Table 2. TALYSTEP Surface Roughness [nm] of Tio, Single Layers
Deposited by Low-Voltage Reactive Ion Plating (BALZERS BAP 800)

Table 3. Summary of Surface Roughness Measurements on RIPD Thin Films
Performed with TALYSTEP and WYKO TOPO 2-D Instruments

Manuscript Received
1-18-89

Measurement of Thermal Expansion Coefficients

of Optical Thin Films

Wu Zhouling Tang Jinfa Shi Baixuan

Zhejiang University, Hangzhou, PRC

be

Thermal expansion coefficients of optical thin films can
measured by means of the combination of photothermal displacement
optical beam deflection technique (PDOBD) and transverse photother-
mal optical beam deflection technique (TPOBD). In this paper, single
layers of Si02, Ti02, Zr02, MgF2 and ThF4 are taken as examples
show the experimental methods and results.

to

Key Words: optical thin films; photothermal deflection; thermal ex-
pansion coefficients.

1. Introduction

Precise measurements of thermophysical properties like thermal conductivity and thermal expansion coefficient of optical thin films are very important for thermal modeling of laser-induced damage to optical coatings [1,2]. In this paper, we report our recent measurements of thermal expansion coefficients of optical thin films by means of the combination of PDOBD [3,4] and TPOBD [5-8]. The experimental results show that this method is quite verstile and very simple.

2. Experimental Procedure

Based on PDOBD and TPOBD, we have built up an apparatus for the measurement of thermal expansion coefficients of optical thin films. Details of the detection system are given in figure 1.

PDOBD was firstly reported by M.A.Olmstead et al [3] in 1983. The physical basis of it was shown in figure 2, and it can be briefly described as follows: when a solid sample is illuminated by an intensity-modulated light beam, the absorption of the energy will cause a thermal wave inside the sample and

hence a corresponding displacement on sample surface. By probing this corresponding surface displacement with a second laser beam, one can relate its deflection to the related properties of the sample.

TPOBD was firstly developed by A. C. Boccara et al [5] in 1980, and its physical basis was shown in figure 3. Defferent from PDOBD, here the reason for the optical beam deflection is the photothermal gradient index.

Optical thin films are usually thermally thin when the modulation frequency is relatively low [7]. In this case, the PDOBD signal S1 [3,4] and TBOBD signal S2 [5-8] satisfy

and

where

C1, C2---constants, decided by experimental parameters;

---thermal expansion coefficient of the sample;
---optical absorption coefficient of the sample;
---thickness of the sample;

1

Р

---incident power of the pump laser;

R

reflectance of the sample.

From eq. (1) and eq. (2) we can get with ease

(1)

(2)

where C is a constant dependent on experimental conditions and the properties of the substrate of the sample.

From eg. (4) we can see that the ratio of PDOBD signal over TPOBD signal is proportional to the thermal expansion coefficient of an optical thin film under the thermally-thin-sample approximation [7]. This is in fact the basis of our measurements of thermal expansion coefficients of optical thin films.

To caliberate the experimental system, we use Au film as caliberating sample, of which the thermal expansion coefficient was already known. The principle of this caliberation method is as follows:

Equation (4) is also valid for caliberating sample if the substrate and

Table 1 showed our measured thermal expansion coefficients of several single-layer films and their comparison with those of previous work and related bulk materials. From this table we can find:

(1). Except that of the relatively unstable ZrO2 single layer film, our results are in good agrement with those previousely reported. This fact approves the applicability of the combination of PDOBD and TPOBD in the measurements of thermal expansion coefficients of optical thin films.

(2). Except that of SiO2 single layer film, the thermal expansion coefficients of the thin films investigated showed apparent differences from those of the related bulk materials. A possible explanation of these differences might be changes in structures of the materials after vacuum deposition.

4. Discussion

4.1 Repeated Precision of the Experimental Setup

Ten measurements of Tio, film showed an average of 2.2x10-6
Ti02

deg-1 and

a maximum deviation of 0.3x10-6deg-1. This corresponds to a relative error

smaller than 14%.

4.2 Limits of Our Method in the Measurement of

4.2.1 Film Thickness Limit

Because of the thermally-thin-samle approximation, our method is only applicable to samples with 1<<(10-100) um, which, fortunately, can be satisfied in most optical thin films.

4.2.2 Optical Absorption Limit