Key Insights
The mobile phone semiconductor industry is experiencing robust growth, driven by increasing demand for advanced smartphones featuring enhanced functionalities like 5G connectivity, high-resolution cameras, and artificial intelligence capabilities. The market, valued at approximately $XX million in 2025 (assuming a logical extrapolation from available data), is projected to maintain a Compound Annual Growth Rate (CAGR) of 7.49% from 2025 to 2033. This growth is fueled by several key trends, including the proliferation of smartphones globally, especially in developing economies, the ongoing development of more energy-efficient and powerful processors, and the increasing integration of advanced semiconductor components into mobile devices. Key segments like mobile processors and memory chips are expected to dominate the market share, contributing significantly to the overall growth. Competition is fierce among leading players such as Qualcomm, Samsung, MediaTek, and Intel, driving innovation and price competitiveness within the industry.
However, the industry faces challenges including supply chain disruptions, geopolitical uncertainties, and the potential for economic slowdowns that could impact consumer spending on mobile devices. While the demand for high-end smartphones remains strong, the mid-range and budget segments also play a crucial role in shaping overall market dynamics. Technological advancements, such as the adoption of advanced packaging technologies and the development of more efficient power management solutions, will continue to be critical in navigating these challenges and sustaining long-term growth. The continued integration of AI and IoT capabilities into mobile devices is likely to further boost demand for sophisticated semiconductors in the coming years. Regional variations exist, with the Asia Pacific region expected to maintain its leading position, followed by North America and Europe.
Mobile Phone Semiconductor Industry: A Comprehensive Market Report (2019-2033)
This insightful report provides a comprehensive analysis of the mobile phone semiconductor industry, offering a detailed look at market trends, leading players, and future growth prospects. Covering the period from 2019 to 2033, with a base year of 2025 and a forecast period from 2025 to 2033, this report is an invaluable resource for stakeholders seeking to understand and capitalize on opportunities within this dynamic sector. The market size in 2025 is estimated at xx Million.

Mobile Phone Semiconductor Industry Market Composition & Trends
This section delves into the competitive landscape of the mobile phone semiconductor market, examining market concentration, innovation drivers, regulatory frameworks, substitute products, end-user profiles, and merger and acquisition (M&A) activities. The report analyzes market share distribution among key players, revealing the dominance of companies like Qualcomm, Samsung, and MediaTek.
- Market Concentration: Highly concentrated, with top 5 players holding approximately xx% of the market share in 2025.
- Innovation Catalysts: Advancements in 5G technology, AI integration in mobile devices, and increasing demand for high-performance mobile processors.
- Regulatory Landscape: Government policies promoting domestic semiconductor manufacturing and data privacy regulations are influencing market dynamics.
- Substitute Products: Limited direct substitutes, but alternative technologies such as improved battery technology can impact demand.
- End-User Profiles: Smartphone manufacturers, mobile network operators, and Original Equipment Manufacturers (OEMs) are the primary end-users.
- M&A Activities: Significant M&A activity has been observed in recent years, with total deal values exceeding xx Million in the period 2019-2024. Deals focused primarily on strengthening supply chains and expanding product portfolios.

Mobile Phone Semiconductor Industry Industry Evolution
This section provides a detailed analysis of the mobile phone semiconductor industry's evolution, examining market growth trajectories, technological advancements, and evolving consumer demands. The industry has witnessed robust growth fueled by the increasing adoption of smartphones globally. The report analyzes growth rates, adoption metrics, and technological breakthroughs driving the sector's expansion. From 2019 to 2024, the CAGR was approximately xx%, and the forecast suggests a CAGR of xx% from 2025 to 2033. Key technological advancements such as the transition to 5G, the integration of Artificial Intelligence (AI), and the development of more power-efficient chips are driving this growth. Consumer demand for improved processing power, longer battery life, and enhanced camera capabilities fuels innovation.
Leading Regions, Countries, or Segments in Mobile Phone Semiconductor Industry
This section identifies the dominant regions, countries, and segments within the mobile phone semiconductor industry. Asia, particularly East Asia, holds a commanding position, driven by strong manufacturing bases and high smartphone adoption rates.
Key Drivers for Asia's Dominance:
- Large manufacturing base: Significant concentration of semiconductor fabrication plants and assembly facilities.
- High smartphone penetration: A large and rapidly growing market for smartphones.
- Government support: Supportive policies and incentives for the semiconductor industry.
- Strong ecosystem: Presence of major players across the value chain.
Segment Analysis: The Mobile Processor segment accounts for the largest revenue share, driven by the constant demand for high-performance processing capabilities in advanced mobile devices.
Mobile Phone Semiconductor Industry Product Innovations
The mobile phone semiconductor industry is characterized by continuous product innovation. Recent advancements include the development of more energy-efficient processors, high-resolution image sensors, and improved memory chips. These innovations deliver enhanced performance, extended battery life, and improved user experiences. Companies are focusing on unique selling propositions like integrated AI capabilities and advanced security features to differentiate their products. Micron Technology's launch of its 1-beta DRAM, improving power efficiency by 15% and bit density by 35%, illustrates this trend.
Propelling Factors for Mobile Phone Semiconductor Industry Growth
Several factors are driving the growth of the mobile phone semiconductor industry. The proliferation of smartphones and other mobile devices globally is a significant driver. Technological advancements, particularly in 5G and AI, are fueling demand for more sophisticated and efficient chips. Furthermore, favorable government policies and investments in semiconductor manufacturing are supporting industry expansion.
Obstacles in the Mobile Phone Semiconductor Industry Market
Despite significant growth potential, the mobile phone semiconductor industry faces several challenges. Supply chain disruptions, geopolitical tensions, and intense competition are key obstacles. Regulatory changes impacting data privacy and trade relations also pose risks. The industry also faces fluctuating raw material prices, potentially impacting profitability and making production more expensive.
Future Opportunities in Mobile Phone Semiconductor Industry
The mobile phone semiconductor industry presents significant future opportunities. The expansion of 5G networks and the growing adoption of the Internet of Things (IoT) are expected to increase demand for advanced semiconductors. Furthermore, advancements in artificial intelligence (AI), augmented reality (AR), and virtual reality (VR) will create new application areas and drive further innovation. The development of more energy-efficient and sustainable semiconductor technologies will also offer promising avenues for growth.
Major Players in the Mobile Phone Semiconductor Industry Ecosystem
- NXP Semiconductors N V
- Samsung Electronics
- Micron Technology Inc
- Skyworks Solutions Inc
- Broadcom Inc
- Qorvo Inc
- Qualcomm Technologies Inc
- Huawei Technologies Co Ltd
- MediaTek Inc
- Intel Corporation
Key Developments in Mobile Phone Semiconductor Industry Industry
- November 2022: Micron Technology launched its 1-beta DRAM, aiming for a 15% improvement in power efficiency and a 35% increase in bit density.
- October 2022: Polymatech, a Japanese-technology-powered semiconductor chip manufacturer, began production of Opto-semiconductors and memory modules, backed by a USD 1 Billion investment.
Strategic Mobile Phone Semiconductor Industry Market Forecast
The mobile phone semiconductor market is poised for continued growth, driven by technological advancements and increasing demand. The forecast period (2025-2033) anticipates strong growth, particularly in segments like 5G-enabled chips and AI-powered processors. Emerging markets and innovative applications will further contribute to market expansion, creating significant opportunities for industry players. The overall market is expected to reach xx Million by 2033.
Mobile Phone Semiconductor Industry Segmentation
-
1. Component Type
- 1.1. Mobile Processors
- 1.2. Memory
- 1.3. Logic Chips
- 1.4. Analog
Mobile Phone Semiconductor Industry Segmentation By Geography
- 1. North America
- 2. Europe
- 3. Asia Pacific
- 4. Latin America
- 5. Middle East and Africa

Mobile Phone Semiconductor Industry REPORT HIGHLIGHTS
Aspects | Details |
---|---|
Study Period | 2019-2033 |
Base Year | 2024 |
Estimated Year | 2025 |
Forecast Period | 2025-2033 |
Historical Period | 2019-2024 |
Growth Rate | CAGR of 7.49% from 2019-2033 |
Segmentation |
|
Table of Contents
- 1. Introduction
- 1.1. Research Scope
- 1.2. Market Segmentation
- 1.3. Research Methodology
- 1.4. Definitions and Assumptions
- 2. Executive Summary
- 2.1. Introduction
- 3. Market Dynamics
- 3.1. Introduction
- 3.2. Market Drivers
- 3.2.1 Rapid Introduction of Next-generation Mobile-communications Standard
- 3.2.2 LTE or 4G; Emergence of 'Multicom' Solutions
- 3.3. Market Restrains
- 3.3.1. Complexity Regarding Manufacturing; Consumer Demand Exceeding Factory Capacity
- 3.4. Market Trends
- 3.4.1. Memory to Significantly Drive the Market
- 4. Market Factor Analysis
- 4.1. Porters Five Forces
- 4.2. Supply/Value Chain
- 4.3. PESTEL analysis
- 4.4. Market Entropy
- 4.5. Patent/Trademark Analysis
- 5. Global Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 5.1. Market Analysis, Insights and Forecast - by Component Type
- 5.1.1. Mobile Processors
- 5.1.2. Memory
- 5.1.3. Logic Chips
- 5.1.4. Analog
- 5.2. Market Analysis, Insights and Forecast - by Region
- 5.2.1. North America
- 5.2.2. Europe
- 5.2.3. Asia Pacific
- 5.2.4. Latin America
- 5.2.5. Middle East and Africa
- 5.1. Market Analysis, Insights and Forecast - by Component Type
- 6. North America Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 6.1. Market Analysis, Insights and Forecast - by Component Type
- 6.1.1. Mobile Processors
- 6.1.2. Memory
- 6.1.3. Logic Chips
- 6.1.4. Analog
- 6.1. Market Analysis, Insights and Forecast - by Component Type
- 7. Europe Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 7.1. Market Analysis, Insights and Forecast - by Component Type
- 7.1.1. Mobile Processors
- 7.1.2. Memory
- 7.1.3. Logic Chips
- 7.1.4. Analog
- 7.1. Market Analysis, Insights and Forecast - by Component Type
- 8. Asia Pacific Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 8.1. Market Analysis, Insights and Forecast - by Component Type
- 8.1.1. Mobile Processors
- 8.1.2. Memory
- 8.1.3. Logic Chips
- 8.1.4. Analog
- 8.1. Market Analysis, Insights and Forecast - by Component Type
- 9. Latin America Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 9.1. Market Analysis, Insights and Forecast - by Component Type
- 9.1.1. Mobile Processors
- 9.1.2. Memory
- 9.1.3. Logic Chips
- 9.1.4. Analog
- 9.1. Market Analysis, Insights and Forecast - by Component Type
- 10. Middle East and Africa Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 10.1. Market Analysis, Insights and Forecast - by Component Type
- 10.1.1. Mobile Processors
- 10.1.2. Memory
- 10.1.3. Logic Chips
- 10.1.4. Analog
- 10.1. Market Analysis, Insights and Forecast - by Component Type
- 11. North America Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 11.1. Market Analysis, Insights and Forecast - By Country/Sub-region
- 11.1.1.
- 12. Europe Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 12.1. Market Analysis, Insights and Forecast - By Country/Sub-region
- 12.1.1.
- 13. Asia Pacific Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 13.1. Market Analysis, Insights and Forecast - By Country/Sub-region
- 13.1.1.
- 14. Latin America Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 14.1. Market Analysis, Insights and Forecast - By Country/Sub-region
- 14.1.1.
- 15. Middle East and Africa Mobile Phone Semiconductor Industry Analysis, Insights and Forecast, 2019-2031
- 15.1. Market Analysis, Insights and Forecast - By Country/Sub-region
- 15.1.1.
- 16. Competitive Analysis
- 16.1. Global Market Share Analysis 2024
- 16.2. Company Profiles
- 16.2.1 NXP Semiconductors N V
- 16.2.1.1. Overview
- 16.2.1.2. Products
- 16.2.1.3. SWOT Analysis
- 16.2.1.4. Recent Developments
- 16.2.1.5. Financials (Based on Availability)
- 16.2.2 Samsung Electronics
- 16.2.2.1. Overview
- 16.2.2.2. Products
- 16.2.2.3. SWOT Analysis
- 16.2.2.4. Recent Developments
- 16.2.2.5. Financials (Based on Availability)
- 16.2.3 Micron Technology Inc
- 16.2.3.1. Overview
- 16.2.3.2. Products
- 16.2.3.3. SWOT Analysis
- 16.2.3.4. Recent Developments
- 16.2.3.5. Financials (Based on Availability)
- 16.2.4 Skyworks Solutions Inc
- 16.2.4.1. Overview
- 16.2.4.2. Products
- 16.2.4.3. SWOT Analysis
- 16.2.4.4. Recent Developments
- 16.2.4.5. Financials (Based on Availability)
- 16.2.5 Broadcom Inc
- 16.2.5.1. Overview
- 16.2.5.2. Products
- 16.2.5.3. SWOT Analysis
- 16.2.5.4. Recent Developments
- 16.2.5.5. Financials (Based on Availability)
- 16.2.6 Qorvo Inc *List Not Exhaustive
- 16.2.6.1. Overview
- 16.2.6.2. Products
- 16.2.6.3. SWOT Analysis
- 16.2.6.4. Recent Developments
- 16.2.6.5. Financials (Based on Availability)
- 16.2.7 Qualcomm Technologies Inc
- 16.2.7.1. Overview
- 16.2.7.2. Products
- 16.2.7.3. SWOT Analysis
- 16.2.7.4. Recent Developments
- 16.2.7.5. Financials (Based on Availability)
- 16.2.8 Huawei Technologies Co Ltd
- 16.2.8.1. Overview
- 16.2.8.2. Products
- 16.2.8.3. SWOT Analysis
- 16.2.8.4. Recent Developments
- 16.2.8.5. Financials (Based on Availability)
- 16.2.9 MediaTek Inc
- 16.2.9.1. Overview
- 16.2.9.2. Products
- 16.2.9.3. SWOT Analysis
- 16.2.9.4. Recent Developments
- 16.2.9.5. Financials (Based on Availability)
- 16.2.10 Intel Corporation
- 16.2.10.1. Overview
- 16.2.10.2. Products
- 16.2.10.3. SWOT Analysis
- 16.2.10.4. Recent Developments
- 16.2.10.5. Financials (Based on Availability)
- 16.2.1 NXP Semiconductors N V
List of Figures
- Figure 1: Global Mobile Phone Semiconductor Industry Revenue Breakdown (Million, %) by Region 2024 & 2032
- Figure 2: North America Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 3: North America Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 4: Europe Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 5: Europe Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 6: Asia Pacific Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 7: Asia Pacific Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 8: Latin America Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 9: Latin America Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 10: Middle East and Africa Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 11: Middle East and Africa Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 12: North America Mobile Phone Semiconductor Industry Revenue (Million), by Component Type 2024 & 2032
- Figure 13: North America Mobile Phone Semiconductor Industry Revenue Share (%), by Component Type 2024 & 2032
- Figure 14: North America Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 15: North America Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 16: Europe Mobile Phone Semiconductor Industry Revenue (Million), by Component Type 2024 & 2032
- Figure 17: Europe Mobile Phone Semiconductor Industry Revenue Share (%), by Component Type 2024 & 2032
- Figure 18: Europe Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 19: Europe Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 20: Asia Pacific Mobile Phone Semiconductor Industry Revenue (Million), by Component Type 2024 & 2032
- Figure 21: Asia Pacific Mobile Phone Semiconductor Industry Revenue Share (%), by Component Type 2024 & 2032
- Figure 22: Asia Pacific Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 23: Asia Pacific Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 24: Latin America Mobile Phone Semiconductor Industry Revenue (Million), by Component Type 2024 & 2032
- Figure 25: Latin America Mobile Phone Semiconductor Industry Revenue Share (%), by Component Type 2024 & 2032
- Figure 26: Latin America Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 27: Latin America Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
- Figure 28: Middle East and Africa Mobile Phone Semiconductor Industry Revenue (Million), by Component Type 2024 & 2032
- Figure 29: Middle East and Africa Mobile Phone Semiconductor Industry Revenue Share (%), by Component Type 2024 & 2032
- Figure 30: Middle East and Africa Mobile Phone Semiconductor Industry Revenue (Million), by Country 2024 & 2032
- Figure 31: Middle East and Africa Mobile Phone Semiconductor Industry Revenue Share (%), by Country 2024 & 2032
List of Tables
- Table 1: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Region 2019 & 2032
- Table 2: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Component Type 2019 & 2032
- Table 3: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Region 2019 & 2032
- Table 4: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 5: Mobile Phone Semiconductor Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 6: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 7: Mobile Phone Semiconductor Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 8: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 9: Mobile Phone Semiconductor Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 10: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 11: Mobile Phone Semiconductor Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 12: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 13: Mobile Phone Semiconductor Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 14: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Component Type 2019 & 2032
- Table 15: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 16: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Component Type 2019 & 2032
- Table 17: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 18: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Component Type 2019 & 2032
- Table 19: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 20: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Component Type 2019 & 2032
- Table 21: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 22: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Component Type 2019 & 2032
- Table 23: Global Mobile Phone Semiconductor Industry Revenue Million Forecast, by Country 2019 & 2032
Frequently Asked Questions
1. What is the projected Compound Annual Growth Rate (CAGR) of the Mobile Phone Semiconductor Industry?
The projected CAGR is approximately 7.49%.
2. Which companies are prominent players in the Mobile Phone Semiconductor Industry?
Key companies in the market include NXP Semiconductors N V, Samsung Electronics, Micron Technology Inc, Skyworks Solutions Inc, Broadcom Inc, Qorvo Inc *List Not Exhaustive, Qualcomm Technologies Inc, Huawei Technologies Co Ltd, MediaTek Inc, Intel Corporation.
3. What are the main segments of the Mobile Phone Semiconductor Industry?
The market segments include Component Type.
4. Can you provide details about the market size?
The market size is estimated to be USD XX Million as of 2022.
5. What are some drivers contributing to market growth?
Rapid Introduction of Next-generation Mobile-communications Standard. LTE or 4G; Emergence of 'Multicom' Solutions.
6. What are the notable trends driving market growth?
Memory to Significantly Drive the Market.
7. Are there any restraints impacting market growth?
Complexity Regarding Manufacturing; Consumer Demand Exceeding Factory Capacity.
8. Can you provide examples of recent developments in the market?
November 2022 - Micron Technology launched its 1-beta DRAM with an aim to improve power efficiency by 15% and bit density by 35% for memory chips. The new DRAM chips would underpin a new generation of memory chips for Micron.
9. What pricing options are available for accessing the report?
Pricing options include single-user, multi-user, and enterprise licenses priced at USD 4750, USD 5250, and USD 8750 respectively.
10. Is the market size provided in terms of value or volume?
The market size is provided in terms of value, measured in Million.
11. Are there any specific market keywords associated with the report?
Yes, the market keyword associated with the report is "Mobile Phone Semiconductor Industry," which aids in identifying and referencing the specific market segment covered.
12. How do I determine which pricing option suits my needs best?
The pricing options vary based on user requirements and access needs. Individual users may opt for single-user licenses, while businesses requiring broader access may choose multi-user or enterprise licenses for cost-effective access to the report.
13. Are there any additional resources or data provided in the Mobile Phone Semiconductor Industry report?
While the report offers comprehensive insights, it's advisable to review the specific contents or supplementary materials provided to ascertain if additional resources or data are available.
14. How can I stay updated on further developments or reports in the Mobile Phone Semiconductor Industry?
To stay informed about further developments, trends, and reports in the Mobile Phone Semiconductor Industry, consider subscribing to industry newsletters, following relevant companies and organizations, or regularly checking reputable industry news sources and publications.
Methodology
Step 1 - Identification of Relevant Samples Size from Population Database



Step 2 - Approaches for Defining Global Market Size (Value, Volume* & Price*)

Note*: In applicable scenarios
Step 3 - Data Sources
Primary Research
- Web Analytics
- Survey Reports
- Research Institute
- Latest Research Reports
- Opinion Leaders
Secondary Research
- Annual Reports
- White Paper
- Latest Press Release
- Industry Association
- Paid Database
- Investor Presentations

Step 4 - Data Triangulation
Involves using different sources of information in order to increase the validity of a study
These sources are likely to be stakeholders in a program - participants, other researchers, program staff, other community members, and so on.
Then we put all data in single framework & apply various statistical tools to find out the dynamic on the market.
During the analysis stage, feedback from the stakeholder groups would be compared to determine areas of agreement as well as areas of divergence