[User] Please transcribe this text

[Assistant] Do you want to come with me? Come.


[User] Please transcribe this text

[Assistant] I do not know what to do. do


[User] Please transcribe this text

[Assistant] I am going out even if it's raining.


[User] Please transcribe this text

[Assistant] I need to find a hotel. find


[User] Please transcribe this text

[Assistant] He finished first in the competition. first


[User] Please transcribe this text

[Assistant] Where can I get a drink? get


[User] Please transcribe this text

[Assistant] Can you give me directions? Give


[User] Please transcribe this text

[Assistant] Hasn't he already arrived? He.


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] his What's his name? his What's his name?


[User] Please transcribe this text

[Assistant] I I don't speak English. I


[User] Please transcribe this text

[Assistant] into Let's go into the woods. into


[User] Please transcribe this text

[Assistant] I'm just about to go out. Just


[User] Please transcribe this text

[Assistant] I don't know where it is. No.


[User] Please transcribe this text

[Assistant] What's that man doing? man


[User] Please transcribe this text

[Assistant] There are many shops in London. many


[User] Please transcribe this text

[Assistant] I would like some more pizza. More.


[User] Please transcribe this text

[Assistant] My. That is my favorite. My.


[User] Please transcribe this text

[Assistant] I have a new job. new


[User] Please transcribe this text

[Assistant] I am now learning English. now


[User] Please transcribe this text

[Assistant] Have you heard of sleep learning? Of.


[User] Please transcribe this text

[Assistant] Let's get on the train. on


[User] Please transcribe this text

[Assistant] 1. I want to go to London one day.


[User] Please transcribe this text

[Assistant] What other restaurants are there?


[User] Please transcribe this text

[Assistant] We have moved into our new house. our


[User] Please transcribe this text

[Assistant] We have moved into our new house.


[User] Please transcribe this text

[Assistant] Do you know where she went? She


[User] Please transcribe this text

[Assistant] There are so many people here. So,


[User] Please transcribe this text

[Assistant] Would you like some food? some


[User] Please transcribe this text

[Assistant] tell Can you tell me the time? tell


[User] Please transcribe this text

[Assistant] Then, Ronaldo is better than Messi.


[User] Please transcribe this text

[Assistant] Where's the train station? the


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming. then


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming.


[User] Please transcribe this text

[Assistant] there There isn't anyone there. there There isn't anyone there.


[User] Please transcribe this text

[Assistant] Do you want some of these eggs? These.


[User] Please transcribe this text

[Assistant] Do you think they were when? They


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] What did you do this morning? this


[User] Please transcribe this text

[Assistant] those Who are those guys? those Who are those guys?


[User] Please transcribe this text

[Assistant] What's wrong with you? What's?


[User] Please transcribe this text

[Assistant] It's time to go home. Time.


[User] Please transcribe this text

[Assistant] to Shall we go to the cinema? to


[User] Please transcribe this text

[Assistant] two Can I have two tickets please? two Can I have two tickets please?


[User] Please transcribe this text

[Assistant] Can I use your pencil? Use.


[User] Please transcribe this text

[Assistant] I want to go home. want


[User] Please transcribe this text

[Assistant] Do you know what the time is? what


[User] Please transcribe this text

[Assistant] Do you know what the time is?


[User] Please transcribe this text

[Assistant] I don't know when I will finish. when


[User] Please transcribe this text

[Assistant] I don't know when I will finish.


[User] Please transcribe this text

[Assistant] Do you know which way is north? Which?


[User] Please transcribe this text

[Assistant] Do you know which way is north?


[User] Please transcribe this text

[Assistant] Do you know who that is? Who.


[User] Please transcribe this text

[Assistant] will Who will win the match? will Who will win the match?


[User] Please transcribe this text

[Assistant] I am with my friend.


[User] Please transcribe this text

[Assistant] I would like a room. would


[User] Please transcribe this text

[Assistant] Can you help me? You.


[User] Please transcribe this text

[Assistant] What's your name? Your.


[User] Please transcribe this text

[Assistant] I like fish and chips. and


[User] Please transcribe this text

[Assistant] as It's as good as new.


[User] Please transcribe this text

[Assistant] Will you be here tomorrow? be


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad. because


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad.


[User] Please transcribe this text

[Assistant] Bye. I will meet you by the post box. Bye. I will meet you by the post box.


[User] Please transcribe this text

[Assistant] Can I use your phone? Can


[User] Please transcribe this text

[Assistant] Do you want to come with me? Come.


[User] Please transcribe this text

[Assistant] day I am at work all day day I am at work all day


[User] Please transcribe this text

[Assistant] I do not know what to do. do


[User] Please transcribe this text

[Assistant] I am going out even if it's raining.


[User] Please transcribe this text

[Assistant] I need to find a hotel. find I need to find a hotel.


[User] Please transcribe this text

[Assistant] He finished first in the competition. first


[User] Please transcribe this text

[Assistant] Can you give me directions? Give


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] his What's his name? his What's his name?


[User] Please transcribe this text

[Assistant] into Let's go into the woods. into


[User] Please transcribe this text

[Assistant] I don't know where it is. No.


[User] Please transcribe this text

[Assistant] Can you look at this? Look.


[User] Please transcribe this text

[Assistant] What's that man doing? man


[User] Please transcribe this text

[Assistant] There are many shops in London. many


[User] Please transcribe this text

[Assistant] more I would like some more pizza. more I would like some more pizza.


[User] Please transcribe this text

[Assistant] I have a new job. new


[User] Please transcribe this text

[Assistant] No. I said no to the job offer. No.


[User] Please transcribe this text

[Assistant] I do not like cats. Not.


[User] Please transcribe this text

[Assistant] I am now learning English. now


[User] Please transcribe this text

[Assistant] Have you heard of sleep learning? Of.


[User] Please transcribe this text

[Assistant] Let's get on the train. on


[User] Please transcribe this text

[Assistant] Other What other restaurants are there?


[User] Please transcribe this text

[Assistant] We have moved into our new house. our


[User] Please transcribe this text

[Assistant] We have moved into our new house.


[User] Please transcribe this text

[Assistant] People I have met lots of new people.


[User] Please transcribe this text

[Assistant] I wanted to say thank you. Say


[User] Please transcribe this text

[Assistant] See. I can see the sea. See.


[User] Please transcribe this text

[Assistant] There are so many people here. So,


[User] Please transcribe this text

[Assistant] Can I take the day off? Take


[User] Please transcribe this text

[Assistant] tell Can you tell me the time? tell


[User] Please transcribe this text

[Assistant] Then, Ronaldo is better than Messi.


[User] Please transcribe this text

[Assistant] Where's the train station? the


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming.


[User] Please transcribe this text

[Assistant] there There isn't anyone there. there There isn't anyone there.


[User] Please transcribe this text

[Assistant] Do you want some of these eggs? These.


[User] Please transcribe this text

[Assistant] Do you think they were when? They.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] What did you do this morning? this


[User] Please transcribe this text

[Assistant] those Who are those guys? those Who are those guys?


[User] Please transcribe this text

[Assistant] What's wrong with you? What's?


[User] Please transcribe this text

[Assistant] It's time to go home. Time.


[User] Please transcribe this text

[Assistant] Shall we go to the cinema? To.


[User] Please transcribe this text

[Assistant] two Can I have two tickets, please? two Can I have two tickets, please?


[User] Please transcribe this text

[Assistant] Can I use your pencil? Use.


[User] Please transcribe this text

[Assistant] I want to go home. want


[User] Please transcribe this text

[Assistant] Do you know what the time is? what


[User] Please transcribe this text

[Assistant] Do you know what the time is?


[User] Please transcribe this text

[Assistant] I don't know when I will finish. when


[User] Please transcribe this text

[Assistant] I don't know when I will finish.


[User] Please transcribe this text

[Assistant] Do you know which way is north? Which?


[User] Please transcribe this text

[Assistant] Do you know which way is north?


[User] Please transcribe this text

[Assistant] will Who will win the match? will Who will win the match?


[User] Please transcribe this text

[Assistant] I would like a room. would


[User] Please transcribe this text

[Assistant] Can you help me? You.


[User] Please transcribe this text

[Assistant] What's your name? Your.


[User] Please transcribe this text

[Assistant] About. I'm about to go to sleep.


[User] Please transcribe this text

[Assistant] all Shall we all meet again? all


[User] Please transcribe this text

[Assistant] I like fish and chips. and


[User] Please transcribe this text

[Assistant] Will you be here tomorrow? be


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad. because


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad.


[User] Please transcribe this text

[Assistant] Bye. I will meet you by the post box. Bye. I will meet you by the post box.


[User] Please transcribe this text

[Assistant] Can I use your phone? Can.


[User] Please transcribe this text

[Assistant] Do you want to come with me? Come.


[User] Please transcribe this text

[Assistant] day I am at work all day day I am at work all day


[User] Please transcribe this text

[Assistant] I do not know what to do. do


[User] Please transcribe this text

[Assistant] I am going out even if it's raining.


[User] Please transcribe this text

[Assistant] I need to find a hotel. find I need to find a hotel.


[User] Please transcribe this text

[Assistant] He finished first in the competition. first


[User] Please transcribe this text

[Assistant] Where can I get a drink? get


[User] Please transcribe this text

[Assistant] Can you give me directions? Give


[User] Please transcribe this text

[Assistant] Hasn't he already arrived? He.


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] Here. I am here now.


[User] Please transcribe this text

[Assistant] his What's his name? his What's his name?


[User] Please transcribe this text

[Assistant] I I don't speak English. I


[User] Please transcribe this text

[Assistant] in What's in there? in What's in there?


[User] Please transcribe this text

[Assistant] into Let's go into the woods. into


[User] Please transcribe this text

[Assistant] I don't know where it is. No.


[User] Please transcribe this text

[Assistant] I like to watch football. like


[User] Please transcribe this text

[Assistant] Shall we make a sand castle? Make.


[User] Please transcribe this text

[Assistant] What's that man doing? man


[User] Please transcribe this text

[Assistant] There are many shops in London. many


[User] Please transcribe this text

[Assistant] more I would like some more pizza. more


[User] Please transcribe this text

[Assistant] I have a new job. new


[User] Please transcribe this text

[Assistant] I do not like cats. Not.


[User] Please transcribe this text

[Assistant] I am now learning English. now


[User] Please transcribe this text

[Assistant] Have you heard of sleep learning? Of.


[User] Please transcribe this text

[Assistant] Let's get on the train. on


[User] Please transcribe this text

[Assistant] One. I want to go to London one day.


[User] Please transcribe this text

[Assistant] Other What other restaurants are there?


[User] Please transcribe this text

[Assistant] We have moved into our new house. our


[User] Please transcribe this text

[Assistant] We have moved into our new house.


[User] Please transcribe this text

[Assistant] I wanted to say thank you. Say


[User] Please transcribe this text

[Assistant] I can see the sea. see I can see the sea.


[User] Please transcribe this text

[Assistant] There are so many people here. So,


[User] Please transcribe this text

[Assistant] tell Can you tell me the time? tell


[User] Please transcribe this text

[Assistant] Then, Ronaldo is better than Messi.


[User] Please transcribe this text

[Assistant] Where's the train station? the


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming. then


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming.


[User] Please transcribe this text

[Assistant] there There isn't anyone there. there There isn't anyone there.


[User] Please transcribe this text

[Assistant] Do you want some of these eggs? These.


[User] Please transcribe this text

[Assistant] Do you think they were when? They.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] What did you do this morning? this


[User] Please transcribe this text

[Assistant] those Who are those guys? those Who are those guys?


[User] Please transcribe this text

[Assistant] What's wrong with you? What's?


[User] Please transcribe this text

[Assistant] It's time to go home. Time.


[User] Please transcribe this text

[Assistant] Shall we go to the cinema? To.


[User] Please transcribe this text

[Assistant] two Can I have two tickets please? two Can I have two tickets please?


[User] Please transcribe this text

[Assistant] Can I use your pencil? Use.


[User] Please transcribe this text

[Assistant] I want to go home. want


[User] Please transcribe this text

[Assistant] Do you know what the time is? what


[User] Please transcribe this text

[Assistant] Do you know what the time is?


[User] Please transcribe this text

[Assistant] I don't know when I will finish. when


[User] Please transcribe this text

[Assistant] I don't know when I will finish.


[User] Please transcribe this text

[Assistant] Do you know which way is north? Which?


[User] Please transcribe this text

[Assistant] will Who will win the match? will Who will win the match?


[User] Please transcribe this text

[Assistant] I would like a room. would


[User] Please transcribe this text

[Assistant] Can you help me? You.


[User] Please transcribe this text

[Assistant] What's your name? Your.


[User] Please transcribe this text

[Assistant] all Shall we all meet again? all


[User] Please transcribe this text

[Assistant] I like fish and chips. and


[User] Please transcribe this text

[Assistant] Will you be here tomorrow? be


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad. because


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad.


[User] Please transcribe this text

[Assistant] But I want to go out, but it's raining.


[User] Please transcribe this text

[Assistant] Bye. I will meet you by the post box. Bye. I will meet you by the post box.


[User] Please transcribe this text

[Assistant] Can I use your phone? Can


[User] Please transcribe this text

[Assistant] Do you want to come with me? Come.


[User] Please transcribe this text

[Assistant] I do not know what to do. do


[User] Please transcribe this text

[Assistant] I am going out even if it's raining.


[User] Please transcribe this text

[Assistant] Find I need to find a hotel. Find


[User] Please transcribe this text

[Assistant] He finished first in the competition. First


[User] Please transcribe this text

[Assistant] Where can I get a drink? get


[User] Please transcribe this text

[Assistant] Can you give me directions? Give


[User] Please transcribe this text

[Assistant] have I have to go to the toilet.


[User] Please transcribe this text

[Assistant] have I have to go to the toilet.


[User] Please transcribe this text

[Assistant] Hasn't he already arrived? He


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] his What's his name? his


[User] Please transcribe this text

[Assistant] I I don't speak English. I


[User] Please transcribe this text

[Assistant] into Let's go into the woods. into


[User] Please transcribe this text

[Assistant] I don't know where it is. No.


[User] Please transcribe this text

[Assistant] Shall we make a sand castle? Make.


[User] Please transcribe this text

[Assistant] What's that man doing? man


[User] Please transcribe this text

[Assistant] There are many shops in London. many


[User] Please transcribe this text

[Assistant] more I would like some more pizza. more I would like some more pizza.


[User] Please transcribe this text

[Assistant] My. That is my favorite. My.


[User] Please transcribe this text

[Assistant] I have a new job. new


[User] Please transcribe this text

[Assistant] No. I said no to the job offer. No.


[User] Please transcribe this text

[Assistant] I do not like cats. Not.


[User] Please transcribe this text

[Assistant] I am now learning English. now


[User] Please transcribe this text

[Assistant] Have you heard of sleep learning? Of.


[User] Please transcribe this text

[Assistant] Let's get on the train. on


[User] Please transcribe this text

[Assistant] One. I want to go to London one day.


[User] Please transcribe this text

[Assistant] What other? What other restaurants are there?


[User] Please transcribe this text

[Assistant] We have moved into our new house. our


[User] Please transcribe this text

[Assistant] We have moved into our new house.


[User] Please transcribe this text

[Assistant] People I have met lots of new people.


[User] Please transcribe this text

[Assistant] See. I can see the sea. See.


[User] Please transcribe this text

[Assistant] Do you know where she went? She


[User] Please transcribe this text

[Assistant] There are so many people here. So,


[User] Please transcribe this text

[Assistant] Can I take the day off? Take


[User] Please transcribe this text

[Assistant] tell Can you tell me the time? tell


[User] Please transcribe this text

[Assistant] Then, Ronaldo is better than Messi.


[User] Please transcribe this text

[Assistant] Where's the train station? the


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming.


[User] Please transcribe this text

[Assistant] Do you want some of these eggs? These.


[User] Please transcribe this text

[Assistant] Do you think they will win? They.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] What did you do this morning? This


[User] Please transcribe this text

[Assistant] those Who are those guys? those Who are those guys?


[User] Please transcribe this text

[Assistant] What's wrong with you? What's?


[User] Please transcribe this text

[Assistant] It's time to go home. time


[User] Please transcribe this text

[Assistant] to Shall we go to the cinema? to


[User] Please transcribe this text

[Assistant] Two. Can I have two tickets please? Two.


[User] Please transcribe this text

[Assistant] Can I use your pencil? Use.


[User] Please transcribe this text

[Assistant] I want to go home. want


[User] Please transcribe this text

[Assistant] Do you know what the time is?


[User] Please transcribe this text

[Assistant] Do you know what the time is?


[User] Please transcribe this text

[Assistant] I don't know when I will finish. when


[User] Please transcribe this text

[Assistant] I don't know when I will finish.


[User] Please transcribe this text

[Assistant] Do you know which way is north? Which?


[User] Please transcribe this text

[Assistant] will Who will win the match? will Who will win the match?


[User] Please transcribe this text

[Assistant] I am with my friend.


[User] Please transcribe this text

[Assistant] I would like a room. would


[User] Please transcribe this text

[Assistant] Can you help me? You.


[User] Please transcribe this text

[Assistant] What's your name? Your.


[User] Please transcribe this text

[Assistant] About. I'm about to go to sleep.


[User] Please transcribe this text

[Assistant] all Shall we all meet again? all


[User] Please transcribe this text

[Assistant] I like fish and chips. and


[User] Please transcribe this text

[Assistant] Will you be here tomorrow? be


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad. because


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad.


[User] Please transcribe this text

[Assistant] But I want to go out, but it's raining.


[User] Please transcribe this text

[Assistant] Bye. I will meet you by the post box. Bye. I will meet you by the post box.


[User] Please transcribe this text

[Assistant] Can I use your phone? Can


[User] Please transcribe this text

[Assistant] Do you want to come with me? Come.


[User] Please transcribe this text

[Assistant] I do not know what to do. do


[User] Please transcribe this text

[Assistant] I am going out even if it's raining.


[User] Please transcribe this text

[Assistant] find I need to find a hotel. find


[User] Please transcribe this text

[Assistant] He finished first in the competition. First


[User] Please transcribe this text

[Assistant] Can you give me directions? Give


[User] Please transcribe this text

[Assistant] have I have to go to the toilet.


[User] Please transcribe this text

[Assistant] have I have to go to the toilet.


[User] Please transcribe this text

[Assistant] Hasn't he already arrived? He.


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] his What's his name? his What's his name?


[User] Please transcribe this text

[Assistant] into Let's go into the woods. into


[User] Please transcribe this text

[Assistant] I'm just about to go out. Just


[User] Please transcribe this text

[Assistant] I don't know where it is. No.


[User] Please transcribe this text

[Assistant] Shall we make a sand castle? Make.


[User] Please transcribe this text

[Assistant] What's that man doing? man


[User] Please transcribe this text

[Assistant] There are many shops in London. many


[User] Please transcribe this text

[Assistant] more I would like some more pizza. more


[User] Please transcribe this text

[Assistant] My. That is my favorite. My.


[User] Please transcribe this text

[Assistant] I have a new job. new


[User] Please transcribe this text

[Assistant] No. I said no to the job offer. No.


[User] Please transcribe this text

[Assistant] I do not like cats. Not.


[User] Please transcribe this text

[Assistant] I am now learning English. now


[User] Please transcribe this text

[Assistant] Have you heard of sleep learning? Of.


[User] Please transcribe this text

[Assistant] Let's get on the train. on


[User] Please transcribe this text

[Assistant] One. I want to go to London one day.


[User] Please transcribe this text

[Assistant] One. I want to go to London one day.


[User] Please transcribe this text

[Assistant] other What other restaurants are there? other What other restaurants are there?


[User] Please transcribe this text

[Assistant] We have moved into our new house. our


[User] Please transcribe this text

[Assistant] We have moved into our new house.


[User] Please transcribe this text

[Assistant] People I have met lots of new people.


[User] Please transcribe this text

[Assistant] See. I can see the sea. See.


[User] Please transcribe this text

[Assistant] Do you know where she went? She


[User] Please transcribe this text

[Assistant] There are so many people here. So,


[User] Please transcribe this text

[Assistant] Would you like some food? some


[User] Please transcribe this text

[Assistant] Can I take the day off? Take


[User] Please transcribe this text

[Assistant] tell Can you tell me the time? tell


[User] Please transcribe this text

[Assistant] Then, Ronaldo is better than Messi.


[User] Please transcribe this text

[Assistant] Where's the train station? the


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming.


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming.


[User] Please transcribe this text

[Assistant] there There isn't anyone there. there There isn't anyone there.


[User] Please transcribe this text

[Assistant] Do you want some of these eggs? These.


[User] Please transcribe this text

[Assistant] Do you think they will win? They.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] What did you do this morning? This


[User] Please transcribe this text

[Assistant] those Who are those guys? those Who are those guys?


[User] Please transcribe this text

[Assistant] What's wrong with you? What's?


[User] Please transcribe this text

[Assistant] It's time to go home. Time.


[User] Please transcribe this text

[Assistant] to Shall we go to the cinema? to


[User] Please transcribe this text

[Assistant] two Can I have two tickets please? two Can I have two tickets please?


[User] Please transcribe this text

[Assistant] Can I use your pencil? Use.


[User] Please transcribe this text

[Assistant] I want to go home. want


[User] Please transcribe this text

[Assistant] Do you know what the time is? what


[User] Please transcribe this text

[Assistant] Do you know what the time is?


[User] Please transcribe this text

[Assistant] I don't know when I will finish. when


[User] Please transcribe this text

[Assistant] I don't know when I will finish.


[User] Please transcribe this text

[Assistant] Do you know which way is north? Which?


[User] Please transcribe this text

[Assistant] will Who will win the match? will Who will win the match?


[User] Please transcribe this text

[Assistant] I would like a room. would


[User] Please transcribe this text

[Assistant] The year is 2019. Year. The year is 2019.


[User] Please transcribe this text

[Assistant] Can you help me? You.


[User] Please transcribe this text

[Assistant] What's your name? Your.


[User] Please transcribe this text

[Assistant] About. I'm about to go to sleep.


[User] Please transcribe this text

[Assistant] all Shall we all meet again? all


[User] Please transcribe this text

[Assistant] I like fish and chips. and


[User] Please transcribe this text

[Assistant] Will you be here tomorrow? be


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad. because


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad.


[User] Please transcribe this text

[Assistant] Bye. I will meet you by the post box. Bye. I will meet you by the post box.


[User] Please transcribe this text

[Assistant] Can I use your phone? Can.


[User] Please transcribe this text

[Assistant] Do you want to come with me? Come.


[User] Please transcribe this text

[Assistant] I do not know what to do. do


[User] Please transcribe this text

[Assistant] I am going out even if it's raining. Even.


[User] Please transcribe this text

[Assistant] I need to find a hotel. find


[User] Please transcribe this text

[Assistant] He finished first in the competition. first


[User] Please transcribe this text

[Assistant] Where can I get a drink? get


[User] Please transcribe this text

[Assistant] Can you give me directions? Give


[User] Please transcribe this text

[Assistant] Hasn't he already arrived? He.


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] his What's his name? his What's his name?


[User] Please transcribe this text

[Assistant] Let's go into the woods. into


[User] Please transcribe this text

[Assistant] I'm just about to go out. Just


[User] Please transcribe this text

[Assistant] I don't know where it is. No.


[User] Please transcribe this text

[Assistant] Can you look at this? Look


[User] Please transcribe this text

[Assistant] Shall we make a sand castle? Make.


[User] Please transcribe this text

[Assistant] What's that man doing? man


[User] Please transcribe this text

[Assistant] There are many shops in London.


[User] Please transcribe this text

[Assistant] more I would like some more pizza. more


[User] Please transcribe this text

[Assistant] My. That is my favorite. My.


[User] Please transcribe this text

[Assistant] I have a new job. new


[User] Please transcribe this text

[Assistant] I am now learning English. now


[User] Please transcribe this text

[Assistant] Have you heard of sleep learning? Of.


[User] Please transcribe this text

[Assistant] Let's get on the train. on


[User] Please transcribe this text

[Assistant] One. I want to go to London one day.


[User] Please transcribe this text

[Assistant] other What other restaurants are there? other What other restaurants are there?


[User] Please transcribe this text

[Assistant] We have moved into our new house. our


[User] Please transcribe this text

[Assistant] We have moved into our new house.


[User] Please transcribe this text

[Assistant] I can see the sea.


[User] Please transcribe this text

[Assistant] Do you know where she went? She


[User] Please transcribe this text

[Assistant] There are so many people here. So,


[User] Please transcribe this text

[Assistant] Can I take the day off? Take


[User] Please transcribe this text

[Assistant] tell Can you tell me the time? tell


[User] Please transcribe this text

[Assistant] Then, Ronaldo is better than Messi.


[User] Please transcribe this text

[Assistant] Where's the train station? the


[User] Please transcribe this text

[Assistant] I went to the beach, then I went swimming.


[User] Please transcribe this text

[Assistant] there There isn't anyone there. there There isn't anyone there.


[User] Please transcribe this text

[Assistant] Do you want some of these eggs? These.


[User] Please transcribe this text

[Assistant] Do you think they were when? They


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] I am tired of hearing the same thing.


[User] Please transcribe this text

[Assistant] What did you do this morning? this


[User] Please transcribe this text

[Assistant] those Who are those guys? those Who are those guys?


[User] Please transcribe this text

[Assistant] What's wrong with you? What's?


[User] Please transcribe this text

[Assistant] It's time to go home. Time.


[User] Please transcribe this text

[Assistant] to Shall we go to the cinema? to


[User] Please transcribe this text

[Assistant] two Can I have two tickets please? two Can I have two tickets please?


[User] Please transcribe this text

[Assistant] Can I use your pencil? Use.


[User] Please transcribe this text

[Assistant] I want to go home. want


[User] Please transcribe this text

[Assistant] Do you know what the time is? what


[User] Please transcribe this text

[Assistant] Do you know what the time is?


[User] Please transcribe this text

[Assistant] I don't know when I will finish. when


[User] Please transcribe this text

[Assistant] I don't know when I will finish.


[User] Please transcribe this text

[Assistant] Do you know which way is north? Which?


[User] Please transcribe this text

[Assistant] Who? Do you know who that is? Who?


[User] Please transcribe this text

[Assistant] will Who will win the match? will Who will win the match?


[User] Please transcribe this text

[Assistant] I am with my friend.


[User] Please transcribe this text

[Assistant] I would like a room. would


[User] Please transcribe this text

[Assistant] The year is 2019. Year. The year is 2019.


[User] Please transcribe this text

[Assistant] Can you help me? You.


[User] Please transcribe this text

[Assistant] What's your name? Your.


[User] Please transcribe this text

[Assistant] About. I'm about to go to sleep.


[User] Please transcribe this text

[Assistant] all Shall we all meet again? all


[User] Please transcribe this text

[Assistant] I like fish and chips. and


[User] Please transcribe this text

[Assistant] Will you be here tomorrow? be


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad. because


[User] Please transcribe this text

[Assistant] I don't like England because the weather is bad.


[User] Please transcribe this text

[Assistant] But I want to go out, but it's raining.


[User] Please transcribe this text

[Assistant] Bye. I will meet you by the post box. Bye. I will meet you by the post box.


[User] Please transcribe this text

[Assistant] Can I use your phone? Can.


[User] Please transcribe this text

[Assistant] Do you want to come with me? Come.


[User] Please transcribe this text

[Assistant] I do not know what to do. do


[User] Please transcribe this text

[Assistant] I am going out even if it's raining. Even.


[User] Please transcribe this text

[Assistant] I need to find a hotel. find


[User] Please transcribe this text

[Assistant] He finished first in the competition. first


[User] Please transcribe this text

[Assistant] Where can I get a drink? get


[User] Please transcribe this text

[Assistant] Can you give me directions? Give.


[User] Please transcribe this text

[Assistant] Hasn't he already arrived? He.


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] Her. What's her name?


[User] Please transcribe this text

[Assistant] his What's his name? his What's his name?


[User] Please transcribe this text

[Assistant] into Let's go into the woods. into


[User] Please transcribe this text

[Assistant] It's, it's raining outside.


[User] Please transcribe this text

[Assistant] I'm just about to go out. Just


[User] Please transcribe this text

[Assistant] I don't know where it is. No.


[User] Please transcribe this text

[Assistant] Can you look at this? Look.


[User] Please transcribe this text

[Assistant] Shall we make a sand castle? Make.


[User] Please transcribe this text

[Assistant] What's that man doing? man


[User] Please transcribe this text

[Assistant] There are many shops in London. many


[User] Please transcribe this text

[Assistant] more I would like some more pizza. more I would like some more pizza.


[User] Please transcribe this text

[Assistant] My. That is my favorite. My.


[User] Please transcribe this text

[Assistant] I have a new job. new


[User] Please transcribe this text

[Assistant] I do not like cats. Not.


[User] Please transcribe this text

[Assistant] I am now learning English. now


[User] Please transcribe this text

[Assistant] Have you heard of sleep learning? Of.


[User] Please transcribe this text

[Assistant] Let's get on the train. on


[User] Please transcribe this text

[Assistant] One. I want to go to London one day.


[User] Please transcribe this text

[Assistant] What other restaurants are there?


[User] Please transcribe this text

[Assistant] We have moved into our new house. our


[User] Please transcribe this text

[Assistant] We have moved into our new house.


[User] Please transcribe this text

[Assistant] See. I can see the sea. See.


[User] Please transcribe this text

[Assistant] Do you know where she went? She


[User] Please transcribe this text

[Assistant] There are so many people here. So,


[User] Please transcribe this text

[Assistant] Would you like some food? some


[User] Please transcribe this text

[Assistant] Today is about the magic of, uh, what's that day again?


[User] Please transcribe this text

[Assistant] Weren't you supposed to thank them for the gift? It seems like you're asking for more.


[User] Please transcribe this text

[Assistant] Save those breadcrumbs, Lucy. There are birds outside who need them. Need breadcrumbs? I never thought of that.


[User] Please transcribe this text

[Assistant] Friends and family is incredibly important. Uhm, in fact many researchers I think if you ask them they would say that social relationships are the biggest factor in happiness and well-being.


[User] Please transcribe this text

[Assistant] Uh, and social support has been shown to be important in coping with loss, coping with illness, with negative events, uhm, and also just with anything, with achieving goals, you know, having, having supportive friends or family that kind of, uhm, you know, that inspire you, that cheer you, uhm, that motivate you, uhm, that give you tangible support.


[User] Please transcribe this text

[Assistant] Gratitude is really critical, uhm, it was one of the critical strategies, uh, to being happy and maintaining happiness. And gratitude is really a thankfulness or appreciation or even kind of a wonder at life.


[User] Please transcribe this text

[Assistant] So in my, it is one type of expression of gratitude. So in my studies I've had people write gratitude letters as a way, as a kind of a technique to make themselves happier.


[User] Please transcribe this text

[Assistant] Counting your blessings is another way to express gratitude, like, which is basically listing, either writing down or telling someone else the things in your life that you're grateful for. But also just savoring and appreciating your life sort of as it happens. You know, when you're with your kids, are you really just sort of savoring


[User] Please transcribe this text

[Assistant] Essentially a semiconductor or any material, you have these energy bands, any solid state material, you have these energy bands. And when you have a situation where one of the bands at zero Kelvin, let's say the valence band, is completely full and a conduction band that's completely empty,


[User] Please transcribe this text

[Assistant] You can, as you raise the temperature, you will have electrons and holes generated. So what you will have is that an electron jumps from the lower band to the higher band, so you will have an electron, and what it leaves behind is a positively charged area, which we'll treat like a particle, we'll call it a hole. Now, with this in mind,


[User] Please transcribe this text

[Assistant] It becomes less resistive, but that's almost all that control you have. Now if you want to make something, if you want to make something useful, you need, you ideally want to be able to control these electrons and holes independently. Right?


[User] Please transcribe this text

[Assistant] And that ability to control these electrons and holes independently is very important because it allows you to design devices, make things that do some useful things. So the question is, how do we come up with a scenario that we can actually control


[User] Please transcribe this text

[Assistant] So one of the things to keep in mind is that the situation we described for carbon, uhm, earlier is also replicated, so this is basically column four of the periodic table. This is column five and three.


[User] Please transcribe this text

[Assistant] So you have carbon, you have silicon, you have germanium, and then you have tin. Right? In this, uh, sorry, uh, SN.


[User] Please transcribe this text

[Assistant] Now, but still, that lattice structure which we will basically show a two dimensional surrogate for, like this,


[User] Please transcribe this text

[Assistant] We'll have electrons and holes generated, but beyond that,


[User] Please transcribe this text

[Assistant] Because you have 4 n states that are full and 4 n states that are empty, if you have electron hole generations, they would be symmetrical and there would not be much to do with that. So now the question is, how can we do something about this? What can we do to change the ratio of electrons and holes?


[User] Please transcribe this text

[Assistant] Because that would be a useful thing to do. You want to create a situation where you can basically have more holes in electrons or vice versa. So, yes.


[User] Please transcribe this text

[Assistant] And I think that's the next one, is antimony here. Uh, here.


[User] Please transcribe this text

[Assistant] So you have nitrogen, phosphorus, uhm, arsenic, and antimony.


[User] Please transcribe this text

[Assistant] So what if I take one of these atoms and replace it with a column 5 element? So what would happen?


[User] Please transcribe this text

[Assistant] So you have still the four electrons that will form, will try to form four covalent bonds, right? But there will be a fifth electron associated with this one that doesn't have anyone to bond with.


[User] Please transcribe this text

[Assistant] So there are four bonds formed already and this is here. So it appears that this electron will be much more loosely bound compared to the other electrons. Now we can actually see this quantitatively. Because if you think about it, if you take away this electron, this will have a positive charge, right?


[User] Please transcribe this text

[Assistant] Because the nucleus, the only difference between a, let's say, phosphorus and silicon, or arsenic and silicon, is that what, you know, phosphorus and silicon would be that phosphorus has one extra proton, and probably possibly a couple of extra neutrons which are, uhm, not


[User] Please transcribe this text

[Assistant] So what happens is that now you have this positively charged thing sitting in the middle, and then you have the electron. So the question is, this electron that you're talking about, how tightly or loosely is it bound? How can we calculate it?


[User] Please transcribe this text

[Assistant] The good news is that we've already done the necessary calculation, almost all of it, right? Just here. So the energy levels


[User] Please transcribe this text

[Assistant] Was given by this divided by n squared. So now, what is different between a hydrogen in free space or whatever, silicon in free space, and when you are inside a material, inside a crystal?


[User] Please transcribe this text

[Assistant] So now, you're going to, this is going to get scaled by epsilon r squared. So your 13.6 eV


[User] Please transcribe this text

[Assistant] It's gonna get scaled by that. So this, the largest energy level that you will have, it will be 13.6 divided by 11.7 to the square, which is roughly 0.1 electron volt. So the bonding energy of this electron is only about 0.1 electron volt.


[User] Please transcribe this text

[Assistant] But a hundred, more than a hundred times smaller than, than a, for example, a hydrogen.


[User] Please transcribe this text

[Assistant] So this electron is much easier to release than these electrons. So these electrons can go around very quickly. Right? They're not tightly bound.


[User] Please transcribe this text

[Assistant] What creates dielectric constant? What is it that's causing that? What would cause materials to have dielectric properties? To have epsilon relatives greater than one. What is it?


[User] Please transcribe this text

[Assistant] So this movement of electron in that space, in that area, despite the fact, I mean, because of the fact that you have all the electronic gases that can displace with respect to the center of gravity, center of charge of the positive and negative, and that displacement can create an electric dipole. So this is, this is still a valid thing to do.


[User] Please transcribe this text

[Assistant] And as a result, you will see that this energy level is much smaller. So what the way it looks like in the energy band diagram,


[User] Please transcribe this text

[Assistant] It's different though. I mean, so now you have these energy levels associated with these dopants. These are called, by the way, donors. The column 5 elements would be called donors. Because obviously they donate electrons. And what happens is that now you have these energy levels.


[User] Please transcribe this text

[Assistant] That are here, very close. This is like, .1 EV.


[User] Please transcribe this text

[Assistant] An electron can jump from here and form a free electron. And what would be left behind?


[User] Please transcribe this text

[Assistant] And positive ion, right? Now, this electron obviously can move around. This is a free electron. But is this also a whole?


[User] Please transcribe this text

[Assistant] Yes. Yes, why can't it move? Because this positive charge is contributed because of what? Because of its nucleus.


[User] Please transcribe this text

[Assistant] Right? So this is fundamentally different, as you pointed out. It can't move.


[User] Please transcribe this text

[Assistant] This guy's bound here, so yes, there would be a positively charged area here, but it's not a charge carrier. It cannot carry any charge. All it does, it just sits there. And that's why this energy level is shown with broken line.


[User] Please transcribe this text

[Assistant] Not with a straight line, because there is no transition across that allowed.


[User] Please transcribe this text

[Assistant] So whatever happens, whatever is released, there's an ion, they're fine. There's an ion. Now,


[User] Please transcribe this text

[Assistant] So that's for that. Now, this way we can create materials that have actually more electrons than holes. So we can artificially


[User] Please transcribe this text

[Assistant] Control the number of electrons and holes this way. Now, what if you wanted to do the opposite? What if you wanted to do, create a material that has more holes than electrons? What do you think we should be doing?


[User] Please transcribe this text

[Assistant] I wanna do the opposite. I wanna create a situation where I have more holes than electrons.


[User] Please transcribe this text

[Assistant] Go to column three, right? So on column three, what are the elements that you have in column three? So,


[User] Please transcribe this text

[Assistant] So, what happens is that you have the column three elements.


[User] Please transcribe this text

[Assistant] In particular- So by the way, when we talk about donors, the donors that are typically used in semiconductor almost always are these guys.


[User] Please transcribe this text

[Assistant] And for acceptors, so these are donors, and these are acceptors, the ones that accept electrons, as we'll see.


[User] Please transcribe this text

[Assistant] So if it's one electron short, there's one of these bonds that cannot be formed. Now, what happens is that, but now this is a bond that can be opened and closed pretty quickly, opened and reformed, broken and formed rather rapidly. So what you can do, one of the adjacent bonds can break. And you will have a positively charged area.


[User] Please transcribe this text

[Assistant] And this guy becomes negatively charged. So this is going to be negative E. Now it's a negative ion. But again, the same way, this ion cannot move. But this hole that you formed here, now can move. So this is an acceptor level, energy level. And the way you show it again,


[User] Please transcribe this text

[Assistant] Column 3 elements, you can actually create a situation where you have more holes than electrons.


[User] Please transcribe this text

[Assistant] So you can control the number of holes and electrons independently. And this is very important.


[User] Please transcribe this text

[Assistant] When this ionization happens, well, it's the temperature, right? If you think about the number, let's say, let's say you have a donor situation, you have a donor introduced, and you're looking at the number of electrons shown with N, versus the absolute temperature. So, what is the number of free electrons at zero Kelvin?


[User] Please transcribe this text

[Assistant] In a situation that you have the donors, let's say you don't have the acceptors.


[User] Please transcribe this text

[Assistant] What would be the number of electrons when they're at zero Kelvin?


[User] Please transcribe this text

[Assistant] Zero, right? Because there's no energy for anything to get ionized, there's not even .1 EV, so nothing's gonna happen. So as you start raising temperature,


[User] Please transcribe this text

[Assistant] What happened? So let's say, just before we do that actually, sorry. Before we do that, let's talk about a special scenario. Let's say you talk about a pure semiconductor for a second.


[User] Please transcribe this text

[Assistant] Now let's say this time you have the donor levels. Now you have the donors in there. What would happen in terms of as you raise the temperature?


[User] Please transcribe this text

[Assistant] It starts going much more rapidly. Why? Because these guys require a lot less energy. It takes a lot less energy to take an electron from here and put it there as opposed to from here to there. Right?


[User] Please transcribe this text

[Assistant] Because they're all ionized, and that's it. And then, how long will this last?


[User] Please transcribe this text

[Assistant] So once you get close to this thing, then now the thermally generated electron hole pairs would come in and they would basically be dominating. So if I ask you


[User] Please transcribe this text

[Assistant] What is a good place to operate a trans- So let's define three regions. Region 1, region 2, and region 3.


[User] Please transcribe this text

[Assistant] So, if you want to use it in a useful structure, where you can control the number of electrons accurately and all those things, which region would you use it in? Region 2, right? Obviously. So, that's the good region to use it.


[User] Please transcribe this text

[Assistant] How about use region one? Let's say you want to do, make a device, make a semiconductor device that's used for cryogenic applications. Let's say you're trying to make a very low noise, something, and you're just trying to make a cryogenic system. What should you do? Does it mean that you can't use it?


[User] Please transcribe this text

[Assistant] If you knew that, if you knew that you're designing a device for cryogenic temperature only, and let's say you wanted to have this level of charges, what would you do?


[User] Please transcribe this text

[Assistant] What's that, what's one of the things that you could do? Let's say you wanted to operate at this temperature.


[User] Please transcribe this text

[Assistant] Now, let's say I want to be at this, at this level, right? So if I start off with an MD that would get me up to that much higher level,


[User] Please transcribe this text

[Assistant] But it is at that level, at that temperature, I can still make it work. They would not be all ionized.


[User] Please transcribe this text

[Assistant] But the number that will be ionized will give me the sufficient level that I need. But then it will work at higher temperature.


[User] Please transcribe this text

[Assistant] I just overcompensate for it, right? Yes.


[User] Please transcribe this text

[Assistant] If, if, yeah, that's a good, that's a great question. So, that device would not be very temperature, because


[User] Please transcribe this text

[Assistant] Slight changes in temperature will change the number of carriers.


[User] Please transcribe this text

[Assistant] So it can get temperature, thermal variation. The, the alternative to that is basically just use what you have. Right?


[User] Please transcribe this text

[Assistant] But if you are operating at very low temperature, let's say liquid hydrogen or liquid nitrogen or something, I mean, liquid nitrogen is not that low, but liquid, liquid helium, not liquid hydrogen, liquid helium.


[User] Please transcribe this text

[Assistant] If you operate at liquid helium, then, then essentially you either have to overcompensate or live with what you have.


[User] Please transcribe this text

[Assistant] Because the number of electrons, the number of free carriers is well controlled and is stable, right?


[User] Please transcribe this text

[Assistant] So you can control it by doping and it will remain stable in that region, the number of free electrons that you have. And regions, how about region 3? Is region 3 useful?


[User] Please transcribe this text

[Assistant] Well-controlled device, probably not, because this is just like, now it's becoming like a, what we call an intrinsic semiconductor. The doping is not doing anything, essentially. For all intents and purposes, doping is not there. So, we wanna operate in region two.


[User] Please transcribe this text

[Assistant] Generally, if you can, region one, there's ways of using it. You have to be careful.


[User] Please transcribe this text

[Assistant] Generally speaking, you want to be in region 2. Now, there's another thing. We talked about semiconductors, so silicon is one of the typical ones.


[User] Please transcribe this text

[Assistant] Before, in the past, germanium by itself was used. When I was a kid, the transistors I used, half of them were germanium transistors. And germanium has a smaller band gap than silicon. So let me ask you this question. What's the problem with a germanium transistor if it has a smaller band gap than silicon? What would be the problem with that?


[User] Please transcribe this text

[Assistant] Yeah, well that temperature is stable, that's correct. So what happens is that this thing happens earlier at a lower temperature, right? This orange curve will come in. So as soon as it heats up, it starts getting pretty bad.


[User] Please transcribe this text

[Assistant] So you should take one gallium and one arsenide and form a gallium arsenide, gallium arsenide, gallium arsenide lattice. So that's one way to form it. Or indium and phosphorous. Indium phosphide. Right? Or gallium and nitrogen. Gallium nitride.


[User] Please transcribe this text

[Assistant] And for example, gallium nitride, one of the advantages of gallium nitride is that it has a very large band gap. So at very high temperatures, it's pretty stable.


[User] Please transcribe this text

[Assistant] So if you want to make power devices that operate at high temperatures, gallium nitride may be a good thing to look at. Uhm, so, but the key point to all of this thing is, is really the question of how we control this, because this ability to dope with


[User] Please transcribe this text

[Assistant] Third column and fifth column, the donors and acceptors, will allow us to design devices.


[User] Please transcribe this text

[Assistant] I will go through the process of device design in the next several lectures, and we'll, in some of your homework problems, you will also design devices. You will make devices that will do certain things.


[User] Please transcribe this text

[Assistant] Target a certain kind of behavior and achieve that by doing this. So any questions on this before we move on? Okay, so


[User] Please transcribe this text

[Assistant] Okay, so one of the, so so far we talked about this energy levels and all those things, but the question is, what distribution do these


[User] Please transcribe this text

[Assistant] In a real system. Particularly in thermal equilibrium. By the way, I want to clarify something and this theme will occur again. Thermal equilibrium and steady state are not the same thing. They're two different things.


[User] Please transcribe this text

[Assistant] For example, when a diode or a transistor is carrying current,


[User] Please transcribe this text

[Assistant] So, right now what we're talking about is thermal equilibrium. So, electrons are fermions. What is the definition of fermions? Anything with a spin of fractional, of one half, three halves, et cetera, et cetera, et cetera. Now, and fermions follow the fermi-dirac distribution. So what is the fermi-dirac distribution?


[User] Please transcribe this text

[Assistant] So Fermi-Dirac distribution basically gives you the probability of finding an electron with energy E. It is defined as 1 over 1 plus E


[User] Please transcribe this text

[Assistant] Is defined essentially the energy at which you have a probability of having one half, the probability of one half of finding an electron. Or fermion in general. Now at lower temperatures,


[User] Please transcribe this text

[Assistant] Let's say at zero Kelvin, if you plot this quantity, you will see that it basically becomes abrupt. At zero Kelvin, it is exactly like this.


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[Assistant] Direct distribution tells you the probability of finding an electron.


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[Assistant] At a given temperature. At a given energy, sorry. At a given energy. For a given temperature.


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[Assistant] In thermal equilibrium. Again, I'd like to emphasize this. Thermal equilibrium.


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[Assistant] It basically shows you that there's a tail, exponential tail.


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[Assistant] Or something. So there will be always electrons with very high energy. But the higher the energy you're targeting, the fewer of those there will be.


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[Assistant] And there will be always the probability of not finding an electron at low energies which basically, for example, can correspond to holes in conduction, in the valence band, down here. Okay?


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[Assistant] So this is the Fermi-Dirac distribution. Now one of the interesting things about this is that if you actually look at the Fermi-Dirac distribution and look at it, say well, let's look at a special case. Let's look at the case where E minus EF is greater than 3kt.


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[Assistant] This exponential, this is e to the power of greater than 3. So this would be significantly larger than 1. So the probability distribution, the probability, uh, of finding something at the energy something, becomes proportional to e to the negative e minus ef over kT. Which, again by definition, is proportional also to the e over kT. What does this look like?


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[Assistant] Probability of something, finding something with an energy of E.


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[Assistant] Of capital E being proportional to E to the negative capital E divided by KT Boltzmann distribution. So this is Boltzmann distribution.


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[Assistant] So you can see that if you are more than 3KT,


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[Assistant] Above EF, the Fermi energy, you can really use the Boltzmann distribution as an approximation for this thing.


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[Assistant] And you will see that actually for most of the calculations that you want to do for devices, the devices that we deal with, you can use the Boltzmann.


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[Assistant] Because we are in that situation. Similarly, for the probability of lack of electron, so the probability of not finding an electron, the same deal.


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[Assistant] The interesting thing is that actually for a lot of device physics results,


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[Assistant] So, if you're gonna be doing that at the end, you might do it at the beginning and get the results much more rapidly, much more directly. Now, there are situations where a firmly direct solution does matter.


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[Assistant] So it's important to know how to deal with that. But in general, a lot of times, actually that's not the case. Many of the practical situations. So,


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[Assistant] The other thing that comes out of this that's quite important is


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[Assistant] What is the probability, so if you have a Boltzmann kind of distribution, the question is, what is the probability of finding an electron with an energy greater than a known energy, a defined, predefined energy E1?


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[Assistant] So basically I have to integrate this from e1, so it would be integral from e1 to plus infinity of e to the negative


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[Assistant] Now, this part of it is constant, so you get e to the e f kt if you wanted to. Keep that. And this part of it is just the integral from e1 to plus infinity of e to the negative e over kt. De.


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[Assistant] And this integral is obviously going to be proportional to e to the negative e1 over kt, with the kt up front.


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[Assistant] Since it's proportionality, we just keep that, so we write it as e to the


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[Assistant] EF minus E1 over kT, oops, not that E, lower kC, which is also proportional by, by definition to, okay, so now this is getting too cramped here.


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[Assistant] So this is a useful result. It says the probability of finding an electron with an energy above E1 is proportional to the E to the negative E1 over kT.


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[Assistant] Current voltage characteristic of a diode or a transistor and things of that sort. So this is a very useful result and we will use it later, soon, uh, to determine that. So,


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[Assistant] So now we want to become a little bit more quantitative. We want to say you have an energy band diagram, you have a valence band, and you have a conduction band. These are the edges of that. And then you have a


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[Assistant] What are those probabilities? So, so the question is that, because this probability of finding an electron in the conduction band


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[Assistant] Tells me what the number of electrons, the density of electrons is. N. Right?


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[Assistant] But according to that equation, this is going to be proportional to


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[Assistant] Minus EC, the energy of the, edge of the conduction band, divided by KT. And I can call this proportionality constant NC.


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[Assistant] Now this NC has a name, it's called the density of states at the edge of the band, but anyway.


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[Assistant] So that's a proportionality constant. And similarly, for the p, for the number of holes, I'll have an nv associated with that. So it would be e of, eh, it would be e, e v minus e f over kt.


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[Assistant] So, there are two relationships that you can obtain.


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[Assistant] This is generally true for any kind of semiconductor with any kind of doping. But so let's talk about the intrinsic semiconductor. So if you have an intrinsic semiconductor, meaning something that's pure,


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[Assistant] What do these correspond to? Well, in the intrinsic semiconductor, we know that the n and p are equal, right? So n is gonna be equal to p.


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[Assistant] Because the generation rate and recombination rate are the same, and also for every electron that you generate, you generate in whole.


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[Assistant] Generate a hole. So their hole and electrons are generated together as pairs. So their numbers have to remain the same. And we call this parameter ni. And intrinsic.


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[Assistant] It's 1.45, 10 to the negative, 10 to the 10 electrons per cubic centimeters, I think. It's 1.45 for silicon, or 10 to the 10, uhm, per cubic centimeter.


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[Assistant] Since that P is also the same thing, it's gonna be NV.


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[Assistant] So now I can use this relationship to simplify what I wrote up there.


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[Assistant] Right? So, and write it in terms of ni. So now, we can say, hey, I know a part of this is here, the nce to the, uh,


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[Assistant] EC, negative EC over KT of it is there, so I can simply write that as NI


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[Assistant] And similarly this would be ni e to the ei minus ef over kt. So this is a useful thing. What it says is that


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[Assistant] The intrinsic energy, the Fermi energy, which is somewhere in the middle, with respect to the Fermi energy wherever it is, your actual Fermi energy, with respect to EI, this difference, this distance in energy,


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[Assistant] This delta in energy determines the number of electrons or holes you will have. So, if my EF is above EI from this equation, do I get more N's or do I get more P's?


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[Assistant] More electrons, right, because it's EF minus EI, so this is a positive thing, it's a positive exponent, and this is a negative exponent.


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[Assistant] So it would be an N-type material. Now if my EF was below EI, this would be a P-type material. So now, but from these two, you can also get something much more, you know, familiar probably.


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[Assistant] Right. So if you get more holes, you get fewer electrons, and vice versa.


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[Assistant] The last thing we are going to talk about, briefly, uh,


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[Assistant] So let's say first they're detached. So let's say you have two pieces and you have some donors introduced here and some acceptors introduced here.


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[Assistant] Electrons, right? Because they have more free electrons. So here you have an N that's greater than P. So it's an N type. That's what we call it. And here you have a P that's greater than N. So you have a P type.


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[Assistant] Now if they are sitting there and nothing is happening, they are going to be in thermal equilibrium. Individually.


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[Assistant] Which would happen very, very, very quickly in semiconductor. Thermal equilibrium happens very quickly. And we'll discuss why later.


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[Assistant] Still, it's in thermal equilibrium, so the Fermi direct distribution still holds, so you have the same Fermi energy across the whole thing. What?


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[Assistant] As you basically go from a situation where your Fermi energy is closer to the n-type


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[Assistant] You will have an energy band diagram like this that we'll discuss in more detail later. Now, but,


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[Assistant] The same way that if you have a hot reservoir and a cold reservoir.


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[Assistant] And if you put some sort of a conductive, thermally conductive material in between,


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[Assistant] There would be a constant flow of energy from one side to the other. So there would be steady state flow of heat. But that system is not in thermal equilibrium.


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[Assistant] So I want to emphasize the difference between thermal equilibrium and steady state, and we'll see this more frequently next time.


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[Assistant] Next time what we'll do, we'll take this and then use the energy distribution as well as the velocity of movement of electrons inside the semiconductor when we calculate that.


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[Assistant] To find the conductivity and resistivity. Which we started with today.


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[Assistant] Now we are going to calculate the conductivity in terms of these microscopic parameters. And we'll see what makes a semiconductor really a semiconductor. Any questions? Alright, well, see you on Thursday. Thank you.


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[Assistant] One of the things that we've done so far is basically develop this basic, very basic feature of solid state devices and the way the carriers behave. So the next thing we do, we are trying to, we saw that we can actually create different regions of the semiconductor with different behavior in terms of the carrier densities, the holes in electrons.


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[Assistant] n-type and regions with more holes than electrons, the p-types. Well, the first device that you probably would want to make has some interesting characteristic would be a piece of n and a piece of p attached to each other. So if you think about them as a p- you already make a p-type material by introducing some, let's say, dopants in there and, you know, some acceptors in the material.


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[Assistant] We actually make them out of a single piece of silicon. If you actually do it that way, it would be a really, really bad p-n junction if any functional one at all.


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[Assistant] That's the way we think about it to just process it. So we are thinking about p-n junctions.


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[Assistant] And we want to understand how they behave. Because they are the basis for the more sophisticated, more complex devices that will come later, that we'll use quite frequently. And of course, p-n junctions are diodes, and then we'll also use them too. So what is a p-n junction? So let's start thinking about a p-n junction. So let's say you have


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[Assistant] Two pieces of semiconductor, so right now I'm keeping them separate, let's say.


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[Assistant] Now, what do we have in a p-type semiconductor? What does it look like?


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[Assistant] Well, you have a whole bunch of semiconductors, let's say silicon or other materials.


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[Assistant] Third column elements. And they basically, you can think about them. So we are starting at zero Kelvin. So let's say we are at zero Kelvin. At absolute zero.


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[Assistant] Now at absolute zero, nothing is ionized, every electron is attached to its associated atom, and they are in a zero state. So what you have is basically you can think about this as a bunch of negatively charged ions with associated holes with them. Right? So you can think about this as a bunch of


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[Assistant] Ions. So this is gonna take me a second to do, and I'm gonna cheat.


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[Assistant] Just bear with me for a second. This is as exciting for me as it is for you.


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[Assistant] Ions that have a whole attachment basically means that they are not ionized. There are third column elements that are not ionized.


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[Assistant] And then you have, and then you show of course these, uh, positive charges here, that are attached to them.


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[Assistant] Okay, and then on the other side, on the n-type side, we also have these positively charged ions.


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[Assistant] Which have an electron attachment. Basically it means that they are a zero Kelvin, they are not ionized.


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[Assistant] And then you have the negatively charted, uhm,


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[Assistant] So nothing is ionized, not very exciting, and what would the energy level look like? So, so now that we are done with the really exciting part, uh,


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[Assistant] We can get on with our business. So what does the energy level, what do the energy levels look like at, in the P side, at zero Kelvin? Let's think about it.


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[Assistant] So, where is the Fermi energy at zero Kelvin?


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[Assistant] So you remember the number of carriers, for example, was given by n i e to the e f minus e i over k t. We did, we derived this in the previous lectures. And then p


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[Assistant] Now, at this temperature, there's nothing ionized, right? So your energy level is basically where your EI is.


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[Assistant] Right, because you're at the N.I. of that temperature. So basically your Fermi energy is in the middle. More or less.


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[Assistant] And the same thing here. And where are the acceptor levels? So acceptor levels, energy levels, are here.


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[Assistant] And they are not ionized. So, they are just sitting there. Now, and the same thing is true here, on this side. So, if I have


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[Assistant] The conduction band and the valence band here. Now I have my donor levels.


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[Assistant] Donor, but they are not ionized. My Fermi energy is here.


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[Assistant] And I'm in thermal equilibrium, nothing is happening, fine. So right now I'm treating them as two separate pieces of semiconductors, right? So now let's say we actually attach them.


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[Assistant] Which is another way of saying that they were made together, anyway, to begin with. And we'll see later on how they're made, but...


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[Assistant] So that's basically when we attach them. When we attach them, nothing exciting happens. This is here, this is here, this is there. This is the junction. That's the energy level. Those are the energy levels at zero Kelvin. It's flat. Nothing is happening.


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[Assistant] Now, let's say you gradually heat it up. You gradually increase the temperature. What's gonna happen now?


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[Assistant] Yes, exactly. Some of the donors and acceptors start getting ionized. So basically what it means in this picture is that some of these dyes will start being ionized.


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[Assistant] And I'm removing them to just put them somewhere else essentially, just some random places. And then here we have the


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[Assistant] Think about that. Now you have two things attached. On one side you have a bunch of electrons, and you have on the other side you have a bunch of holes. And now they're not just stationary. They are moving around. Why? Because of their


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[Assistant] Thermal energy, right? They have thermal energy. And they're very light. So a little bit of thermal energy gives them a lot of speed.


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[Assistant] So when they are bouncing around, there's a chance that this hole will end up on the other side. Every so often.


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[Assistant] And there's a chance that an electron from this side will end up on the other side.


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[Assistant] So at some point, these guys, there's a good chance that the electrons that end up on the other side will recombine. Will find a hole and they hit each other and they recombine. And the same thing is true about the holes on this side. So gradually what happens, and this is most likely to happen where? At the borderline, right?


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[Assistant] So you gradually start forming a region, which is basically the free charge carriers are gone because


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[Assistant] I've heard this being explained at times as, yeaah, the electrons see that there's less electrons on the other side, so they go to the other side, or the holes, see, see, electrons are pretty dumb. They're not that smart. Uhm, so, they're just moving randomly around.


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[Assistant] And what happens is that they're just gonna end up on the other side and there's a higher chance of recombination.


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[Assistant] What do you, what about diffusion? So what about diffusion? So the question is what about diffusion?


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[Assistant] This is diffusion. The random thermal movement of electrons is diffusion.


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[Assistant] Actually, in this explanation, I actively stay away from the word diffusion.


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[Assistant] Because I want exactly for people to realize that there's nothing magical happening about it.


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[Assistant] This random thermal movement is in fact a diffusion.


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[Assistant] But I don't call it diffusion because I want people not to think that this is something very fancy or special.


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[Assistant] This is a very, very simple thing happening. Now, the fusion equation describes the flow due to random thermal movement.


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[Assistant] Yes, that's what we're going to do next. Great. Quick question. So,


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[Assistant] So the next question is, the question was, how does it look like in terms of energy band diagrams?


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[Assistant] So let's, let's find out. So, but for that to have to think about, for that to be found out, just let's think about one thing. Now, once this region is formed that's mostly depleted of carriers, and you're showing it kind of like an abrupt thing, but it's really a transition. It's a gradual thing.


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[Assistant] This abrupt transition is a good approximation and we'll know why, we'll soon, but it really goes back to this exponential.


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[Assistant] Because you have an exponential drop and the exponential drops happen really rapidly. So it basically did this, but it's called a depletion approximation. That you can just basically assume that this is a


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[Assistant] Well defined region. It's a pretty good approximation because of this exponential.


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[Assistant] Going to this thing, what is happening here? What is going on here in this region? What do you have?


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[Assistant] You have a little bit of an electric field, right? Because now you have positively charged ions here that cannot move.


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[Assistant] Tied down. And the same thing here but negatively charged. So what happens to the electric field? There is an electric field, right?


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[Assistant] This random movement of electrons from one side to the other and the holes from one side to the other, or does it impede?


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[Assistant] Think about it. Now, if there's an electric field here in this direction, is it easier for


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[Assistant] A positive charge to go from this side to that side, does it experience a resistive force? A repelling force?


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[Assistant] Yeah, no, it says, yeah, go back, we were here first. And this guy says, oh, no, no, go back. Right? There's a built-in potential. So now, let's see how it's reflected in the energy band diagram.


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[Assistant] So now still, there's no external potential applied to this thing. This is just sitting there.


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[Assistant] Now the energy band diagram, so if it's sitting there and it's in thermal equilibrium, one thing needs to be constant across this thing, which is the Fermi energy, right?


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[Assistant] So now what happens is that we said there's some ionization happening on this side. So we are at T above zero Kelvin, but still below room temperature. So there's some ionization happening.


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[Assistant] You have a Fermi energy that looks like. The band gap really doesn't change. The band gap is a property of the material. What is happening here is that now the Fermi energy is getting closer to the conduction band on this side because this is n-type.


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[Assistant] And it's getting closer to the valence band on the other side. Let me just make this a little bit less like that because we are not still at room temperature.


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[Assistant] So you can see here, EF is above EI, the intrinsic energy level, which is kind of like half way through. It's not exactly in the middle of the conduction band and valence band, but it's kind of close. And the reason it's not half exactly in the middle is that the energy states, the density of states in this state and that state, the NC and NV are not exactly the same.


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[Assistant] The band gap. The Fermi energy remains constant across the thing. So this is our Fermi energy.


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[Assistant] And here what you see is that on this side you have EI that's greater than EF. So what you will have? What will you have? You will have a lot more P's, holes, than N's, right? And on this side you have EF that's above EI. So you will have a larger number of electrons.


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[Assistant] So there's this built-in electrostatic potential as a result of this thing. So there's, there's, there's this built-in potential that's there. Part of it is on the p-side and part of it is on the n-side. So we can actually even give it a name and calculate it. So we can say this is psi, uhm, q psi p and this is q psi n.


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[Assistant] Now, psi, psi is basically measured in voltages. And this is electric, this is the energy, right? So we want to convert from the energy to the


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[Assistant] The energy band diagram for this. Now as the temperature goes to the room temperature, so let's say it goes to the room temperature, what happens is that at room temperature


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[Assistant] And as a result, what happens is that you will be in a situation where these are a little bit farther up.


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[Assistant] And with respect to the acceptor and donor energy, so this is where the acceptor energy levels are. And this is where the donor energy levels are. What was the appropriate color for that? I don't know.


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[Assistant] So at that point you have formed a slightly larger depletion region. Let's say like this. And you have basically


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[Assistant] An ionization happening in this region, and you have an electric field built in. So now let's look at this energy band diagram, see if it makes sense.


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[Assistant] It seems to show that this side is higher than that side. But if you think from an energy perspective, if you take a positive charge,


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[Assistant] If I move it, is it harder to move it from this side to that side or is it from left to right or from right to left?


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[Assistant] So, it's easier to move it from right to left, right? Because electric fuel will help it.


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[Assistant] So, this appears to be upside down, right?


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[Assistant] Because it should be the other way around, it should be downhill, going from here to there. But it looks uphill. Why?


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[Assistant] So this is a common question, common confusion, uhm, just, yes.


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[Assistant] Correct, these are the energies of electrons. These are the energy band diagrams of the energy band diagrams of band energies of the electrons. Electrons are negatively charged. So for an electron,


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[Assistant] So these are energy band diagrams for the electrons. The energy levels for electrons. So that's why they're upside down. Because electrons are negatively charged. Fine.


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[Assistant] But, so other than that, this should make sense.


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[Assistant] What happens? Does, does this process stop once the depletion region is formed?


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[Assistant] If you think about it, the depletion region is formed, let's say we are at room temperature, there's a depletion region, and


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[Assistant] It's there. So everything is static, everything is sitting there, nothing is happening? No, right?


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[Assistant] There are electrons moving around very rapidly still, right?


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[Assistant] So there's still a chance that an electron will jump from this side to that side.


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[Assistant] And recombine. And the same thing for a hole. Because some of them still have enough energy. Some of them are hot enough.


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[Assistant] To just jump from this side to the other, across this potential barrier. Because see, this is uphill for the electrons, and this is also uphill for the holes. So the holes want to go this way, but this is their uphill. If you flip it upside down.


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[Assistant] So what does it, what happens? Does it mean that the depletion region keeps growing and growing and growing and growing?


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[Assistant] No, doesn't make sense, right? Why, what stops it from growing? What is the thing that opposes this process?


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[Assistant] Which means that you're losing more electrons from this side and losing more holes from that side.


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[Assistant] There must be something that counters this process. Yes.


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[Assistant] Correct, thermal, thermal generation of electron hole generation, particularly in the depletion region.


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[Assistant] Because yes, this is depleted because they moved here and they're close to the hostile region, they will just get absorbed most of the time. But there's nothing that said that every so often, because of the thermal energy, an electron cannot jump from here to there.


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[Assistant] From a conduction, from valence band to the conduction band. So when that happens, what do you have? You have a hole, and you have an electron, right?


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[Assistant] Right? So you have a hole and you have an electron. So which way would they go? Downhill.


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[Assistant] The electric field will just basically, if you look at the electric field, you see that's the direction it will go.


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[Assistant] Uh, what happens is that you are, that this, this current, this generation, thermal generation current is gonna oppose the diffusion current. Now what is that, where is that diffusion current that we talked about earlier comes from? What is that thermal energy current coming from? Because if you think about it, these electrons on the P side, on the N side,


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[Assistant] Have a Fermi-Dirac distribution, which we set for energy levels that are sufficiently far away from the


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[Assistant] Fermi level, which is 3KT, which is not that much, 75 millivolts.


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[Assistant] And the same thing for the holes. So the holes also experience a similar situation. So there's a distribution of these guys, and


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[Assistant] This, this built, we call this a built-in potential, right? Because there's an electric field difference. How can we calculate that? How can we calculate what this built-in potential is?


[User] Please transcribe this text

[Assistant] Do you agree that this built-in potential is q, psi n, psi n minus psi p, right? Psi p minus psi n. Or the sum of these two. So what is this one? Let's say psi p. What is it? Let's calculate that. If you say q, psi p,


[User] Please transcribe this text

[Assistant] Do you, but look at this equation, or look at this equation perhaps, and tell me what that is. Well you can solve for EI minus EF from this equation.


[User] Please transcribe this text

[Assistant] Right? And use it there. So if we solve for that, what do we get? Now, we get p, which is the density of the holes in the bulk of the p-type. What is the density of the holes in the bulk of the p-type? At room temperature.


[User] Please transcribe this text

[Assistant] Na, right? Because you've doped it, and we said at room temperature, if you design, if you have the right kind of material, then all of them are ionized, the number of holes is essentially dictated by that density. So, this is going to be Na. And this is gonna be Nd also.


[User] Please transcribe this text

[Assistant] Which is the intrinsic level. It's 1.45 10 to the minus 10 per cubic centimeter.


[User] Please transcribe this text

[Assistant] It's a fixed amount, fixed quantity. So you know psi p. So psi p is basically q, uh, that divided by q, the charge of the electron.


[User] Please transcribe this text

[Assistant] And then similarly for psi n, the built-in potential, electric potential on the other side, it's gonna be EF minus EIN. This difference.


[User] Please transcribe this text

[Assistant] And similarly from this, you can calculate what that is. Which basically is going to be KT.


[User] Please transcribe this text

[Assistant] And therefore, psi n minus, plus psi p, which is the sum of these two, is going to be kt over q.


[User] Please transcribe this text

[Assistant] This is in volts, right? NA ND divided by NI squared.


[User] Please transcribe this text

[Assistant] So this is the voltage, this is the voltage across this thing has to be equal, which is some of these two built-in potentials, has to be equal to that. So this is the built-in potential.


[User] Please transcribe this text

[Assistant] So this is the height of this barrier that gets built naturally when you actually have this random thermal movement.


[User] Please transcribe this text

[Assistant] So you can calculate the height of this electric built in potential.


[User] Please transcribe this text

[Assistant] And of course, this quantity, how many, what is this? What, how much, how many electrons are there that are hot enough that can go through? The number of these hot electrons that can still pass potential barrier. What is it proportional to?


[User] Please transcribe this text

[Assistant] You remember from last time we did a calculation, we said that the number of electrons above a certain E1, or it's not charge carriers,


[User] Please transcribe this text

[Assistant] In Boltzmann distribution, was proportional to e to the negative e1 divided by kT. That's Boltzmann distribution.


[User] Please transcribe this text

[Assistant] So this is proportional, the number of these things is proportional to the e, the negative. Now this is the potential barrier. e to the q sine-naught divided by kt. Call this sine-naught.


[User] Please transcribe this text

[Assistant] So that is the height of the potential barrier, which we calculated. So this, the number of electrons that can pass is proportional to that, so is the number of holes, because they also experience the same potential barrier height. The barrier height is the same for both of them. Right?


[User] Please transcribe this text

[Assistant] But it's not still particularly useful. Why it's not particularly useful? Because it just shows what it is in thermal equilibrium without any external influence. If you're making a device, you want to do something with it.


[User] Please transcribe this text

[Assistant] And doing something with it in electrical engineering means applying electric voltage and currents to it, right? So now let's see what happens if you apply some voltage to that.


[User] Please transcribe this text

[Assistant] So we are going to stay with this picture and say, look, I'm not going to do all of those again.


[User] Please transcribe this text

[Assistant] Negatively charged ions here, positively charged ions there.


[User] Please transcribe this text

[Assistant] And then you have a bunch of free electrons and free holes going around.


[User] Please transcribe this text

[Assistant] Here, and then we have the electrons.


[User] Please transcribe this text

[Assistant] Here, our energy band diagram looked like this.


[User] Please transcribe this text

[Assistant] Initially, when we are in thermal equilibrium. And then that's the p-type.


[User] Please transcribe this text

[Assistant] And I'm gonna apply a voltage called, let's call it VD. The voltage across the diode. Because this is a diode, as we'll see.


[User] Please transcribe this text

[Assistant] The positive is going to P, positive is going to positive, negative is going to negative, so it's forward. So I'm forward biasing it from an electrical, from a circuit perspective. So what does that do to the potential barrier?


[User] Please transcribe this text

[Assistant] And the depletion region. If you think about the depletion region. Now what does this do? So injecting positive charge into here and negative charge into here.


[User] Please transcribe this text

[Assistant] Shrink the depletion region, right? Exactly, because you have now more electrons and holes that are available so they can come in and just like fill up these empty spaces where they were kind of ionized before so they can come in and be here and neutralize the charge here. So the electric field will go down. The potential barrier will be lowered. By how much? The potential barrier will be lowered by


[User] Please transcribe this text

[Assistant] So this potential barrier now is lowered compared to before. So this is where it was before, and this is where it was before. Now it's lowered by QVD.


[User] Please transcribe this text

[Assistant] So now remember, let's think about those charge carriers and the distribution. So before, you had this distribution, and these were the guys who could pass.


[User] Please transcribe this text

[Assistant] Right? These were proportional to e to the negative q psi naught over kT. Now a whole bunch of new electrons can pass too. Because now I've lowered the potential barrier.


[User] Please transcribe this text

[Assistant] So now that I've lowered the potential barrier by QVD, now how many can pass? So now, basically all the stuff that's kind of happening is they're going to be proportional to the e to the psi naught minus VD over kT. Minus.


[User] Please transcribe this text

[Assistant] So what is the net increase in the number that can pass?


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[Assistant] Do you agree that this, if this is this whole thing, and this is the top part, this net part is the difference of these two?


[User] Please transcribe this text

[Assistant] Proportional to the difference of these two. So the net flow of electrons, let's say Jn, is going to be proportional to the e, to the q,


[User] Please transcribe this text

[Assistant] Psi naught minus VD over kT minus e to the negative q Psi naught over kT.


[User] Please transcribe this text

[Assistant] Which I can write as e to the negative q psi naught over kT times


[User] Please transcribe this text

[Assistant] And the same thing is true for the holes. If you think about the holes, so before,


[User] Please transcribe this text

[Assistant] These were the ones that would go, which is proportional to that, but now the new ones that can go are


[User] Please transcribe this text

[Assistant] So this is the net extra current that can be carried by the snake.


[User] Please transcribe this text

[Assistant] Now, we give it a proportionality constant called Is, the saturation constant.


[User] Please transcribe this text

[Assistant] So it would be QVD over KT minus one.


[User] Please transcribe this text

[Assistant] So, that's the equation that's used for a diode. That's a diode equation. Describing the current. And what you see, there's some, so, okay, so,


[User] Please transcribe this text

[Assistant] Equations, et cetera, et cetera. What is the takeaway from this? What's the meaning of this?


[User] Please transcribe this text

[Assistant] Does all the work because of the immense amount of thermal energy that is there in the electrons. It's just a way of utilizing that thermal energy.


[User] Please transcribe this text

[Assistant] All you're just doing when you apply a forward bias, you're luring the potential barrier and they just pour in. The electrons from one side and the holes from the other side.