Measurements of infrared emissions have been used in various research fields, such as semiconductors, material characterization, chemical analysis, and life sciences. Applications that involve low-level light detection require high sensitivity to infrared detectors [1–4]. Photon-counting InGaAs avalanche photodiodes (APDs) provide high sensitivity for very-low-level light detection at wavelengths between 1 and 1.6 μm [5,6]. The detection limit of photon counters at a measurement time of 1 s is expressed as $(h\nu /\eta )R^{1/2}$ ($h\nu$: photon energy; $R$: dark-count rate (DCR); $\eta$: single photon detection efficiency). This expression indicates that the photon counters cannot measure the number of detected photons below the fluctuation of the dark counts. In practice, the detection limits of photon-counting InGaAs APDs cannot go below ${10}^{-17}\mathrm{W}$ at present due to a high DCR [5–7]. The DCR of the APDs is increased by high electric field effects, namely, band-to-band tunneling and trap-assisted tunneling [7]. To enable photon counting, a high APD internal gain is necessary to overcome the electrical noise of a readout circuit; a high electric field is then needed to achieve the high gain.

Cooled InGaAs $p\text{-}i\text{-}n$ photodiodes (PDs) have the advantages of high quantum efficiency, low dark current, and a very linear response to detected photons, even for short pulse emissions. However, they have not been utilized for low-level light experiments because of their low sensitivity. In previous measurements by our group, the detection limits of photodetection systems with an InGaAs $p\text{-}i\text{-}n$ PD were higher than those of photon-counting InGaAs APDs because of the high levels of dielectric polarization noise [8] or the large dark currents of the InGaAs $p\text{-}i\text{-}n$ PDs. The dielectric polarization noise is generated in materials with dielectric losses [9]. Dielectric losses may be large in materials with a high defect density, and dark currents are large in semiconductors with high defect and impurity densities. Therefore, the high noise levels of the InGaAs $p\text{-}i\text{-}n$ PDs we used may have been due to the high defect and impurity densities.

The noises of commercially available InGaAs $p\text{-}i\text{-}n$ PDs have since been reduced. We successfully fabricated an ultra-low-noise infrared photodetection system with an InGaAs $p\text{-}i\text{-}n$ PD by optimizing the device temperature to reduce the dielectric polarization noise and the DCR.

The readout circuit used for this experiment is shown in Fig. 1. We used an 80-μm diameter InGaAs $p\text{-}i\text{-}n$ PD manufactured by Kyosemi Corporation (KPDE008). This circuit, which is a kind of charge amplifier, is the same as the one we used previously [10], apart from a reset circuit. The resetting for discharging the feedback capacitor is carried out using a two-step operation wherein the output voltage of the operational amplifier is set to zero. First, a forward bias voltage is applied to the InGaAs $p\text{-}i\text{-}n$ PD for resetting (KPDE10GC-V2), so that the output voltage is positive regardless of any voltage fluctuations due to charge injection through the PD. Second, light from an infrared LED is injected into the PDs until the output voltage is zero. The reset sequence is controlled using a reset control circuit.

 

Fig. 1. Schematic of apparatus used to measure the noise characteristics of the infrared detection system. All the devices in the cryostat were mounted on an alumina platform, which was set on the work surface of a liquid nitrogen cryostat with a thermal insulator between the platform and the work surface. The degree of thermal isolation was varied with the temperature at which each measurement was carried out. The temperature was controlled using a heater resistor on the platform.

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Figure 2 shows the temperature and the sampling rate dependence of the readout noise at a bias voltage of 14 V applied to the InGaAs $p\text{-}i\text{-}n$ PD. The readout noise was calculated using a correlated double sampling [11], with two successive data points that were averaged over a time interval corresponding to the inverse of the sampling rate. The readout noise at low sampling rates is low at low temperatures, whereas the readout noise at high sampling rates is low at high temperatures.

 

Fig. 2. Dependence of the readout noise on the temperature and the sampling rate. The readout noise was obtained using a correlated double sampling.

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The noises that mainly contribute to the readout noise at low sampling rates are the dielectric polarization noises of the readout circuit with the PD and shot noise due to the dark current of the PD. Figure 3 shows the noise spectral densities with and without the PD at 80 K and 90 K. The noise spectra with the PD are represented at bias voltages of 14 V and 0 V. The noise spectra of the readout circuit with and without the PD exhibited $1/f$ characteristics around 1 Hz. This shows that the PD also had $1/f$ polarization noise. On the other hand, the Lorentzian noise spectra around 100 Hz at 80 K and around 1 kHz at 90 K were attributed only to the PD, because the Lorentzian spectrum was not observed in the noise spectra of the readout circuit without the PD. The cutoff frequencies of the Lorentzian spectra were 180 Hz at 80 K and 1550 Hz at 90 K. The increase in the readout noise at sampling rates of 100 Hz at 80 K and 1 kHz at 90 K was due to the noise component having Lorentzian spectra.

 

Fig. 3. Noise spectral densities of the readout circuit with and without the InGaAs $p\text{-}i\text{-}n$ PD at 80 K and 90 K, and at bias voltages of 0 V and 14 V.

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The polarization noises of PDs arise from the electrodes as well as the $p\text{-}n$ junctions of the detectors [12]. To differentiate between the noise sources, it is necessary to know the dependence of the noise on the capacitance of the $p\text{-}n$ junction [12]. Polarization noises of electrodes, unlike those of the $p\text{-}n$ junction, do not depend on the capacitance. The capacitances of the $p\text{-}n$ junction at bias voltages of 14 V and 0 V were 0.56 pF and 1.23 pF, respectively, including the capacitance of the electrode. Therefore, the dependence of the polarization noise on the bias voltage at 80 K and 90 K indicates that the polarization noise attributed to the PD should be attributed to the $p\text{-}n$ junction.

The polarization noise voltage with a Lorentzian spectrum can be derived from the Debye susceptibility. The frequency dependence of the square of the noise voltage measured by a charge amplifier is expressed as ${\epsilon }^{\prime \prime }(f)/f$, where ${\epsilon }^{\prime \prime }(f)$ is the imaginary part of the dielectric constant—here that of the InGaAs crystal [9]. The imaginary parts of the dielectric constant and susceptibility are proportional to each other when dc conductance is negligible; then the frequency dependence of the noise is ${(1+{(2\pi f\tau )}^2)}^{-1}$ for the Debye susceptibility, where $\tau$ is a Debye relaxation time [13]. If $\tau$ is determined by thermally activated processes with an activation energy, the energy can be calculated to be 0.13 eV using an Arrhenius plot for $1/\tau$, which corresponds to a cutoff frequency of a Lorentzian spectrum of the noise. To determine the origin of the Debye process in the InGaAs crystal, further study is necessary.

The readout noises at low sampling rates increased with increasing temperature above 120 K owing to the increases in the polarization noise and shot noise of the dark current. The noise spectral densities with and without the PD at 120 K and 140 K are shown in Fig. 4, together with shot noises calculated from the dark currents of $6.9\mathrm{e}/\mathrm{s}$ at 120 K and $43\mathrm{e}/\mathrm{s}$ at 140 K. The temperature dependence of the dark current is also shown in Fig. 4. The $1/f$ polarization noise of the readout circuit without the PD increased with an increase in temperature. This feature has been commonly observed in our previous measurements on silicon devices. On the other hand, the $1/f$ polarization noise of the PD was almost constant between 80 K and 120 K. At 140 K, the polarization noise of the PD observed at low frequencies may be attributed to the electrode of the PD because of the independence of the bias voltage. Furthermore, the square of the noise voltage was proportional to $f^{-1.25}$ below 1 kHz. A frequency dependence of polarization noise, $f^{-\alpha -1}$, corresponds to $f^{-\alpha }$ for ${\epsilon }^{\prime \prime }$, and $\alpha =0$ below 120 K and 0.25 at 140 K in our case. Values of $\alpha$ between 0 and 1 have been widely observed for crystalline materials and glasses, and the increase in $\alpha$ with increase in temperature has also been observed for such materials, though the origin of the frequency dependence has not been clear [14].

 

Fig. 4. Noise spectral densities of the readout circuit with and without the InGaAs $p\text{-}i\text{-}n$ PD at 120 K and 140 K, and at bias voltages of 0 V and 14 V. Inset: The dark current versus temperature.

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The noise spectral density of the readout circuit at high frequencies was mainly attributed to the junction field effect transistor (JFET) channel, because the polarization noise components decreased with an increase in frequency. Because the high-frequency noise of the JFET channel increased from 140 K to 80 K, the readout noise increased with decreasing temperature at high sampling rates. This feature was possibly due to an increase in the noise resistance of the JFET channel caused by the mobility-saturation effect and increased free-carrier temperature [15].

The light detection limits of the photodetection system at different temperatures can be estimated from the readout noises at a measurement time of 1 s and the quantum efficiencies of the PD. Readout noises at a sampling rate of 1 Hz do not directly correspond to readout noises at 1 s; the readout noise at 1 Hz corresponds to that at a measurement time of 2 s, because two data points are necessary to obtain the charge value in a correlated double sampling. To calculate readout noises at 1 s, we fitted a straight line to the measured data over a time interval of 1 s and obtained the fluctuations of the slope values (Table 1). The quantum efficiencies of the PD were indirectly determined from the room-temperature quantum efficiency given in the manufacturer’s catalog (88%) and the relative responsivities between room temperature and low temperatures at a wavelength of 1.3 μm. The light detection limits at 1.3 μm are listed in Table 1.

Table 1. Readout Noise and Light Detection Limit

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We measured the readout noise and noise spectral density of the readout circuit to operate the ultra-high sensitivity infrared detection system at an optimum temperature. The InGaAs $p\text{-}i\text{-}n$ PD had a dielectric polarization noise with a Lorentzian spectrum in addition to a $1/f$ polarization noise. Because of the Lorentzian polarization noise, the optimum temperature for the readout noises at sampling rates below 100 Hz was 100 K, and the readout noises were as low as 2.5 e. A light detection limit of $8.2\times {10}^{-19}\mathrm{W}$ was obtained at 1.3 μm and 80 K. At sampling rates above 10 kHz, the readout noise decreased with increasing temperature, and the readout noise at the 1 MHz sampling rate was 49.4 e at 140 K.