Supplementary Information

Transcription

1 Supplementary Information Supplementary Figure 1. Modal simulation and frequency response of a high- frequency (75- khz) MEMS. a, Modal frequency of the device was simulated using Coventorware and shows 74.6 khz for the fundamental torsional mode. b, The oscillation amplitudes were calculated by reflecting a HeNe laser beam off the mirror surface and measuring the scan angle at varying frequencies. 1

2 Supplementary Figure 2 Schematic of x- ray measurement of the grazing- incidence reflectivity of MEMS mirror and the diffractive MEMS static rocking curves and dynamic diffraction during its oscillation. Specific energies of the x- ray beam produced by the undulator source on the APS storage ring are filtered using the double crystal monochromator. The aperture is used to define the beam diameter at the surface of MEMS, which is mounted on a diffractometer. Reflected/diffracted pulses are measured with a CCD or APD detector. 2

3 Supplementary Figure 3. Definition of angles. Diagram illustrating the relationships between the offset angle Δθ = θ 0 θ B, MEMS amplitude α(t), and MEMS crystal position θ(t) for a, the general case (Δθ 0) and b, special case (Δθ = 0). 3

4 Supplementary Figure 4. Pulse picking by Bragg diffraction of the MEMS Si (100) element. a, Incident X- ray pulse train from the APS measured using the APD detector shown single X- ray pulses separated by 153 ns (inset). b, The separation between X- ray pulses diffracted by the oscillatory MEMS Si 100 crystal is μs, equal to half the time period of the device at khz. 4

5 Supplementary Figure 5. Dynamic profile measurements of the MEMS during different phases of its oscillation cycle. a, The stroboscopic optical surface profile of the mirror when passing through the equilibrium position. In dynamic actuation, the Bragg diffraction takes place in a short time window when the MEMS device passes through this phase of the oscillation cycle allowing a non- distorted reflection of the x- ray pulse impinging at the center of the device. b, The surface profile of the mirror at a phase away from the equilibrium position. The figure is plotted with the tilt component removed and shows large deformation. Note the different vertical scales in the two cases. 5

6 Supplementary Discussion High- frequency MEMS. The fast torsional MEMS device consists of a single- crystal- silicon mass with a smooth surface suspended on opposite sides by a pair of torsional springs. The basic structure of the two devices used in this study is similar. The thickness of the higher frequency device (75- khz) was increased to 25 µm and the dimensions of the torsional springs were varied to significantly increase stiffness. The crystal can be rotated in an oscillatory motion about the torsional springs by applying a time- varying electric potential to the comb- drive actuators. Finite Element Analysis (FEA) was conducted to determine the modal response of the MEMS (Supplementary Figure 1a). CoventorWare simulations show the first harmonic resonance occurring at 74.6 khz which was verified from experimental measurements to be ca khz with a Q- factor of in air. The MEMS device was designed by the authors and fabricated at the commercial foundry MEMSCAP using the SOIMUMPS process. The process includes a phosphorus doping and diffusion step, which explains the dopant induced strain measured in the rocking curves. The measured oscillation amplitude of about ±4 required a 70 V (peak- to- peak) driving voltage. The frequency response of this device is shown in Supplementary Figure 1b. Definition of two MEMS crystal angles. The angles terms are illustrated in more detail in Supplementary Figure 3. One of them, θ θb, is the deviation of the MEMS crystal angle (θ) from the Bragg angle (θ B ). This term is used in Fig. 2b as the variable to measure the crystal rocking curve and its width. When the MEMS crystal is at its equilibrium or rest position, the angle θ is adjusted by using the diffractometer around the Bragg angle. When the MEMS crystal is oscillating, the angle θ is scanned by the sweeping crystal so that the dynamic rocking curve is measured in time. Even with the dopant induced side peaks there is no diffraction beyond and for θ θb as shown in Fig. 2b. The second angular term, Δθ = θ0 θb, is introduced to test the MEMS crystal diffraction quality affected by dynamic deformation. The term denotes the offset between the MEMS equilibrium angle (θ0) at its resting position and the Bragg angle (θb). During the experiment, this angle is set by the diffractometer that holds the MEMS device. The larger the amplitude of Δθ is, the further the crystal has to rotate in the opposite direction from its resting position to overcome the offset to satisfy the Bragg condition. The limits of the offset are determined by the amplitude of the crystal oscillation, which is measured to be 2.69 in either direction. Figs. 4b 4d illustrated the results measured at different offset angles. In Fig. 4b, the crystal oscillates a full cycle in µs (within the ±2.69 oscillation range), within which time Bragg condition is satisfied twice for a given Δθ (if within the ±2.69 oscillation range). But the Bragg condition is fulfilled in very short instances (Δt w ) as shown as the dynamic rocking curves. In fact, Δt w is so small compared to the oscillation period that the time axis of the dynamic rocking curves needs to be scaled up 20 times to show the width in Fig. 4b. The same statement can be made for the rotation angles because they are correlated with the diffractive- time- window through only the angular velocity, a known quantity 6

7 throughout the cycle. Therefore, in Figs. 4c and 4d, the variable is the offset angle, Δθ, rather than the incident angle. A brief explanation is now added to the text (pages 4 and 5) and the figure legends to state that Δθ is not the incident angle, rather it is the offset angle that we use to test the dynamic properties of the MEMS when the crystal is away from its equilibrium. Two cases are included in Supplementary Figure 3: a) θ 0 does not coincide with θ B (or Δθ 0), and b) θ 0 coincides with θ B (or Δθ = 0). X- ray measurements. The x- ray experiments were performed at Sector 7- ID beamline of the Advanced Photon Source (APS), a dedicated beamline for ultrafast x- ray experiments. Schematically shown in Supplementary Figure 2, the x- ray beam, produced by an undulator source, was monochromatized by a flat diamond double- crystal monochromator tuned to a photon energy E of 8 or 10 kev with a bandwidth ΔE/E of ca The static grazing incidence x- ray reflection was measured with a 10- kev x- ray beam while the MEMS was not energized. The unfocused x- ray beam was defined by a pair of X- Y slits to a size of 100 µm (horizontal) 10 µm (vertical) before impinging on the MEMS device. We used a CCD camera to record the reflected beam as two- dimensional patterns, as shown in Fig. 1B. As the mirror is rotated to slightly higher angles (below the critical angle of the mirror, 0.18 ), the x- ray beam showed a well- defined spot on the area detector at higher reflection angles indicating a high- quality mirror surface. This is confirmed quantitatively from the measurement with a point detector that can record the reflected beam intensity in a conventional θ- 2θ scan, shown in Fig. 1c, which demonstrates close- to- theory reflection efficiency. The static rocking curves around the Si(400) Bragg angle were measured by using a high- resolution diffractometer with a minimum angular step size of 3.125x10-5. The diffracted photons were detected by an avalanche photodiode (APD) operated in photon- counting mode. For dynamic measurements, the transient x- ray diffraction signal when the Bragg condition was met was measured by another APD but operated in charge- integration mode [Supplementary Reference]. The integration mode is needed because every diffracted x- ray pulse contained multiple photons. The APD has a fast response with temporal resolution of approximately 5 ns. The APD signal output was recorded with a 1- ns interval by a transient digitizer (500- MHz bandwidth) that leads to a systematic error of 0.5 ns in determining the delay time between the MEMS driver pulse and the x- ray pulse diffracted by the MEMS crystal element, and adds to the measured temporal resolution. The oscilloscope trace of 1 ms was integrated over 20 times to improve the signal- to- noise ratio. 7

8 Time- domain pulse modulation of synchrotron x- ray photons. The 75- khz device is tested as a fast X- ray pulse modulator by using an incident X- ray beam containing 100 ps pulses with a repetition- rate of MHz in a train of 24 pulses per synchrotron cycle of μs and an inter- pulse separation of ns, as shown in Supplementary Figure 4a. The diffracted x- ray beam from the Si 100 crystal then has a pulse- to- pulse separation shown in Supplementary Figure 4b is measured to be μs, which is half the oscillation period of the device, when the incident angle coincides with the Bragg angle of Si(440) diffraction as the device is at rest. Dynamic deformation. Dynamic deformation does not adversely affect the performance of the MEMS as a diffractive optics. As shown in Supplementary Figure 5, the stroboscopic optical profile measurements (Veeco Wyko NT1100 DMEMS) of the MEMS mirror under actuation reveals the shape of the deformation at two different instances in the oscillation cycle. Dynamic deformation is a limiting factor for MEMS scanners in display applications due to added distortion of the beam at angles away from the equilibrium position. For x- ray optics however, the MEMS device is oriented so that the Bragg condition is satisfied at the equilibrium positions (i.e. flat profile) of the oscillation cycle Supplementary Figure 5a, resulting in a non- distorted reflected beam. Supplementary Reference: Powell, C. F., Yue, Y., Poola, R. and Wang, J. Time- resolved measurements of supersonic fuel sprays using synchrotron X- rays, J. Synchrotron Rad. 7, (2000). 8