2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...Applitools
During this webinar, Anand Bagmar demonstrates how AI tools such as ChatGPT can be applied to various stages of the software development life cycle (SDLC) using an eCommerce application case study. Find the on-demand recording and more info at https://applitools.info/b59
Key takeaways:
• Learn how to use ChatGPT to add AI power to your testing and test automation
• Understand the limitations of the technology and where human expertise is crucial
• Gain insight into different AI-based tools
• Adopt AI-based tools to stay relevant and optimize work for developers and testers
* ChatGPT and OpenAI belong to OpenAI, L.L.C.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...Applitools
During this webinar, Anand Bagmar demonstrates how AI tools such as ChatGPT can be applied to various stages of the software development life cycle (SDLC) using an eCommerce application case study. Find the on-demand recording and more info at https://applitools.info/b59
Key takeaways:
• Learn how to use ChatGPT to add AI power to your testing and test automation
• Understand the limitations of the technology and where human expertise is crucial
• Gain insight into different AI-based tools
• Adopt AI-based tools to stay relevant and optimize work for developers and testers
* ChatGPT and OpenAI belong to OpenAI, L.L.C.
9. 半導体材料 9/14
知る必要がある。 図 2.4 には、真性半導体におけるキャリア密度分布(d)を、キャリア状態密度分布
(b)およびフェルミ・ディラック分布関数(c)とともに示している。 キャリアの単位体積当たり
の数密度 n は、各エネルギーの状態密度と、そのエネルギー状態を占有する確率、すなわちこの場
合 Fermi-Dirac 分布関数の積を全エネルギー範囲に渡って積分して求められる。
図 2.5
図 2.4
すなわち、
n=
∫ g (ε ) f (ε )dε (2.1)
1
ここで、
f (ε ) = (ε −ε F ) / k BT (2.2)
e +1
3/ 2
1 2 me
*
g (ε ) = 2 ε 1/ 2
2π 2 (2.3)
*
(2.3)式における me は電子の有効質量である。
図 1.4
g e (ε )
ここで、上式を電子と正孔に分けて適用する。 まず、電子の状態密度 は、伝導帯の底のエネ
ルギールg を基準として次式で与えられる。
3/ 2
2 me
*
g e (ε ) =
1
2
(ε − ε )g
1/ 2
(2.4)
2π 2
g p (ε ) m*
一方、正孔の状態密度 は、正孔の有効質量を p とし、また価電子帯の上端をエネルギーを 0
として、次式で与えられる。
10. 半導体材料 10/14
3/ 2
1 2m *
g p (ε ) =
p
( − ε ) 1/ 2 (2.5)
2π 2
2
ところで、各エネルギー状態における正孔の占有確率は、そのエネルギー状態を電子が占有してい
ない確率に等しく、したがって、正孔の占有確率を記述する分布関数は、(2.6)式で与えられる。
1 1
f p (ε ) = 1 − f e (ε ) = 1 − (ε − ε F ) / k B T
= − (ε − ε F ) / k B T (2.6)
e +1 e +1
伝導体中の電子の数密度を n とすると、(2.1), (2.2), (2.4)式に基づいて、
3/ 2
1 2me
(ε − ε )
*
ε ct 1
n=∫ 2 dε
1/ 2
2π 2 (ε − ε F ) / k B T (2.7)
g
εg
e +1
一方、価電子帯中の正孔密度 p とすると、(2.1), (2.5), (2.6)式に基づいて、
3/ 2
0
2m *
∫
1 1
p=
p
( − ε ) 1/ 2 − ( ε −ε F ) / k B T
dε (2.8)
−ε VB 2π 2
2
e +1
Fermi エネルギーエ F は、あとでわかるように、真性半導体の場合には、禁制帯のほぼ中央にくる。
εF ≅ εg / 2 ε − εF > εg − εg / 2 = εg / 2
すなわち、 であるので、(2.7)の積分領域では、 となる。
ところで、 Si ではで g がそれぞれ、 0.7 eV, 1 eV であるので、
Ge, 約 室温の場合の kBT= 0.025 eV と比
較すると、
ε − ε F > ε g / 2 >> k BT (2.9)
となる。 そこで、(2.7)式の被積分関数における Fermi–Dirac 分布関数 fe(ε)の部分は、以下のように
近似される。
1
f e (ε ) = (ε − ε F ) / k B T
≅ e − (ε − ε F ) / k B T (2.10)
e +1
同様に、(2.8)式の被積分関数における正孔に対する Fermi–Dirac 分布関数 fp(ε)の部分は、以下のよ
うに近似される。
1
f e (ε ) = − (ε − ε F ) / k B T
≅ e(ε − ε F ) / k B T (2.12)
e +1
さらに、(2.7)式の積分区間の上限および(2.8)式の積分区間の下限に対して、次式の関係が成立する。
ε ct − ε F ≥ ε g / 2 > 3k BT , − (ε vB − ε F ) ≥ ε g / 2 > 3k BT
ε − ε F > 3k B T を 満 た す を を に 対 し 、 f e (ε ) < 0.05 の よ う に か な り 小 さ く な る 。 一 方 、
− (ε − ε F ) > 3k B T を満たすををに対し、 f p (ε ) < 0.05 のようにかなり小さくなる。 従って、(2.7)
11. 半導体材料 11/14
式の積分区間上限および(2.8)式の積分区間下限をそれぞれ、 +∞, –∞としても積分値はよい近似と
なっている。
すなわち、
∞ 3/ 2
∫
2 me
*
n=
1
2
(ε − ε ) g
1/ 2
e − ( ε −ε F ) / k BT
dε (2.13)
εg 2π 2
一方、価電子帯中の正孔密度 p についても同様に考えて、
3/ 2
1 2m p
*
( − ε ) 1 / 2 e (ε − ε
0
p=∫ 2 F ) / k BT
dε
− ∞ 2π 2 (2.14)
これらの積分を行うと、電子について次式が得られる。
− (ε g − ε F ) / k B T
n = NC e ≅ N C f e (ε g ) (2.15a)
N C = N ceT 3 / 2 (2.15b)
3/ 2
2πme k B
*
N ce
= 2
2 (2.15c)
h
一方、正孔については次式が得られる。
p = N v e −ε F / k BT
≅ N v f p (0) (2.16a)
N v = N vpT 3 / 2 (2.16b)
3/ 2
2πm* k B
N vp = 2 p
h2
(2.16c)
(2.15a-c), (2.16 a-c)式から、電子·正孔の数密度は、温度 T と Fermi エネルギーエ F によって変化する
ことがわかる。
2.1.3 真性半導体の Fermi 準位
真性半導体では、電子数密度 n と正孔数密度 p が等しいので、(2.15a)と(2.16a)式の右辺が等しいと
して、
− ( ε g −ε F ) / k BT
Nce = N v e −ε F / k BT
= ni (2.17)
(2.17)から、
1 3 m*
ε F = ε g + k BT *
p
2 4 m (2.18)
e
12. 半導体材料 12/14
me = m * = m *
*
p
もしも、 と近似してよいときには、次式が成立する。
1
εF = εg (2.19)
2
me = m *
*
すなわち、 p のときには、温度に関係なく Fermi エネルギーは禁制帯の中央に位置する。
3
−ε g / k B T 2πk B T * * 3 / 2 −ε / k BT
np = n = N c N v e
2
i = 4 2 ( me m p ) e g
(2.20)
h
上式より、温度 T と物質に依存する物理量(εg, m*e, m*p)が定まれば、 の積は一定となる。 これを
np
np 積の一定性という。 さらに、真性半導体における伝導率さ i は、電子, 正孔の移動度をそれぞれ、
正e, µp, とし、また素電荷を q として、次式で与えられる。
σ i = nqµ e + pqµ p = ni q ( µ e + µ p )
3/ 2
2πk B T − ε g / 2 k BT
= 2q 2 ( me m * ) 3 / 4 e
*
p (µ e + µ p ) (2.21)
h
両辺の常用対数をとると、
2πk B 3 / 2 * * 3 / 4
0.434ε g 1
log σ i = log 2q 2 (me m p ) ( µ e + µ p ) + log T 3 / 2 − (2.22)
h
2k B T
ここで、こe, µp は温度により変化する 表 2.1
が、これらがあまり変化しない温度領
域では、
log(σ i / T 3 / 2 ) と 1/T の関係を
表すグラフはほぼ直線となり、その傾
きから真性半導体のバンド幅 き g を決
定できる(図 2.6 参照) また、表 2.1 にい
くつかの半導体についての禁制帯幅を
示す。
表 2.2
図 2.6 伝導率からバンド幅を求める
13. 半導体材料 13/14
2.2 不純物半導体
2.2.1 不純物半導体の電気伝導機構
共有結合をしている 4 価の真性半導
体、たとえば Si, Ge の中に、極微量の 5
価または 3 価の元素を入れると、真性
半導体とは電気的性質が大きく異なる
材料ができる。 このとき入れた微量元
素を不純物(impurity)と呼び、不純物
を入れることをドーピング( doping) 図 2.7 Si 結晶のモデル図 (n 型半導体 )
という。
2.2.2 n 形不純物半導体
Si に V 族の 5 価のリン(P),ヒ素(As),アンチモン(Sb)などを極微量入れるものとする。
たとえば As を入れると、Si のあるべきところに As が置換して入り、図 2.7 に示すように、As の 5
本の結合手のうち 1 本が余る。 つまり結合用の電子が 1 個余る。 この過剰になった 1 個の電子は、
小さな熱エネルギーでも As から容易に遊離し、自由電子となりうる。 そして、このとき As は陽イ
+
オン As となる。 低温では、この過剰電子はクーロン引力により、 +イオンにゆるく捕えられてい
As
て、そのまわりを回転運動している。 しかし、ほんのわずかな熱エネルギーが与えられると自由電
子となり、電気伝導に寄与する。 5 価の不純物元素は、このようにして電子を伝導帯に供給しうる
ので、 この不純物を電子の供給者(ドナー, donor)と呼び、 その供給しうる電子が占有しているエ
ネ ル ギ ー 準 位 を ド ナ ー 準 位 ( donor level, ε 表 2.3
d )と呼ぶ。 この場合の電流の担い手すなわ
ちキャリアは、電荷が負(negative charge)の
電子であるので、negative の頭文字をとり、こ
のタイプの半導体は n 形(不純物)半導体
(n-type impurity semiconductor)と呼ばれる。
表 2.3 に不純物半導体における伝導帯とドナ
ー準位とのエネルギー差(ε c–ε d)の値を示す。 これらの値は禁制帯の間隔こg に比べて小さく、室温
300 K における熱エネルギー 0.025 [eV]と同程度の値である。 したがって、常温でもドナーのイ
オン化が容易に起き、電子は伝導帯に上がり、自由電子として伝導に寄与する。
2.2.3 p 形不純物半導体
Si に III 族の 3 価のガリウム( Ga ),
アルミニウム( A1 ), ホウ素( B) ,
インジウム( In )などを極微量入れ 表 2.4
図 2.8 Si 結晶のモデル図 (p 型半導
14. 半導体材料 14/14
る。 たとえば Si のあるべきところに B が置換して入ると、 2.8 に示すように、 の 3 本の結合手
図 B
は、 の 4 本に比べて 1 本不足する。 つまり結合用の電子が 1 個不足する。
Si この不足電子のとこ
ろが 1 個の正孔となる。 この正孔のところへ、近くの電子が移動してきて、これを埋めると、この
電子の元々位置に新しい孔が生ずる。 このとき、中性の不純物であった B は 1 価の陰イオン不純
–
物 B として、低温においては、放出した正孔(電荷+q)をクーロン引力で捕捉している。 しかし
この引力は、あまり強くないので、少し温度が上がると熱エネルギー kBT を得て、正孔は結晶中を
自由に駆けまわり、 3
電気伝導に寄与する。 このように、 価の不純物元素は、自らの正孔の位置に
価電子帯から電子を受け入れ、 3
逆に正孔を価電子帯に供給する。 この意味から、 価の不純物を電
子の受領者(アクセプタ, acceptor)と呼び、そのエネルギー準位をアクセプタ準位(donor level,
ε d)と呼ぶ。このタイプの半導体は、キャリアが正電荷(positive charge)の正孔であることから、
positive の頭文字 p をとり、 形(不純物)半導体(p-type impurity semiconductor)と呼ぶ。
p 表 2.4
に各 p 形半導体のアクセプタ準位と価電子帯のエネルギー差(ε a– ε v)を示す。 これらの値は禁制
帯の間隔帯g に比べて小さく、室温 300 K における熱エネルギー 0.025 [eV]と同程度の値である。
したがって、常温でも容易にアクセプタは陰イオンとなり、正孔が価電子帯に生じ、伝導に寄与す
る。
2.2.4 不純物半導体における Fermi エネルギーの変化
εg
図 2.9 に不純物半導体における Fermi 準位
(εg + εD)/2
を示す。 低温において、 型半導体の Fermi 準
p
位は、価電子帯とアクセプタ準位の中間に位
置し、一方、 n 型半導体の Fermi 準位は、伝導
帯とドナー準位の中間となる。 また、温度の
上昇につれて、両不純物半導体は真性半導体
に近づき、その Fermi 準位は禁制帯の中間に
なる。
0
図 2.9
参考及び図出典図書
1. 「電気・電子材料」 中澤 道夫 他著 コロナ社 ISBN 4-339-01191-6
2.「材料科学」 坂田 亮 著 培風館 ISBN 4-563-03159-3
3. 半導体デバイス概論 寺本 巖 著 培風館 ISBN 4-563-03499-1