Spectral Reflectance of Silicon Photodiodes

Spectral reflectance of silicon photodiodes Atte Haapalinna, Petri Ka¨rha¨, and Erkki Ikonen

A precision spectrometer was used to measure the spectral reflectance of a silicon photodiode over the wavelength range from 250 to 850 nm. The results were compared with the corresponding values predicted by a model based on thin-film Fresnel formulas and the known refractive indices of silicon and silicon dioxide. The good agreement at the level of 2 3 1023 in the visible wavelength range verifies that the reflection model can be used for accurate extrapolation of the spectral reflectance and responsivity of silicon photodiode devices. In addition, characterization of the photodiode reflectance in the ultraviolet region improves the accuracy of the spectral irradiance measurements when filter radiometers based on trap detectors are used. © 1998 Optical Society of America OCIS codes: 120.5630, 040.6040, 040.7190, 230.5170.

1. Introduction

Silicon photodiodes are among the most popular photodetectors that combine high performance over a wide wavelength range with unparalleled ease of use. High-quality photodiodes, in the form of a trap detector,1,2 have many significant applications in precision radiometry. Their predictable responsivity in visible and near-infrared ~NIR! wavelengths allows the realization of high-accuracy spectral responsivity scales.3,4 The spectral responsivity scales can be utilized in, for example, realization of luminous intensity5,6 and spectral irradiance scales.7,8 The spectral responsivity of a silicon photodiode is determined by the reflectance of the diode surface r~l! and the internal quantum deficiency d~l!. The values of d~l! and r~l! can be extrapolated4 by mathematical models. To extrapolate the values of r~l!, Fresnel equations9 and known refractive indices10,11 of silicon dioxide ~SiO2! and silicon ~Si! can be used. The responsivity of a trap detector is a combination of the responsivities of the component photodiodes. In precision radiometry, the responsivity of trap detectors is calibrated against the cryogenic radiometer at certain laser wavelengths. Accurate knowledge of the spectral reflectance of the trap detector facilitates

The authors are with Metrology Research Institute, Helsinki University of Technology, P.O. Box 3000, FIN-02015 HUT, Finland. Received 8 July 1997; revised manuscript received 7 October 1997. 0003-6935y98y040729-04$10.00y0 © 1998 Optical Society of America

the extrapolation of the responsivity to other wavelengths. High-accuracy filter radiometers constructed from trap detectors benefit from the low backreflection of the trap detector. This makes possible separate characterization of the trap detector and the interference filter even at UV wavelengths.12 The residual correction due to interreflections can be reliably determined if the spectral reflectance of the photodiodes in the trap detector is known. Our purpose was to study the spectral reflectance of silicon photodiodes both experimentally and theoretically. Accurate characterization of this parameter allows precise extrapolation of the spectral responsivity of trap detectors and accurate modeling of interreflections for filter radiometers based on trap detectors. We present the results of spectral reflectance measurements and compare them with the reflectance values obtained with a calculation model based on Fresnel formulas. In Section 2 we describe the calculation model used in the extrapolation of spectral reflectance. The measurement setup is described in Section 3. The measurement results and the comparison between the experiments and the calculated results are included in Section 4. Finally, conclusions are drawn from the comparison results and presented in Section 5. 2. Calculation of the Reflectance of a Silicon Photodiode

From the optical point of view, a photodiode can be described as a Si substrate with a thin layer of SiO2 on the surface. The reflectance of the photodiode is calculated from the thickness of the SiO2 layer and the known refractive indices n2 for SiO2 and n# 3 for Si. 1 February 1998 y Vol. 37, No. 4 y APPLIED OPTICS

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The values for n2 and n# 3 used in this study were taken from Refs. 10 and 11, respectively. In the visible region, the refractive index of SiO2 is practically real; however, for Si, the complex refractive index n# 3 5 n3 2 ik3,

(1)

where k3 is the extinction coefficient, has to be used. Consider a ray coming from the air ~refractive index n1! to the surface of the photodiode at an angle of u1 with respect to the normal of the surface. Part of the beam is reflected from the surface of SiO2. The transmitted beam is again partly reflected from the interface between SiO2 and Si. The amplitude reflectance and the transmittance coefficients rmn and tmn from medium m to n~m, n 5 1, 2, 3! in the interface of two media can be calculated by using Fresnel equations.9 For p-polarized beams the coefficients are nn cos um 2 nm cos un , nn cos um 1 nm cos un

(2)

2nm cos um , tmn 5 nn cos um 1 nm cos un

(3)

rmn 5

and for s-polarized beams rmn 5

nm cos um 2 nn cos un , nm cos um 1 nn cos un

(4)

tmn 5

2nm cos um . nm cos um 1 nn cos un

(5)

Note that at the interface between Si and SiO2 the reflectance and the transmittance coefficients are complex. The refraction angles u2 and u# 3 in SiO2 and Si, respectively, can be calculated from the Snell’s law as

S S

D D

u2 5 arcsin

n1 sin u1 , n2

(6)

u# 3 5 arcsin

n1 sin u1 . n# 3

(7)

The partial reflections result in an infinite series of interreflections between the surfaces of the SiO2 layer. The phase difference between two subsequent wave fronts exiting the front surface of the SiO2 layer is b5

2p n2t cos u2, l1

(8)

where l1 is the wavelength in air and t is the thickness of the layer. Evaluating the resulting geometrical series yields the amplitude reflection coefficient for the photodiode r# 5 r12 1 730

t12t21r# 23 exp~22ib! . 1 1 r12r# 23 exp~22ib!

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(9)

Fig. 1. Reflectance measuring accessory of the reference spectrometer. The turntable assembly, including the tracking mirrors and the integrating sphere detector, is shown in both the sample measurement position ~turned to the left! and the reference measurement position ~turned to the right!. In the reference measurement position, the sample is removed from the beam.

The intensity reflection coefficient can be calculated from the amplitude reflection coefficient as rs,p~u1! 5 ur# u2.

(10)

In a polarization-independent reflection trap detector2 the light intensity is attenuated by five reflections on the photodiode surfaces before the residual intensity exits the device. Because of the geometry of the device, the angle of incidence of these reflections is twice 45° for the s plane of polarization, once normal incidence, and twice 45° for the p plane of polarization. Thus the reflectance of the trap detector is rtrap 5 r~0°!rs2~45°!rp2~45°!.

(11)

3. Measurement Setup

The measurements were made with our specially built precision reflectance spectrometer. The measurement principle of the reflectance spectrometer is similar to the National Institute of Standards and Technology ~NIST! specular reflectometer– spectrophotometer for transmittance measurements.13 The measurement system consists of a light source, a single grating monochromator, and a reflectance measuring accessory used to control the measurement geometry. The light sources and the grating monochromator are the same as in our reference spectrometer.14 The lamps used as light sources are of two types: a halogen filament lamp for the measurements in the NIR and visible wavelengths, and a deuterium arc lamp for the measurements in the UV wavelengths. Order-sorting filters are used to reduce the level of stray light. In the exit optics of the monochromator, an off-axis parabolic mirror is used to create a collimated measurement beam of approximately 8 mm in diameter. The measurement beam is polarized with a calcite prism. The reflectance measurement accessory ~Fig. 1! is used to direct the light beam into the integrating sphere both directly as a reference and after being reflected by the sample. The intensities are measured as the signal obtained from the Si photodiode of the integrating sphere detector. The incident inten-

Fig. 2. Spectral reflectance of an S6337 photodiode for light polarized in the s plane. The solid curves denote reflectance values calculated with thin-film Fresnel formulas. The oxide layer thickness ~28.5 nm! used in the calculation was determined by leastsquares fitting.

Fig. 3. Spectral reflectance of an S6337 photodiode for light polarized in the p plane. The solid curves denote reflectance values calculated with thin-film Fresnel formulas. The oxide layer thickness ~28.5 nm! used in the calculation was determined by leastsquares fitting.

sity corresponds to the reference measurement position, whereas the intensity of the reflected beam is measured at the sample measurement position. The measured quantity, the absolute specular reflectance of the sample surface, is obtained as the ratio of these intensities, after being corrected for dark signals. 4. Measurement Results

As a sample, a windowless, large-area silicon photodiode ~Hamamatsu S6337-11! with an active area of 18 mm 3 18 mm was used. This type of photodiode is similar to type S1337-11 commonly used in trap detectors, except for the larger dimensions. The spectral reflectance was measured over a wavelength range extending from 250 to 850 nm with a 3-nm bandwidth of the monochromator. The measurement beam was polarized either in the plane parallel to the plane of incidence ~ p plane! or in the plane perpendicular to the plane of incidence ~s plane!. Measurements were performed at two angles of incidence: 45° and an angle close to 0°. The choice of these two angles was determined by the geometry of the trap detector. The measurement results together with the corresponding reflectance values calculated by use of the equations given in Section 2 are presented in Figs. 2 and 3 for s- and p-polarized measurement beams, respectively. The thickness of the oxide layer was determined by least-squares fitting, in which the squared differences between the modeled and the measured reflectances were minimized. The oxide layer thickness was used as a parameter in the fitting, and for this sample the value 28.5 nm gave the best agreement for all the measurement geometries. The uncertainty components of reflectance measurements are discussed in more detail in Ref. 15. For a photodiode sample, the relative uncertainties ~2s! were estimated to be 0.7%, 0.6%, and 0.9% in the UV, visible, and NIR wavelengths, respectively. The relative deviation between the calculation model and the measurement results is presented in Fig. 4 as

Fig. 4. Relative deviation between the calculated and the measured spectral reflectance values of the S6337 photodiode sample. The symbols are as in Figs. 2 and 3.

a function of wavelength. The standard deviations are 1%, 0.2%, and 0.3% in the UV, visible, and NIR parts of the spectrum, respectively. In the visible and the NIR wavelengths, the averaged deviations are 20.04% and 20.2%, respectively, whereas in the UV region the average deviation is 10.4%. 5. Conclusions

The spectral reflectance of a Si photodiode has been studied both experimentally and by means of mathematical modeling. The measurements confirm the validity of the calculation model used to estimate photodiode reflectances. The measured reflectance values are in excellent agreement with the calculated values in the visible and the NIR wavelengths. In the UV wavelengths the agreement is still good, although the maximum relative deviation at approximately 250 nm is somewhat higher, i.e., 4%. For these wavelengths the discrepancy between predicted and measured values can be explained qualitatively with a small amount of strongly absorbing silicon monoxide present in the SiO2 layer, as this component is not included in the refractive index of the oxidized layer. 1 February 1998 y Vol. 37, No. 4 y APPLIED OPTICS

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In visible wavelengths the standard deviation of relative difference between the calculated and the measured reflectances is 0.2%, and the average difference is 20.04%. The corresponding relative error in the predicted responsivity of a trap detector is below 2 3 1025. This is adequate for even the most demanding measurements of optical power because other uncertainty components with trap detectors are generally larger. As the reflectance of the silicon photodiode is high in the UV region, the corresponding corrections made in the characterization of UV-filter radiometers are also correspondingly large. The measured reflectances allow this correction to be more precisely defined, thus improving the accuracy of the filter radiometry. The financial support of the Centre for Metrology and Accreditation is acknowledged with gratitude. The excellent workmanship of Seppo Metsa¨la¨ in manufacturing the turntable mechanics of the reflectance spectrometer is greatly appreciated. References 1. E. F. Zalewski and C. R. Duda, “Silicon photodiode device with 100% external quantum efficiency,” Appl. Opt. 22, 2867–2873 ~1983!. 2. N. P. Fox, “Trap detectors and their properties,” Metrologia 28, 197–202 ~1991!. 3. D. H. Nettleton, T. R. Prior, and T. H. Ward, “Improved spectral responsivity scales at the NPL, 400 nm to 20 mm,” Metrologia 30, 425– 432 ~1993!. 4. T. R. Gentile, J. M. Houston, and C. L. Cromer, “Realization of a scale of absolute spectral response using the National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 4392– 4403 ~1996!.

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5. P. Ka¨rha¨, A. Lassila, H. Ludvigsen, F. Manoochehri, H. Fagerlund, and E. Ikonen, “Optical power and transmittance measurements and their use in detector-based realization of the luminous intensity scale,” Opt. Eng. 34, 2611–2618 ~1995!. 6. C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, and A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109 – 132 ~1996!. 7. B. C. Johnson, C. L. Cromer, R. D. Saunders, G. Eppeldauer, J. Fowler, V. I. Sapritsky, and G. Dezsi, “A method for realizing spectral irradiance based on an absolute cryogenic radiometer,” Metrologia 30, 309 –315 ~1993!. 8. P. Ka¨rha¨, P. Toivanen, F. Manoochehri, and E. Ikonen, “Development of a detector-based absolute spectral irradiance scale in the 380 –900 nm spectral range,” Appl. Opt. 36, 8909 – 8918 ~1997!. 9. M. Born and E. Wolf, Principles of Optics, 3rd ed. ~Pergamon, Oxford, 1965!, pp. 40, 632– 633. 10. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 ~1965!. 11. G. E. Jellison, Jr., “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41– 47 ~1992!. 12. P. Ka¨rha¨, R. Visuri, K. Leszcynski, F. Manoochehri, K. Jokela, and E. Ikonen, “Detector-based calibration method for highaccuracy solar UV measurements,” Photochem. Photobiol. 64, 340 –343 ~1996!. 13. J. J. Hsia and V. R. Weidner, “NBS specular reflectometer– spectrophotometer,” Appl. Opt. 19, 1268 –1273 ~1994!. 14. F. Manoochehri and E. Ikonen, “High-accuracy spectrometer for measurement of regular spectral transmittance,” Appl. Opt. 34, 3686 –3692 ~1995!. 15. F. Manoochehri, A. Haapalinna, and E. Ikonen, “Highaccuracy measurement of regular spectral transmittance and reflectance in UV–visible–NIR,” in Proceedings of the XIV IMEKO World Congress, Vol. 2, J. Halttunen, ed. ~Finnish Society of Automation, Helsinki, Finland, 1997!, pp. 108 –113.