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Koshizaki and T. Sasaki National Institute of Advanced Industrial Science and Technology, Nanoarchitectonics Research Center, Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan

G. Martı´nez-Montes and U. Pala) Instituto de Fı´sica, Universidad Auto´noma de Puebla, Apdo. Postal J-48, Puebla, Pue. 72570, Me´xico (Received 22 March 2001; accepted 28 September 2001)

The optical constants of Si/ZnO composite films grown on quartz glass substrates were determined in the spectral range 1.5–5.0 eV by spectroscopic ellipsometry using a rotating-analyzer ellipsometer. The structure of the samples was modeled by a two-phase (substrate–film) model, and the optical functions of the film were parameterized through different effective medium approximations. The results allowed us to estimate the microstructural film parameters, such as film thickness, the volume fractions of each of the constituents, and optical constants.

I. INTRODUCTION

Nano- and microcomposites doped with semiconductor or metal have been extensively investigated in recent years due to their unique optical and dielectric properties, which favor their applications in electronics and gas sensors.1 The study of the optical properties of composite films prepared on substrates requires the use of nondestructive characterization techniques that allow determination of the film parameters. One optical technique used for this purpose is spectroscopic ellipsometry, which is very sensitive to film thickness, surface roughness, optical constants, and other properties of interest. Spectroscopic ellipsometry measures the change in polarization of a linearly polarized, collimated beam after reflection from a sample surface.2 The resulting state of polarization is characterized by the two so-called ellipsometric parameters, tan⌿ and cos⌬; the first one describes the ratio of the resulting amplitudes of two mutually perpendicular components of the reflected beam, whereas ⌬ represents the phase shift introduced by the reflection between these components. The ellipsometric parameters are related to the sample structure by tan⌿exp共i⌬兲 = rp Ⲑ rs = ␳

respectively. In the case in which the system is ambientfilm-substrate (Fig. 1), these reflection coefficients are described by the equations: rp = rs =

共r01兲P + 共r12兲Pe−2i␤

1 + 共r01兲P共r12兲Pe−2i␤ 共r01兲S + 共r12兲Se−2i␤

1 + 共r01兲S共r12兲Se−2i␤

,

(2)

,

(3)

where ␤ is the phase change that the multiply reflected wave inside the film experiences as it traverses the film once from one boundary to the other and is given in terms of the free-space wavelength ␭, the film thickness d1, the

(1)

where rp and rs are the complex reflection coefficients2 for the electric field of the incoming light polarized parallel and perpendicular to the plane of incidence, Address all correspondence to this author. e-mail: [email protected] 3554

J. Mater. Res., Vol. 16, No. 12, Dec 2001

FIG. 1. Schematic diagram of the reflection at different interfaces of an ambient-film-substrate system. © 2001 Materials Research Society

J. Garcı´a