Physical thickness and group refractive index measurement of individual layers for double-stacked microstructures using spectral-domain interferometry

Abstract

A non-destructive method for measuring the physical thickness and group refractive index of individual layers was proposed based on spectral-domain interferometry, which was realized to achieve real-time measurements using a mode-locked laser and an optical spectrum analyzer. As a double-stacked specimen, a microfluidic channel mold composed of a SU-8 photoresist and a silicon wafer was chosen. With areal scanning of the sample, a physical thickness map and a representative group refractive index value for each layer were obtained at the same time. The sample was measured 30 times consecutively at pre-determined points to estimate the repeatability of the physical thickness, for which the standard deviation was less than 10 nm. Moreover, a measurement comparison with two calibrated reference instruments was conducted. According to the comparative measurement results, physical thickness values obtained by the proposed method and with each comparative method were found to be in good agreement within expanded uncertainty levels.

Introduction

In recent years, multi-layered structures have been widely utilized to fabricate smart devices for a variety of purposes. There are numerous applications, such as stacked semiconductor devices, flexible display devices, OLED or AMOLED display panels, solar cells, electronic paper, RFID and MEMS devices, and optical filters [1], [2], [3], [4]. Particularly, with regard to optical elements such as display panels and waveguides among these applications, their performance capabilities are sensitive to the physical thickness and refractive index of each stacked layer [5], [6]. Therefore, for optical elements having multiple layers, the quantities of both the physical thickness and the refractive index for each layer should be monitored and controlled to achieve the desired performance outcomes.

An optical interferometer is a well-established non-destructivemethod for measuring the optical thickness given its advantages of good precision and traceability to length standards. In this case, the physical thickness can only be determined from the optical thickness when the refractive index of the medium is provided with high precision [7], [8], [9], [10], [11], [12]. To circumvent this fundamental problem, several measurement methods have been proposed and realized using several optical path differences obtained by inserting and removing the sample [13], [14], [15], [16], [17], [18], [19], by rotating the sample [20], [21], and by blocking some beam paths in the interferometer layout [22], [23]. However, most of these studies utilized only single-layered samples [12], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23] or measured the total thickness of multi-layered samples [13]. An interferometric method to measure the refractive index and thickness of a specific layer within a multi-layered specimen was reported in the field of optical coherence tomography, but it has practical limits when used to improve the measurement speed due to the estimation of the focus shift using numerically corrected images [24].

In this paper, a non-destructive method which can be used to measure the physical thickness and group refractive index of separate layers in a double-stacked sample is proposed based on spectral-domain interferometry, which facilitates high-speed measurements through a straightforward analysis of the interference spectra without any numerical optimization. This study builds on previous works by the authors [13], [14], [15], [16], [17], [18] on physical thickness measurements of silicon wafers [14], [15], [16], [17], large glass panels [18], and multi-layered samples [13]. There are several examples of the originality of this work. First, it seeks to measure and verify the physical thickness and refractive index of each layer, unlike in the authors’ previous works. Secondly, it seeks to provide a theoretical means of extracting two quantities of each layer with appropriate assumptions. For a feasibility test, as a double-stacked sample of the type widely used for bio-MEMS sensors, a microfluidic channel mold composed of SU-8 film and a silicon wafer was chosen.