Open Access
Add to BibSonomyAbstract
We demonstrate the use of a dual-mode detector for determining the internal quantum deficiency of a silicon photodiode without the use of an external reference. This is achieved by combining two different principles for measuring optical power in one device, where the photodiode is used as absorber for both thermal and photon detection. Thermal detection is obtained by the same principle as for an electrical substitution radiometer (ESR), with a type A measurement uncertainty of 0.34 % in unstabilized room temperature. The optical power measured in thermal mode was around 3 % ± 0.5 % higher than what was measured in photocurrent mode. Heat transfer simulations revealed a difference of up to 2.2 % between optical and electrical heating, and based on these simulations we give recommendations for improvements of the detector thermal design.
© 2017 Optical Society of America
1. Introduction
There are currently two detector-based primary standard methods for measuring optical power [1, 2]. Of these two, the most established standard method is the cryogenic radiometer (CR), which has been used as a primary standard since 1985 [3]. The CR is an electrical substitution radiometer (ESR) operated at cryogenic temperatures, and the working principle is to heat a black absorber with radiative power and then match the temperature rise with electrical heating. The second primary standard detector is the Predictable Quantum Efficient Detector (PQED), which is based on induced junction photodiodes [4–7] and is designed and operated with the aim of minimizing the internal and external losses. Simulations by Gran et al. [7] show that the internal losses of the PQED photodiode for the visible range are expected to be less than 100 ppm (parts per million) at room temperature, matching the uncertainty of the CR. These simulations were verified experimentally by Müller et al. [6].
The CR and PQED are based on two different areas of physics, and hence they provide different advantages in terms of spectral range, dynamic range, functionality and cost. On one hand, the silicon-based PQED can be operated at optical powers from 100 pW to 400 μW [6] and is predictable for wavelengths between 400 nm and 900 nm. One complete measurement is performed in a few seconds. On the other hand, the CR is normally operated from 100 μW to the milliwatt range, and has a spectral range determined by the absorbing material. One complete measurement requires minutes to hours, and the measurement uncertainties are highly affected by temperature stability. With the proper implementation of these two measurement methods into one device, as demonstrated by White et al. [8], the final device can benefit from the measurement capability of both methods. Ultimately, this results in a device with expanded spectral and dynamic range, and with the properties of a primary standard. Such a detector can be operated in two different modes using the measurement principles from the PQED and the CR (hereby called photocurrent and thermal mode, respectively), thus a dual-mode detector.
In the dual-mode detector, there is an overlapping range where both the photocurrent mode and the thermal mode operates ideally. This important range can be exploited for comparing the two primary standards. Furthermore, in the range where the photocurrent mode is operating non-ideally, for instance at room temperature and/or at power levels in the mW range, the thermal mode can be used to perform a self-calibration.
When performing a comparison measurement of the photocurrent mode and thermal mode, all losses due to diffuse and specular reflection will be identical in both modes, and can therefore be disregarded. Also, the uncertainty contribution from the instruments is reduced by using the same ammeter for current measurements in both modes. Another advantage is that the source-specific responsivity in A/W can be measured directly using the dual-mode detector, given by the ratio between the photocurrent and the optical power measured in thermal mode. This responsivity is wavelength dependent, yet it will be constant for a constant spectral distribution. This means that the detector is not only limited to monochromatic sources, but can also be used to measure broadband sources such as LEDs.
The PQED photodiode has approximately the same cost and functionality as many standard silicon photodiodes used in a wide range of applications today, and this opens up for implementing the dual-mode primary standard detector directly into current applications. This would be of great benefit; not only would it introduce an unprecedented accuracy, but it would also eliminate a long traceability chain. However, to make use of a primary standard installed directly in applications, we need a reliable technique for monitoring drift, without sacrificing traceability. The combination of the two primary standards for optical power in the dual-mode detector presents one solution to this challenge, with its self-calibration procedure.
By performing an optical power measurement using the thermal mode of the detector, and then comparing the result from photocurrent mode, the internal quantum deficiency (IQD) of the photodiode can be determined for that specific wavelength and power level. For the PQED photodiode, the IQD limits the accuracy of the optical power measurement for power levels above the microwatt range and for measurements performed in room temperature. However, when using the thermal mode as a reference, the IQD of the dual-mode detector can be determined with high accuracy even under conditions where the IQD previously would limit the measurement accuracy. Hence, the dual-mode detector can be used in photocurrent mode for wavelengths down to 200 nm, and at power levels limited only by the thermal design of the detector, stretching beyond the limits of the linear range of the photodiode.
The first realization of the dual-mode detector was done by White et al. [8]. Their main goal was to demonstrate the principle of an ultimate comparison between two primary standards. They used a PQED photodiode working both as a thermal detector and photocurrent detector, and measured the optical power from an LED source with both modes. Their experiment was performed at 50 K, and they reported a deviation of 1.5 % between the optical power obtained from the two methods. They attributed this difference to the limited knowledge about the radiation wavelength during cooling, and suggest using a stabilized laser source for increased accuracy. Furthermore, due to the large thermal conductivity of Si at 50 K compared to room temperature, they assume negligible non-equivalence between electrical and optical heating.
In this work, we use a stabilized 488 nm laser to demonstrate the ability to use the dual-mode detector in unstabilized room temperature, with the aim of predicting the IQD of the photodiode. The absorbed optical power from the laser beam is measured using both photocurrent mode and thermal mode, and the two results are compared. Due to the much lower thermal conductivity of Si at room temperature compared to 50 K, we use computer simulations in Comsol Multiphysics to study the heat transfer in the detector. We also use simulations in Cogenda Genius TCAD to study the IQD in photocurrent mode.
2. Theory
For an ideal photodiode, the responsivity is given by the ratio between the elementary charge e and the photon energy, hc/λ, since each photon will contribute with one electron in the measurement circuit. Here h is Planck’s constant, c is the speed of light in vacuum and λ is the wavelength of the incoming radiation. However, in most cases a photodiode is not ideal, and the responsivity deviates from the ideal case through loss correction factors in the following way:
Here δ(λ) is the IQD and ρ(λ) represents all losses that prevents photons from being absorbed in the substrate, such as reflectance and dust particles on the surface. The measured optical power of the incoming radiation is given by the photocurrent divided by the responsivity,White et al. [8] demonstrated that a silicon photodiode can work as an ESR and that the detector thereby can be operated in dual-mode. This is achieved by implementing a temperature sensor to the photodiode, along with a heat sink, a heat link, and a way of heating the absorber electrically. The electrical heating can be done by applying a forward bias voltage across the photodiode, which will cause the resistivity of the silicon to dissipate heat inside the detector.
Since the dual-mode detector uses the same absorbing element in both measurement modes, the reflectance will be equal in both modes, and hence it can be disregarded. This is valid as long as the measurement is a pure comparison measurement and the reflectance has negligible time variations. For an absolute optical power measurement however, the reflectance must be taken into account. In that case, the reflectance can be reduced to a few tens of ppm by using two or more detectors in a trap configuration, as shown in [5,9–11].
An essential requirement for optimal ESR functionality is equivalence between heat transfer in optical and electrical heating. This means that equal optical and electrical power will give equal temperature rise in the position of the temperature sensor. When this requirement is fulfilled, the optical power in thermal mode will be given by PT = U · I(U). Here U is the applied voltage across the photodiode needed to achieve the same temperature rise as with optical heating, and I(U) is the corresponding current through the photodiode.
When all other error sources have been eliminated or accounted for, the IQD of the photodiode can be found from the heating and photocurrent power measurements by
The self-calibration procedure is therefore a true measurement of the IQD of photodiodes - a quantity that has up to now been difficult to measure.3. Experiment
The photodiode used in this experiment was a test sample of an induced junction PQED photodiode developed in the EMRP project Qu-Candela [1,5,6]. The sample had an active area of 11 × 11 mm2, with an oxide thickness of 300 nm. A more detailed description of the photodiode can be found in reference [5]. Figure 1(a) shows the photodiode with heat link and heat sink, while Fig. 1(b) shows a cross-sectional schematic of the photodiode and dedicated heat link. The photodiode was mounted on a printed circuit board (PCB), serving both as a chip carrier and heat link. A 7 mm hole in the PCB allowed for a Ge thermistor to be mounted on the back of the photodiode. The PCB heat link was extended by a polylactic acid (PLA) stage, mounted on a second PCB. The photodiode with heat link was placed on top of a brass block serving as a heat sink. A second Ge thermistor was mounted on the brass block, so that system variations in temperature could be monitored and accounted for. The detector with heat link and heat sink was then placed in a vacuum chamber. Another photodiode, functioning as a mirror, was placed above the photodiode to increase the amount of light being absorbed by the photodiode. All measurements were performed in unstabilized room temperature, and the light source was a 488 nm power stabilized laser with a beam size of approximately 1.9 mm full width of half maximum (FWHM). Since the aim was to demonstrate that the IQD can be determined with the self-calibration procedure, we were not limited to operate within the linear range of the photodiode. A power level of 0.5 mW was chosen, close to the linear range of a typical Si photodiode.
Fig. 1 (a) Photodiode with carrier. (b) Schematic showing a cross-section of the photodiode and PLA/PCB heat link.
The detector was run through three operational steps – first photocurrent mode, and then thermal mode with optical heating followed by electrical substitution:
- In photocurrent mode, Fig. 2(a), the laser beam was directed onto the detector surface, and the resulting photocurrent, iphoto, was measured. Dark current was also measured and subtracted. A reverse bias of VRB = −19 V was applied to the photodiode to increase the width of the depletion region, and hence reduce electron-hole recombination in the substrate.
- In thermal mode, Fig. 2(b), the photodiode was heated both optically and electrically. When heated optically, the photodiode was set in open circuit, so no current could flow. The absorbed optical power was then transformed to heat instead of a photocurrent. Having the same absorbing substrate in both modes of operation ensures that the field of view of the sensor, as well as the size and power of the beam, is the same in both cases. When the heat lost through the heat link equals the heat produced from the incoming light, the temperature will saturate. The difference between this saturation temperature and the initial temperature, ΔTOPT, was measured.
- Our next step was to relate the measured temperature rise to the optical power, through electrical substitution. A forward voltage bias was used to heat the photodiode electrically. Two different power levels were applied, and the optical power was found from a linear fit based on these levels. Both power levels ensured close proximity to optical power, and because of this it was sufficient to assume system linearity over a narrow dynamic range around the nominal optical power. When measuring the actual voltage across the diode, we performed a four-terminal measurement directly on the aluminum contacts on the photodiode, to avoid measuring the voltage drop along the electrical wires.
Fig. 2 The two modes for measuring optical power with the dual-mode detector. (a) Photocurrent mode. Incoming light is converted to a photocurrent, iphoto. (b) Thermal mode. Incoming light is converted to heat, followed by electrical substitution to relate heat to optical power.
The complete measurement series started with a photocurrent measurement, followed by nine succeeding cycles of electrical and optical heating (thermal mode), and finished with a second photocurrent measurement.
The photocurrent measurements consisted of three succeeding measurements, where the laser shutter was closed, opened and closed, respectively. Each of these three measurements had a duration of six seconds. A six second measurement time is sufficient for a reliable photocurrent measurement and ensures that the temperature increase during illumination is limited. In this way the temperature increase can be assumed negligible with regards to the temperature dependence of the IQD. The average current signal with the shutter closed was subtracted from the current signal with the shutter open to find the photocurrent signal. The photocurrent of the complete measurement series was then found from the average of the two photocurrent measurements, one performed before and one after the thermal mode measurement. The optical power from photocurrent mode, PPC, was determined by inserting the photocurrent iphoto into Eq. (2) together with the ideal responsivity, R(λ). By using the ideal responsivity, PPC represents the amount of optical power that is directly measured by the circuit.
Before starting the thermal mode measurements, we allowed 20 minutes of temperature stabilization of the system, to reduce the effects from heating during photocurrent mode below the detection limit. There was no temperature stabilization between thermal mode and the second photocurrent measurement, since the temperature change during the thermal measurements was well below 1 K, and hence was assumed to give negligible variations in the IQD.
In thermal mode, each heating step had a duration of ten minutes, including five minutes for stabilization between each heating step. A weighted mean of the last five minutes was found for each heating, and a value for the optical power was determined for each of the nine steps. An average of these nine gave the final value for the optical power, PT, from thermal mode.
When using the principle of electrical substitution, there are several requirements that need to be fulfilled to obtain equivalence between optical and electrical heating [12]. One of these requirements is that the heat flow path from the detector to the reference temperature should be identical for optical and electrical heating. This means that equal applied optical and electrical power should give an equal temperature signal from the temperature sensor. In our dual-mode detector, a difference in heat transfer is expected, since heat is dissipated from different areas of the photodiode in the two cases. During optical heating, the heat is generated where the beam is absorbed in the substrate, as illustrated in Fig. 3(a), whereas during electrical heating, the heat is dissipated along the edges of the photodiode and spreads towards the center, as illustrated in Fig. 3(b). To investigate the effect of this difference in heating profiles, we performed computer simulations of the heat transport through the detector using Comsol Multiphysics. In addition, we studied the IQD of the photodiode in photocurrent mode using simulations in Cogenda Genius TCAD. Simulation details can be found in the appendix, section 6.
Fig. 3 Top view of photodiode, illustrating heating profiles for (a) optical heating and (b) electrical heating. During optical heating, the heat is generated where the beam is absorbed in the substrate, whereas during electrical heating, the heat is dissipated along the edges of the photodiode and spreads towards the center.
4. Results and discussion
Figure 4 shows the temperature signal for two cycles of a thermal mode measurement as a function of time, alternating between electrical and optical heating. The low and high electrical power levels were 482 μW and 512 μW, respectively.
Fig. 4 Two cycles of the thermal mode measurement, with optical heating and electrical heating of two different power values.
The optical power for each of the nine succeeding heating cycles are shown in Fig. 5. The arithmetic mean of these nine, giving PT, and the optical power from photocurrent mode, PPC, are shown as solid lines in the figure. The numerical values of the measured optical power in the two modes are listed in Table 1. All uncertainties are given by standard deviation of the mean, k = 1. Even with a relatively high noise level in the temperature reading, as seen in Fig. 4, the standard deviation of the mean of the optical power in thermal mode at ∼0.5 mW in unstabilized room temperature was found to be 0.34 %. As can be seen in Table 1 and Fig. 5, there is a deviation between the results from the two modes which is much larger than the type A relative measurement uncertainty. The estimated optical power in thermal mode is actually 3.5 % higher than what is measured in photocurrent mode. This deviation is higher than expected and requires further examination.
Table 1. Measured absorbed optical power in photocurrent mode and thermal mode
Fig. 5 Optical power from thermal mode, PT, for nine cycles (blue asterisk), and the average over these nine cycles (blue solid line). The same result, when adjusted for the non-equivalence between optical and electrical heating, is shown as a gray dashed-dotted line. The optical power from photocurrent mode, PPC, is shown by the green solid line. The standard deviation of the mean (k = 1) is indicated by dashed lines.
The low temperature rise during heating combined with the high sensitivity of the temperature sensor makes measurements in unstabilized room temperature challenging. In Fig. 5 there seems to be a trend that the individual points with higher values have higher uncertainty than those with lower values. This could be a result of temperature drift in the system, in combination with the signal processing procedure and the method used for calculating the values. The estimated power value for thermal mode, PT, was calculated using the arithmetic mean of each of the individual points. We also tested the outcome when making a weighted mean of the points, where each point was weighted by the inverse of the standard deviation of that point. This procedure shifted the estimated value for PT closer to the photocurrent mode estimation and resulted in a deviation of 2.5 % between the two modes. By using two different methods of calculating the thermal mode optical power we got a deviation of 2.5 % and 3.5 % compared to the photocurrent mode. This suggests that the optimized algorithm of estimating the thermal mode optical power has not yet been found.
The unexpectedly large deviation between the two operational modes lead us to investigate the heating profiles during optical and electrical heating. We developed a model of the system in Comsol Multiphysics and performed an analysis of the heat transfer during optical and electrical heating using two different simulation models. Initially, we used a simulation model with the dedicated PLA/PCB heat link between the photodiode and heat sink. This gave a time constant of ∼7 minutes (1/e), which was not consistent with the experimental time constant that we found to be approximately one minute. In the second simulation model, we included the bonding wires that were connected to the photodiode. Results from these simulations are shown in Fig. 6, with temperature response as a function of time for optical and electrical heating. For comparison, an experimental result from electrical heating is also shown. As seen from the figure, the time constant when including the bonding wires agrees well with the experimental data, with a value of approximately 65 s. The vertical axis for the experimental data (right) is given in arbitrary units, since our thermistor was not calibrated, due to the fact that we only measured temperature differences and not absolute values. However, the agreement between the experiment and simulation time constants suggests a thermal sensitivity of approximately 0.16 K/mW.
Fig. 6 Simulation results from Comsol Multiphysics for temperature rise for optical heating (red solid line) and electrical heating (blue dashed line), as well as an experimental result from electrical heating (green dotted line, right axis). The inset shows the temperature profile along the center of the back of the photodiode at t = 10 min. The temperature sensor position is at x = 0, and the bonding wires are connected to the top surface of the photodiode close to x = 5 mm.
The fact that it is necessary to include the wiring to get a time constant matching the experiment indicates that it is the electrical wires that functions as the main route for heat transport between the photodiode and heat sink. This is supported by the inset in Fig. 6, which shows the temperature profile after 10 minutes of heating, along the center of the back of the photodiode. The bonding wires are connected to aluminum rings on the photodiode close to x = 5 mm. From the figure it is evident that there is a heat loss through these bonding wires, resulting in a lower temperature close to the bonding wires. The heat transport route along the wires was not accounted for in our design of the experiment. As a result, we have an undefined coupling between the photodiode (absorber) and the brass block (heat sink). This can explain the unexpectedly high noise level in the temperature measurements, as can be seen in Fig. 4, and it is therefore likely that the noise level can be reduced by improving the heat link design.
Even though the simulations have given us new insight to the heat link of the system, our intention with the simulations was to compare the heat transfer in the two thermal modes to reveal any non-equivalence. The simulation results in Fig. 6 show that a difference in temperature response exists between optical and electrical heating. The estimated difference is 1.83 mK, which leads to an over-estimation of up to 2.2 % in PT, depending on the exact position of the temperature sensor. By accounting for this non-equivalence in heating, the optical power from thermal mode will be shifted downwards, as shown by the gray dash-dotted line in Fig. 5. However, the detail level of the simulation model was limited to the purpose of studying the heat transfer through the detector. Using the simulation results in a quantitative way should be done with caution, but nevertheless they give an indication about the level of non-equivalence between optical and electrical heating. The consequence when correcting for the non-equivalence is that the remaining deviation between the thermal mode and photocurrent mode will be 0.3–1.3 %, depending on the algorithm for calculating PT.
To study the internal losses in more detail, we performed computer simulations of the internal losses in Cogenda Genius, with an incoming radiation of 500 μW and a reverse bias of −19 V, as in the experiment. The simulation procedure was similar to the one described by Tang et al. [13]. In general, the internal losses can be separated into surface and bulk recombination. The reverse bias ensures that bulk recombination is reduced to a minimum, meaning that the internal losses are attributed mainly to surface recombination. This was evident from the Cogenda Genius simulations, where the total recombination was practically equal to the surface recombination, and the bulk recombination was found to be below 1 ppm. The simulations showed that in order to attribute the remaining deviation of 0.3–1.3 % to surface recombination loss, the surface recombination velocity for holes and electrons needs to be in the range of 107–108 cm/s. These high values are unlikely, indicating that the deviation between the photocurrent mode and thermal mode is caused by other effects.
Another possible explanation for the deviation between PPC and PT is associated with dust and other impurities on the detector surface. Impurities will be heated by absorbing some of the incoming radiation, while also shielding the substrate from that radiation. This means that radiation captured by an impurity will, through heat, contribute to the measured optical power in thermal mode, but will not produce a signal in photocurrent mode. However, this is highly dependent on the thermal coupling efficiency between the impurity and the oxide surface, and the effect is expected to be small. If, however, the impurities introduce negative charges on the surface, the effect can be more prominent. A build-up of negative charges at the surface will counteract the positive charges in the oxide, reducing the effective charge of the oxide. The Cogenda Genius simulations revealed that the linearity of the photodiode is sensitive to the fixed oxide charge. Any negatively charged impurities on the surface, resulting from long-lasting use of the photodiode in a harsh lab environment, would therefore result in an increase of the internal losses.
The thermal simulations have revealed that the non-equivalence between optical and electrical heating is far from ideal. The findings of the thermal simulations suggest that a new design must be developed to improve the equivalence between optical and electrical heating. Furthermore, an improved design is expected to reduce the thermal noise in the measurement as the heat will flow in a controlled path as compared to the design presented here. After an optimized thermal design is developed and realized, an independent measurement of the non-equivalence could be carried out experimentally. This could be done by moving a localized spot at different positions over the surface of the diode and measuring the absorbed optical power using thermal mode in each spot. By also monitoring the reflectance at the different locations, we would be able to account for reflectance differences due to oxide thickness non-uniformity. If the beam variations do not result in changes in the measurement, we could reliably conclude that the non-equivalence is below the detection limit.
Overall, the lack of agreement between photocurrent mode and thermal mode of the detector, in the order of 2.5–3.5 %, is most likely caused by a combination of the improper thermal design, low temperature signals, and operation in unstabilized room temperature without an optimized analysis algorithm. A detailed uncertainty evaluation is not feasible with the current design. However, this study has shown a proof of concept.
The ultimate goal is to produce a thermal design and a reliable measurement algorithm that meets most of the high accuracy optical power applications to better than 0.1 %. That would generate a convenient and easy to use method that matches the uncertainty given by the best National Metrology Institutes in spectral response intercomparisons [14]. Combined with photocurrent simulations, a measurement at one wavelength can be used to predict the response over the full predictable spectral range.
5. Conclusion
We have demonstrated that the self-calibrating dual-mode detector principle works well in unstabilized room temperature. Even though this was the first demonstrating experiment, we were able to measure the absorbed optical power in thermal mode with an estimated type A relative uncertainty of 0.34 %. Our thermal simulations revealed that the mechanical design of the photodiode and heat link gave a non-equivalence between optical and electrical heating of up to 2.2 %. In future work we will use thermal simulations as a tool to optimize the heat link/heat sink design, with the aim of eliminating the non-equivalence between electrical and optical heating. A new design is also expected to improve the uncertainty in the optical power estimation in thermal mode, by providing a more defined link between the absorber and the heat sink. The uncertainty in thermal mode can be further reduced by introducing temperature stabilization.
In addition to optimizing the design, an optimal algorithm for estimating the optical power in thermal mode should be found. Also, the suitability of other types of photodiodes can be examined. Until now, studies on combining thermal and photocurrent measurements in one device have looked only at induced photodiodes. Other designs and photodiodes could give smaller non-equivalence in optical and electrical heating. Future work will also include studies of the detector response at various temperatures, which should affect the internal losses. In addition, future work will include a detailed uncertainty evaluation and a thorough examination over a wider dynamic and spectral range.
6. Appendix
6.1. Comsol Multiphysics simulations
The computer simulations of heat transfer through the detector were performed using the Heat transfer in solids physics in Comsol Multiphysics. Heating of the surface was introduced by heat flux through the detector surface. For optical heating, the heat flux was defined as a centered, gaussian function with 1.9 mm FWHM, as illustrated in Fig. 3(a). This was approximately the size of the laser beam in the experiment. For electrical heating, the heat flux was confined to the aluminum connection area along the edges of the photodiode, as illustrated in Fig. 3(b). The flux was defined such that the total applied power was equal to 500 μW in both cases. The initial and surrounding temperature was set to 295 K.
Material and thermal properties of the materials used in the model are listed in Table 2. Silicon was used in the photodiode, FR4 and PLA was used in the dedicated heat link, gold was used for bonding wires, and copper was used to simulate leads connected to the bonding wires.
Table 2. Material and thermal properties of the materials used in the model
6.2. Cogenda Genius TCAD simulations
Cogenda Genius TCAD was used to perform simulation of charge carrier transport in photocurrent mode. The software can solve the Poisson’s equation coupled with the continuity equation for holes and electrons in both 2D and 3D. Table 3 shows the parameters of the simulation model. Due to symmetry, only the center quarter of the photodiode was simulated. Optical generation was applied normal to the diode and as a uniform square. Variation of incident optical power and surface recombination velocity was performed to investigate their effects on the internal quantum deficiency (IQD). The IQD was calculated from the ratio of recombined and photo-generated electron-hole-pairs.
Table 3. Simulation parameters for Cogenda Genius
Funding
UNIK - The University Graduate Center at Kjeller, Norway.
Acknowledgments
The authors thank prof. Aasmund Sudbø for useful discussions.
References and links
1. S. Kueck, ”The Qu-Candela project,” http://www.quantumcandela.org.
2. CCPR Working Group on Strategic Planning, ”Mise en pratique for the definition of the candela and associated derived units for photometric and radiometric quantities in the International System of Units (SI),” http://www.bipm.org/en/publications/mises-en-pratique.
3. J. E. Martin, N. P. Fox, and P. J. Key, ”A Cryogenic Radiometer for Absolute Radiometric Measurements,” Metrologia 21(3), 147–155 (1985). [CrossRef]
4. J. Geist, G. Brida, and M. L. Rastello, ”Prospects for improving the accuracy of silicon photodiode self-calibration with custom cryogenic photodiodes,” Metrologia 40(1), S132–S135 (2003). [CrossRef]
5. M. Sildoja, F. Manoocheri, M. Merimaa, E. Ikonen, I. Müller, L. Werner, J. Gran, T. Kübarsepp, M. Smîd, and M.L. Rastello, ”Predictable quantum efficient detector: I. Photodiodes and predicted responsivity,” Metrologia 50(4), 385–394 (2013). [CrossRef]
6. I. Müller, U. Johannsen, U. Linke, L. Socaciu-Siebert, M. Smîd, G. Porrovecchio, M. Sildoja, F. Manoocheri, E. Ikonen, J. Gran, T. Kübarsepp, G. Brida, and L. Werner, ”Predictable quantum efficient detector: II. Characterization and confirmed responsivity,” Metrologia 50(4), 395–401 (2013). [CrossRef]
7. J. Gran, T. Kübarsepp, M. Sildoja, F. Manoocheri, E. Ikonen, and I. Müller, ”Simulations of a predictable quantum efficient detector with PC1D,” Metrologia 49(2), S130–S134 (2012). [CrossRef]
8. M. White, J. Gran, N. Tomlin, and J. Lehman, ”A detector combining quantum and thermal primary radiometric standards in the same artefact,” Metrologia 51(6), S245–S251 (2014). [CrossRef]
9. E.F. Zalewski and C.R. Duda, ”Silicon photodiode device with 100 % external quantum efficiency,” Applied Optics 22(18), 2867–2873 (1983). [CrossRef]
10. M. Sildoja, F. Manoocheri, and E. Ikonen, ”Reducing photodiode reflectance by Brewster-angle operation,” Metrologia 45(1), 11–15 (2008). [CrossRef]
11. M. Sildoja, F. Manoocheri, and E. Ikonen, ”Reflectance calculations for a predictable quantum efficient detector,” Metrologia 46(4), S151–S154 (2009). [CrossRef]
12. A.C. Parr, R.U. Datla, and J.L. Gardner, ”Optical Radiometry,” in Experimental Methods in the Physical Sciences, Vol. 41 (Elsevier, 2005).
13. C. K. Tang, J. Gran, I. Müller, U. Linke, and L. Werner, ”Measured and 3D modelled quantum efficiency of an oxide-charge induced junction photodiode at room temperature,” in Proceedings of International Conference on Numerical Simulation of Optoelectronic Devices (2015), pp. 177–178.
14. R. Goebel and M. Stock, ”Report on the key comparison CCPR-K2.b of spectral responsivity measurements,” http://kcdb.bipm.org/AppendixB/appbresults/ccpr-k2.b/ccpr-k2.b_final_report.pdf.
