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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

Optimal environmental and economic performance trade-offs for fifth generation district heating and cooling network topologies with waste heat recovery

Network topology greatly influences both the economic and environmental performance of fifth generation district heating and cooling (5GDHC) systems. In this study the optimal trade-offs between the environmental and economic performance of 5GDHC network topologies for a five-building district with waste heat recovery were explored. A life cycle assessment method was used to calculate the total life cycle CO 2 emissions (LCCO2) associated with the installation and operation of various network topologies. Twelve months of empirical data from a data center cooling system were analyzed to assess its suitability for integration into a 5GDHC system. The most suitable method for utilizing this waste heat was selected based on the ambient loop warm pipe setpoint, waste heat temperature, and district energy system configuration. A multi-objective optimization algorithm was used to select the 5GDHC network topology that provided the optimal trade-off between LCCO2 and life cycle cost (LCC). A trade-off parameter was employed to weigh the importance of each objective in the selection process. The results showed waste heat from the data center was suitable for integration into the 5GDHC system due to its availability and consistent temperature profile. When return temperatures of 25 °C or higher were available from the liquid-cooled system, direct pre-heating of the ambient loop warm pipe was found to be the most effective waste heat integration method. The selection of the network topology that provided the optimal trade-off between LCCO2 and LCC (optimal trade-off topology) was highly dependent on factors such as fuel prices, CO 2 prices, electricity CO 2 emissions factors, availability of waste heat, embodied CO 2 emissions associated with network installation and network infrastructure costs. Optimal trade-off topologies produced substantial LCCO2 reductions relative to corresponding LCC increases. LCCO2 reduction to LCC increase ratios from 5.78 to 117.79 were identified with CO 2 offset costs ranging from 4.77 to 60.08 ($/tCO 2 e).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Bacterial population-level trade-offs between drought tolerance and resource acquisition traits impact decomposition

Microbes drive fundamental ecosystem processes, such as decomposition. Environmental stressors are known to affect microbes, their fitness, and the ecosystem functions that they perform; yet, understanding the causal mechanisms behind this influence has been difficult. We used leaf litter on soil surface as a model in situ system to assess changes in bacterial genomic traits and decomposition rates for 18 months with drought as a stressor. We hypothesized that genome-scale trade-offs due to investment in stress tolerance traits under drought reduce the capacity for bacterial populations to carry out decomposition, and that these population-level trade-offs scale up to impact emergent community traits, thereby reducing decomposition rates. We observed drought tolerance mechanisms that were heightened in bacterial populations under drought, identified as higher gene copy numbers in metagenome-assembled genomes. A subset of populations under drought had reduced carbohydrate-active enzyme genes that suggested—as a trade-off—a decline in decomposition capabilities. These trade-offs were driven by community succession and taxonomic shifts as distinct patterns appeared in populations. We show that trait–trade-offs in bacterial populations under drought could scale up to reduce overall decomposition capabilities and litter decay rates. Using a trait-based approach to assess the population ecology of soil bacteria, we demonstrate genome-level trade-offs in response to drought with consequences for decomposition rates.

59 BASIC BIOLOGICAL SCIENCES↗

Implications of an emission trading scheme for India’s net-zero strategy: a modelling-based assessment

To help meet its near-term NDC goals and long-term net-zero 2070 target, the Government of India has planned to establish a Carbon Credit Trading Scheme (CCTS), i.e. a domestic emission trading scheme (ETS). An ETS is an inherently cost-effective policy instrument for emission reduction, providing the greatest flexibility to reduce emissions from within and across sectors. An effective ETS requires design features that consider country-specific challenges and reflect its role within the larger policy package to achieve long-term emission reduction. Within the Indian context and in this study we therefore investigate—(i) what might be the role of the ETS in achieving India’s long-term mitigation targets? (ii) How might the various sectors interact under an emissions cap? (iii) How might the ETS interact with existing energy and climate policies? We do this analysis by running four main scenarios using the integrated assessment model GCAM (v6.0), adapted to India-specific assumptions and expectations. These scenarios are—(i) NZ (net-zero), (ii) NZ + ETS, (iii) NZ + CC (command and control), and (iv) NZ + RPO (renewables purchase obligations) + ETS. The NZ scenario assumes India’s near-term and long-term climate commitments of net zero by 2070. Scenarios with ETS (ii) and (iv) apply an emissions cap on four sectors—electricity, iron and steel, cement, and fertilizer. The scenario with CC applies a homogenous emission cap on each of the chosen sectors but does not allow cross-sectoral trading. The last scenario includes renewables purchase obligations (RPOs along with an ETS. We show that under a specific ETS emissions cap: (i) the electricity sector emerges as the largest source of cost-effective greenhouse gas (GHG) reduction options; (ii) ETS with trading across sectors is around 24% more cost-effective than ETS with trading only within sectors, (iii) RPOs can be complementary to an ETS although the impact of RPOs on GHG reductions in the electricity sector would need to be considered when setting the level of the ETS cap (or emissions intensity targets) or the RPO targets to avoid low carbon prices, and (iv) the direction and volume of financial transfers across sectors depends on allocation targets set by the government. Based on these results we provide design recommendations for India’s ETS.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A Blockchain and PKI-Based Secure Vehicle-to-Vehicle Energy-Trading Protocol

With the increasing awareness for sustainable future and green energy, the demand for electric vehicles (EVs) is growing rapidly, thus placing immense pressure on the energy grid. To alleviate this, local trading between EVs should be encouraged. In this paper, we propose a blockchain and public key infrastructure (PKI)-based secure vehicle-to-vehicle (V2V) energy-trading protocol. A permissioned blockchain utilizing the proof of authority (PoA) consensus and smart contracts is used to securely store data. Encrypted communication is ensured through transport layer security (TLS), with PKI managing the necessary digital certificates and keys. A multi-leader, multi-follower Stackelberg game-based trade algorithm is formulated to determine the optimal energy demands, supplies, and prices. Finally, we propose a detailed communication protocol that ties all the components together, enabling smooth interaction between them. Key findings, such as system behavior and performance, scalability of the trade algorithm and the blockchain, smart contract execution costs, etc., are presented through numerical results by implementing and simulating the protocol in various scenarios. This work not only enhances local energy trading among EVs, encouraging efficient energy usage and reducing burden on the power grid, but also paves a way for future research in sustainable energy management.

Stackelberg game↗

Understanding the Conductivity and Transference Trade-Off in Polymer Electrolytes Using a Robeson-Inspired Upper Bound

The development of high-performance electrolytes is crucial for advancing next-generation lithium and sodium battery technologies. Since the cation is the working ion in both technologies, electrolytes exhibiting the rapid cation transport are essential for making progress. Pathways to optimize electrolytes are unclear due to the inherent trade-off between conductivity and cation transference. While this trade-off is sometimes recognized, there are no well-accepted methodologies for quantifying it. Inspired by the Robeson upper bound for the permeability–selectivity trade-off in gas separation membranes, we propose an approach for quantifying the trade-off in electrolytes using Newman’s concentrated solution theory. We suggest calling this the Newman upper bound. By analyzing published data from 30 polymer electrolytes containing univalent lithium and sodium salts, the Newman upper bound is expressed as κ = 2.0­(1/ρ+ – 1) where κ (mS/cm) is conductivity and ρ+ is the current fraction measured in a symmetric cell as first described by Bruce et al. [J. Electroanal. Chem. Interfacial Electrochem. 1987, 225 (1), 1–17]. This formulation of the upper bound introduces a critical guiding metric for designing next-generation polymer electrolytes; it highlights factors underlying the trade-off, including the salt diffusion coefficient (D), cation transference number relative to solvent velocity ( t + 0 ), and thermodynamic factor (1 + (d lnγ+–)/(d lnm)), where γ+– is the mean molar activity coefficient and m is the molality. These parameters have been measured for very few electrolytes. We posit that establishing the molecular properties that govern these parameters will lead to improved electrolytes that greatly exceed the current upper bound.

He, Zirong↗

Environmental and socio-economic Pareto-front trade-off analysis of U.S. PET packaging material in a circular economy

Various recycling technologies are emerging to implement circular economy in plasticssupply chain systems. However, the environmental and socio-economic trade-offs of in circular economy are not well understood at a systems level. Particularly, quantifying these trade-offs as a function of end-of-life (EOL) management decisions, including transition of recycling technologies, systems level metrics such as circularity, recycled content, and the need for fossil-derived plastics are not well understood. Here, the present study addressed these research gaps by applying a systems analysis modeling approach that utilizes material flow analysis, life cycle assessment, socioeconomic data, and system optimization techniques for polyethylene terephthalate (PET) packaging supply chains in the United States. Pareto-front trade-offs between conflicting environmental and socio-economic impacts as well as those between socioeconomic impacts and circularity were explored using the epsilon constraint method. The Pareto-front trade-off analysis revealed the transition of EOL management strategies for PET packaging systems, including changes in selection of recycling technologies, to aid decision making process by quantifying studied system metrics. Transitioning from environmentally optimal to socio-economically optimal systems led to increased employment (by 17%), wages (by 26%), and revenues (by 6%) but also led to increased global warming potential (GWP; by 65%), energy consumption (by 59%), and reliance on fossil PET in the system (by 78%). Finally, the results show that there is not a unique set of recycling technologies to achieve a sustainable circular economy of PET packaging system, instead it depends on the decision maker’s objectives and targeted metrics of the system.

54 - ENVIRONMENTAL SCIENCES/GLOBAL CLIMATE CHANGE ↗

A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.

Bilevel multistage stochastic programming problem↗

Ecological trade-offs drive phenotypic and genetic differentiation of Arabidopsis thaliana in Europe

Plant diversity is shaped by trade-offs between traits related to competitive ability, propagule dispersal, and stress resistance. However, we still lack a clear understanding of how these trade-offs influence species distribution and population dynamics. In Arabidopsis thaliana , recent genetic analyses revealed a group of cosmopolitan genotypes that successfully recolonized Europe from its center after the last glaciation, excluding older (relict) lineages from the distribution except for their north and south margins. Here, we tested the hypothesis that cosmopolitans expanded due to higher colonization ability, while relicts persisted at the margins due to higher tolerance to competition and/or stress. We compared the phenotypic and genetic differentiation between 71 European genotypes originating from the center, and the south and north margins. We showed that a trade-off between plant fecundity and seed mass shapes the differentiation of A. thaliana in Europe, suggesting that the success of the cosmopolitan groups could be explained by their high dispersal ability. However, at both north and south margins, we found evidence of selection for alleles conferring low dispersal but highly competitive and stress-resistance abilities. This study sheds light on the role of ecological trade-offs as evolutionary drivers of the distribution and dynamics of plant populations.

59 BASIC BIOLOGICAL SCIENCES↗

Persistent trade-offs balance competition and colonization across centuries

When a microbe colonizes a host, it must both establish infection and outcompete other organisms. Short-term experiments show that gains in competitive ability can reduce colonization, creating trade-offs, but whether microbes resolve these conflicts over long evolutionary timescales is unknown. We show that a trade-off between competitive killing and host colonization has been stably maintained for centuries in natural Pseudomonas populations infecting Arabidopsis thaliana. Tailocins—phage-derived weapons—provide strong competitive advantages, yet their production reduces colonization success, explaining why the most broadly lethal variants remain rare. Genomic surveys and historical genomes spanning two centuries reveal that the polymorphisms underlying this trade-off have persisted across 10⁵-10⁶ generations. Understanding such long-lived constraints can inform antimicrobial strategies that exploit evolutionary trade-offs.

Backman, Talia↗

Improving I/O-aware Workflow Scheduling via Data Flow Characterization and trade-off Analysis

The scientific computing paradigm has transitioned from compute-intensive to I/O-intensive and memory-intensive in the past decade, especially when data-driven science has become common practice. Numerous empirical I/O-aware scheduling optimizations have been developed by incorporating I/O capacity and bandwidth as constraints into scheduling. Unfortunately, there is a lack of data flow (I/O) characterization tool and an understanding of trade-offs between concurrency, locality, and I/O bandwidth. To bridge the gap, this work 1) presents a set of descriptors to characterize, organize, and visualize I/O profiles, including flow size, I/O bandwidth, and operation count, which group data flows by I/O types, tasks, and files; 2) proposes an I/O Roofline model-based trade-off analysis to find the optimal trade-off between flow operational intensity, concurrency, and flow performance. The I/O descriptors generate useful insights into complicated I/O behaviors, suggesting distinct concurrency, storage, and scheduling to be used by types, tasks, and files. The proposed trade-off analysis guides scheduling decisions that generate resource assignment with the best flow parallelism. We evaluate our I/O-aware scheduling methodology on a highly I/O-intensive workflow–1000 Genomes. The experimental results demonstrate speedups of up to 2.4× compared to the state-of-the- art methods.

Guo, Luanzheng [BATTELLE (PACIFIC NW LAB)]↗

Quantitative Trade-Off in Distributed Secondary Control for Autonomous AC Microgrids

In this paper, we propose to quantify the trade-off between voltage regulation and reactive power sharing in autonomous AC microgrids with distributed secondary control. It is known that voltage regulation and reactive power sharing in droop-controlled autonomous AC microgrids are two conflicting control objectives that present a natural trade-off between voltage regulation towards the voltage magnitude reference and reactive power sharing accuracy. This trade-off is commonly shown qualitatively without sufficient quantification. In this work, to quantify the trade-off between the two objectives, we focus on distributed secondary control and utilize regression and polynomial surface fitting to identify the requisite parameter area to satisfy the predefined error bands for voltage magnitude regulation and reactive power sharing. Extensive case studies are presented to validate the proposed method.

autonomous AC microgrids↗

Trade-offs among restored ecosystem functions are context-dependent in Mediterranean-type regions

Global biodiversity hotspots, including Mediterranean-type ecosystems worldwide, are highly threatened by global change that alters biodiversity, ecosystem functions, and services. Some restoration activities enhance ecosystem functions by reintroducing plant species based on known relationships between plant traits and ecosystem processes. Achieving multiple functions across different site conditions, however, requires understanding how abiotic factors like climate and soil, along with plant assemblages, influence ecosystem functions, including their trade-offs and synergies. We used the ModEST ecosystem simulation model, which integrates carbon, water, and nutrient processes with plant traits, to assess the relationships between restored plant assemblages and ecosystem functions in Mediterranean-type climates and soils. We investigated whether maximised carbon increment, water use efficiency, and nitrogen use efficiency, along with their trade-offs and synergies, varied across different abiotic contexts. Further, we asked whether assemblages that maximised functions varied across environments and among these functions. We found that maximised ecosystem carbon increment and nitrogen use efficiency occurred under moist, warm conditions, while water use efficiency peaked under drier conditions. Generally, the assemblage that maximised one function differed from those for other maximised functions. Synergies were rare, except between water and nitrogen use efficiencies in loam soils across most climates. Trade-offs among maximised functions were common, varying in strength with abiotic context and plant assemblages, and were more pronounced in sandy loam soils compared to clay-rich soils. Our findings suggest that due to variation in abiotic conditions within and across Mediterranean-type regions at the global scale, site-specific plant assemblages are required to maximise ecosystem functions. Thus, lessons from a single site cannot be transferred to another site, even where the same plant functional types are available for restoration. Our simulation results offer valuable insights into potential ecosystem performance under specific abiotic conditions following restoration with particular plant functional types, thereby informing local restoration efforts.

54 ENVIRONMENTAL SCIENCES↗

Soil moisture-atmosphere interactions drive terrestrial carbon-water trade-offs

Soil moisture is coupled with vegetation and atmosphere, influencing global cycling of water, carbon, and energy. However, it remains unclear how soil moisture-atmosphere interactions affect land-atmosphere carbon and water exchanges simultaneously. Using Earth system model experiments, we show widespread carbon-water trade-offs between net ecosystem production and precipitation-minus-evapotranspiration driven by soil moisture dynamics. Soil moisture positively controls net ecosystem production and negatively affects precipitation-minus-evapotranspiration, through direct soil water stress and indirect soil moisture-atmosphere feedbacks. While soil moisture variability magnifies the interannual variability of net ecosystem production, it moderates that of precipitation-minus-evapotranspiration over land. These opposing effects lead to a pronounced carbon-water trade-off, which originates from the interplay between carbon acquisition through photosynthesis and water extraction through evapotranspiration. This trade-off is projected to intensify in a warming and drying future, as soil moisture increasingly regulates carbon and water exchanges, posing a serious challenge to sustaining both terrestrial carbon sink and water supply.

54 ENVIRONMENTAL SCIENCES↗

Allometric relationships and trade‐offs in 11 common M editerranean‐climate grasses

Abstract Biomass allocation in plants is the foundation for understanding dynamics in ecosystem carbon balance, species competition, and plant–environment interactions. However, existing work on plant allometry has mainly focused on trees, with fewer studies having developed allometric equations for grasses. Grasses with different life histories can vary in their carbon investment by prioritizing the growth of specific organs to survive, outcompete co‐occurring plants, and ensure population persistence. Further, because grasses are important fuels for wildfire, the lack of grass allocation data adds uncertainty to process‐based models that relate plant physiology to wildfire dynamics. To fill this gap, we conducted a greenhouse experiment with 11 common California grasses varying in photosynthetic pathway and growth form. We measured plant sizes and harvested above‐ and belowground biomass throughout the life cycle of annual species, while for the establishment stage of perennial grasses to quantify allometric relationships for leaf, stem, and root biomass, as well as plant height and canopy area. We used basal diameter as a reference measure of plant size. Overall, basal diameter is the best predictor for leaf and stem biomass, height, and canopy area. Including height as another predictor can improve model accuracy in predicting leaf and stem biomass and canopy area. Fine root biomass is a function of leaf biomass alone. Species vary in their allometric relationships, with most variation occurring for plant height, canopy area, and stem biomass. We further explored potential trade‐offs in biomass allocation across species between leaf and fine root, leaf and stem, and allocation to reproduction. Consistent with our expectation, we found that fast‐growing plants allocated a greater fraction to reproduction. Additionally, plant height and specific leaf area negatively influenced the leaf‐to‐stem ratio. However, contrary to our hypothesis, there were no differences in root‐to‐leaf ratio between perennial and annual or C 4 and C 3 plants. Our study provides species‐specific and functional‐type‐specific allometry equations for both above‐ and belowground organs of 11 common California grass species, enabling nondestructive biomass assessment in California grasslands. These allometric relationships and trade‐offs in carbon allocation across species can improve ecosystem model predictions of grassland species interactions and environmental responses through differences in morphology.

54 ENVIRONMENTAL SCIENCES↗

Design trade-offs for residential retail tariffs and virtual power plants

Retail rate design and virtual power plants (VPPs) have the potential to shift customer electricity demand and provide economic benefits to utility customers. As the adoption of distributed energy resources (DERs) and flexible loads increases, retail tariff and program design can impact Bonbright's rate design principles including affordability, fairness, and economic efficiency. We model the effects of residential retail rates and VPP programs on power system costs in Massachusetts under a potential future system with high renewable energy and DER adoption. We model interactions among retail rate design, demand flexibility, and utility costs and identify trade-offs across different rate designs and VPP programs. We estimate that time-of-use (TOU) rates and VPP programs designed to avoid critical peak rates can lower overall system costs by 3.5 %-4.8 %. These lower costs translate to lower electricity bills for 62 %-91 % of customers, depending on the scenario. Although TOU rates with a critical peak VPP program can benefit all customer segments and are economically efficient, a VPP program with flat rates leads to the lowest overall bills for customers. We find that customers with loads that align with peak demand and who participate in critical peak VPP programs can underpay for their contribution to utility costs and shift costs to other customers. While our assumptions about mandatory TOU and/or critical peak pricing likely impact the magnitude of the results, the results highlight the trade-offs of these tariffs and programs and the importance of tariff and program design as demand becomes more flexible and responsive.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Microphysics Dominates Sub‐Cloud Rain Evaporation in Trade Cumuli Over Barbados

This study investigates the microphysical and thermodynamic influences on North Atlantic trade-cumulus rain evaporation in the sub-cloud layer over Barbados from January to November 2020. Using radar observations and a 1-D model, the results reveal that microphysical properties, namely geometric mean diameter (D g ) and raindrop concentration, primarily control evaporation processes under conditions of limited thermodynamic variability. Thermodynamic factors like cloud base height and relative humidity exert a smaller influence due to their narrow observed ranges. Small D g leads to rapid increases in rain evaporation fraction (REF), as small drops evaporate completely, while larger D g yields slower, more gradual REF changes. Frequent weak-rain cases reduce the mean evaporation flux, whereas infrequent intense-rain events substantially enhance it. These findings highlight the pivotal role of microphysical variability in shaping sub-cloud evaporation in this trade cumulus regime, while thermodynamic effects may be more important in other environments.

54 ENVIRONMENTAL SCIENCES↗

Application-specific machine-learned interatomic potentials: exploring the trade-off between DFT convergence, MLIP expressivity, and computational cost

Machine-learned interatomic potentials (MLIPs) are revolutionizing computational materials science and chemistry by offering an efficient alternative to ab initio molecular dynamics (MD) simulations. However, fitting high-quality MLIPs remains a challenging, time-consuming, and computationally intensive task where numerous trade-offs have to be considered, e.g., How much and what kind of atomic configurations should be included in the training set? Which level of ab initio convergence should be used to generate the training set? Which loss function should be used for fitting the MLIP? Which machine learning architecture should be used to train the MLIP? The answers to these questions significantly impact both the computational cost of MLIP training and the accuracy and computational cost of subsequent MLIP MD simulations. In this study, we use a configurationally diverse beryllium dataset and quadratic spectral neighbor analysis potential. We demonstrate that joint optimization of energy versus force weights, training set selection strategies, and convergence settings of the ab initio reference simulations, as well as model complexity can lead to a significant reduction in the overall computational cost associated with training and evaluating MLIPs. This opens the door to computationally efficient generation of high-quality MLIPs for a range of applications which demand different accuracy versus training and evaluation cost trade-offs.

36 MATERIALS SCIENCE↗

Understanding Reliability Trade-Offs in 1T-nC and 2T-nC FeRAM Designs

Ferroelectric random access memory (FeRAM) is a promising candidate for energy-efficient nonvolatile memory, particularly for logic-in-memory and compute-in-memory (CIM) applications. Among the available cell architectures, One-Transistor–n-Capacitor (1T-nC) and two-transistor–n-capacitor (2T-nC) FeRAMs each offer distinct trade-offs in density, scalability, and reliability. In this work, we present a comparative study of these two architectures under both dimensional scaling ( XY/Z shrinkage) and vertical integration (increasing stacked capacitors per cell). Using technology computer-aided design (TCAD) and circuit-level simulations, we analyze how scaling impacts ferroelectric capacitance, parasitic coupling, and floating-node (FN) dynamics, which together dictate sense margin (SM) and read stability. A key mitigation strategy—floating unselected capacitors—is applied to both architectures, effectively decoupling the SM from the number of stacked capacitors and enabling tractable analysis across scaling regimes. Results show that 1T-nC suffers more from charge sharing with the bitline (BL), while 2T-nC benefits from transistor isolation and stronger low-voltage sensing at the cost of increased area. By systematically evaluating these behaviors across scaling directions, this work establishes the reliability trade-offs of 1T-nC and 2T-nC cells and provides design guidelines for high-density, vertically integrated FeRAM systems.

1T-nC↗