Monitoring subwavelength grating structures for vertical-cavity surface-emitting laser applications by spectroscopic ellipsometry Emeric Balogh, Peter Basa, Attila Suto, Benjamin Powell, Anna Bölcskei-Molnár, and Szilvia Biró Citation: Journal of Vacuum Science & Technology B 37, 062928 (2019); doi: 10.1116/1.5122771 View online: https://doi.org/10.1116/1.5122771 View Table of Contents: https://avs.scitation.org/toc/jvb/37/6 Published by the American Vacuum Society Monitoring subwavelength grating structures for vertical-cavity surface-emitting laser applications by spectroscopic ellipsometry Emeric Balogh, Peter Basa,a) Attila Suto, Benjamin Powell, Anna Bölcskei-Molnár, and Szilvia Biró Semilab Semiconductor Physics Laboratory Co. Ltd., Budapest H-1117, Hungary (Received 31 July 2019; accepted 6 November 2019; published 22 November 2019) GaAs based vertical cavity surface emitting lasers (VCSELs) have one of the fastest growing markets due to their numerous applications in imaging technology, optical sensors, and interconnects. Stable, single-mode operation of these laser diodes is often achieved by forming subwavelength structures on the surface of the GaAs semiconductor. Quick and preferably noncontact inspection of the formed nanostructures is desired during the fabrication process. Nanostructure characterization by spectral ellipsometry-based metrologies has become an indispensable tool in the semiconductor industry. An advanced method of ellipsometry is the application of Mueller-matrix ellipsometry, which enables the characterization of structure details difficult to measure or not reachable by using standard ellipsome- try measurements. In this paper, the authors present the results of nanostructure characterization by model-based dimension metrology using spectral ellipsometry and Mueller-matrix spectral ellipsometry of line gratings formed on GaAs substrates during the process of VCSEL fabrication. Published by the AVS. https://doi.org/10.1116/1.5122771 I. INTRODUCTION compare the two methods and highlight the performance and GaAs based vertical cavity surface emitting lasers (VCSELs) potential advantages and disadvantages of each. have been widely studied recently due to their numerous dem- The paper is organized as follows: in Sec. II, we present onstrated and prospective applications. They have many advan- the sample fabrication process and details of the measure- tageous properties like narrow emission bandwidth, which ment apparatus and describe ellipsometry quantities essential enables very sensitive time of flight detection with applications for the understanding of the result. In Sec. III, we provide a in imaging and depth sensors, and they are even used in atomic brief theoretical description of ellipsometry-based MBD clocks.1,2 Another outstanding feature is the quick response models. In Sec. IV, measurement results are described, and time to driving current modulations, which makes them a very we conclude our results in Sec. V. promising light source in high-speed optical communication.3,4 Many of these applications demand stable, single-mode opera- II. SAMPLE FABRICATION AND MEASUREMENT tion of VCSEL devices. In the case of GaAs VCSELs, laser TECHNIQUES emission can occur along both the ⟨100⟩ and ⟨010⟩ crystalline A. Sample fabrication planes.5 Single-mode operation can be achieved by forming subwavelength gratings on the surface of the semiconductor to During the fabrication of the VCSEL devices, GaAs wafers 6 suppress emission in modes perpendicular to the grating lines. are used and coated with SiO2 using the solgel method. The This is a proven, efficient method of mode suppression and is refractive index of the material deposited with the solgel already applied in mass production. Preparation of these subwa- method can be slightly different from the literature values of velength gratings requires cost-efficient, yet industry level SiO2; therefore, during the discussions in this paper, we are quality method which in most cases is realized by nanoimprint- going to refer to the material simply as SolGel. Then, pattern- ing.7 Monitoring of the parameters of the imprinted gratings is ing of the SolGel surface is done by nanoimprinting. After the necessary for efficient process control. There are two main formation of the grating in the SolGel coating, grating lines in types of metrologies currently in use which are capable of pro- the GaAs substrate are formed using the reactive ion etching ducing accurate and fast measurement results required to main- method. During these processes, some uncertainty by the tain high throughput of VCSEL production lines: automatized imprinting process is introduced and therefore the orientation atomic force microscopy (AFM) and model-based dimension of the grating lines inside the sample may shift by a few (MBD) characterization metrology. degrees. This grating angle orientation and uncertainty has to In this contribution, we present MBD metrology based on be accounted for by any metrology to achieve reliable results spectral ellipsometry (SE-MBD) and on Mueller-matrix spec- of structure parameters and grating period, and it is especially tral ellipsometry (MM-MBD), measurement data of real-life important in SE-based metrology of nanogratings for reasons product wafers, and MBD analysis of the measurements. We discussed in Secs. II B and II C. B. Spectral ellipsometry Note: This paper is part of the Conference Collection: 8th International Conference on Spectroscopic Ellipsometry 2019, ICSE. Samples were measured with the spectral ellipsometry a)Electronic mail: [email protected] tool (Semilab SE-2000) capable of SE measurement in the 062928-1 J. Vac. Sci. Technol. B 37(6), Nov/Dec 2019 2166-2746/2019/37(6)/062928/7/$30.00 Published by the AVS. 062928-1 062928-2 Balogh et al.: Monitoring subwavelength grating structures for VCSEL applications by spectroscopic ellipsometry 062928-2 region of 193–2500 nm. The spectral region needed to accu- incidence. The 2 by 2 matrix in Eq. (2) is often referred to as rately characterize the structure depends on the sample; in the Jones matrix and can accurately describe nondepolarizing general, we have used data in the region of 250–550 nm, anisotropic samples. The normalized Jones matrix of a with an incidence angle of 75°. This restricted spectral range sample is measured in generalized ellipsometry. was found to be a good compromise between precision and When using SE measurement in the case of anisotropic model computation time for this application. The same samples, the measured quantities depend on all four terms of ellipsometry tool was used for the measurements of the 15 the Jones matrix. The strong parameter correlation between element Mueller matrix, described in Sec. II C. structure parameters and grating angle makes it difficult or In spectral ellipsometry measurement, light incident on a even impossible to accurately characterize samples from a sample is interacting with the material and reflected toward single SE measurement if the orientation of grating lines is the detector. The relative amplitudes and phases of s and p uncertain. One of the solutions is to align the samples prior to polarized waves are varying during the reflection, transform- SE measurement based on an independent measurement ing the incident (usually linearly polarized) light into the capable of accurate grating angle characterization or to make elliptically polarized one. Let us denote the amplitudes of s multiple SE measurements by rotating the samples in the azi- i and p polarization light waves incident on a sample as Es muthal direction. Both of these methods require a more i fi and Ep, respectively. In the same manner, we de ne the complex mechanical hardware and increase total measurement fl r r re ected light amplitudes Es and Ep. time and are, therefore, not desirable in a production line. The complex reflection coefficients are defined as r ¼ Er=Ei and r ¼ Er =Ei . In spectral ellipsometry, the s s s p p p C. Mueller-matrix ellipsometry ratio ρ of the reflection coefficients is measured,8 which is a complex quantity. The ellipsometric quantities Ψ and Δ are Another possibility to characterize the anisotropy of the related to ρ as samples is by using Mueller-matrix spectral ellipsometry. In this case, the Mueller matrix is used to determine the grating r ρ ; tan (Ψ)exp(ÀiΔ) ¼ p , (1) line orientation and structure parameters from a single mea- rs surement. This measurement technique is an advanced method of spectral ellipsometry, designed specifically for the fl fi where rp and rs describe the complex re ection coef cients purpose of measuring samples showing optical anisotropy. for p- and s-polarized waves, respectively. Equation (1) is The Mueller matrix is a 4 by 4 matrix describing the trans- complete only in cases when p- and s-polarized waves can formation of the Stokes vector of light interacting with a be treated independently during the interaction of light with material, in our case, the sample. the sample. This is the case for isotropic samples and also The four component Stokes vector completely describes the for samples showing optical anisotropy, when the anisot- polarization state of light. The Stokes vector is described as 9 T ropy axis is normal to the surface of the sample. S ¼ ½Is þ Ip, Is À Ip, Iþ45 À IÀ45 , IR À IL ,whereIs Subwavelength gratings are known to show optical aniso- and Ip are the light intensities in s and p polarizations, Iþ45 tropic behavior (different optical properties parallel and per- and IÀ45 are the intensities of polarization components ori- pendicular to the grating lines), which is sometimes termed ented at ±45°, and IR and IL are the intensities of left and right geometrical anisotropy, for the reason that it is linked to the circular components of the wave. The benefit of using Stokes geometric properties of the subwavelength (quasi-)periodic vectors for describing light polarization is that when the last features of the sample. Gratings with periodicity comparable three Stokes vectors are plotted in a spherical coordinate to the wavelength of incident light may exhibit several types system, then the resulted sphere (the so-called Poincaré 10,11 of resonance phenomena, known as Wood’s anomalies.