IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 6, DECEMBER 1994 I99

Measurement of the Thickness of Dielectric Thin Films on Silicon Photodetectors Using the Angular

Response to Incident Linearly Polarized Light R. M. A. Azzam and M. M. K. Howlader

Abstmct-A simple and accurate technique for measuring the thickness of dielectric thin films on solid state photodetectors is described. It is based on the angled-incidence-dependent response of the detector to incident p(TM)- or s(TE)-polarized monochromatic light. The method is applied to determine the thickness of Si02 films on planar-difhrsed Si photodiodes to within fl nm.

I. INTRODUCTION OLD state semiconductor photodetectors, and in particu- S lar silicon junction photodiodes, have broad application in

many areas of science and technology. Because of their sim- plicity, ruggedness, and low cost, they have largely replaced the photomultiplier tube [l]. The topmost layer of a planar- diffused silicon photodiode is a passivation oxide film (see Fig. 1). The thickness d of that film is often selected to be a quarterwave for minimum reflectance at normal incidence; i.e., d = X/(4N1), where X is the vacuum wavelength of the monochromatic light of interest (or the center wavelength in the spectrum of a broad-band source), and N I is the film refractive index.

Beyond their standard widespread use in photometry and radiometry, Azzam et al., [2]-[6] have recently introduced novel instruments, in which arrangements of one or more re- flective silicon photodiodes are employed at oblique incidence to measure the state of polarization of the incoming light. This opens up a new era of application for the silicon detector technology. (A four-detector photopolarimeter is available commercially under the trade name “StokesMeter” [7].) The detectors are made intentionally reflective by simply control- ling the thickness of the dielectric oxide film. Although the thickness of the dielectric oxide film can be measured optically using reflectance [8] or ellipsometric [9] methods, a simple and accurate photoelectric technique is described in this paper that uses a thickness-dependent normalized angular response function for incident linearly polarized monochromatic light.

n. THEOREnCAL BASIS OF THE METHOD

Consider a monochromatic and collimated light beam that is incident on the planar surface of a photodetector D at an angle 4, Fig. 2. Here, p and s indicate the hea r polarization states with the electric vector parallel (TM) and perpendicular (TE) to the plane of incidence, respectively. The nonreflected light is absorbed by the detector and generates a proportional electrical signal i. The detector is assumed to have a linear response (which is true to within 1% over 8-10 decades of incident power for silicon detectors [lo]) so that

(1)

Here, IC is the responsivity of the detector, 10, is the intensity (power) of the incident linearly polarized light, and RY(4) is the intensity reflectance of the detector surface for the U polarization (U = p or s) at the angle of incidence 4. A normalized angular response function is defined as

i v ( 4 ) = kIov[1 - ‘ R V ( 4 ) l .

From (1) and (2), we obtain

(3)

Because it is this normalized function which is measured, the output power of a stable source, the detector responsivity, and any postdetection gain need not be known. This simplifies the measurement technique and eliminates several sources of error.

The intensity reflectance ‘R, is determined by

‘R, = R,R: (4)

where R, is the complex amplitude reflection coefficient of the dielectric film-semiconductor substrate system for the U polarization. When coherent multiple reflections between the film boundaries are accounted for, R, is given by

7-01, + 7-12, exP(-m&)

1 + 7-Olv7-12, eXP(-m&) R, = (5)

Manuscript received February 11, 1994, revised July 5, 1994. The work was supported by the. Electric Power Research hstit~te (EPRI) and ~nergy Copration.

The authors are with the Department of Electrical Enginering, University of New Orleans, New Orleans, LA 70148 USA.

where 7-01, and 7-12, are the Fresnel reflection Coefficients at the air-film and film-substrate interfaces, respectively;

IEEE Log Number 9406557. ~4 = (S) (N: - sin2 41-4 (6)

0018-9456/94$04.00 0 1994 IEEE

800 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 6, DECEMBER 1994

CONTACT

OXIDE

PASSIVATION

ACTIVE AREA DIA

>

\& t+j I 1

P-TYPE SILICON

P* DIFFUSION

Fig. 1. Structure of a planar-diffused silicon photodiode.

D

& I

Fig. 2. Response z(4) of a tilted photodetector D to incident light which is liiearly polarized parallel (p or TM) or perpendicular (s or TE) to the plane of incidence. Here 4 is the angle of incidence.

1.4

1.2

1 .o

0.8

f*@)

0.6

0.4

0.2

0.0

Fig. 3. Calculated normalized angular response function, fd(4), of the Si detector for incident s-polarized light at 633-nm wavelength for different values of the thickness of the topmost Si& film from 0 to 500 nm in steps of 50 nm.

1.50 1'75 1 1 .oo 1.25 1 0.50 1

fi., 11.50

' 1 0 5 0 . .... .... . _.:._. I , , , , I , , , , I , , , , , , , , , I , , , , I I , , , I , , , I I , , , , I , ;. /

/.. ... i is the angle-of-incidence-dependent film thickness period, and 0.25 s, 0.25

N I is the film refractive index [9]. Figs. 3 and 4 show families of normalized response func-

tively, for different values of the thickness d of the Si02

0.00 0.00 0 0 0 0 0 0 0 0 0 0 tions fs(+) and fp(+) for the s and p polarizations, respec- - ~ m + m m r - m m

f#J

f ih-from 0 to 500 nm in steps of 50 nm. These resulk

using the known refractive indices NI = 1.46 and N2 = 3.85

Fig. 4. Calculated normalized angular response function, fp(4), of the Si

values of the thickness of the topmost Si& film from 0 to 500 nm in steps of 50 nm.

are calculated for He-Ne laser fight of 633-nm wavelength for incident P-Plarized light at 633-nm for different

-j(0.02) of Si02 and Si, respectively [ll]. Except for thin films in the 0-100 nm range, the s polarization gives a higher sensitivity. The film thickness can be accurately determined from data obtained in the 10-75' range of incidence angle.

Detector 3 the film thickness is neither a quarterwave nor a halfwave.

Fig. 5 shows the experimental setup. Here L is a 1-mW He-

111. EXPERIMENTAL RESULTS

Planar-diffused silicon (PIN) photodiodes, optimized for photovoltaic unbiased operation are used. Each windowless Si detector has a 2.5-cm-diameter active area, and a 75' clear field of view. Three different detectors are tested with different thicknesses of the oxide layer. The Si02 film on the first detector (Detector 1) is nominally quarterwave thick for minimum reflectance at normal incidence for the 633- nm wavelength. Detector 2 is made reflective with a layer of nominal halfwave thickness at the same wavelength. For

Ne laser, and P is a crystal polarizer mounted in a graduated circle (0.005' resolution). The polarizer is rotatable so that the transmitted electric field vector is selected as horizontal (p) or vertical (s). (A small error of the azimuth angle of the polarizer is inconsequential, to the first order.) The silicon photodiode under test D is attached to a rotary stage or goniometer G, with an angle resolution of 0.002'. The circuit diagram of the postdetection low-noise transimpedence operational amplifier A appears in Fig. 6. The amplified output is recorded at discrete angular positions from 0 to 70' in 5' steps. Measurements are taken in ascending order of +

AZZAM AND HOWLADER: DELECTRlC THIN FILMS 801

1.025 ~ 1.025

Fig. 5. Instrument for measuring the angle-dependent photoelectric response. L is a 633-nm He-Ne laser source, P is a polarizer in a rotatable mount, and D is the photodetector under test. A and DV are an operational amplifier and digital voltmeter, respectively.

ClP "DC

T

Fig. 6. Circuit diagram of the transhpedence operational amplifier A in Fig. 5.

from 0 to 70", then in descending order from 70" to 0, and the results are averaged. This eliminates the effect of small errors associated with any possible goniometer hysteresis. The detector surface is initially set normal to the (horizontal) laser beam by autocollimation, so that the reflected beam coincides with the incident beam at q5 = 0. The detector surface is also positioned to contain the (vertical) axis of rotation of the goniometer by observing that the light spot on the detector surface does not move as the detector is rotated.

Fig. 7 shows the experimental points and best-fit curves for Detector 1 for incident p and s-polarized light. The best-fit curves, in the standard least-sum-of-squares sense, are obtained with a film thickness d =110.5 nm for the s polarization, and d =110.2 nm for the p polarization data. These independently obtained thicknesses are in excellent agreement, and are only slightly shifted from the quarterwave thickness of 633/(4 x 1.46) = 108.4 nm.

Fig. 8 shows the results that we obtain for Detector 2. The thicknesses for the best-fitting curves for the s and p polarization data are 222.2 nm and 221.0 nm, respectively. The agreement of these independently obtained thickness values gives confidence in this technique. The nominal halfwave thickness is 216.8 nm.

1 .ooo

0.975

0.950

0.925

U49 0.900

0.875

0.825

0850 1 0.850

0.825

0 800 0 800 o o o o o u 7 o ~ o o o o o m o

- - N N V l P 7 d b o O * W b

9 Fig. 7. N o d i angular response functions for the s and p polarizations, fa(q5) and fp(q5), versus the angle of incidence 4 for Detector 1. The data pits (0 ) are the experimental results, and the continuous l i e s are calculated to achieve a least-squares best fit. The theoretical curves are obtained when the Si& film thickness is 110.5 nm for the s data and 110.2 nm for the p data.

0 9 0 -

0 8 5 -

U400 80 -

0 7 5 -

0 7 0 -

1.250

1.225

1.200

1 1 7 5 q w

1150

1125

1100

1075

0.65 1 \t 1.050

0 60 o * ~ o o o o o o ~ o o o m o

9 Fig. 8. Normalized angular response functions for the s and p polarizatiOns, fd(q5) and fp(q5), versus the angle of incidence q5 for Detector 2. The data pomts ( 0 ) are the experimental results, and the continuous lines are calculated to achieve a least-squares best fit. The theoretical curves are obtained when the Si02 film thickness is 222.2 nm for the s data, and 221.0 nm for the p data.

- " m m f b o " n * b

Finally, Fig. 9 shows the results that we get for Detector 3. The film thicknesses derived from fitting the s and p polarization data are in perfect agreement in this case; the same d = 310.7 nm is obtained.

These results, which are repeatable to within fl nm, con- firm the validity and precision of the proposed technique. The normalized residual rms error in fitting the data in Figs. 7-9 is in the range 0.002 to 0.006. This level of uncertainty can be reduced further; e.g., by using a chopper to interrupt the source beam and a lock-in amplifier for detection.

When iteration is allowed on both the film refractive index and thickness, we are able to independently confirm the 1.46 value for the Si02 refractive index at the 633-nm wavelength

- ,,I-

802 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43. NO. 6, DECEMBER 1994

1 .o 1.06 j i, I 1 ::::

* \ v c 0.97

0.96

0.95

0.94

0.93

0 92 o “ “ ~ ~ g ~ ~ U l g ” o “ 0

9 m w w r .

Fig. 9. Normalized angular response functions for the s and p polarizations, f. (4) and fp (4). versus the angle of incidence 4 for Detector 3. The data points ( 0 ) are the experimental results, and the continuous lines are calculated to achieve a least-squares best fit. The theoretical curves are obtained for the same Si& film thickness of 310.7 nm for both polarizations.

to within fO.O1.

Iv. SUMMARY

The angle-of-incidence-dependent normalized photoelectric response of a silicon photodetector for incident linearly polar- ized light is a sensitive function of the thickness of the topmost oxide layer. This provides the basis for a relatively simple technique for determining the thickness of that layer, without recourse to conventional reflectance or ellipsometric methods. Except for thin films in the 0-100 nm range, the incident light should preferably be linearly polarized perpendicular to the plane of incidence (i.e., s or TE) to achieve higher sensitivity. Measurements on three different planar-diffused PIN silicon photodiodes c o b the validity of this technique of film thickness determination to a precision of the order of 1 nm. The method is obviously applicable to the characterization of Si-based photovoltaic solar cells and to other solid state photodetectors as well.

ACKNOWLEDGMENT We are pleased to acknowledge the assistance of Francis

Grosz, Frank Sebro, and Ron Guidry with the electronics.

REFERENCES

[l] W. Budde, Physical Detectors of Optical Radiation. New York Aca- demic, 1983.

[2] R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Len., vol. 10, pp. 309-311, Jul. 1985.

[3] R. M. A. Azzam, E. Masetti, I. M. Elminyawi and F. G. Grosz, “Con- struction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum., vol. 59, pp. 84-88, Jan. 1988.

[4] R. M. A. Azzam, “Tlvo-detector ellipsometer,” Rev. Sei. Instrum., vol. 56, pp. 1746-1748, Sept. 1985.

[5] D. C. Nick and R. M. A. ham, “Performance of an automated rotathg- detector ellipsometer,” Rev. Sci. Instrum., vol. 60, pp. 3625-3632, Dec. 1989.

[6] -, “Stokes-parameter photopolarimeter using an optically or mechanically rotatable two-detector assembly,” IEEE Trans. Instrum. Meas., vol. 39, pp. 722-725, Oct. 1990.

[7] Gaertner Scientific Corporation, Chicago, Illinois 60614. [8] W. A. Pliskin and E. E. Conrad, “Nondestructive determination of thick-

ness and refractive index of transparent films,” IBM J. Res. Develop.,

[9] R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light.

[lo] W. Budde, “Multidecade linearity measurements on si photodiodes,”

[l 1 J G. Gergely, Ed., Ell@sometric Tables of the Si-Si02 System for Mercury

vol. 8, pp. 43-51, Jan. 1964.

A”: North-Holland, 1987.

Appl. Opr., vol. 18, pp. 1555-1558, 15 May 1979.

and He-Ne Laser Spectral Lines. Budapest: Akademiai Kiado, 1971.

R. M. A. Azuun received his B.Sc. from Cairo University, Egypt, in 1967, and Ph.D. from the University of Nebraska-Lincoln in 1971, both in electrical engineering.

He is currently a distinguished professor of elec- trical engineering at the University of New Orleans. He is also the Polarization Optics topical editor for Applied Optics (Optical Technology Division), and was the topical editor of the Journal of the Optical Society of America A for Polarization and Thin Films from 1985 to 1989. Azzam served as coorganizer,

cochairman, and pfwedhgs coeditor of several national and intemational conferences on ellipsometry, polarized light, and optical polarimetry. He was also guest coeditor of special issues of Optical Engineering and the Journal of the Optical Society of America A, and editor of Vol. MS27 of the SPIE’s Milestone Series Selected Papers on Ellipsometry, published in 1991. Azzam was a Fulbright senior research scholar and visiting professor at Universit6 de Provence, Marseille, France, from 1985 to 1986. He has four patents and is author or coauthor of over 200 journal papers, and the monograph Ellipsometry and Polarized Light, which was first published by North-Holland in 1977, translated into Russian by Mir, Moscow, in 1981, and appeared in paperback in 1987. Dr. h a m is a Fellow of the Optical Society of America. h a m was

recogmzd as an Outstanding American Inventor, and placed as a finalist in the competition for America’s 1988 Inventor of the Year Award, sponsored by Intellectual Propeaty Owners, Inc., for his fourdetector photopolarimeter, which lead to the commercial development of the StoResMeter by Gaemer. He received a Photonics Circle of Excellence Award and one of the R&D 100 Awards for this invention, in 1993.

Mohammed M. K. Howlader received his B.Sc. in electrical and electronics engineering from Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh, in 1991, and his M.Sc. in electrical engineering from the University of New Orleans in August, 1994.

He is currently pursuing a Ph.D degree in electrical engineering from the University of Central Florida.

He is a student member of the Optical Society of America. In 1994, he received a graduate fellowship

at the Center for Research and Education in Optics and Lasers (CREOL).