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Characterization of silicon photodiode-based trap detectors and establishment of spectral responsivity scale
ARTICLE IN PRESS
Optics and Lasers in Engineering 43 (2005) 131–141
Characterization of silicon photodiode-based trap detectors and establishment of spectral responsivity scale O¨zcan Bazkır, Farhad Samadov TU¨BI˙TAK-Ulusal Metroloji Enstitu¨su¨ (UME), Gebze, 41470, Kocaeli, Turkey Received 8 March 2004; accepted 29 July 2004 Available online 2 October 2004
Abstract Spectral responsivity scale was established at National Metrology Institute of Turkey (UME) between 350 and 850 nm wavelength ranges. The scale is based on UME made reflection type trap detector consisting of three single element silicon photodiodes. Various measurements systems were established in order to make optical characterization of trap detectors like linearity, polarization sensivity, uniformity and spectral responsivity. The absolute responsivity linked to the absolute optical power was obtained using improved laser stabilization optics and electrical substitution cryogenic radiometer system at discrete laser wavelengths. Using physical models for the trap detectors, reflectance and internal quantum efficiency the scale was realized with an expanded uncertainty of 0.05%. r 2004 Elsevier Ltd. All rights reserved. Keywords: Photodiode; Trap detector; Spectral responsivity; Optical characterization
1. Introduction Responsivity standards have been changed significantly in the past two decades from single element detectors to reflection or transition type trap detectors. Compared to other optical radiation detectors, trap detectors constructed from Corresponding author. Tel.: +90-262-679-5000; fax: +90-262-679-5001
E-mail address: [email protected] (O¨. Bazkır). 0143-8166/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2004.08.004
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silicon photodiodes have better optical properties [1,2]. Having good stability and spectral response to intensity from 1013 w/cm2 to 10 mw/cm2, these detectors have been used from deep ultraviolet through the visible to the near infrared regions for many applications. Reflection type trap detectors have been used since the development of the silicon photodiode self-calibration technique [3]. Having the highest accuracy, they have been used for the realization of optical power [4,5], spectral responsivity [6,7] and spectral irradiance scales in optical radiometry [8] and transferring the scale to test detectors [2]. The responsivity of optical radiation detectors is the ratio of their output electrical signal to input radiometric signal known as radiant (optical) power. Optical power can be measured accurately on metrological level traceable to electrical substitution cryogenic radiometers (ESCR). Using this system the uncertainty of optical power measurements at laser wavelengths that can be achieved is typically on the order of 0.001% (k=1) [9,10]. In this paper, we present both measurement techniques for optical characterizations and the realization of spectral responsivity scale. Our absolute responsivity scale is based on UME made reflection type reference trap detectors calibrated against ESCR. The scale was obtained using suitable mathematical models for the calculated internal quantum efficiency from measured absolute responsivity values and reflectance measurements at the tuneable Ar+ and He–Ne laser wavelengths.
2. Characterization of trap detectors In order to realize spectral responsivity scale trap detectors consisting of three Hamamatsu S1337-11 windowless photodiodes as shown in Fig. 1 were constructed. The number of photodiodes and their geometrical arrangements are decided such that to remove the polarization sensivity of trap detectors to incident light and reduce the high reflection losses of silicon photodiodes, which is about 30% in the visible region [11], and thereby increase external quantum efficiency. In this kind of trap detectors incoming beam undergoes five reflections where most of the radiation
Fig. 1. Internal structure of trap detector and photodiode.
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is being absorbed by photodiodes and the remaining beam returns back along the incoming beam. Due to these reasons the response of the detector to incident light can be determined more effectively. The spectral responsivity R (l) of trap detector in terms of reflectance and internal losses is given by [12] el ; (1) nhc where e is the elementary charge, l is the wavelength in vacuum, h is the Planck constant, c is the speed of light in vacuum, n is the refractive index of medium, r(l) is the spectral reflectance, d(l) is the internal quantum deficiency of trap detector, and 1d(l) is the internal quantum efficiency. Spectral responsivity of a trap detector as given in Eq. (1) is defined with the reflectance and the internal quantum efficiency. These parameters have to be modeled so as to interpolate and extrapolate the absolute responsivity data. In this work in order to realize the responsivity scale, initially the optical characterizations of trap detectors like; linearity polarization sensivity, homogeneity, reflectance and IQE were done then interpolation and extrapolation of responsivity scale from 350 to 850 nm wavelengths were described. R ¼ ½1 rðlÞ½1 dðlÞ
2.1. Nonlinearity measurements A detector is said to be linear if its output signal is directly proportional to the incident power. Detectors are often linear within certain power level limits, which are often termed as their dynamic range. Noise will determine the lowest level of incident light that is detectable. The upper limit of the linearity is determined by the maximum current, that the detector can handle without becoming saturated. Saturation is a condition in which there is no further increase in detector response as the input light is increased [13]. Linearity may be quantified in terms of the maximum percentage deviation from a straight line over a range of input light levels, which is called nonlinearity. We have measured nonlinearity of trap detectors using the flux-addition technique. The schematic representation of optical setup for the nonlinearity measurements is shown in Fig. 2. The intensity stabilized He–Ne laser with a stability of 0.009% was used as the light source. Laser beam was divided into two parts (A and B) with about the same powers by applying a polarization beam-splitting cube. Blocking one each time and superimposing them on the detector, photocurrents IA, IB and IAB were measured. In the measurements, 10 different neutral-density filters were used to change power levels from 0.1 to 1.1 mW. From recorded data the nonlinearity N is calculated from the following relation [14–17]: NðI AB Þ ¼
ðI AB I A I B Þ : I AB
(2)
Four silicon-based trap detectors (TD-1, TD-2, TD- 3 and TD-4) were placed on a computer controlled linear translation stage of having 10 mm motion sensivity with
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Fig. 2. Nonlinearity measurement set up. A1–A5 are apertures, S1 and S2 are shutters.
Fig. 3. Nonlinearity measurement of silicon photodiode-based trap detectors.
step motors. The nonlinearity of these detectors was measured and the results are shown in Fig. 3. At about 0.80 mW power level the nonlinearity varies between 1 105 and 2 105. This means that the responsivity of trap detectors is linear to within few parts in 105. There are many factors that affect the nonlinearity of silicon photodiodes. Most important are series resistance of photodiodes, the diameter of the incident beam, photocurrent and size of the active area [15–17]. 2.2. Polarization sensivity measurements The responsivity of transfer standards should not depend on the polarization state of the beam to be measured. In trap detector construction both the number of photodiodes and their geometrical arrangement are decided to remove the polarization sensivity. UME made reflection type trap detectors as shown in Fig. 1 consist of three photodiodes and they are arranged such that the incident beam after five specular reflections emerge from the trap detector with the same polarization as incident beam.
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Fig. 4. Polarization sensivity results of trap detectors.
Fig. 5. Spatial uniformity measurement set up.
Power stabilized He–Ne laser at 632.8 nm wavelengths was used as a light source. Detectors were sequentially placed in the beam way and rotated around its optical axis (the z-axis in Fig. 5) to examine the effect of rotation of the plane of polarization. The responsivity was measured simultaneously in each position at 22.51 steps. Signals from trap detectors were recorded as a function of the rotation angle and normalized to a value obtained at an arbitrarily chosen origin to detect relative variation of responsivity (Fig. 4). The maximum relative variations that were obtained are7few parts in 104. This means that any misalignment of detectors would lead to a relative standard uncertainty of about 104 in the determination of the responsivity. Therefore, in order to avoid changes due to misalignment, the detectors must always be oriented the same way with respect to the direction of polarization thought calibrations. 2.3. Uniformity measurements Spatial uniformity is the variation of responsivity as a function of position across the detecting surface. In this case trap detectors were mounted on X–Y translation stage, which was driven by PC-controlled step motors given in Fig. 5. Using power
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Fig. 6. Spatial uniformity representations of each trap detectors.
stabilized He–Ne laser (632.8 nm) beam having spot size of 1.0 mm diameter, the spatial uniformity of trap detectors was investigated by scanning their entrance aperture with a step length of 0.5 mm. The uniformity of trap detectors was obtained by dividing their response at the selected point to the maximum responsivity value. Fig. 6 shows the results of the uniformity measurements of a S1337 photodiode’s based trap detectors. Within the 6 mm diameter the change in the spatial uniformity of trap detectors were obtained as about 0.02%.
2.4. Reflectance measurements The absolute responsivities of trap detectors as described in Section 2.5 were measured at discrete laser wavelengths. In order to expand responsivity scale, the reflectance losses of trap detectors should be measured and modeled. The reflectance of trap detectors were measured using Ar+ (at 457.1, 488 and 514.5 nm wavelengths), and He–Ne (at 632.8 nm wavelength) lasers using the set up given in Fig. 7. A stabilized laser beam was aligned to incident a point close to the rim of a mirror so as to get the small angle (about 11) between the incident and reflected beam from the first trap detector. Any reflected beam from this trap detector was measured using another trap detector. The measurements were repeated by interchanging the
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Fig. 7. Laser-based spectral reflectance measurements set-up. A1–A4 are apertures.
Fig. 8. Illustration of reflectance of silicon photodiode-based trap detectors. Solid line indicates the theoretical model fitted to the measured values and black points inside box indicate the measured data at laser wavelengths.
detectors. The repeatability in these measurements was of the order of 105. The obtained measurement results are shown in the Fig. 8. In order to use these measured reflectance values in Eq. (1) for the realization of spectral responsivity scale, these reflectance values have to be modeled. This is achieved as follows. In a trap detector, incoming beam undergoes five reflections due to the geometry of device. The angle of incidence of these reflections is twice 451 for the perpendicular (s) plane of polarization, once normal incidence, and twice 451 for
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the parallel (p) plane of polarization. Thus the reflectance of a trap detector is written as rref ¼ rð0o Þr2s ð45o Þr2p ð45o Þ:
(3)
To calculate these r(01), rs(451) and rp(451) reflections the Fresnell’s reflection, transmission equations and known refractive indices of Si and SiO2 were used [11]. The calculated reflectance data were fitted to the measured data by adjusting the oxide thickness parameter. The difference between measured and calculated data after the best fit was at 10-5 level. The oxide thicknesses after the fitting were obtained as 30.10, 29.68, 28.99 and 28.08 nm for TD-1, TD-2, TD-3 and TD-4, respectively. Both the measurements and calculations showed that the reflectance of trap detectors are below 0.5% over the wavelengths under the study, this means that in this region the responsivity is insensitive to the reflectance changes, but increases at short wavelengths. 2.5. Internal quantum efficiency calculation Quantum efficiency is defined as the ratio of countable events produced to number of photons incident on the detector. The quantum efficiency is basically another way of expressing the effectiveness of the incident radiant energy for producing electrical current in a circuit. The most important advantage of silicon-based trap detectors over the single silicon photodiodes is that internal quantum efficiency is close to unity [9,18,19]. This means the spectral responsivity of trap detectors would not be changed in time and it would be linear over many orders of irradiance. Any deflection from unity is called internal quantum deficiency, which is assumed to be due to the trap charges at the SiO2/Si interface [2]. This charge attracts the electrons (the minority carrier in this region) and reduces the number reaching the depletion region. To calculate the quantum efficiency of the photodiode it is necessary to quantify this loss mechanism. The IQE is related to the responsivity by the equation IQE ¼ 1 dðl ¼Þ
R hc : ð1 rÞnel
(4)
In the Eq. (4) the absolute responsivity values were obtained by measuring the trap detectors response in terms of either current or voltage against the absolute optical power from ESCR at power stabilized Ar+ (457.1, 488, 514.5 nm) and He–Ne (632.8 nm) lasers. Using these responsivity values and reflectance r values measured as described in Section. 2.4 the IQE values were calculated. In order to expand the IQE between 350 and 850 nm (Fig. 9), the model described by Geist [9,20,21] was used, which is given as IQE ¼ 1 d ¼ K½A1 expðl=l1 Þ þ A2 expðl2 =l22 Þ:
(5)
This equation is fitted to the IQE values obtained from Eq. (4) by adjusting the parameters K, A1, A2, l1 and l2. Having seen that both the internal quantum efficiency and the reflectance of trap detector obtained effectively by the combination of measurements and developed
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Fig. 9. Measured and modeled IQE of trap detectors.
Fig. 10. Responsivity of trap detectors obtained from combination of measured and modeled values.
models, the spectral responsivity scale can be realized using Eqs. (1), (3) and (5). Comparing the calculated and measured values, it was seen that there is a good agreement between them. Hence, we decided to use this model for the realization of spectral responsivity from 350 to 850 nm as shown in Fig. 10.
3. Conclusions The realization of the spectral responsivity of silicon-based reflection type trap detectors were studied in this paper. Four trap detectors were used so as to compare
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the effectiveness of the realized responsivity scale. Different measurement systems were established in order to optically characterize these detectors and to calculate their effects on the uncertainty. For the nonlinearity measurements, flux addition technique was used and it was found that trap detectors in the 0.1–0.8 mW power ranges are linear within 105. The polarization sensivity was obtained by measuring the responsivity as a function of rotation of trap detectors around the beam axis. Results shows that any misalignment of trap detectors leads to a maximum polarization sensivity of 104 in the responsivity. The uniformity measurements obtained by scanning of entrance aperture of trap detectors provides us the variation of responsivity across the detecting surface of trap detectors which is about 3 105 within the 6 mm diameter. After optical characterizations, trap detectors were calibrated against ESCR at Ar+ and He–Ne laser wavelengths in order to establish absolute responsivity scale. The scale then expanded from 350 to 850 nm with an uncertainty of 0.05% by using interpolation and extrapolation models that give measured reflectance and internal quantum efficiency of trap detectors.
References [1] Zalewski EF, Duda CR. Silicon photodiode device with 100% external quantum efficiency. Appl Opt 1983;19:2867–73. [2] Fox NF. Trap detectors and their properties. Metrologia 1991;28:197–202. [3] Zalewski EF, Geist J. Spectral response self-calibration and interpolation of silicon photodiodes. Appl Opt 1980;19:3795–9. [4] Ko¨hler R, Goebel R, Pello R. Results of an international comparison of spectral responsivity of silicon photodetectors. Metrologia 1995/1996;32:463–8. [5] Lassila A, Hofer H, Ikonen E, Liedquist L, Stock KD, Varpula T. Intercomparisons of cryogenic radiometers using silicon trap detectors. Meas Sci Technol 1997;8:123–7. [6] Nettleton DH, Prior TR, Ward TH. Improved spectral responsivity scales at the NPL, 400 nm to 20 mm. Metrologia 1993;30:425–32. [7] Gentile TR, Houston SM, Cromer CL. Realisation of a scale of absolute spectral response using NIST high-accuracy cryogenic radiometer. Appl Opt 1996;35:4392–403. [8] Karha P, Toivanen P, Monoochehri F, Ikonen E. Development of a detector based absolute spectral irradiance scale in the 380–900 nm spectral range. Appl Opt 1997;36:8809–918. [9] Varpula T, Seppa H, Saari J- M. Optical power calibrator based on a stabilized green He- Ne laser and a cryogenic absolute radiometer. IEEE Trans Instrum Meas 1989;38:558–64. [10] Martin JE, Fox NP, Key RJ. A cryogenic radiometer for absolute radiometric measurements. Metralogia 1985;21:147–55. [11] Haapalinna A, Karha P, Ikonen E. Spectral reflectance of silicon photodiodes. Appl Opt 1998;31:729–32. [12] Karha P, Fagerlund H, Lassila A, Ludvigsen H, Monoochehri F, Ikonen E. Optical power and transmittance measurements and their use in detector-based realization of the luminous intensity scale. Opt Eng 1995;34:2611–8. [13] Budde W. Definition of the linearity range of Si photodiodes. Appl Opt 1983;22:1780. [14] Boivin LP. Automated abslolute and relative spectral linearity measurements on photovoltaic detectors. Metrologia 1993;30:355–60. [15] Ku¨barsepp T, Haapalinna A, Karha P, Ikonen E. Non linearity measurements of photodiodes. Appl Opt 1998;37:2716–22.
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[16] Fischer J, Fu L. Photodiodes nonlinearity measurement with an intensity stabilized laser as a radiation source. Appl Opt 1993;32:4187–90. [17] Haapalinna A, Ku¨barsepp T, Karha P, Ikonen E. Measurement of the absolute linearity of photodetectors with a diode laser. Meas Sci Technol 1999;10:1075–8. [18] Palmer JM. Alternative configurations for trap detectors. Metrologia 1993;30:327–33. [19] Zalewski EF, Hoyt CC. Comparison between cryogenic radiometry and predicted quantum efficiency of pn silicon photodiode light traps. Metrologia 1991;28:203–6. [20] Geist J. Quantum efficiency of p-n junction in silicon as an absolute radiometric standard National Brureau at Standards. Appl Opt 1979;18:760–2. [21] Werner L, Fischer J, Johannsen U, Hartmann J. Accurate determination of the spectral responsivity of silicon trap detectors between 238 and 1015 nm using a laser based cryogenic radiometer. Metrologia 2000;37:279–84.
Optics and Lasers in Engineering 43 (2005) 131–141
Characterization of silicon photodiode-based trap detectors and establishment of spectral responsivity scale O¨zcan Bazkır, Farhad Samadov TU¨BI˙TAK-Ulusal Metroloji Enstitu¨su¨ (UME), Gebze, 41470, Kocaeli, Turkey Received 8 March 2004; accepted 29 July 2004 Available online 2 October 2004
Abstract Spectral responsivity scale was established at National Metrology Institute of Turkey (UME) between 350 and 850 nm wavelength ranges. The scale is based on UME made reflection type trap detector consisting of three single element silicon photodiodes. Various measurements systems were established in order to make optical characterization of trap detectors like linearity, polarization sensivity, uniformity and spectral responsivity. The absolute responsivity linked to the absolute optical power was obtained using improved laser stabilization optics and electrical substitution cryogenic radiometer system at discrete laser wavelengths. Using physical models for the trap detectors, reflectance and internal quantum efficiency the scale was realized with an expanded uncertainty of 0.05%. r 2004 Elsevier Ltd. All rights reserved. Keywords: Photodiode; Trap detector; Spectral responsivity; Optical characterization
1. Introduction Responsivity standards have been changed significantly in the past two decades from single element detectors to reflection or transition type trap detectors. Compared to other optical radiation detectors, trap detectors constructed from Corresponding author. Tel.: +90-262-679-5000; fax: +90-262-679-5001
E-mail address: [email protected] (O¨. Bazkır). 0143-8166/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2004.08.004
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silicon photodiodes have better optical properties [1,2]. Having good stability and spectral response to intensity from 1013 w/cm2 to 10 mw/cm2, these detectors have been used from deep ultraviolet through the visible to the near infrared regions for many applications. Reflection type trap detectors have been used since the development of the silicon photodiode self-calibration technique [3]. Having the highest accuracy, they have been used for the realization of optical power [4,5], spectral responsivity [6,7] and spectral irradiance scales in optical radiometry [8] and transferring the scale to test detectors [2]. The responsivity of optical radiation detectors is the ratio of their output electrical signal to input radiometric signal known as radiant (optical) power. Optical power can be measured accurately on metrological level traceable to electrical substitution cryogenic radiometers (ESCR). Using this system the uncertainty of optical power measurements at laser wavelengths that can be achieved is typically on the order of 0.001% (k=1) [9,10]. In this paper, we present both measurement techniques for optical characterizations and the realization of spectral responsivity scale. Our absolute responsivity scale is based on UME made reflection type reference trap detectors calibrated against ESCR. The scale was obtained using suitable mathematical models for the calculated internal quantum efficiency from measured absolute responsivity values and reflectance measurements at the tuneable Ar+ and He–Ne laser wavelengths.
2. Characterization of trap detectors In order to realize spectral responsivity scale trap detectors consisting of three Hamamatsu S1337-11 windowless photodiodes as shown in Fig. 1 were constructed. The number of photodiodes and their geometrical arrangements are decided such that to remove the polarization sensivity of trap detectors to incident light and reduce the high reflection losses of silicon photodiodes, which is about 30% in the visible region [11], and thereby increase external quantum efficiency. In this kind of trap detectors incoming beam undergoes five reflections where most of the radiation
Fig. 1. Internal structure of trap detector and photodiode.
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is being absorbed by photodiodes and the remaining beam returns back along the incoming beam. Due to these reasons the response of the detector to incident light can be determined more effectively. The spectral responsivity R (l) of trap detector in terms of reflectance and internal losses is given by [12] el ; (1) nhc where e is the elementary charge, l is the wavelength in vacuum, h is the Planck constant, c is the speed of light in vacuum, n is the refractive index of medium, r(l) is the spectral reflectance, d(l) is the internal quantum deficiency of trap detector, and 1d(l) is the internal quantum efficiency. Spectral responsivity of a trap detector as given in Eq. (1) is defined with the reflectance and the internal quantum efficiency. These parameters have to be modeled so as to interpolate and extrapolate the absolute responsivity data. In this work in order to realize the responsivity scale, initially the optical characterizations of trap detectors like; linearity polarization sensivity, homogeneity, reflectance and IQE were done then interpolation and extrapolation of responsivity scale from 350 to 850 nm wavelengths were described. R ¼ ½1 rðlÞ½1 dðlÞ
2.1. Nonlinearity measurements A detector is said to be linear if its output signal is directly proportional to the incident power. Detectors are often linear within certain power level limits, which are often termed as their dynamic range. Noise will determine the lowest level of incident light that is detectable. The upper limit of the linearity is determined by the maximum current, that the detector can handle without becoming saturated. Saturation is a condition in which there is no further increase in detector response as the input light is increased [13]. Linearity may be quantified in terms of the maximum percentage deviation from a straight line over a range of input light levels, which is called nonlinearity. We have measured nonlinearity of trap detectors using the flux-addition technique. The schematic representation of optical setup for the nonlinearity measurements is shown in Fig. 2. The intensity stabilized He–Ne laser with a stability of 0.009% was used as the light source. Laser beam was divided into two parts (A and B) with about the same powers by applying a polarization beam-splitting cube. Blocking one each time and superimposing them on the detector, photocurrents IA, IB and IAB were measured. In the measurements, 10 different neutral-density filters were used to change power levels from 0.1 to 1.1 mW. From recorded data the nonlinearity N is calculated from the following relation [14–17]: NðI AB Þ ¼
ðI AB I A I B Þ : I AB
(2)
Four silicon-based trap detectors (TD-1, TD-2, TD- 3 and TD-4) were placed on a computer controlled linear translation stage of having 10 mm motion sensivity with
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Fig. 2. Nonlinearity measurement set up. A1–A5 are apertures, S1 and S2 are shutters.
Fig. 3. Nonlinearity measurement of silicon photodiode-based trap detectors.
step motors. The nonlinearity of these detectors was measured and the results are shown in Fig. 3. At about 0.80 mW power level the nonlinearity varies between 1 105 and 2 105. This means that the responsivity of trap detectors is linear to within few parts in 105. There are many factors that affect the nonlinearity of silicon photodiodes. Most important are series resistance of photodiodes, the diameter of the incident beam, photocurrent and size of the active area [15–17]. 2.2. Polarization sensivity measurements The responsivity of transfer standards should not depend on the polarization state of the beam to be measured. In trap detector construction both the number of photodiodes and their geometrical arrangement are decided to remove the polarization sensivity. UME made reflection type trap detectors as shown in Fig. 1 consist of three photodiodes and they are arranged such that the incident beam after five specular reflections emerge from the trap detector with the same polarization as incident beam.
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Fig. 4. Polarization sensivity results of trap detectors.
Fig. 5. Spatial uniformity measurement set up.
Power stabilized He–Ne laser at 632.8 nm wavelengths was used as a light source. Detectors were sequentially placed in the beam way and rotated around its optical axis (the z-axis in Fig. 5) to examine the effect of rotation of the plane of polarization. The responsivity was measured simultaneously in each position at 22.51 steps. Signals from trap detectors were recorded as a function of the rotation angle and normalized to a value obtained at an arbitrarily chosen origin to detect relative variation of responsivity (Fig. 4). The maximum relative variations that were obtained are7few parts in 104. This means that any misalignment of detectors would lead to a relative standard uncertainty of about 104 in the determination of the responsivity. Therefore, in order to avoid changes due to misalignment, the detectors must always be oriented the same way with respect to the direction of polarization thought calibrations. 2.3. Uniformity measurements Spatial uniformity is the variation of responsivity as a function of position across the detecting surface. In this case trap detectors were mounted on X–Y translation stage, which was driven by PC-controlled step motors given in Fig. 5. Using power
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Fig. 6. Spatial uniformity representations of each trap detectors.
stabilized He–Ne laser (632.8 nm) beam having spot size of 1.0 mm diameter, the spatial uniformity of trap detectors was investigated by scanning their entrance aperture with a step length of 0.5 mm. The uniformity of trap detectors was obtained by dividing their response at the selected point to the maximum responsivity value. Fig. 6 shows the results of the uniformity measurements of a S1337 photodiode’s based trap detectors. Within the 6 mm diameter the change in the spatial uniformity of trap detectors were obtained as about 0.02%.
2.4. Reflectance measurements The absolute responsivities of trap detectors as described in Section 2.5 were measured at discrete laser wavelengths. In order to expand responsivity scale, the reflectance losses of trap detectors should be measured and modeled. The reflectance of trap detectors were measured using Ar+ (at 457.1, 488 and 514.5 nm wavelengths), and He–Ne (at 632.8 nm wavelength) lasers using the set up given in Fig. 7. A stabilized laser beam was aligned to incident a point close to the rim of a mirror so as to get the small angle (about 11) between the incident and reflected beam from the first trap detector. Any reflected beam from this trap detector was measured using another trap detector. The measurements were repeated by interchanging the
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Fig. 7. Laser-based spectral reflectance measurements set-up. A1–A4 are apertures.
Fig. 8. Illustration of reflectance of silicon photodiode-based trap detectors. Solid line indicates the theoretical model fitted to the measured values and black points inside box indicate the measured data at laser wavelengths.
detectors. The repeatability in these measurements was of the order of 105. The obtained measurement results are shown in the Fig. 8. In order to use these measured reflectance values in Eq. (1) for the realization of spectral responsivity scale, these reflectance values have to be modeled. This is achieved as follows. In a trap detector, incoming beam undergoes five reflections due to the geometry of device. The angle of incidence of these reflections is twice 451 for the perpendicular (s) plane of polarization, once normal incidence, and twice 451 for
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the parallel (p) plane of polarization. Thus the reflectance of a trap detector is written as rref ¼ rð0o Þr2s ð45o Þr2p ð45o Þ:
(3)
To calculate these r(01), rs(451) and rp(451) reflections the Fresnell’s reflection, transmission equations and known refractive indices of Si and SiO2 were used [11]. The calculated reflectance data were fitted to the measured data by adjusting the oxide thickness parameter. The difference between measured and calculated data after the best fit was at 10-5 level. The oxide thicknesses after the fitting were obtained as 30.10, 29.68, 28.99 and 28.08 nm for TD-1, TD-2, TD-3 and TD-4, respectively. Both the measurements and calculations showed that the reflectance of trap detectors are below 0.5% over the wavelengths under the study, this means that in this region the responsivity is insensitive to the reflectance changes, but increases at short wavelengths. 2.5. Internal quantum efficiency calculation Quantum efficiency is defined as the ratio of countable events produced to number of photons incident on the detector. The quantum efficiency is basically another way of expressing the effectiveness of the incident radiant energy for producing electrical current in a circuit. The most important advantage of silicon-based trap detectors over the single silicon photodiodes is that internal quantum efficiency is close to unity [9,18,19]. This means the spectral responsivity of trap detectors would not be changed in time and it would be linear over many orders of irradiance. Any deflection from unity is called internal quantum deficiency, which is assumed to be due to the trap charges at the SiO2/Si interface [2]. This charge attracts the electrons (the minority carrier in this region) and reduces the number reaching the depletion region. To calculate the quantum efficiency of the photodiode it is necessary to quantify this loss mechanism. The IQE is related to the responsivity by the equation IQE ¼ 1 dðl ¼Þ
R hc : ð1 rÞnel
(4)
In the Eq. (4) the absolute responsivity values were obtained by measuring the trap detectors response in terms of either current or voltage against the absolute optical power from ESCR at power stabilized Ar+ (457.1, 488, 514.5 nm) and He–Ne (632.8 nm) lasers. Using these responsivity values and reflectance r values measured as described in Section. 2.4 the IQE values were calculated. In order to expand the IQE between 350 and 850 nm (Fig. 9), the model described by Geist [9,20,21] was used, which is given as IQE ¼ 1 d ¼ K½A1 expðl=l1 Þ þ A2 expðl2 =l22 Þ:
(5)
This equation is fitted to the IQE values obtained from Eq. (4) by adjusting the parameters K, A1, A2, l1 and l2. Having seen that both the internal quantum efficiency and the reflectance of trap detector obtained effectively by the combination of measurements and developed
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Fig. 9. Measured and modeled IQE of trap detectors.
Fig. 10. Responsivity of trap detectors obtained from combination of measured and modeled values.
models, the spectral responsivity scale can be realized using Eqs. (1), (3) and (5). Comparing the calculated and measured values, it was seen that there is a good agreement between them. Hence, we decided to use this model for the realization of spectral responsivity from 350 to 850 nm as shown in Fig. 10.
3. Conclusions The realization of the spectral responsivity of silicon-based reflection type trap detectors were studied in this paper. Four trap detectors were used so as to compare
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the effectiveness of the realized responsivity scale. Different measurement systems were established in order to optically characterize these detectors and to calculate their effects on the uncertainty. For the nonlinearity measurements, flux addition technique was used and it was found that trap detectors in the 0.1–0.8 mW power ranges are linear within 105. The polarization sensivity was obtained by measuring the responsivity as a function of rotation of trap detectors around the beam axis. Results shows that any misalignment of trap detectors leads to a maximum polarization sensivity of 104 in the responsivity. The uniformity measurements obtained by scanning of entrance aperture of trap detectors provides us the variation of responsivity across the detecting surface of trap detectors which is about 3 105 within the 6 mm diameter. After optical characterizations, trap detectors were calibrated against ESCR at Ar+ and He–Ne laser wavelengths in order to establish absolute responsivity scale. The scale then expanded from 350 to 850 nm with an uncertainty of 0.05% by using interpolation and extrapolation models that give measured reflectance and internal quantum efficiency of trap detectors.
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