise nature of the detector modes has been made. However, there are a few ways of minimising the noise, such as feedback capacitance, composite amplifier and decoupling phase compensation [46], which have been widely used in the conventional photoconductive mode detectors.
In the specific circumstance mentioned above, for the photoconductive mode detector, the maximum gain is $5.55$ with a background RMS IRN of ${613}\;\mu \textrm {V}$. For the zero-mode detector, the maximum gain is around $209.9$ which makes the RMS IRN only ${24}\;\mu \textrm {V}$. The key parameters of the measurement are shown in TABLE 3. The above results have been obtained from case 1 and case 3, respectively. As for case 2, the resistor $R$ has the same value as in case 1 but is in zero-mode detection. In this case, the gain is smaller than in photoconductive mode because of the loading effect of the capacitor but still has a low IRN level. The higher IRN of the photoconductive detector may come from three sources: the dark current, the DC photocurrent shot noise, the power supply ripple.
Table 3. Comparison between photoconductive mode and zero-mode detector under a specific circumstance.
4. Conclusion
We proposed a new mode of operation for photodiodes. This ’zero-mode’ is particularly useful when trying to isolate the variable part (AC) of an optical signal containing a strong constant background component (DC). We showed that this mode of operation has many advantages. The main advantage is the simplicity. Except for this, it also has shorter settling time, larger maximum output signal voltage swing and potentially lower noise. We also provided a working model that enables us to estimate the output of the detector including its bandwidth, time domain response, frequency domain response and non-linearity of the gain under increasing illumination.
Funding
Office of Naval Research Global (N62909-18-1-2147).
Acknowledgement
We would like to thank Dr Ivan Perez-Wurfl for helping us measuring and characterising the photodiodes.
Disclosures
YW, TL and LS are inventors of a patent application related to the zero-mode detector described in the present article, and the applicant is NewSouth Innovations Pty Limited. Other authors have no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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