The purpose of this chapter was to establish some basic steady-state optical properties of dielectric films, dielectric mirrors, two-mirror optical cavities, and the compound “membrane-in-the-middle”
cavity. We have alluded to an apparatus described in Chapter 5, in which a short, high-finesse cavity (F = 103 −104) is integrated with a thin (50 nm) dielectric film with low optical loss (Im[nm]∼10−5). In the next chapter we will discuss the mechanical properties of these films. In Chapters 5 and 6 we’ll describe design/construction of the apparatus and its characterization using the numerical models developed above.
Chapter 4
Mechanical Properties of High-Stress Silicon Nitride Membranes
Mechanical dissipation poses a critical impediment to observing quantum behavior in optomechani- cal systems. The task is made more challenging by confining the parameter space to MEMS/NEMS structures which can be coupled strongly to a light field while introducing minimal optical loss. A significant breakthrough was introduced by the Harris group at Yale [23]. In their optomechani- cal system, a flexible, ∼nanogram mass, commercially available SiN membrane with exceptional mechanical properties is coupled to a standard high-finesse Fabry-Perot cavity [13, 7, 23], thereby separating the task of fabricating the oscillator from integrating it into an optical system. Our group’s point of entry into the field in 2008 was a demonstration that these SiN membranes could be optimized to realize one of the key minimum requirements for optomechanical cooling to the ground state fromroom temperature, namely a mechanical quality factorQmlarger than the number of room temperature thermal phonons: Qm >n¯m=kBTroom/~Ωm [14, 24]. In this chapter I elaborate on those results, providing an overview of the membrane resonator and its mechanical description as well as a detailed description of the apparatus for characterizing mechanical quality factors. I will also summarize an ongoing investigation into clamping-related losses, which we believe limit the mechanical quality of the resonators we’ve studied.
Broadly speaking, the approach we’ve taken is to extend the work done at Yale [23] to include films with high tensile stress. SiN under tensile stress has been recognized for some time for its unusually low mechanical dissipation, particularly among amorphous materials [7, 39, 40, 41]. Initial optomechanical experiments with SiN membranes used the fundamental mode of a 1-mm-square film with Qm = 1.1×106 at Ωm/2π = 130 kHz [7], corresponding to a relatively low tensile stress of T ≈ 100 MPa . In our experiments [14] we use a SiN film in its stoichiometric form, Si3N4, which when deposited by low-pressure chemical vapor deposition (LPCVD) on silicon has a large tensile
dm = 50 nm wm = 500 �m
dchip = 200 �m wchip = 5 mm e-beam etch
e-beam resist
KOH etch LPCVD
plasma etch
Si wafer Si3N4 Si3N4
fabrication steps
Norcada Membrane Chip
drum vibrational modes (6,6) (4,4) (2,2)
Figure 4.1: Overview of the mechanical element: a membrane resonator constructed from a thin film of silicon nitride deposited a silicon wafer. Basic fabrication procedure is shown at left. At top right, we show a photograph of a “membrane chip” purchased commercially from Norcada, Inc.
Dimensions of this device are shown at bottom left. This particular membrane chip consists of a 50 nm layer of stoichiometric Si3N4 deposited on a square silicon substrate with dimensions 5 mm× 5 mm×200 µm. A 500-µm-square window of thin film is exposed. This window is what we refer to as the “membrane” — it exhibits transverse (drum) vibrations, a subset of which are shown at bottom right.
stress ofT ∼1 GPa. In addition, we use sub-mm membranes and focus on the high-order modes (as illustrated in Figure 4.1); this along with the increased tension has allowed us to increase the resonant frequency of our mechanical mode by more than an order of magnitude over the mode cooled in [7], while simultaneously realizing improved room-temperature quality factors. The method of using tension to increase the frequency of mechanical modes while maintaining low dissipation has been recognized as an important tool for seeing quantum effects in a variety of mechanical systems [7, 39, 42, 43].
4.1 SiN Membranes: Architecture and Material Properties
The mechanical element in our optomechanical system is a silicon nitride membrane. As pictured in Figure 4.1, each membrane consists of a square “window” of thin-film silicon nitride deposited on a
silicon wafer (a.k.a. “chip”). The thicknessdand widthwof the window and chip shown in the figure are{dm, wm}={50 nm,0.5 mm} and{dchip, wchip}={200µm,5 mm}, respectively. We purchase these devices commercially from a Canadian MEMs company — Norcada, Inc. [34] — which develops them for use as sample holders for transmission electron microscopy and as vacuum windows for X-ray spectroscopy. Their utility for these applications inherits from the exceptional surface quality of LPCVD SiN thin films and because these films offer unparalleled optical transparency in the soft X-ray band. Typically SiN membranes are manufactured with low tensile stress (T ∼100 MPa) to improve yield and overall mechanical robustness. Our focus has been on high-stress films (T ∼ 1 GPa), the product of a slightly modified fabrication process.
4.1.1 Fabrication
The mechanical properties of silicon nitride films are closely related to the LPCVD process [35, 41].
LPCVD occurs at high temperature (700 – 800 K) and low pressure (∼200 mTorr); under these conditions, the procedure consists of exposing a combination of volatile compounds — ammonia and dichlorosilane — to a bare silicon wafer. The volatiles react to create a thin film of silicon nitride on the wafer. Upon cooling the device to room temperature, the film acquires tensile stress due to the thermal expansion mismatch between silicon and silicon nitride. The absolute magnitude of the tension can be controlled via the deposition temperature and the ratio and flow rate of the volatile chemicals. Low stress is desirable for many commercial applications. This is accomplished by using a LPCVD recipe which dopes the film with extra nitride. High-stress silicon nitride is produced using a slightly modified recipe [41] which results in a stoichiometric Si3N4 chemistry. Whereas low-stress films exhibit a tensile stress ofT ∼100 MPa, high-stress stoichiometric films obtain a tensile stress as high asT ≈1.2 GPa. This has been routinely achieved in the academic NEMs community, for instance in the context of high-stress nano-strings [41, 40]. By contrast, the included stress in our commercial high-stress films is closer to T ≈900 MPa. To date, we have not been able to find a vendor for higher stress films.
To expose the membrane window, a standard sequence of e-beam, plasma, and chemical etching is followed. We usually have Norcada perform this procedure, but have recently had success developing our own membranes in the KNI facility at Caltech using raw LPCVD-coated wafers (also purchased from Norcada). Oskar Painter’s graduate student Richard Norte and our post-doc Kang-Kuen Ni have helmed this effort. As illustrated in Figure 4.1, the procedure consists of (1) depositing an e-beam resist atop the silicon nitride film (the substrate is coated on both sides but polished on only one; we operate on the unpolished surface); (2) using the e-beam to write square holes in the resist (oriented along the (111) crystal planes of the silicon wafer), thus exposing square regions of Si3N4; (3) plasma-etching through the exposed Si3N4 until the underlying Si is exposed; (4) washing away the excess resist; and (5) dipping the wafer into KOH, which etches away at the exposed Si at an
Material Property LPCVD Si3N4 Silicon (111 crystal) Young’s Modulus, E (GPa) 270-290 (210 [39]) 160-190
Poisson Ratio,ν 0.27 0.26 (||to 111 plane)
0.18 (⊥to 111 plane)
density, ρ(kg/m3) 2700-3200 2330
specific heat per unit volume,cV (J/kg/K) 540-700 700
thermal conductivity,κc (W/m/K) 3-35 14
thermal expansion coefficient,α(m/K) 2.3×10−6 @ 300K 2.6×10−6 @ 300K
Table 4.1: Table of material properties for high stress LPCVD Si3N4film and the underlying silicon (111 crystal) substrate. Spread reflects a survey of values cited in [35, 44, 39, 45, 46, 47] and [35, 44], respectively.
angle of 54.7o with respect to both crystal planes, until it reaches the opposite Si3N4 surface. The wafer is then dried, cleaned, and diced into the square chips pictured.
4.1.2 Material Properties
As a quick reference for this chapter, in Table 4.1 we present a collection of material properties for high-stress LPCVD silicon nitride films and the silicon wafer substrate. Values for LPCVD silicon nitride films do not generally coincide with bulk properties; nor do values for low-stress and high-stress LPCVD films coincide with one another. Properties such as the thermal conductivity appear to vary substantially between these three cases and depend on the detail of the fabrication process or geometry (e.g., film thickness) and measurement procedure. As comprehensive resources, we’ve found the textbooks [35, 44] and the websitewww.memsnet.org to be useful. For comparative purposes, we often assume the properties cited in [39].