Modeling and Simulation

Research Projects with Sandia National Lab in partnership with Metroscientific

Collaboration & Innovation

Mean Estimation and Nominal Device Selection with the Pairwise Midpoint Method

Variation characteristics curves

Figure 1: Variation of product characteristics curves due to tolerance of parameter.

CSM vs PMM Method

Figure 2: CSM (Cross Sectional Mean) & PMM (Pairwise Midpoint Method) mean of Figure 1.

In order to manufacture a product, there may be some variation in its characteristics (Figure 1) due to manufacturing parameter tolerances. To determine the ideal behavior curve for this product, we need to find an ideal example/measurement/characteristic from a set of curves.

One approach is to find the mean curve, but for a 2D dataset, simply calculating the normal mean (Cross Sectional Mean) won't work (Figure 2) as it doesn't consider both axes. The Karcher mean (KM) is a popular method for calculating mean curves for 2D datasets, but it is computationally burdensome due to the large number of calculations involved. We proposed an alternative method for calculating the mean curve which is much less computationally expensive than KM.

Purpose of this research:

Accurate device modeling is an important prerequisite of electronic circuit design. Analog circuit simulators based on SPICE (Simulation Program with Integrated Circuit Emphasis) used in the electrical design process support numerous canonical compact models, i.e., models for individual devices within the design. Often for high reliability and large-scale commercial designs, a series of circuit level simulations are performed using calibrated corner models to bound circuit responses and ensure performance remains within the required specifications.

Before leaving the factory, an electrical product produced in foundries are subjected to a Product Acceptance Test (PAT) to assess their electrical performance.

Only products that pass the PAT test are sent to the packaging plant. The output behavior of the chipset is compared with a nominal device response, and it must fall within a tolerance bound for the chipset to meet the required specifications. Therefore, it is necessary to determine the nominal behavior of the chipset with the corresponding tolerance bound.

Purpose illustration top
Purpose illustration bottom

Figure 3: Purpose of this research

Pairwise Midpoint Method illustration

Figure 4: Comparison among CSM, KM and PMM

Pairwise Midpoint Method

In the principled analysis of functional data, both amplitude (y-axis) variability and phase (x-axis) variability must be considered. The Cross-sectional mean (CSM) at a given time point is computed by averaging all observed function values at that point (in practice, the independent variable is not restricted to a measure of time – it is simply used here as a generic stand-in). This clearly does not account for phase variability, and the resulting mean is often a poor description of the average behavior of the observed functions.

The KM provides a much-improved representation of the mean compared to the CSM. The PMM is a method that accounts for phase variability while being simpler to both understand and implement than the KM. This has multiple upsides over the traditional timeseries method:

  • ✓ Easy to understand and implement.
  • ✓ Alleviate computational burden.

Comparison among CSM, PMM and KM:

A key purpose for developing the PMM method as an alternative to formal methods is to gain an advantage in computational time. The output curves of simulated data and real-life data are shown in Figures 4, 5 respectively. Specially Figure 5 represents the characteristic curves of Zener diode devices. From these curves, we can see the CSM can't determine mean due to its only one-dimension consideration.

To assess the computation time required by each method, CSM, PMM and KM, a single data set was chosen. Each method was run 500 times on this data set, and the computation time was recorded. This analysis was carried out on a laptop with 2.5 GHz and 32 GB of RAM, running on a 64-bit operating system. The timing analysis results are given in Table 1. Clearly, PMM requires far less computation time than KM.

CSM <0.001 (<0.001)
KM 209.919 (0.580)
PMM 0.257 (0.011)

PMM is a novel technique to determine the mean and select a nominal device from a set of electrical devices. It gives output similar to KM but alleviates the computational burden. Though a negligible amount of dependency exists in the output curve with the input point selection pattern, it gives excellent output considering both axis variations.

Comparison among CSM, PMM and KM

Figure 5: Comparison among CSM, PPM & KM in Zener diode dataset

Mixed Signal Benchmark Circuit Simulation

Compensated CMOS Operational Amplifier Circuit

Compensated CMOS Operational Amplifier

The integrated operational amplifier is practicable in linear active circuit in today's mixed-signal systems. The configuration represents a classical two-stage CMOS operational amplifier (OA). As the op amp is compensated, its transfer function can be approximated to a single pole transfer function.

The op amp has the effect of increasing the phase shift as the frequency increases. So, at some higher end frequency, the negative feedback may be converted to positive feedback and make an amplifier turn into an oscillator.

Compensation is done by putting a capacitor between the input and the intermediate stages. This can be done by the chip manufacturer by fixing a capacitor internally or the user may be asked to use one external to the chip.

CMOS Operational Amplifier

The operational amplifier is the most widely used linear active circuit in today's mixed-signal systems. The schematic represents CMOS operational amplifier (OA). The CMOS operational amplifier is the most intricate, and in many ways the most important building block of linear CMOS and switched-capacitor circuits.

Its performance usually limits the high-frequency application and the dynamic range of the overall circuit and hence the benchmark circuit should have to be implemented.

CMOS Operational Amplifier Circuit Top
CMOS Operational Amplifier Layout
State Variable Filter Circuit Top
State Variable Filter Response

Continuous Time State Variable Filter

The state variable filter is a type of multiple-feedback filter circuit that can produce all three filter responses - Low Pass, High Pass and Band Pass simultaneously from the same single active filter design. State variable filters use three operational amplifier circuits (the active element) cascaded together to produce the individual filter outputs but if required an additional summing amplifier can also be added to produce a fourth Notch filter output response as well.

One of the main advantages of a state variable filter design is that all three of the filters main parameters, Gain (A), corner frequency (ƒc) and the filters Q can be adjusted or set independently without affecting the filter performance. In fact if designed correctly, the -3dB corner frequency (ƒc) point for both the low pass amplitude response and the high pass amplitude response should be identical to the center frequency point of the band pass stage.

Leapfrog Filter

The leapfrog filter is used to remove high-frequencies from a system. This filter transfers anything from DC to any desired device operation with a low frequency. The proposed design approach is quite simple and systematic which has no passive element requirements.

The basic building blocks of all circuits mainly consist of Operational Amplifier (OA). For not having any passive elements, this filter is usually used in audio amplifiers and in some multi-media set-top boxes which operate in baseband mode.

Therefore, the Benchmark Circuit of Leapfrog Filter should be implemented.

Leapfrog Filter Circuit Top
Leapfrog Filter Response
Single State Common Emitter Amplifier Circuit

Single State Common Emitter Amplifier

The most common amplifier configuration for an NPN transistor is that of the Common Emitter Amplifier circuit. This common emitter configuration is highly useful due to its moderate current and voltage gain.

It can increase the strength of input signal of a frequency generation circuit. Moreover, this benchmark circuit is commonly practicable in order to increase the speed of fans, motors, and time circuits.

Differential Amplifier

The electronic device that amplifies the difference between two input voltages is a differential amplifier but suppresses any voltage common to the two inputs. It is an analog circuit with two inputs and one output.

It is used in amplitude modulation, automatic gain control circuit and volume control circuit.

Differential Amplifier Circuit

Investigations of Nanowire Gate-All-Around Negative Capacitance GaAs/InN Tunnel FET

Nanowire Gate-All-Around Negative Capacitance GaAs/InN Tunnel FET

In the rapidly advancing world of electronic devices, researchers are constantly searching for new and improved technologies that can offer higher speeds and lower power consumption. In recent years, one promising option has been the use of tunnel field-effect transistors (TFETs), which can overcome the subthreshold swing limitations of traditional metal-oxide-semiconductor field-effect transistors (MOSFETs).

This article demonstrated a nanowire gate-all-around (GAA) negative capacitance (NC) TFET based on the GaAs/InN heterostructure using TCAD simulation. In the gate stacking, we proposed a tri-layer HfO2/TiO2/HfO2 as a high-K dielectric and hafnium zirconium oxide (HZO) as a ferroelectric (FE) layer. The proposed GAA-TFET overcomes the thermionic limitation (60 mV/decade) of conventional MOSFETs' subthreshold swing (SS) thanks to its improved electrostatic control and quantum mechanical tunneling. Simultaneously, the NC state of ferroelectric materials improves TFET performance by exploiting differential amplification of the gate voltage under certain conditions. This optimized device structure produced an ION/IOFF ratio on the order of 10^11 and a larger on-state current of about 135 micro-ampere, indicating better channel and current control capacities. With a 9 nm HZO in the gate stack, the lowest SS of 20.56 mV/dec and the maximum voltage gain of 6.58 were achieved, making this TFET structure promising as energy-efficient switches. The output characteristics also revealed a substantial transconductance (gm) of 7.87 mS, a DIBL of 9.7 mV, and a threshold voltage of 0.53 V (37.65% lower than the baseline TFET), all of which are notable in comparison to all other state-of-the-art TFETs. The proposed GaAs/InN nanowire GAA NCTFET has the potential to ameliorate the limitations of scaling down transistor size and reduce power consumption. This makes it a unique route for the ongoing advancement of electronic devices and a promising option for an Internet of Things (IoT) technological platform.

In conclusion, the hybrid nanowire GAA NCTFET structure demonstrated by our team shows great potential for improving the performance of electronic devices, and could lead to higher speeds and lower power consumption. As research in this field continues, we can expect to see further advances that build on the promising results of this study.

Cutting-Edge Advance Materials to Drive Technological Advancement

Nanowire Research Image 1
Nanowire Research Image 2

Advancing Nanowire Research: Investigating Novel Properties for Future Nanotechnological Advancement

Nanowires are extremely fine structures with diameters ranging from 1 to 100 nanometers. These wire-like structures, which can be made of various materials such as metals or semiconductors, have remarkable properties. Their high surface-to-volume ratio improves reactivity and sensitivity, making them ideal for applications such as sensors, solar cells, and batteries. Because of quantum confinement effects at the nanoscale, nanowires have unique electronic and optical properties. This capability enables precise control and tuning of their behavior, resulting in advancements in electronics, optoelectronics, and photonics. Furthermore, nanowires are being used in energy harvesting and storage, allowing for more efficient solar cells and higher-capacity batteries. They are extremely sensitive to changes in their surroundings, making them ideal for sensing and detection applications in healthcare, security systems, and environmental monitoring. Nanowires have also shown promise in the field of nanomedicine, where they can help with targeted drug delivery, diagnostics, and imaging for better medical treatments. Overall, nanowires have numerous applications and have the potential to revolutionize a variety of industries.

Our research endeavors in the field of Nanowire experimentation have encompassed the generation and examination of a diverse range of compound Nanowire materials. These materials have undergone meticulous scrutiny under a multitude of extreme conditions, leading to significant and compelling findings. By subjecting the Nanowires to these rigorous experimental conditions such as AC and ZZ tensile test with varying subject temperature, we have attained profound insights into their behavior and performance characteristics. Our comprehensive investigations in this domain have contributed to the advancement of knowledge regarding the distinctive properties and prospective applications of compound Nanowire materials.

In the design and development of a product, it is essential to take into account the mechanical properties of various materials. These properties include strength, hardness, elasticity, toughness, and thermal conductivity. Understanding these properties and selecting the appropriate material for a particular application is essential for developing durable, efficient, and reliable products. High mechanical properties can also improve product performance and reduce the risk of failure. These materials are particularly valuable for applications such as NEMS, MEMS, power electronics, high-temperature environments, nano-generators, and high-speed electronics, where their unique mechanical properties enable high performance and reliability. They are also used in applications such as sensors, optoelectronics, and aerospace due to their high thermal stability and resistance to radiation. In summary, the mechanical properties of materials are of great importance in product design and development, and should be carefully considered in any application, including those in NEMS, MEMS, power electronics, high-temperature environments, nano-generators, high-speed electronics, sensors, optoelectronics, and aerospace.

Our research has concentrated on the development and characterization of a diverse set of promising materials. These include silicon carbide (SiC), silicon germanium (SiGe), beryllium oxide (BeO), zinc sulfide (ZnS), indium nitride (InN), and gallium nitride (GaN). We have explored the properties of these materials under various conditions, such as extreme temperatures, impurity doping, the introduction of vacancies, and different grain sizes with random orientations. Additionally, we have investigated the behavior of these materials in hetero bi-layer configurations. Through our comprehensive analyses, we have gained valuable insights into the properties and potential applications of these materials in diverse fields.

Materials Research Image 1
Materials Research Image 2

Investigating Compound Nanotubes: Thermal Conductivity, Characterization, and Promising Applications

Nanotubes, which are cylinder-shaped nanostructures mostly composed of carbon atoms, have remarkable properties and find various uses. Their high mechanical strength makes them a promising material for use in aerospace components and composite structures. Their remarkable thermal conductivity benefits thermal management applications and allows for faster electronics and transparent coatings. Photonics and optoelectronics both benefit from nanotubes with controllable optical properties. Nanoelectromechanical systems, supercapacitors, gas sensors, and drug delivery systems are just a few examples of the many ways this technology can be put to use in the fields of electronics, energy storage, environmental sensing, and medicine. Nanotubes' adaptability makes them an intriguing research topic in nanotechnology.

Compound Nanotubes Research

In our experimental research on Nanotubes, there involved a careful selection of specific materials, and then we synthesized hetero MW-Nanotubes exhibiting diverse growth orientations. These nanotubes were subjected to specific thermal heat flux, then comprehensive computations are conducted to determine the thermal conductivity of these nanotubes. Furthermore, we conducted extensive characterization studies under varying loading conditions. The outcomes of these experiments have yielded novel insights into the properties of different compound nanotubes, offering exciting prospects for their application in future Nanotechnological advancements, particularly in the development of smart sensors and electronic devices.

Modelling & Simulation

We use Comsol, Silvaco, QUANTUM Espresso, PSpice, HSpice, LTspice, Ngspice, Xyce, ModelSim, Matlab Simulink, gpvdm, and VASP to provide following modeling and simulation services:

  • Simulation of analog, digital and mixed-signal circuits
  • Optical Sensor design
  • Characteristics analysis of FET, JFET, OFET, MOSFET, FINFET, TFET devices
  • Performance Analysis of Solar cells
  • Exploration of Nanomaterial Property
  • Simulation of 1D, 2D, and 3D material
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