Segments - by Component (Software, Hardware, Services), by Application (Semiconductor Design, FPGA Design, ASIC Design, SoC Design, Others), by Deployment Mode (On-Premises, Cloud), by End-User (Semiconductor Companies, Foundries, EDA Vendors, Research Institutes, Others)
This report is updated with the latest market data and insights as of June 2026. Base year: 2025 | Forecast period: 2026-2034
According to our latest research, the global ML-Driven Place & Route Tool market size is valued at USD 2.14 billion in 2025, with a robust CAGR of 15.7% anticipated through the forecast period. By 2034, the market is expected to reach USD 7.89 billion, reflecting the rapid adoption of artificial intelligence and machine learning technologies in electronic design automation (EDA). The primary growth factor fueling this surge is the increasing complexity of integrated circuits (ICs) and the urgent demand for more efficient, intelligent automation in semiconductor design workflows. As chipmakers push deeper into sub-3 nm process nodes and embrace heterogeneous integration, the limitations of conventional place and route methodologies are becoming acutely apparent, making ML-driven alternatives not just advantageous but essential.
The rapid evolution of semiconductor technologies, particularly in advanced-node fabrication and 3D-IC packaging, is a significant driver for the ML-Driven Place & Route Tool market. As chip designs grow more intricate, traditional place and route tools struggle to optimize performance, power, and area (PPA) within feasible timeframes. Machine learning-driven solutions are uniquely positioned to address these challenges by leveraging data-driven optimization techniques, enabling faster convergence and improved design outcomes. This shift is also propelled by the growing need for design teams to manage escalating design rule checks (DRC) and layout-versus-schematic (LVS) complexities, which ML algorithms can streamline with far greater efficiency than manual or rule-based approaches. Vendors exploring AI-driven EDA solutions are finding that ML-based routing and placement represent one of the highest-impact areas for automation investment.
Another crucial growth factor is the intensifying competition within the semiconductor industry, which compels companies to accelerate time-to-market while minimizing costs. ML-driven place and route tools are increasingly integrated into the design flow to automate repetitive tasks, predict bottlenecks, and optimize resource allocation. These tools not only reduce manual intervention but also enhance the predictability and reproducibility of design results, thereby lowering the risk of costly design iterations. The proliferation of AI-driven consumer electronics, IoT devices, and automotive electronics further amplifies demand for advanced EDA tools that can handle high-volume, high-complexity designs with minimal errors. The convergence of generative AI with EDA in 2025 is opening new possibilities for fully automated design space exploration, pushing the boundaries of what ML-driven automation can achieve.
Furthermore, the rise of cloud-based place and route solutions and the democratization of AI technologies are expanding the addressable market significantly. Cloud deployment enables scalable compute resources and collaborative workflows, making it easier for startups, research institutes, and smaller semiconductor companies to access state-of-the-art design tools without significant upfront investments. This trend is particularly pronounced in emerging markets, where cloud adoption is accelerating digital transformation. Additionally, partnerships between EDA vendors and hyperscale cloud providers are fostering innovation and broadening the global reach of ML-driven EDA solutions. The concurrent maturation of photonic integrated circuits is also creating demand for specialized tools, as reflected in the growing interest in AI-driven place and route solutions for photonic design.
In the realm of electronic design automation, the concept of Design Rule Checking Acceleration AI is gaining traction as a pivotal innovation. As integrated circuits become more complex, traditional methods of design rule checking are often inadequate to keep pace with rapid design cycles. AI-driven acceleration in DRC processes is transforming how design teams approach verification challenges, offering significant reductions in time and resource expenditure. By leveraging machine learning algorithms, these systems can predict potential rule violations early in the design process, allowing for proactive adjustments and minimizing costly iterations. This not only enhances the efficiency of semiconductor workflows but also ensures higher compliance with stringent design standards, ultimately leading to more reliable and robust chip designs.
Regionally, Asia Pacific dominates the ML-Driven Place & Route Tool market, driven by the concentration of semiconductor manufacturing hubs in China, Taiwan, South Korea, and Japan. North America follows closely, benefiting from its leadership in EDA software development and a vibrant ecosystem of fabless semiconductor companies. Europe is witnessing steady growth, particularly in automotive and industrial applications, while Latin America and the Middle East & Africa are gradually embracing advanced EDA tools as part of their broader digital infrastructure development. The interplay of local semiconductor policies, government investments, and global supply chain realignment will continue to shape regional dynamics over the 2026-2034 forecast period.
The ML-Driven Place & Route Tool market is segmented by component into software, hardware, and services, each playing a distinct role in the overall ecosystem. The software segment holds the largest share at approximately 58.5% of 2025 revenue, underpinned by the continuous evolution of machine learning algorithms and their deep integration into EDA platforms. ML-driven software solutions are at the forefront of automating design tasks, optimizing layout, and reducing cycle times, which are critical for meeting aggressive market timelines. Vendors are investing heavily in R&D to enhance the accuracy and efficiency of these tools, embedding features such as reinforcement learning, graph neural networks, and predictive analytics to further differentiate their offerings. The software segment is expected to maintain its dominance through 2034, driven by recurring subscription and license revenues and the industry-wide shift toward AI-powered design automation.
The hardware segment, representing roughly 21% of the 2025 market, is gaining traction as specialized accelerators and high-performance computing infrastructure become essential for training and deploying complex ML models. Advanced place and route algorithms require significant computational resources, especially when handling large-scale designs and extensive design rule sets at sub-5 nm nodes. Hardware innovations, including the use of NVIDIA GPUs, AMD FPGAs, and custom AI inference chips, are enabling faster processing and real-time feedback during the design process. Leading EDA vendors are collaborating with hardware manufacturers to optimize tool performance, ensuring seamless integration and scalability for enterprise customers. The growing availability of purpose-built AI hardware platforms is expected to further accelerate adoption across the forecast period. Complementary developments in RFIC layout automation hardware and software are also contributing to broader hardware ecosystem growth within EDA.
The services segment, at approximately 20.5% of 2025 market value, is emerging as a key growth area, reflecting the need for technical support, customization, and training as organizations adopt ML-driven EDA workflows. Consulting services are in high demand, particularly among companies transitioning from traditional to AI-powered design methodologies. Service providers are offering tailored solutions, including workflow integration, design data management, and model fine-tuning, to maximize the value of ML-driven place and route tools. As the technology matures, managed services and design-as-a-service models are gaining prominence, enabling companies to outsource complex design tasks and focus on core innovation activities.
The interplay between these components is fostering a vibrant ecosystem, with software providers increasingly partnering with hardware vendors and service integrators to deliver end-to-end solutions. This collaborative approach is essential for addressing the diverse needs of semiconductor companies, foundries, and research institutes, each of which requires a unique blend of software, hardware, and services. As the market evolves through 2034, interoperability, scalability, and ease of integration will be key differentiators, shaping vendor strategies and influencing customer adoption patterns.
| Attributes | Details |
| Report Title | ML-Driven Place & Route Tool Market Research Report 2034 |
| By Component | Software, Hardware, Services |
| By Application | Semiconductor Design, FPGA Design, ASIC Design, SoC Design, Others |
| By Deployment Mode | On-Premises, Cloud |
| By End-User | Semiconductor Companies, Foundries, EDA Vendors, Research Institutes, Others |
| Regions Covered | North America, Europe, APAC, Latin America, MEA |
| Base Year | 2025 |
| Historic Data | 2019-2024 |
| Forecast Period | 2026-2034 |
| Number of Pages | 298 |
| Number of Tables & Figures | 316 |
| Customization Available | Yes, the report can be customized as per your need. |
The ML-Driven Place & Route Tool market spans a wide range of applications, including semiconductor design, FPGA design, ASIC design, SoC design, and others. Semiconductor design remains the largest application segment in 2025, driven by the relentless push toward smaller process nodes and higher transistor densities at leading foundries. ML-driven tools are instrumental in optimizing floorplanning, routing, and timing closure, enabling designers to meet stringent performance and power targets. The complexity of modern semiconductor devices, such as 5G modems, AI accelerators, and high-bandwidth memory controllers, necessitates advanced automation and intelligent optimization that ML-based tools are uniquely equipped to provide. The parallel expansion of AI-based pattern matching in DRC verification is further complementing ML-driven routing by catching layout errors earlier in the design flow.
In FPGA design, ML-driven place and route tools are revolutionizing the prototyping and deployment of custom logic circuits. FPGAs are widely used in applications requiring rapid iteration and flexibility, including telecommunications infrastructure, adaptive automotive systems, and aerospace electronics. ML algorithms can significantly reduce the time required for placement and routing, enabling faster turnaround and more efficient resource utilization. This is particularly valuable in industries where time-to-market is critical and design cycles are increasingly compressed. The integration of ML-driven EDA tools with modern FPGA development environments is expected to accelerate adoption throughout the forecast period.
ASIC design is another major application area, characterized by high-volume production and stringent quality requirements. ML-driven place and route tools are enhancing the predictability and reliability of ASIC design flows, reducing the risk of costly respins and improving overall yield. These tools leverage historical design data and real-time feedback to optimize layout, minimize routing congestion, and ensure compliance with foundry-specific design rules at advanced nodes. As ASICs become more prevalent in autonomous vehicles, edge AI inference chips, and satellite communications, the demand for intelligent automated design tools will continue to accelerate through 2034.
SoC design presents unique challenges due to the integration of multiple functional blocks, IP cores, and heterogeneous interfaces on a single die. ML-driven place and route tools are addressing these challenges by enabling hierarchical design methodologies, optimizing interconnects, and managing complex power domains more effectively. The ability to predict and mitigate design bottlenecks early in the process is a significant advantage, reducing development time and enhancing overall system performance. Other applications, such as photonic integrated circuits and mixed-signal analog design, are also beginning to benefit from ML-driven automation, further expanding the addressable market.
The ML-Driven Place & Route Tool market is segmented by deployment mode into on-premises and cloud solutions, each offering distinct advantages. On-premises deployment remains the preferred choice for large semiconductor companies and foundries with stringent data security and IP protection requirements. These organizations often maintain dedicated EDA infrastructure to ensure compliance with internal policies and regulatory standards. On-premises solutions offer greater control over hardware resources and tighter integration with existing design environments, making them ideal for mission-critical projects involving sensitive intellectual property.
However, the cloud deployment segment is experiencing rapid growth, driven by the need for scalability, flexibility, and cost efficiency. Cloud-based EDA tools enable organizations to access high-performance computing resources on demand, eliminating the need for significant upfront investments in hardware and infrastructure. This is particularly attractive to startups, research institutes, and small-to-medium enterprises seeking to leverage advanced ML-driven design tools without incurring prohibitive costs. Cloud deployment also facilitates collaboration among geographically dispersed design teams, streamlining workflows and accelerating project timelines in an era of distributed engineering.
The transition to cloud-based EDA is further supported by the increasing availability of secure, industry-compliant cloud platforms specifically tailored for semiconductor design. Major cloud providers are partnering with EDA vendors to offer integrated solutions, including pre-configured design environments, automated elastic scaling, and robust data protection features. This collaboration is lowering barriers to entry and enabling a broader range of organizations to adopt ML-driven place and route tools. As cloud adoption accelerates through 2034, hybrid deployment models are also emerging, allowing companies to balance the benefits of both on-premises control and cloud scalability.
Despite the advantages of cloud deployment, challenges remain around data privacy, design latency, and integration with legacy EDA systems. Vendors are addressing these concerns through customizable deployment architectures, enhanced end-to-end encryption, and seamless interoperability interfaces with established EDA flows. Over the 2026-2034 forecast period, the cloud segment is expected to outpace on-premises deployment in terms of growth rate, driven by ongoing digital transformation initiatives and the increasing compute demands of sub-3 nm design programs.
The ML-Driven Place & Route Tool market serves a diverse array of end-users, including semiconductor companies, foundries, EDA vendors, research institutes, and others. Semiconductor companies constitute the largest end-user segment in 2025, as they are at the forefront of adopting advanced EDA tools to maintain competitiveness and accelerate product development cycles. These organizations rely heavily on ML-driven automation to manage growing chip design complexity, optimize resource allocation, and reduce time-to-market. The ability to leverage large volumes of historical design data and predictive analytics is particularly valuable in driving continuous improvement and achieving first-pass silicon success.
Foundries play a critical role in the ecosystem, providing manufacturing services to fabless semiconductor companies and integrated device manufacturers. ML-driven place and route tools are increasingly being adopted by foundries to ensure manufacturability, optimize yield, and streamline the handoff between design and fabrication. The integration of ML algorithms into foundry-specific design flows enables more accurate rule checking, faster design closure, and improved collaboration with fabless design partners. As foundries expand service offerings to support advanced process nodes at 2 nm and below, along with heterogeneous packaging services, the demand for intelligent EDA tools will continue to rise.
EDA vendors are simultaneously developers and users of ML-driven place and route tools, investing heavily in R&D to develop cutting-edge solutions and maintain technological leadership. These companies are at the forefront of integrating machine learning into traditional EDA workflows, offering differentiated products that cater to the evolving needs of semiconductor designers. By collaborating with hardware manufacturers, cloud providers, and academic researchers, EDA vendors are driving innovation and expanding the capabilities of ML-driven automation. The competitive landscape is characterized by rapid product development cycles, strategic acquisitions, and a relentless focus on customer-centric design outcomes.
Research institutes and academic organizations represent a growing end-user segment in 2025, leveraging ML-driven place and route tools for exploratory research, algorithm development, and prototyping. These institutions play a pivotal role in advancing the state of the art, validating emerging techniques, and nurturing the next generation of EDA engineers. The availability of cloud-based EDA platforms and open-source design frameworks is enabling broader access to advanced design tools, fostering global collaboration. Other end-users, including system integrators and IP vendors, are also increasingly adopting ML-driven automation to enhance their design and verification workflows as chip complexity grows.
One of the most significant opportunities in the ML-Driven Place & Route Tool market lies in the integration of advanced deep learning and generative AI techniques to further improve design automation and optimization. As semiconductor architectures become increasingly complex, the ability to leverage large volumes of design data and extract actionable insights is invaluable. Vendors that successfully embed graph neural networks, large language model-assisted design assistance, and transfer learning into their EDA tools can deliver superior performance, faster convergence, and greater design flexibility. Additionally, the rise of chiplets, 3D-IC integration, and heterogeneous packaging presents new challenges and opportunities for ML-driven automation, enabling vendors to develop specialized solutions tailored to these emerging design paradigms. The growing ecosystem around open-source EDA frameworks is also fostering community-driven innovation that commercial vendors can leverage.
Another key opportunity is the continued expansion of cloud-based EDA offerings, which can democratize access to advanced design tools and foster innovation across the semiconductor value chain. By leveraging scalable cloud infrastructure, vendors can offer flexible subscription pricing, on-demand compute, and collaborative design environments that cater to customers ranging from well-funded startups to global fabless giants. The integration of ML-driven place and route tools with other AI-powered EDA solutions, including verification, testing, and sign-off, can create end-to-end automated design flows, further enhancing productivity. Strategic partnerships with cloud providers, specialized hardware manufacturers, and academic institutions can accelerate innovation and expand market reach through 2034.
Despite these opportunities, the market faces several restraining factors. The complexity of integrating ML-driven tools into established design workflows remains a significant barrier, as many organizations have deep investments in legacy EDA infrastructure and may be hesitant to adopt new technologies that require process changes or retraining of design teams. Data privacy and security concerns, particularly in cloud-based deployments, also pose challenges, as semiconductor companies are highly protective of their intellectual property. Additionally, the rapid pace of technological change can lead to tool fragmentation and interoperability issues, making it difficult for end-users to evaluate and select the most suitable solutions. A global shortage of engineers with combined expertise in ML and semiconductor physical design is also constraining adoption rates, particularly among mid-sized companies and organizations in emerging markets.
The Asia Pacific region is the undisputed leader in the ML-Driven Place & Route Tool market, accounting for approximately USD 856 million in 2025, or nearly 40% of the global market share. This dominance is driven by the concentration of semiconductor manufacturing powerhouses in China, Taiwan, South Korea, and Japan, which collectively account for the majority of global chip production capacity. Aggressive investments in advanced-node fabrication, government initiatives to bolster local semiconductor ecosystems, and the rapid adoption of AI-powered design automation are key factors fueling market growth in the region. The Asia Pacific market is expected to maintain a strong CAGR of 16.4% through 2034, outpacing other regions due to ongoing capacity expansions, technology upgrades, and government-backed semiconductor self-sufficiency programs.
North America follows as the second-largest market, with a 2025 valuation of approximately USD 556 million. The region's strength lies in its leadership in EDA software development, a vibrant ecosystem of fabless semiconductor companies, and strong collaboration between academia, industry, and government agencies. The United States is home to several leading EDA vendors and innovative startups that are driving adoption of ML-driven place and route tools. The market is further buoyed by the presence of major cloud service providers, a robust venture capital ecosystem, and the CHIPS and Science Act, which is stimulating domestic semiconductor investment. North America's market is projected to grow at a CAGR of 14.9% through 2034, fueled by advancements in AI chip design, 5G infrastructure, and high-performance computing.
Europe, Latin America, and the Middle East & Africa collectively account for the remaining market share, with Europe leading among these regions at approximately USD 385 million in 2025. The European market is characterized by strong demand from automotive, industrial automation, and IoT sectors, where the integration of AI and ML into chip design is increasingly critical. Government funding for semiconductor R&D through initiatives such as the European Chips Act and the presence of leading automotive OEMs are key growth drivers. Latin America and the Middle East & Africa together represent around USD 343 million in 2025. These regions are gradually embracing advanced EDA tools as part of broader digital transformation initiatives, with cloud adoption playing a pivotal role in lowering entry barriers and accelerating technology transfer to local design communities.
The competitive landscape of the ML-Driven Place & Route Tool market in 2025 is characterized by intense innovation, strategic partnerships, and a relentless focus on differentiation through advanced machine learning capabilities. Leading EDA vendors are investing heavily in R&D to incorporate state-of-the-art ML algorithms into their toolchains, enhancing automation, accuracy, and scalability across the full design flow. The market includes a mix of established players with comprehensive EDA suites and a growing number of specialized startups. These companies compete not only on performance and features but also on cloud integration, hardware accelerator support, and the quality of customer success services. The pace of technological advancement is rapid, with frequent product updates aimed at addressing the evolving needs of semiconductor designers working at advanced nodes.
Strategic collaborations and partnerships are a hallmark of the market, as vendors seek to leverage complementary strengths and accelerate innovation cycles. EDA companies are partnering with major cloud service providers to offer integrated, elastically scalable solutions. Hardware manufacturers are working closely with EDA vendors to optimize tool performance on specialized accelerators including NVIDIA GPUs and AMD FPGAs. These partnerships are fostering a vibrant ecosystem that supports end-to-end automation and seamless design workflow integration. The broader trend toward AI-powered physical design is also spurring investment in adjacent areas such as AI-powered PCB layout, with tools like those covered in the AI automatic PCB placement software and hardware market increasingly sharing underlying ML infrastructure with IC place and route platforms.
The market is also witnessing increased consolidation, with larger EDA vendors acquiring startups and niche players to expand ML capabilities and broaden product portfolios. This trend is driven by the need to stay ahead of competition, address emerging design challenges at 2 nm and below, and offer comprehensive solutions spanning the entire semiconductor design lifecycle. The competitive landscape is further shaped by the entry of cloud hyperscalers and AI hardware vendors who bring substantial compute assets and ML research expertise to the EDA domain.
Major companies in the ML-Driven Place & Route Tool market include Synopsys, Cadence Design Systems, Siemens EDA (Mentor Graphics), Ansys, and Empyrean Technology. Synopsys and Cadence are widely recognized as industry leaders, offering comprehensive EDA suites with advanced ML-driven automation embedded throughout the physical design flow. Siemens EDA is known for its strong presence in the European and automotive markets and its focus on integrating AI into traditional design verification and place and route flows. Ansys is leveraging its expertise in simulation and sign-off to enhance ML-driven physical design capabilities, while Empyrean Technology is gaining significant traction in the Asia Pacific region with localized solutions tailored to regional foundry requirements. These companies are continually expanding their product offerings, forging strategic alliances, and investing in next-generation AI to maintain competitive advantage.
In addition to these established players, a number of innovative firms are making significant contributions to the market. Movellus is pioneering ML-based timing closure and clock architecture automation, while Pulsic focuses on AI-driven analog and custom digital layout. Plunify is providing cloud-based FPGA optimization services that leverage ML to improve compilation and placement results. Arteris IP and Celus are applying ML to network-on-chip design and electronics design automation respectively, reflecting the broadening scope of AI-driven physical design. As demand for intelligent automated design tools continues to grow through 2034, the competitive landscape is expected to intensify further, with ongoing innovation and strategic consolidation driving the next wave of growth in the ML-Driven Place & Route Tool market.
The ML-Driven Place & Route Tool market has been segmented on the basis of
Yes. The report can be customized to meet specific research requirements. Customization options include additional country-level or sub-regional breakdowns, deeper competitive profiling of selected vendors, custom segmentation by process node or design complexity tier, technology benchmarking, and expanded end-user analysis. Please contact our research team with your specific requirements to receive a tailored proposal.
Leading companies include Synopsys, Cadence Design Systems, Siemens EDA, Ansys, NVIDIA, Intel, AMD (Xilinx), Samsung Electronics, Amazon Web Services, Achronix Semiconductor, Flex Logix Technologies, Tenstorrent, Empyrean Technology, Movellus, Pulsic, Plunify, Arteris IP, and Celus. Synopsys and Cadence are the dominant EDA incumbents, while NVIDIA and AMD provide critical hardware acceleration. Empyrean Technology is a key player in the Asia Pacific region, and specialized startups such as Movellus and Pulsic are driving niche ML innovations in timing closure and physical design.
Major opportunities include the integration of deep learning and generative AI to automate hierarchical design tasks, the democratization of advanced EDA through cloud platforms, and the emergence of chiplet and 3D-IC packaging as new design paradigms requiring specialized ML-driven routing solutions. Key challenges include the difficulty of integrating ML tools into legacy EDA workflows, IP security concerns in cloud deployments, a global shortage of engineers skilled in both ML and semiconductor design, and the rapid pace of change that can create tool fragmentation and interoperability issues.
The main end-users are semiconductor companies (the largest segment), foundries, EDA vendors, research institutes, and others including system integrators and IP vendors. Semiconductor companies rely on ML-driven automation to manage growing chip complexity and shorten time-to-market. Foundries use these tools to optimize yield and ensure design-for-manufacturability. EDA vendors are simultaneously developers and users of the technology, embedding ML into their core toolchains, while research institutes drive algorithmic innovation and prototyping.
Tools are deployed either on-premises or via the cloud. On-premises deployment remains preferred by large semiconductor companies and foundries that require strict IP protection and regulatory compliance. Cloud deployment is the faster-growing mode, enabling scalable compute on demand and lowering the barrier for startups, research institutes, and SMEs. Hybrid models are also emerging, letting organizations keep sensitive IP on-premises while offloading compute-intensive ML training workloads to cloud infrastructure.
The primary applications are semiconductor design, ASIC design, SoC design, FPGA design, and other emerging domains such as photonic and mixed-signal layout. Semiconductor design holds the largest share, driven by advanced-node programs at 3 nm and below. SoC and ASIC design are the fastest-growing sub-segments, reflecting demand from AI accelerator, automotive, and edge computing chip programs. FPGA design adoption is also accelerating as ML reduces routing turnaround time significantly.
The market is segmented into three components: software, hardware, and services. Software is the largest segment at roughly 58.5% of the 2025 market, encompassing ML-powered layout optimization, timing closure, and reinforcement-learning-based routing engines. Hardware accounts for approximately 21%, covering GPU, FPGA, and custom AI accelerator infrastructure used to train and run ML models. Services represent around 20.5%, including integration consulting, workflow customization, managed design services, and ongoing technical support.
Asia Pacific leads the market, commanding roughly 40% of global revenue in 2025 (approximately USD 856 million), driven by semiconductor manufacturing hubs in Taiwan, South Korea, China, and Japan. North America is the second-largest region at around USD 556 million in 2025, supported by dominant EDA software vendors and a vibrant fabless semiconductor ecosystem. Europe ranks third, with strong demand from automotive and industrial chip design segments.
Key growth drivers include the escalating complexity of advanced-node semiconductor designs, the urgent need to compress design cycle times, and the widespread integration of reinforcement learning and deep learning into EDA workflows. The surge in AI accelerator, 5G, and automotive chip programs is compelling design teams to adopt intelligent place and route automation to meet stringent performance, power, and area targets while controlling costs.
The global ML-Driven Place & Route Tool market is valued at USD 2.14 billion in 2025 and is projected to reach USD 7.89 billion by 2034, expanding at a robust CAGR of 15.7% over the 2026-2034 forecast period. This growth is fueled by rising integrated circuit complexity, accelerating AI adoption in electronic design automation, and the rapid expansion of cloud-based EDA platforms across all major regions.