Modeling & Simulation

SC Solutions provides modeling and simulation services for a wide range of applications. A key enabling technology is our capability of physics-based modeling which allows us to accurately capture input-output behavior. Our models are based on finite-element and/or finite-volume methods, and are developed using both commercial and SC Solutions’ proprietary modeling software. We are a certified COMSOL consultant, and a Matlab Partner.

Physics-based Models including heat, flow and species transport, chemical kinetics, and mechanical modeling for manufacturing processes (such as semiconductor and advanced materials). These dynamic models are used for equipment design, model-based control, virtual sensing, and process optimization. Our capabilities include other cross-disciplinary areas such as electromagnetics, electrochemical processes, optics, and multi-scale phenomena. Some specific applications include:

Sample Projects on Modeling & Simulation:

Under this NSF-funded SBIR Phase II program, SC has developed a commercial prototype of a novel software tool for integrated model-based control design for Rapid Thermal Processing (RTP) systems to be used by semiconductor process engineers and RTP equipment design engineers.

Currently, the design and development of advanced process controllers is a relatively slow and complicated process. There is no high-level tool that allows the process engineer to design, tune and deploy advanced controllers and develop fast, low-order physical models to be used for control. Based on customer feedback and its own experience, SC Solutions, an industry leader in RTP temperature control solutions, has leveraged this grant to fill a strong need for an integrated modeling and control tool that is customized for various processes involved in semiconductor wafter processing (e.g., RTP).

The prototype developed by SC contains implementation of relevant model-order reduction algorithms, and algorithms for speeding up the Monte Carlo ray tracing computations for accurate modeling of radiative heat transfer in the RTP chamber.  The prototype also contains a control design toolbox, and a graphical user interface for the integrated software tool.

SC worked closely with its industrial partner in testing the prototype tool in the design of next-generation RTP equipment.

Under this NSF sponsored Small Business Innovation Research (SBIR) Phase II project, SC Solutions proposed a product development effort for physical modeling and model-based sensing and control of chemical mechanical planarization (CMP) systems. CMP is a rapidly emerging technology playing an increasingly critical role in global planarization for microelectronics fabrication. In Phase I, SC demonstrated the feasibility of modeling and real-time control using actual experimental data from the Applied Materials’ MirraTM CMP system. The results of our 3D contact mechanical models correlate closely with experimental results for removal rate distribution across the wafer. Reduced input-output models relating the within wafer nonuniformity (WIWNU) to the pressure ratio and pad conditioning, obtained from the detailed 3D models, were used as a basis for real-time and run-to-run control. In Phase II, extended these models and control methods, and develop a model-based embedded controller for within-wafer and within-die uniformity control. The Phase II development effort culminated in the following products tested on the MirraTMsystem at Applied Materials: advanced process modeling and control software, and an embedded controller for CMP. The successful commercial application of our technology in the semiconductor industry is tremendous, resulting in improved and repeatable performance, increased throughput, and improved yields.

Related Publications

SC Solutions provides controls and physical modeling solutions to its customers for silicon epitaxy. SC Solutions’ engineers have designed temperature controllers for a RTCVD equipment manufacturer for their next-generation, single-wafer epitaxy chamber. The dynamic finite-volume heat transfer model, and the model-based, multiple-input, multiple-output, feedback controllers were computer tested for performance (temperature ramp-up and ramp-down rates, wafer temperature uniformity, etc). Multiple design iterations were explored quickly, and suitable modifications were made to the chamber design before constructing a prototype. This integrated approach, with an eye towards design-for-controllability, resulted in considerable time and money savings for our customer. Apart from real-time feedback controllers, we also provide run-to-run controllers for increased repeatability of wafer properties.

In addition, SC Solutions develops reactor-scale CVD models for the industry using CFDRC’s popular simulation software, CFD-ACE. These models provide insight into a variety of issues such as performance limits, troubleshooting, design improvements, etc. The graphic above describes a physical model of a horizontal, hot-wall reactor for silicon epitaxy. This relatively simple 2D case study was taken from the literature solely to show SC Solutions’ modeling capabilities.

Hot Wall Epitaxial Reactor

Two-dimensional Reactor-scale Transport Model

Figure 1 shows the geometry used in the 2-D model obtained from Habuka et al [1]. The end-to-end length of the radiantly-heated chamber is 0.705 m and the total height is 0.4 m. The top part of the left wall and the entire right wall are at 300 K, and the sections of the top and the bottom wall immediately above the susceptor are at specified temperatures. The rest of the walls are adiabatic. The flow enters at atmospheric pressure from the top left corner of the chamber, and exits from the bottom right corner. The 8" wafer is located at the center of the 12" susceptor, 0.205 m from the left end of the chamber.

Figure 1. Schematic of a two-dimensional horizontal CVD reactor [1]. The figure is not to scale. Shaded walls are adiabatic. The part of the walls next to the IR heaters are semi-transparent and at elevated temperatures.

A gaseous mixture, consisting of trichlorosilane (SiHCl3, nominal mass fraction=0.71) and hydrogen, is injected into the chamber at room temperature (300K) and a velocity of 0.67 m/s. The wafer temperature is isothermally elevated to a nominal value of 1423K. The temperatures of the hot sections of the top and bottom walls, Twall, were measured by Habuka et al [1], and expressed as the following linear function of the susceptor temperature, Tsus:

Twall = 730 + (770-730)(Tsus-1393)/(1453-1393) For Tsus = 1423K, Twall = 750K. The other sections on the top and the bottom walls are kept at 300K. The susceptor (and hence, the wafer) temperatures are here assumed to be independently controlled to excellent uniformity.

Figure 2. Mesh for numerical solution using CFD-ACE. The 90 X 53 mesh (with 3399 cells or control volumes in all) is clustered near the walls and near regions of high temperature gradients at the edges of the wafer. For clarity, the vertical dimensions are magnified five times the horizontal dimensions.

Figure 2 shows the mesh generated for the control-volume solution. The solution converged after 600 iterations in about half-an-hour on a Pentium PC. Figure 3 shows the velocity vectors with superposed temperatures for nominal conditions (trichlor mass fraction of 0.71, wafer temperature of 1423K, and top and bottom quartz wall temperatures of 750K). The gas is heated up considerably by the susceptor and the wall, and speeds up along the wafer surface. Figure 4 shows comparison of deposition rate uniformity with Habuka et al [1]. Figure 5 shows that wafer rotation significantly improves deposition uniformity, assuming that the rotation period is much smaller than the deposition period (which is almost always the case). The CFD-ACE results compares quite well with those Habuka et al [1], the average deposition rate difference being about 10%.

Figure 3. Gas velocity vectors with superposed temperature.

Figure 4. Deposition profile along flow direction. Comparison with Habuka, et al [1].

Figure 5. Effect of wafer rotation on deposition rate uniformity.

The deposition rates were calculated by varying the trichlor mass fraction. The results are plotted in Figure 6. These results agree well with Habuka’s experimental data. The slight over-prediction of the deposition rate may be attributed be due to two possible causes. First, the temperatures at the adiabatic parts of the wall are relatively high, and in reality, there is probably some deposition on the walls leading to reactant depletion downstream. Second, there is always a small amount of HCL etching of deposited silicon that reduces the overall deposition rate.

Figure 6. Average deposition rate as function of average molecular weight of gas at inlet. Nominal molecular weight is 6.67 kg/kg-mole (when trichlor mass fraction = 0.71).

Several tests were carried out on the model to establish convergence on the basis of mesh refinement and number of iterations needed. The results are shown in Figure 7.

Figure 7. Convergence study using deposition rates and gas temperatures.

We find that reducing iterations from 5000 to 1000 results in an average difference of 0.5% in the deposition rate. Based on this result, it is arbitrarily decided that for this geometry, 1500 iterations are sufficient. Reducing the number of cells from 3399 to 1381 changed the average deposition rate by 0.8%, and the average horizontal centerline temperature by 0.7%. Hence, 1381 cells are deemed sufficient. It is also noted that the time per iteration rises non-linearly for more refined mesh, which is to be expected from this solver.


[1] M. Habuka, Katayama, M. Shimda, K. Okuyama, "Numerical Evaluation of
ON Silicon Thin Growth from SiHCl3-H2 Gas Mixture in a Horizontal Chemical
Vapor Deposition Reactor," Jpn. J. Appl. Phys., 1994. 33: p.1977-1985.

MOCVD of BSTO Thin Films

The team of SC Solutions, Stanford University, and ATMI (Danbury, CT) has developed chemical mechanisms, reactor-scale models and control strategies for MOCVD of Barium Strontium Titanate/Oxide (BSTO) thin-films. There is considerable interest in polycrystalline BSTO films because they exhibit low dielectric losses and tunable dielectric constants that make them very useful for a wide range of applications.

Our approach has involved concurrent ab initio research into the chemical mechanisms for oxide formation using quantum chemistry calculations, together with reactor-scale modeling of transport properties and chemical kinetics. Prior to this work, no studies had been undertaken to determine the decomposition mechanism from a fundamental standpoint. This integrated approach has enabled realistic simulations of BSTO deposition, the results of which compare favorably with experimental data. The model was subsequently used for development of a control architecture for realizing deposition with enhanced oxide uniformity and accurate stoichiometries. Additionally, the model was used to study ways in which minor chamber modifications would enhance deposition uniformity.

The reactor-scale simulations, used to determine both reactor design as well as process optimization, require kinetic and transport properties of the barium, strontium and titanium beta-diketonate precursors and their decomposition products. These are generally not known, however there is some experimental data of the overall rate of film growth and several mechanisms for film deposition have been proposed.

We have used quantum chemical methods to study the decomposition mechanisms of beta-diketonate precursors and found that decomposition is likely to begin with the cleavage of M-O bonds. The M-O bond in the monodentate ligand is considerably strengthened after the other M-O bond (of the same ring) is broken due to the charge donation of the oxygen into empty metal d states. The co-polymerization model found in the literature assumed that Ba(dpm)2 and Sr(dpm)2 copolymerize preferentially with TiO(dpm)2. Our calculations have shown that Ti (OH)2-O-M and Ti(OH)2-O2-M where M= Sr or Ba, dimers are indeed stable and energetically favored over the homogeneous dimers.

SC Solutions has developed reactor-scale models developed for studying species transport and chemical kinetics within the reactor. A popular software platform, CFD-ACETM, was used for developing the models. Both two-dimensional (2D) and three dimensional (3D) models were developed. However, the 2D model was considered sufficiently accurate for most of the simulations of this nominally axisymmetric reactor. The model incorporates all the essential physics, and the kinetics models and transport properties were based on the DFT studies and data from the literature. The deposition rates and uniformities obtained from the simulations were similar to those obtained on the ATMI's reactor. The model was used to perform 'what-if' experiments for testing sensitivity of deposition uniformity and precursor utilization. The model was used to recommend minor modifications to the ATMI reactor for better uniformity, as well as developing a run-to-run controller.

Model-Based Control for BSTO MOCVD

The primary objective is to obtain a uniformly distributed BSTO deposition of desired thickness and stoichiometry on a wafer, with little variation from wafer-to-wafer. Thickness non-uniformity is primarily caused by species depletion and by temperature non-uniformity on the wafer at lower temperatures. Stoichiometry non-uniformity may be caused by unequal diffusivities of the gas-phase intermediates and fluctuations or drifts in the precursor supply.

The inputs available to control deposition are the flow rate and/or pressure of the carrier gas, the temperature of the susceptor, and the concentration of the precursor gases. The outputs that are measured are the flow rates of carrier gas (in-situ), susceptor temperatures measured using thermocouples (in-situ), and the deposition thickness (ex-situ). The wafer temperature may or may not be measured using a pyrometer, or has to be modeled from the susceptor temperature. The expected sources of noise and disturbances include measurement noise on all measurements, random fluctuations in flow rate, random fluctuations in precursor concentration, and drifts in wafer and susceptor temperatures. The control problem is to obtain deposition thickness with desired deposition uniformity using the available control inputs and measured outputs, in the face of the expected noise and disturbances. The physical model described in the previous section approximates the static global behavior of the MOCVD reactor, and is used in the controller design.

Although the deposition process as a function of control inputs can be considered as a static system, all disturbances are dynamic, which implies that dynamic "slave" controllers are needed locally to obtain tight regulation at the desired operating points, as shown in figure 1. The control structure shows both dynamic controllers using in-situ sensing as well as a run-to-run controller employing ex-situ sensors. The vaporizers are controlled by local (inner-loop) controllers, there are in-situ temperature sensors measuring substrate temperature corresponding to substrate (segmented) heaters, and metrology is employed to measure wafer properties of interest (deposition thickness and uniformity, stoichiometry). Integral control and (notch) filtering possibly extended with some phase compensation should give tight regulation. For this design, it is preferable to have (low-complexity) dynamic models available that relate measured outputs to manipulated inputs and disturbances/noise.

Run-to-run Control for BSTO MOCVD

Run-to-run control has been shown to be an excellent means to achieve desired film properties. Here, the values of the nominal operating set-points (called recipe variables) are adjusted after one run of the process based on ex-situ measurements of wafer properties before processing the next wafer. SC Solutions has developed a model-based run-to-run controller for BSTO thin film manufacturing.

MOCVD of High Temperature Superconducting Thin Films

SC Solutions, in partnership with MIT, developed techniques and tools for modeling, model-order reduction and control of MOCVD of YBCO (yttrium barium copper oxide) high temperature superconducting (HTS) thin-films. This was one of the first such modeling efforts for HTS manufacturing. As further example of SC Solutions' CVD modeling capabilities, some results for a 2D reactor using a seven-step finite-rate kinetics model are shown below.

Gas velocities in a 2D version of Thomas Swan MOCVD reactor (vertical dimensions exaggerated). Temperature contours for same flow. The 50 m diameter wafer sits 175 mm from the left end of reactor.
Precursor mass fraction at mid-height along reactor. Oxide mass fractions in the vertical direction at the wafer center.
YBCO deposition rate uniformity with wafer rotating. Operating conditions are as follows: the gas mixture of precursors, oxygen, nitrogen, and argon enter the reactor at a pressure of 10 torr with velocity 2 m/s and temperature 513 K. Inlet mole fractions are: O2 = 0.44, N2 = 0.47, Ar = 0.088, Y(dpm)3 = 2.72X10-5, (Ba(dpm)2)4 = 4.41X10-5, Cu(dpm)2 = 2.35X10-5. The wafer (and the chamber walls) are kept at a temperature of 1073 K.

This work was funded by a DARPA contract and administerd by ONR.

Related Projects

Related Publications

The objective of this DARPA-sponsored work was to develop a physics-based reactor-scale, physical model of Metal-Organic Chemical Vapor Depostion (MOCVD) of superconducting thin films composed of Yttrium Barium Copper Oxides (YBCO). A Thomas Swan reactor used by STI (Santa Barbara, CA) was modeled. The model predicts deposition rate and stoichiometry along the wafer surface when the operating conditions and inflow gas composition are specified.

The physical model addressed precursor decomposition and oxide formation chemistry, and the transport processes (fluid mechanics, species diffusion, and heat transfer) associated with CVD. For modeling chemistry, we used kinetics data developed from quantum chemistry calculations, supplemented by other data in the literature. Stanford University was a collaborator on this project.

Related Publications

Polycrystalline Barium Strontium Titanate/Oxide (BSTO) films exhibit low dielectric losses and tunable dielectric constants, and can be used as a frequency agile materials for manufacturing RF and microwave communication components. These properties have a strong dependence on stoichiometry and microstructure. Additionally, precise control of composition over a large area and enhanced growth rates are important in reducing manufacturing costs.

A methodology was developed and implemented under this DARPA-funded program to perform reactor-scale physical modeling and model-based process control for barium strontium titanate (Ba1-xSrxTiO3 or BSTO) thin film deposition. This novel approach, demonstrated for the first time on YBCO deposition in an earlier program, began from first-principles quantum chemistry computations led by Stanford University to determine the pathways of the complex chemical processes involved in precursor decomposition and BSTO formation.

We developed an accurate physical model of the chamber for predicting film deposition rate and uniformity. A run-to-run controller was development in conjunction with the modeling effort, and its performance demonstrated using MATLAB™ simulations.

Related Publications

The team of SC Solutions, HRL Laboratories and UCLA have developed and implemented model-based controllers for depositing reproducible III-V thin films by molecular beam epitaxy (MBE). To achieve and control the atomic scale features that are required, processing must be founded upon a fundamental understanding of the atom-by-atom assembly of these engineering structures. For purposes of control, the problem is to develop a model which relates morphology variables at the atomistic scale and sensor variables at the device scale to the control variables at the reactor scale.

Epitaxial growth of a single layer includes the following processes: deposition and diffusion of adatoms, nucleation of islands through collisions of adatoms, and attachment of adatoms to the island leading to island growth and coalescence.

The control problem addressed here is to grow a specified number of layers such that the resulting surface meets a specified "roughness'' criteria. The control uses a RHEED or PEO (photoemission) sensor to measure step edge density which signifies roughness. The figure below shows the MBE chamber and the associated sensors used for this work. The sensors are Reflection High Energy Electron Diffraction (RHEED), Photoemission Oscillation sensor (PEO), Absorption Band-Edge Spectroscopy (ABES, for temperature), Reflection Mass Spectroscopy (REMS) sensor, all of which are in-situ sensors, and Scanning Tunneling Microscopy (STM) which is an ex-situ sensor.

Schematic of the MBE system.

The variables that strongly effect the layer growth are the substrate temperature and adatom flux. In the MBE reactor, it is not possible to rapidly change the diffusion (by controlling surface temperature) over the time period of typical 5-10 monolayer growth because of the slow thermal dynamics of the substrate. Hence, substrate temperature is useful as a "run-to-run" control variable. Flux, can be rapidly changed by adjusting the effusion cell cracker valves or shutters, and more slowly changed by controlling the cell temperature. Hence, flux is the effective control variable. A change in flux will effect the deposition time to achieve a desired coverage, i.e., decreasing flux increases the deposition time to reach a coverage goal, thereby lowering the step edge density.

Surface conditions are monitored from RHEED and PEO signals. The oscillation period of the RHEED signal is directly related to the growth rate of layers of atoms on he surface. The PEO sensor scans a smaller area of the wafer but is more sensitive to surface changes yielding accurate period data at the beginning of a growth cycle, is more robsut to changing growth conditions, and can be used with wafer rotation. However, the PEO is a relatively new sensor compared to RHEED, the latter being used in period control described below.

Closed-loop Feedback Control for MBE

The oscillation period of the RHEED signal was controlled during III-V growth. Using the error between the desired period and the period calculated from the RHEED signal, the controller was able to adjust in real-time the set-point temperature of the Group III material effusion cell.

The model-based controller algorithm used results from a KMC simulation model of atom-by-atom film growth together with a dynamic thermal model of the effusion cell. The controller, which controls growth from layer to layer, has two important features:

  • it is very robust to chamber variations and uncertainties
  • the system may be conveniently modeled as a discrete-time system where sample times are replaced by layer number. There is well-developed control theory applicable to such systems.

The figure below shows details of the RHEED oscillation controller including the various control inputs and sensor outputs and computer configuration.

The figure below shows the results of a control experiment performed on the MBE system. The controller shows good performance by keeping the oscillation period close to the reference period. The experimental data and the simulation results are in good agreement.

This work was funded by a DARPA contract as part of the Virtual Integrated Prototyping (VIP) Program.

Phase III: Control of Interface Morphology in III-V Nanoelectronic Devices

One of the primary goals of this DARPA sponsored project was to produce a controller that will demonstrate real-time control of morphology of MBE-grown semiconductor interfaces.The scope of this project included modeling and simulation of epitaxial growth, device performance and sensors, development of reduced order models and control, validation through extensive experimentation and microscopy, implementation and demonstration of controls.The project is led by Hughes Research Laboratory (HRL) with UCLA, SC Solutions, and University of Colorado as subcontractors.

Physical Vapor Deposition (PVD)

SC Solutions has developed techniques and tools for physical modeling and model-based control for advanced materials processing. This technology has been successfully applied to the manufacturing of Giant MagnetoResistive (GMR) thin films. The results of the physical model provided guidelines for selecting process parameters, and identifying causes for wafer-to-wafer variability in film properties. This variability was reduced by more than 50% using SC’s controller.

GMR Production Using RF Diode Sputtering

The cornerstone of SC Solutions’ technology is Model-Based Control Design. With this approach a physical model of the GMR chamber and the sputter process is used directly in the control design. This "virtual" integrated prototyping environment can also be used to evaluate or optimize performance for either existing equipment or for the next generation equipment. GMR materials have tremendous potential for application to technologies such as hard disk read heads for computer data storage, computer memory, and sensors. A common method of producing thin-film GMR material is by RF diode sputtering.

SC Solutions has developed, in collaboration with Nonvolatile Electronics (NVE) of Eden Prairie, MN and the University of Virginia, Charlottesville, VA, a set of computer models for the physical processes that occur in radio-frequency (RF) diode sputtering for thin film deposition. The resulting RF integrated-voltage controller implemented at NVE reduced wafer-to-wafer variability in film properties by more than 50%. In addition, within-wafer thickness uniformity was substantially improved by adopting equipment modifications suggested by the simulations. This work was funded by DARPA, Applied & Computational Mathematics Program.

Model of the RF Sputtering Chamber

An integrated model of the GMR RF sputtering chamber was developed that consists of the following modules which simulate the various physical phenomena occurring during thin film deposition:

  • fluid flow model,
  • RF plasma & sputter models,
  • direct simulation Monte Carlo (DSMC) model,
  • thermal model of the chamber.

Integrated Voltage Controller

Guided by the results of the integrated model, careful measurements were made to detect correlations between the process parameters (performance variables) and the critical device properties, viz, the GMR ratio, saturation magnetic field strength (hsat), and the sheet resistance (rhos). The data showed that three of the four variables were relatively well-controlled, with the integrated target bias voltage correlating with variations in wafer hsat. An integrated voltage controller was developed that compensates for the RF bias voltage fluctuations by adjusting the plasma on-time so as to regulate the time-integrated voltage (for all layers of the same material deposited). This approach keeps the total RF energy input into the plasma constant.

Within-Wafer Uniformity

The integrated model indicated that reduced electrode spacing would significantly improve deposition uniformity. Experiments were conducted and the results show that this closer spacing produced wafers with excellent GMR. Calculations using the model also showed that a concave shaped target would reduce deposition non-uniformity across the wafer, since the reduced spacing at the edges would compensate for the flux of atoms escaping from the plasma boundary. Deposition (and hence film property) uniformity within a wafer has shown significant improvement following recommendations obtained from simulations with the model.

Related Publications

Under this Army-sponsored Small Business Technology Transfer Research (STTR) Phase II project, a unique combination of technical expertise developed at Cornell University, SC Solutions, and CryoIndustries of America are being capitalized to produce a powerful new type of scanned probe microscope.

The Magnetic Resonance Force Microscope (MRFM) is a sensitive new technique for detecting nuclear magnetic moments (and unpaired electrons). In this program we developed the prototype of a variable-temperature MRFM capable of detecting and imaging at a sensitivity of a few thousand protons. Our microscope gives researchers the unprecedented ability to non-destructively acquire a three-dimensional image of subsurface nanoscale features with isotopic, and potentially chemical, selectivity. This unique instrument potentially has wide application for researchers and product developers in the semiconductor, materials, and biotechnology industries.

In MRFM and other Scanned Force Microscopes (SFM), interaction forces acting between a scanned probe tip and a sample are exploited for imaging purposes, similar to the tunneling current in STM. Other examples of SFM are atomic force microscopy (AFM) and electric force microscopy (EFM).

The key component in SFM is a tip on a cantilever, which acts as a force sensor. When the tip is brought close to the surface of the sample under investigation, the interaction force between the tip and the sample causes a deflection of the cantilever, which behaves as a soft spring. It can be shown that the force gradients acting on the cantilever, in effect, change the cantilever’s spring constant, and hence its resonance frequency.

Within SFM, active control of the cantilever is needed for several reasons:

  • Fast damping of the cantilever is needed to increase imaging speed in AFM. Cantilevers with a high quality factor have lengthy ring-down time (many 10’s of seconds) that slows imaging.
  • AFM imaging with constant frequency and/or imaging with constant amplitude will provide different images. Both types of imaging require feedback control.
  • In MRFM mode, the cantilever thermo-mechanical oscillations can be many nanometers. These random oscillations must be damped to below 0.1 nm rms if atomic-scale imaging resolution is to be achieved.
  • As the cantilever approaches a surface, its natural frequency can change significantly. For many applications it is favorable or required to track and measure the cantilever frequency continuously.

All-in-one Digital Cantilever Controller

To accommodate these requirements, SC Solutions has developed a generic all-in-one digital cantilever controller, a schematic of which is shown in Figure 1.

ematic of generic cantilever controller.

Figure 1. Schematic of generic cantilever controller, including low-level motion controllers, as well as high-level characterization and detection algorithms.

Current analog cantilever controllers suffer from significant thermal drift and are not easily tunable. To overcome this, an all-in-one-digital cantilever was developed that combines frequency shift measurements, phase shifting and amplitude control, as well as positive feedback control for driving the cantilever at its resonance frequency. This versatile controller is comprised of a Field Programmable Gate Array (FPGA) connected via a low-latency interface to an analog input, an analog output, and a Digital Signal Processor (DSP) with additional analog outputs.

Hardware & Software

The cantilever controller hardware consists of a Texas Instruments (TI) C6711 DSP based system tightly coupled to a Xilinx Virtex-II FPGA. The FPGA communicates directly through digital data lines to a high speed (80 MHz) ADC (Analog-to-Digital-Converter) and DAC (Digital-to-Analog-Converter). As can be seen in Figure 2, the signal path is SPM—ADC—FPGA—DAC—SPM.

Block diagram of the cantilever controller.

Figure 2. Block diagram of the cantilever controller. The Scanned Probe Microscope provides a cantilever position signal, digitized at 80MHz by the ADC, which passes it to the FPGA. The FPGA sends a phase-shifted AC signal to a fast DAC which is used to drive the cantilever at its resonance frequency, thus closing the control loop. A DSP is used to set registers in the FPGA as well as control slow DACs.

The Scanned Probe Microscope (SPM) system provides a signal which is proportional to a cantilever position. The ADC digitizes this signal at 80 MHz and passes it to the FPGA. The FPGA computes an estimate of the cantilever’s frequency, amplitude, and phase. It also sends a phase-shifted AC signal to a fast DAC which is used to drive the cantilever at its resonance frequency, thus closing the control loop. By using the FPGA to perform all the calculations in the critical path of the control loop, the overall system latency is reduced by eliminating the need to pass data to and from the DSP over its input/output bus.

The DSP controls the FPGA by setting the values of several registers in the FPGA that determine the characteristics of the control loop. The DSP also sets the values in three slow (1 MHz) DACs. The slow DAC’s will be used for other aspects of the scanned probe microscope. One is used to produce a voltage proportional to the cantilever frequency, and another controls RF power levels. This leaves the third DAC free to control, for example, the height of the cantilever.

The 10 MHz clock reference for the ADC/DAC is an externally provided from a stable, low phase noise crystal. The FPGA multiplies the 10 MHz up to 80 MHz using a digitally locked loop (DLL) and this 80 MHz signal becomes the clock for the ADC/DAC. We chose to provide the 10 MHz from an external source instead of using a DSP-generated clock reference to guarantee that the reference had low phase noise. To obtain the rated accuracy of the ADC/DAC low phase noise clocks must be used. A photo of the completed all-digital cantilever controller hardware is shown in Figure 3.

Photo of controller hardware.

Figure 3. Photo of controller hardware installed at Cornell University. The stacked FPGA/DSP cards can be seen slightly right from the center.

Screenshot of the LabView User Interface.

Figure 4. Screenshot of the LabView User Interface, which controls the hardware by setting control registers in the FPGA. This software also monitors the estimated frequency shift of the resonating cantilever.

Figure 4 shows the main user interface. A key feature is the selection of the mode of operation. Another common feature is the display of relevant data, e.g., the current estimate of the cantilever frequency and/or frequency shift, as well as the magnitude of the cantilever signal. Another common feature is setting up the connection with the target.

Experimental Results

A prototype controller has been tested on one of Cornell’s ultra-sensitive cantilevers. The all-digital cantilever controller quickly locked into the cantilever’s resonance frequency, see Figure 5. The controller successfully measured 5 to 10 millihertz shifts in a 5 Hz detection bandwidth in the resonance frequency of these ultra-sensitive microcantilevers on a millisecond timescale. Independently, a noise floor of 40 microhertz in one second was measured for this controller.

Frequency shift detection result.

Figure 5. Frequency shift detection result. The three columns show the results of a 100 mHz, a 20 mHz, and a 5 to 10 mHz shift, respectively. The first row shows the step in tip voltage applied to induce a frequency shift in the cantilever. The second row shows the frequency shift estimated by the FPGA algorithm, without any filtering. The third row shows the same frequency shift estimate, but now post-processed using a moving average filter with a 10 Hz frequency gate and 1 Hz frequency gate.

Related Publications

SC Solutions' staff participated in a research and development effort at Delft University of Technology, Netherlands in cooperation with Philips Research Laboratories (Eindhoven, Netherlands) aimed at developing faster and more accurate positioning of wafer stages through advanced control methods. The desired speed requirement is a throughput of 60–80 wafers/hr, and the desired positioning error (accuracy) must not exceed 50 nm with a measurement accuracy of 13 nm.

A new methodology for designing 3-Degree-of-Freedom controllers integrating Feedback control, Feedforward control, and Position-time trajectory design was developed and implemented on a Phillips wafer stepper. The implementation of the advanced control methodology resulted in improvement of state-of-the-art Motion Controllers from Philips: faster settling, and better vibration control.

Joint effort with Princeton University and Oxford University, under support from the DARPA QUIST (Quantum information Science & Technology) Program, this research is concerned with combining control concepts and quantum information systems. Particular emphasis is being given to closed loop laboratory techniques for obtaining the maximum performance from quantum information systems.

SC Solutions Inc. is a key team member in the 2008 NIST-TIP Cyber-Enabled Wireless Monitoring Systems for the Protection of Deteriorating National Infrastructure Systems. This $19-million project is funded by $9-million from NIST (National Institute of Standards and Technology), and is expected to run from 2009 -- 2013. It is a Joint Venture (JV) led by the University of Michigan (UofM), Ann Arbor, MI, in partnership with five private firms in Michigan, New York and California.

Under this project the JV team is developing a comprehensive system for monitoring and assessing the structural health and integrity of major infrastructure elements such as bridges on a regional basis, with innovations ranging in scale from “smart material”-based sensors at the level of individual structural components up through structure-level data integration and interpretation to a Web-based system for information aggregation and decision support at the regional level.

SC Solutions is contributing its extensive and unique experience in both bridge engineering and control engineering, and developing methods and tools for effective model-based data analysis and health monitoring. As part of the project we are working with Caltrans (California Department of Transportation) and the JV team members to test this new technology on the New Carquinez Bridge, a long-span bridge that connects the Solano and Contra Costa Counties, located between Vallejo (on the North side) and Crockett (on the South side) in California.

This project has been featured as a special report in the evening news of KTVU, a local San Francisco Bay Area TV station.



J. L. Ebert, S. Ghosal, D. de Roover, and A. Emami-Naeini, “Experimental Validation of Model of Electro-Chemical-Mechanical Planarization (ECMP) of Copper,” Proceedings of the 2012 COMSOL Conference, Boston, October 3-5, 2012.

G. W. van der Linden, A. Emami-Naeini, R .L. Kosut, H. Sedarat, and J. P. Lynch, Optimal Sensor Placement for Health Monitoring of Civil Structures, 2011 American Control Conference, San Francisco, CA, USA, June 29 - July 01, 2011, pp. 3116 -3121, 2011.

In this paper we focus on comparing three candidate approaches to the optimal placement of sensors for state estimation-based continuous health monitoring of structures. The first aims to minimize the static estimation error of the structure deflections, using the linear stiffness matrix derived from a finite element model. The second approach aims to maximize the observability of the derived linear state space model. The third approach aims to minimize the dynamic estimation error of the deflections using a Linear Quadratic Estimator. Both nonlinear mixed-integer and relaxed convex optimization formulations are presented. A simple search-based optimization implementation for each of the three approaches is demonstrated on a model of the long-span New Carquinez Bridge in California.

M. Kurata, J. P. Lynch, T. Galchev, M. Flynn, P. Hipley, V. Jacob, G. W. van der Linden, A. Mortazawi, K. Najafi, R. L. Peterson, L.-H. Sheng, D. Sylvester, E. Thometz, A Two-Tiered Self-Powered Wireless Monitoring System Architecture for Bridge Health Management, In: "Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security 2010", Ed. Peter J. Shull, Aaron A. Diaz, H. Felix Wu, doi: 10.1117/12.848212, Proc. of SPIE Vol. 7649, San Diego, CA, USA, March 7-11, 2010.

Bridges are an important societal resource used to carry vehicular traffic within a transportation network.  As such, the economic impact of the failure of a bridge is high; the recent failure of the I-35W Bridge in Minnesota (2007) serves as a poignant example.  Structural health monitoring (SHM) systems can be adopted to detect and quantify structural degradation and damage in an affordable and real-time manner.  This paper presents a detailed overview of a multi-tiered architecture for the design of a low power wireless monitoring system for large and complex infrastructure systems.  The monitoring system architecture employs two wireless sensor nodes, each with unique functional features and varying power demand.  At the lowest tier of the system architecture is the ultra-low power Phoenix wireless sensor node whose design has been optimized to draw minimal power during standby.  These ultra low-power nodes are configured to communicate their measurements to a more functionally-rich wireless sensor node residing on the second-tier of the monitoring system architecture. While the Narada wireless sensor node offers more memory, greater processing power and longer communication ranges, it also consumes more power during operation.  Radio frequency (RF) and mechanical vibration power harvesting is integrated with the wireless sensor nodes to allow them to operate freely for long periods of time (e.g., years).  Elements of the proposed two-tiered monitoring system architecture are validated upon an operational long-span suspension bridge.

S. Ghosal, N. Acharya, T. E. Abrahamson, L. Porter II, H. W. Schreier, “An Integrated Tool for Estimation of Material Model Parameters,” Proceedings of the SEM Annual Conference, Indianapolis, IN, June 7-10, 2010.

G. W. van der Linden, A. Emami-Naeini, R. L. Kosut, H. Sedarat, J. P. Lynch, Near-Optimal Sensor Placement for Health Monitoring of Civil Structures, In: "Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security 2010", Ed. Peter J. Shull, Aaron A. Diaz, H. Felix Wu, doi: 10.1117/12.847704, Proc. of SPIE Vol. 7649, San Diego, CA, USA, March 7-11, 2010.

In this paper we focus on the optimal placement of sensors for state estimation-based continuous health monitoring of structures using three approaches.  The first aims to minimize the static estimation error of the structure deflections, using the linear stiffness matrix derived from a finite element model.  The second approach aims to maximize the observability of the derived linear state space model. The third approach aims to minimize the dynamic estimation error of the deflections using a Linear Quadratic Estimator.  Both nonlinear mixed-integer and relaxed convex optimization formulations are presented.  A simple search-based optimization implementation for each of the three approaches is demonstrated on a model of the long-span New Carquinez Bridge in California.

Copyright 2010 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

J. L. Ebert, N. Acharya, D. de Roover, A. Emami-Naeini, R. L. Kosut, J. Zhang, Model-Based Control and Virtual Sensing with Application to a Vertical Furnace, AEC/APC Symposium, Salt Lake City, Utah, 2008.

de Roover, D.; Emami-Naeini, A.; Ebert, J.L., Model-based control for chemical-mechanical planarization (CMP), Proceedings of the 2004 American Control Conference, Volume 5, 30 June-2 July 2004, pp. 3922-3929, 2004.

The research described in this tutorial paper involves an effort for physical modeling and model-based sensing and control of CMP systems.  A dynamic model of a rotational CMP process is developed, as well as simulation software. This dynamic model is used for feedback control design based on  in-situ thickness measurements, as well as run-to-run control using in-line metrology. Simulation results of open-loop, feedback control, and combined feedback and run-to-run control are presented and compared. A multivariable LQ (linear quadratic) feedback controller was designed and showed improvement of Within-Wafer-Non-Uniformity (WIWNU) at the end of a run in simulation over existing open-loop control of a CMP process.  It also showed the possibility of using feedback control as a means of end-pointing the CMP process.  Furthermore, a run-to-run (R2R) controller was designed and simulated. Additional improvement of WIWNU and tracking a desired average wafer thickness was obtained, showing the merits of a combined feedback / run-to-run control process.

S. Ghosal, R. L. Kosut, J. L. Ebert, and L. L. Porter II, Multiscale Modeling and Control of RF Diode Sputter Deposition for GMR Thin Films, Proceedings of the 2004 American Control Conference, 30 June-2 July 2004, Volume: 5,  pp. 3930-3941, 2004.

Radio frequency (RF) diode sputtering is widely used for depositing Giant Magneto-Resistive (GMR) thin films for multilayers, spin valves,  and spin-dependent tunneling (SDT) devices used in data storage, computer memory, etc.  However, the thin films thus produced often show unacceptably high variation in GMR properties from wafer to wafer.  This paper describes a modeling and control effort that was undertaken for improving run-to-run repeatability.  A multiscale input-output model was developed for the primary physical phenomena in the deposition process − gas flow, plasma discharge, sputtering, and atom transport.  The model predicts the deposition rate, the energy distribution of sputtered atoms, and their sensitivity to deposition conditions such as power, working gas type, pressure, gas temperature, and electrode spacing.  Simulations with this model were used to determine the process parameters to which the wafer properties have the maximum sensitivity.  Experiments were performed to determine the relative importance of these parameters.  Based on the results, a controller was designed to regulate the time-integrated target bias voltage.  Implementation of the controller reduced wafer-to-wafer variation of GMR properties by over 50%.  Additionally, application of control to SDT wafers led to improvement and optimization of the process.

A. Emami-Naeini, J. L. Ebert, D. de Roover, R. L. Kosut, M. Dettori, L. M. Porter, S. Ghosal, Modeling and control of distributed thermal systems, IEEE Transactions on Control Systems Technology, Volume 11,  Issue 5, Page(s):668 - 683, Sept. 2003.

This paper investigates the application of model-based control design techniques to distributed temperature control systems. Multivariable controllers are an essential part of modern-day rapid thermal processing (RTP) systems. We consider all aspects of the control problem beginning with a physics-based model and concluding with implementation of a real-time embedded controller. The thermal system used as an example throughout is an RTP chamber widely used in semiconductor wafer processing. With its exceptionally stringent performance requirements (low nonuniformity of wafer temperature, high temperature ramp rates), RTP temperature control is a challenging distributed temperature control problem. Additionally, it is important in the semiconductor industry because of the progressively smaller "thermal budget" resulting from ever decreasing integrated circuit dimensions. Despite our emphasis on faster cold wall single-wafer processing RTP chambers, the approach described here for solving distributed temperature control problems is equally applicable to slower distributed thermal systems, such as hot-wall batch-processing furnaces. For the physical model, finite volume techniques are used to develop high-fidelity heat transfer models that may be used for both control design and optimal chamber design. Model-order reduction techniques are employed to reduce these models to lower orders for control system design. In particular, principal orthogonal decomposition techniques have been used to derive low order models. Techniques such as linear quadratic Gaussian H2/H methods are employed for feedback control design. While the methods are illustrated here using a generic RTP system, they have been successfully implemented on commercial RTP chambers.

S. Ghosal, R. L. Kosut, J. L. Ebert, A. Kozak, T. E. Abrahamson, W. Zou, X. W. Zhou, J. F. Groves, Y. G. Yang, H. N. G. Wadley, D. Brownell, and D. Wang, Multi-Scale Model of the RF Diode Sputter Deposition of GMR Thin Films, Application notes, 2000.

SC Solutions, Inc., "Reactor-scale Model of Silicon Epitaxy Process", Application Notes, 1999.

In this white paper, we describe the numerical simulation of CVD process for epitaxial growth of silicon using trichlorosilane (SiHCl3). This study uses the one-step, finite-rate chemistry for the 2-D reactor geometry from the literature, and successfully reproduces the published results. A commercial software package, CFD-ACEe, popular in the semiconductor industry, was used for our modeling work. Several tests were carried out on the model to establish convergence on the basis of mesh refinement and number of iterations needed.  We concluded that our results agree very well with those published in the literature. This validation study served as a starting point for other commercial projects for modeling CVD and MOCVD processes.

Reactor-scale Modeling and Control for MOCVD of YBCO High Temperature Superconductors, Application Notes, SC Solutions, Inc., 1999.

This whitepaper details a systematic methodology for concurrent development of reactor-scale physical model and model-based process control development for metal-organic chemical vapor deposition (MOCVD). The example used for illustrating the approach is the deposition of yttrium-barium-copper oxide (YBa2Cu3O7-x or YBCO) thin films with high temperature superconducting (HTS) properties. Information about the gas-phase chemical mechanisms, obtained from experimental data in the literature, is used in the reactor-scale transport and kinetics model developed using the CFD-ACE™ software package. These models were used to design model-based controllers for desired deposition rate, and for uniformity of deposition rate and stoichiometry within wafer. These simulation tools and the results obtained from the studies provide a clearer understanding of the chemical mechanism, species transport, and film growth. This understanding enables design and implementation of optimized controllers that meet both process specifications as well as run-to-run repeatability, which are essential for large-scale production.

S. Ghosal, A. Emami-Naeini, Y. P. Harn, B. Draskovich, and J. P. Pollinger, A Physical Model for Drying of Gelcast Ceramics, Journal of the American Ceramic Society, Vol. 82, No. 3, pp. 513-520, 1999.

Gelcasting is a promising new technology for manufacturing advanced structural ceramic components. The process involves drying of the ‘green’ gelcast part before densification. The physical mechanisms controlling this relatively long drying process are not well understood. In this study, several controlled experiments were performed to elucidate the key mechanisms. A one-dimensional drying model was formulated based on evaporation and gaseous diffusion through the part. Experimental data were used to obtain correlations for model parameters. This model predicts the instantaneous moisture content of a gelcast sample with an accuracy of better than 10% when dryer humidity and temperature, and sample thickness are specified.

D. de Roover, A. Emami-Naeini, J. L. Ebert, S. Ghosal, and G. W. van der Linden, Model-Based Control of Fast-Ramp RTP Systems, Proceedings of the Sixth International Conference on Advanced Thermal Processing of Semiconductors, RTP '98, Kyoto, Japan, September 9-11, 1998.

Seismic analysis of complex structures: Practical application issues and case study, A. V. Krimotat and R. M. Mutobe of SC Solutions, Inc., 1451 Grant Road, Mountain View, CA 94040, U.S.A.

All large structures are vulnerable to earthquake damage. Local failures or total collapses of such structures represent not only immediate concern for loss of life and repair costs, but also major economic impacts due to loss of service. The 1989 Loma Prieta and 1994 Northridge earthquakes in California provided dramatic examples of the vulnerability of engineered structures and the extensive impact of their failure in regions classified as high seismic risk zones. Today, engineers throughout the world are faced with increasing requirements to assess the seismic vulnerability of existing structures, even in regions of relatively low seismic risk classification, and to design new, more sophisticated structures. The purpose of this paper is to discuss the particular features and benefits of ADINA with respect to the requirements of advanced seismic analysis. Major aspects of earthquake related analysis are discussed, i.e. static lateral push-over analysis, ground motion specification for dynamic analysis, and significant structural behavior phenomena associated with contact and ductile energy dissipation. The modelling of typical structural components is presented and analysis strategies are delineated via case study of a large public building.

In addition to issues related to the as-built structure analysis, the philosophy of accommodating displacements via the deformation of highly ductile components or dampers introduced at existing expansion joint hinges and other appropriate structural locations is presented along with the requisite modelling requirements. With respect to post-processing, typical structural component performance is illustrated via monotonic and hysteretic energy characterizations as well as with standard displacement and force demand data. A summary of the analytical issues and their simulation within ADINA especially with respect to new capabilities, is also provided.

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