際際滷

際際滷Share a Scribd company logo
Continuity equation
kamlesh singh rawat
INTRODUCTION
The continuity equation which describes the
distribution of electrons and holes when there is
excess carrier generation recombination and
carrier movement. We will consider some of the
simplifications which are used for deriving the
characteristics, how the equations can be
simplified. And finally we will summarize the
characteristic material parameters which
describe a semiconductor device. So let us begin
with the continuity equation.
As per law of conservation of charge rate
of change of number of electrons inside
the semiconductor is equal to the no of
electrons entering per second minus
number of electrons leaving per second
plus number of electrons generated per
second by generation process minus
number of electrons lost per second by
recombination process.
Derivation of Continuity Equation
 Consider carrier-flux into/out-of an infinitesimal volume:
Jn(x) Jn(x+dx)
dx
Area A, volume Adx
  AdxRAdxGAdxxJAxJ
qt
n
Adx nnnn 緒







)()(
1
Continuity Equation TEC-101
n
n
n
nn
R
x
xJ
qt
n
dx
x
xJ
xJdxxJ






緒


緒
)(1
)(
)()(
Lp
p
Ln
n
GR
x
xJ
qt
p
GR
x
xJ
qt
n
)(1
)(1












Continuity
Equations:
TEC-101Continuity Equation
Summary: Continuity Equations
 The continuity equations are established based on
conservation of carriers, and therefore hold generally:
 The minority carrier diffusion equations are derived from
the continuity equations, specifically for minority carriers
under certain conditions (small E-field, low-level injection,
uniform doping profile):
Lp
n
Ln
n
GR
x
xJ
qt
p
GR
x
xJ
qt
n )(1)(1












Lp
n
P
n
Ln
p
N
p
GR
x
p
D
t
p
GR
x
n
D
t
n
2
2
2
2












TEC-101Continuity Equation
Continiuty Equation

More Related Content

What's hot (20)

Unit-I Characteristics of opamp
Unit-I Characteristics of opampUnit-I Characteristics of opamp
Unit-I Characteristics of opamp
Dr.Raja R
Maxwell's equations
Maxwell's equationsMaxwell's equations
Maxwell's equations
Bruna Larissa Cris坦stomo
Optical Detector PIN photodiode
Optical Detector PIN photodiodeOptical Detector PIN photodiode
Optical Detector PIN photodiode
Dhruv Upadhaya
Reflection and Transmission coefficients in transmission line
Reflection and Transmission coefficients in transmission lineReflection and Transmission coefficients in transmission line
Reflection and Transmission coefficients in transmission line
RCC Institute of Information Technology
transmission-line-and-waveguide-ppt
transmission-line-and-waveguide-ppttransmission-line-and-waveguide-ppt
transmission-line-and-waveguide-ppt
ATTO RATHORE
SHORT CHANNEL EFFECTS IN MOSFETS- VLSI DESIGN
SHORT CHANNEL EFFECTS IN MOSFETS- VLSI DESIGNSHORT CHANNEL EFFECTS IN MOSFETS- VLSI DESIGN
SHORT CHANNEL EFFECTS IN MOSFETS- VLSI DESIGN
NITHIN KALLE PALLY
Oscillators
OscillatorsOscillators
Oscillators
ForwardBlog Enewzletter
Wave guide tees
Wave guide teesWave guide tees
Wave guide tees
Keval Patel
Pin photodiode.pptx ashvani
Pin photodiode.pptx ashvaniPin photodiode.pptx ashvani
Pin photodiode.pptx ashvani
Ashvani Shukla
Basics of semiconductor, current equation, continuity equation, injected mino...
Basics of semiconductor, current equation, continuity equation, injected mino...Basics of semiconductor, current equation, continuity equation, injected mino...
Basics of semiconductor, current equation, continuity equation, injected mino...
Nidhee Bhuwal
Poissons and Laplaces Equation
Poissons and Laplaces EquationPoissons and Laplaces Equation
Poissons and Laplaces Equation
Abhishek Choksi
Pn junction diode
Pn junction diodePn junction diode
Pn junction diode
Poojith Chowdhary
Signals & Systems PPT
Signals & Systems PPTSignals & Systems PPT
Signals & Systems PPT
Jay Baria
Small signal analysis of bjt amplifiers
Small signal analysis of bjt amplifiersSmall signal analysis of bjt amplifiers
Small signal analysis of bjt amplifiers
PRAVEENA N G
microwave-tubes
 microwave-tubes microwave-tubes
microwave-tubes
ATTO RATHORE
Hall effect
Hall effect Hall effect
Hall effect
Harsh Shukla
Trapatt diode
Trapatt diodeTrapatt diode
Trapatt diode
Ankit Pandey
SEMICONDUCTOR PHYSICS
SEMICONDUCTOR PHYSICSSEMICONDUCTOR PHYSICS
SEMICONDUCTOR PHYSICS
Vaishnavi Bathina
Stick Diagram
Stick DiagramStick Diagram
Stick Diagram
Kalyan Acharjya
Photodetectors
PhotodetectorsPhotodetectors
Photodetectors
Engr Syed Absar Kazmi
Unit-I Characteristics of opamp
Unit-I Characteristics of opampUnit-I Characteristics of opamp
Unit-I Characteristics of opamp
Dr.Raja R
Optical Detector PIN photodiode
Optical Detector PIN photodiodeOptical Detector PIN photodiode
Optical Detector PIN photodiode
Dhruv Upadhaya
transmission-line-and-waveguide-ppt
transmission-line-and-waveguide-ppttransmission-line-and-waveguide-ppt
transmission-line-and-waveguide-ppt
ATTO RATHORE
SHORT CHANNEL EFFECTS IN MOSFETS- VLSI DESIGN
SHORT CHANNEL EFFECTS IN MOSFETS- VLSI DESIGNSHORT CHANNEL EFFECTS IN MOSFETS- VLSI DESIGN
SHORT CHANNEL EFFECTS IN MOSFETS- VLSI DESIGN
NITHIN KALLE PALLY
Wave guide tees
Wave guide teesWave guide tees
Wave guide tees
Keval Patel
Pin photodiode.pptx ashvani
Pin photodiode.pptx ashvaniPin photodiode.pptx ashvani
Pin photodiode.pptx ashvani
Ashvani Shukla
Basics of semiconductor, current equation, continuity equation, injected mino...
Basics of semiconductor, current equation, continuity equation, injected mino...Basics of semiconductor, current equation, continuity equation, injected mino...
Basics of semiconductor, current equation, continuity equation, injected mino...
Nidhee Bhuwal
Poissons and Laplaces Equation
Poissons and Laplaces EquationPoissons and Laplaces Equation
Poissons and Laplaces Equation
Abhishek Choksi
Signals & Systems PPT
Signals & Systems PPTSignals & Systems PPT
Signals & Systems PPT
Jay Baria
Small signal analysis of bjt amplifiers
Small signal analysis of bjt amplifiersSmall signal analysis of bjt amplifiers
Small signal analysis of bjt amplifiers
PRAVEENA N G
microwave-tubes
 microwave-tubes microwave-tubes
microwave-tubes
ATTO RATHORE

Similar to Continiuty Equation (20)

Basic potential step and sweep methods
Basic potential step and sweep methodsBasic potential step and sweep methods
Basic potential step and sweep methods
Getachew Solomon
Modeling Of Transfer Function Characteristic of Rlc-Circuit
Modeling Of Transfer Function Characteristic of Rlc-Circuit Modeling Of Transfer Function Characteristic of Rlc-Circuit
Modeling Of Transfer Function Characteristic of Rlc-Circuit
IOSR Journals
E017122733
E017122733E017122733
E017122733
IOSR Journals
Lecture 30 ac power. resonance. transformers.
Lecture 30   ac power. resonance. transformers.Lecture 30   ac power. resonance. transformers.
Lecture 30 ac power. resonance. transformers.
Albania Energy Association
Quantitative Modeling and Simulation of Single-Electron Transistor
Quantitative Modeling and Simulation of Single-Electron TransistorQuantitative Modeling and Simulation of Single-Electron Transistor
Quantitative Modeling and Simulation of Single-Electron Transistor
IRJET Journal
Resonant Response of RLC Circuits
Resonant Response of RLC Circuits Resonant Response of RLC Circuits
Resonant Response of RLC Circuits
Sachin Mehta
Kinetics of X-ray conductivity for an ideal wide-gap semiconductor irradiated...
Kinetics of X-ray conductivity for an ideal wide-gap semiconductor irradiated...Kinetics of X-ray conductivity for an ideal wide-gap semiconductor irradiated...
Kinetics of X-ray conductivity for an ideal wide-gap semiconductor irradiated...
Andrii Sofiienko
Mobility
MobilityMobility
Mobility
Amarendra Kumar
eco system The hamper is built from eco-friendly bamboo and includes two slid...
eco system The hamper is built from eco-friendly bamboo and includes two slid...eco system The hamper is built from eco-friendly bamboo and includes two slid...
eco system The hamper is built from eco-friendly bamboo and includes two slid...
Satyendra Singh
Chapter5 carrier transport phenomena
Chapter5 carrier transport phenomenaChapter5 carrier transport phenomena
Chapter5 carrier transport phenomena
K. M.
Dft calculation by vasp
Dft calculation by vaspDft calculation by vasp
Dft calculation by vasp
MIHIR RANJAN SAHOO
Other RLC resonant circuits and Bode Plots 2024.pptx
Other RLC resonant circuits and Bode Plots 2024.pptxOther RLC resonant circuits and Bode Plots 2024.pptx
Other RLC resonant circuits and Bode Plots 2024.pptx
DrOmarShAlyozbaky
Transmissions line power system btech notes
Transmissions line power system btech notesTransmissions line power system btech notes
Transmissions line power system btech notes
ShivamRai624135
wireless power transfer
wireless power transferwireless power transfer
wireless power transfer
Mimar Sinan Sara巽
Dynamics
DynamicsDynamics
Dynamics
nguyendattdh
wep153
wep153wep153
wep153
Raffaello Secondo
NAS-Ch3-Solutions of Equations
NAS-Ch3-Solutions of EquationsNAS-Ch3-Solutions of Equations
NAS-Ch3-Solutions of Equations
Hussain K
Lecture 3: Fundamental Limitations of Solar Cells
Lecture 3: Fundamental Limitations of Solar CellsLecture 3: Fundamental Limitations of Solar Cells
Lecture 3: Fundamental Limitations of Solar Cells
University of Liverpool
study of conductivity of fe2o3 using impedance spectroscopy
study of conductivity of fe2o3 using impedance spectroscopystudy of conductivity of fe2o3 using impedance spectroscopy
study of conductivity of fe2o3 using impedance spectroscopy
Priyanka Suri
Ch34 ssm
Ch34 ssmCh34 ssm
Ch34 ssm
Marta D鱈az
Basic potential step and sweep methods
Basic potential step and sweep methodsBasic potential step and sweep methods
Basic potential step and sweep methods
Getachew Solomon
Modeling Of Transfer Function Characteristic of Rlc-Circuit
Modeling Of Transfer Function Characteristic of Rlc-Circuit Modeling Of Transfer Function Characteristic of Rlc-Circuit
Modeling Of Transfer Function Characteristic of Rlc-Circuit
IOSR Journals
Lecture 30 ac power. resonance. transformers.
Lecture 30   ac power. resonance. transformers.Lecture 30   ac power. resonance. transformers.
Lecture 30 ac power. resonance. transformers.
Albania Energy Association
Quantitative Modeling and Simulation of Single-Electron Transistor
Quantitative Modeling and Simulation of Single-Electron TransistorQuantitative Modeling and Simulation of Single-Electron Transistor
Quantitative Modeling and Simulation of Single-Electron Transistor
IRJET Journal
Resonant Response of RLC Circuits
Resonant Response of RLC Circuits Resonant Response of RLC Circuits
Resonant Response of RLC Circuits
Sachin Mehta
Kinetics of X-ray conductivity for an ideal wide-gap semiconductor irradiated...
Kinetics of X-ray conductivity for an ideal wide-gap semiconductor irradiated...Kinetics of X-ray conductivity for an ideal wide-gap semiconductor irradiated...
Kinetics of X-ray conductivity for an ideal wide-gap semiconductor irradiated...
Andrii Sofiienko
eco system The hamper is built from eco-friendly bamboo and includes two slid...
eco system The hamper is built from eco-friendly bamboo and includes two slid...eco system The hamper is built from eco-friendly bamboo and includes two slid...
eco system The hamper is built from eco-friendly bamboo and includes two slid...
Satyendra Singh
Chapter5 carrier transport phenomena
Chapter5 carrier transport phenomenaChapter5 carrier transport phenomena
Chapter5 carrier transport phenomena
K. M.
Other RLC resonant circuits and Bode Plots 2024.pptx
Other RLC resonant circuits and Bode Plots 2024.pptxOther RLC resonant circuits and Bode Plots 2024.pptx
Other RLC resonant circuits and Bode Plots 2024.pptx
DrOmarShAlyozbaky
Transmissions line power system btech notes
Transmissions line power system btech notesTransmissions line power system btech notes
Transmissions line power system btech notes
ShivamRai624135
NAS-Ch3-Solutions of Equations
NAS-Ch3-Solutions of EquationsNAS-Ch3-Solutions of Equations
NAS-Ch3-Solutions of Equations
Hussain K
Lecture 3: Fundamental Limitations of Solar Cells
Lecture 3: Fundamental Limitations of Solar CellsLecture 3: Fundamental Limitations of Solar Cells
Lecture 3: Fundamental Limitations of Solar Cells
University of Liverpool
study of conductivity of fe2o3 using impedance spectroscopy
study of conductivity of fe2o3 using impedance spectroscopystudy of conductivity of fe2o3 using impedance spectroscopy
study of conductivity of fe2o3 using impedance spectroscopy
Priyanka Suri

Recently uploaded (20)

TPR Data strategy 2025 (1).pdf Data strategy
TPR Data strategy 2025 (1).pdf Data strategyTPR Data strategy 2025 (1).pdf Data strategy
TPR Data strategy 2025 (1).pdf Data strategy
Henry Tapper
Essentials of a Good PMO, presented by Aalok Sonawala
Essentials of a Good PMO, presented by Aalok SonawalaEssentials of a Good PMO, presented by Aalok Sonawala
Essentials of a Good PMO, presented by Aalok Sonawala
Association for Project Management
South Hornsey: The Lost Local Authority that Merged with Stoke Newington by T...
South Hornsey: The Lost Local Authority that Merged with Stoke Newington by T...South Hornsey: The Lost Local Authority that Merged with Stoke Newington by T...
South Hornsey: The Lost Local Authority that Merged with Stoke Newington by T...
History of Stoke Newington
Mate, a short story by Kate Grenville.pptx
Mate, a short story by Kate Grenville.pptxMate, a short story by Kate Grenville.pptx
Mate, a short story by Kate Grenville.pptx
Liny Jenifer
Rass MELAI : an Internet MELA Quiz Finals - El Dorado 2025
Rass MELAI : an Internet MELA Quiz Finals - El Dorado 2025Rass MELAI : an Internet MELA Quiz Finals - El Dorado 2025
Rass MELAI : an Internet MELA Quiz Finals - El Dorado 2025
Conquiztadors- the Quiz Society of Sri Venkateswara College
FESTIVAL: SINULOG & THINGYAN-LESSON 4.pptx
FESTIVAL: SINULOG & THINGYAN-LESSON 4.pptxFESTIVAL: SINULOG & THINGYAN-LESSON 4.pptx
FESTIVAL: SINULOG & THINGYAN-LESSON 4.pptx
DanmarieMuli1
Database population in Odoo 18 - Odoo slides
Database population in Odoo 18 - Odoo slidesDatabase population in Odoo 18 - Odoo slides
Database population in Odoo 18 - Odoo slides
Celine George
Reordering Rules in Odoo 17 Inventory - Odoo 際際滷s
Reordering Rules in Odoo 17 Inventory - Odoo 際際滷sReordering Rules in Odoo 17 Inventory - Odoo 際際滷s
Reordering Rules in Odoo 17 Inventory - Odoo 際際滷s
Celine George
CBSE Arabic Grammar - Class 10 ppt.pptx
CBSE Arabic Grammar - Class 10   ppt.pptxCBSE Arabic Grammar - Class 10   ppt.pptx
CBSE Arabic Grammar - Class 10 ppt.pptx
suhail849886
cervical spine mobilization manual therapy .pdf
cervical spine mobilization manual therapy .pdfcervical spine mobilization manual therapy .pdf
cervical spine mobilization manual therapy .pdf
SamarHosni3
Principle and Practices of Animal Breeding || Boby Basnet
Principle and Practices of Animal Breeding || Boby BasnetPrinciple and Practices of Animal Breeding || Boby Basnet
Principle and Practices of Animal Breeding || Boby Basnet
Boby Basnet
PUBH1000 Module 3: Public Health Systems
PUBH1000 Module 3: Public Health SystemsPUBH1000 Module 3: Public Health Systems
PUBH1000 Module 3: Public Health Systems
Jonathan Hallett
N.C. DPI's 2023 Language Diversity Briefing
N.C. DPI's 2023 Language Diversity BriefingN.C. DPI's 2023 Language Diversity Briefing
N.C. DPI's 2023 Language Diversity Briefing
Mebane Rash
How to use Init Hooks in Odoo 18 - Odoo 際際滷s
How to use Init Hooks in Odoo 18 - Odoo 際際滷sHow to use Init Hooks in Odoo 18 - Odoo 際際滷s
How to use Init Hooks in Odoo 18 - Odoo 際際滷s
Celine George
Computer Network Unit IV - Lecture Notes - Network Layer
Computer Network Unit IV - Lecture Notes - Network LayerComputer Network Unit IV - Lecture Notes - Network Layer
Computer Network Unit IV - Lecture Notes - Network Layer
Murugan146644
How to Manage Putaway Rule in Odoo 17 Inventory
How to Manage Putaway Rule in Odoo 17 InventoryHow to Manage Putaway Rule in Odoo 17 Inventory
How to Manage Putaway Rule in Odoo 17 Inventory
Celine George
Research & Research Methods: Basic Concepts and Types.pptx
Research & Research Methods: Basic Concepts and Types.pptxResearch & Research Methods: Basic Concepts and Types.pptx
Research & Research Methods: Basic Concepts and Types.pptx
Dr. Sarita Anand
English 4 Quarter 4 Week 4 Classroom Obs
English 4 Quarter 4 Week 4 Classroom ObsEnglish 4 Quarter 4 Week 4 Classroom Obs
English 4 Quarter 4 Week 4 Classroom Obs
NerissaMendez1
Year 10 The Senior Phase Session 3 Term 1.pptx
Year 10 The Senior Phase Session 3 Term 1.pptxYear 10 The Senior Phase Session 3 Term 1.pptx
Year 10 The Senior Phase Session 3 Term 1.pptx
mansk2
The Broccoli Dog's inner voice (look A)
The Broccoli Dog's inner voice  (look A)The Broccoli Dog's inner voice  (look A)
The Broccoli Dog's inner voice (look A)
merasan
TPR Data strategy 2025 (1).pdf Data strategy
TPR Data strategy 2025 (1).pdf Data strategyTPR Data strategy 2025 (1).pdf Data strategy
TPR Data strategy 2025 (1).pdf Data strategy
Henry Tapper
South Hornsey: The Lost Local Authority that Merged with Stoke Newington by T...
South Hornsey: The Lost Local Authority that Merged with Stoke Newington by T...South Hornsey: The Lost Local Authority that Merged with Stoke Newington by T...
South Hornsey: The Lost Local Authority that Merged with Stoke Newington by T...
History of Stoke Newington
Mate, a short story by Kate Grenville.pptx
Mate, a short story by Kate Grenville.pptxMate, a short story by Kate Grenville.pptx
Mate, a short story by Kate Grenville.pptx
Liny Jenifer
FESTIVAL: SINULOG & THINGYAN-LESSON 4.pptx
FESTIVAL: SINULOG & THINGYAN-LESSON 4.pptxFESTIVAL: SINULOG & THINGYAN-LESSON 4.pptx
FESTIVAL: SINULOG & THINGYAN-LESSON 4.pptx
DanmarieMuli1
Database population in Odoo 18 - Odoo slides
Database population in Odoo 18 - Odoo slidesDatabase population in Odoo 18 - Odoo slides
Database population in Odoo 18 - Odoo slides
Celine George
Reordering Rules in Odoo 17 Inventory - Odoo 際際滷s
Reordering Rules in Odoo 17 Inventory - Odoo 際際滷sReordering Rules in Odoo 17 Inventory - Odoo 際際滷s
Reordering Rules in Odoo 17 Inventory - Odoo 際際滷s
Celine George
CBSE Arabic Grammar - Class 10 ppt.pptx
CBSE Arabic Grammar - Class 10   ppt.pptxCBSE Arabic Grammar - Class 10   ppt.pptx
CBSE Arabic Grammar - Class 10 ppt.pptx
suhail849886
cervical spine mobilization manual therapy .pdf
cervical spine mobilization manual therapy .pdfcervical spine mobilization manual therapy .pdf
cervical spine mobilization manual therapy .pdf
SamarHosni3
Principle and Practices of Animal Breeding || Boby Basnet
Principle and Practices of Animal Breeding || Boby BasnetPrinciple and Practices of Animal Breeding || Boby Basnet
Principle and Practices of Animal Breeding || Boby Basnet
Boby Basnet
PUBH1000 Module 3: Public Health Systems
PUBH1000 Module 3: Public Health SystemsPUBH1000 Module 3: Public Health Systems
PUBH1000 Module 3: Public Health Systems
Jonathan Hallett
N.C. DPI's 2023 Language Diversity Briefing
N.C. DPI's 2023 Language Diversity BriefingN.C. DPI's 2023 Language Diversity Briefing
N.C. DPI's 2023 Language Diversity Briefing
Mebane Rash
How to use Init Hooks in Odoo 18 - Odoo 際際滷s
How to use Init Hooks in Odoo 18 - Odoo 際際滷sHow to use Init Hooks in Odoo 18 - Odoo 際際滷s
How to use Init Hooks in Odoo 18 - Odoo 際際滷s
Celine George
Computer Network Unit IV - Lecture Notes - Network Layer
Computer Network Unit IV - Lecture Notes - Network LayerComputer Network Unit IV - Lecture Notes - Network Layer
Computer Network Unit IV - Lecture Notes - Network Layer
Murugan146644
How to Manage Putaway Rule in Odoo 17 Inventory
How to Manage Putaway Rule in Odoo 17 InventoryHow to Manage Putaway Rule in Odoo 17 Inventory
How to Manage Putaway Rule in Odoo 17 Inventory
Celine George
Research & Research Methods: Basic Concepts and Types.pptx
Research & Research Methods: Basic Concepts and Types.pptxResearch & Research Methods: Basic Concepts and Types.pptx
Research & Research Methods: Basic Concepts and Types.pptx
Dr. Sarita Anand
English 4 Quarter 4 Week 4 Classroom Obs
English 4 Quarter 4 Week 4 Classroom ObsEnglish 4 Quarter 4 Week 4 Classroom Obs
English 4 Quarter 4 Week 4 Classroom Obs
NerissaMendez1
Year 10 The Senior Phase Session 3 Term 1.pptx
Year 10 The Senior Phase Session 3 Term 1.pptxYear 10 The Senior Phase Session 3 Term 1.pptx
Year 10 The Senior Phase Session 3 Term 1.pptx
mansk2
The Broccoli Dog's inner voice (look A)
The Broccoli Dog's inner voice  (look A)The Broccoli Dog's inner voice  (look A)
The Broccoli Dog's inner voice (look A)
merasan

Continiuty Equation

  • 2. INTRODUCTION The continuity equation which describes the distribution of electrons and holes when there is excess carrier generation recombination and carrier movement. We will consider some of the simplifications which are used for deriving the characteristics, how the equations can be simplified. And finally we will summarize the characteristic material parameters which describe a semiconductor device. So let us begin with the continuity equation.
  • 3. As per law of conservation of charge rate of change of number of electrons inside the semiconductor is equal to the no of electrons entering per second minus number of electrons leaving per second plus number of electrons generated per second by generation process minus number of electrons lost per second by recombination process.
  • 4. Derivation of Continuity Equation Consider carrier-flux into/out-of an infinitesimal volume: Jn(x) Jn(x+dx) dx Area A, volume Adx AdxRAdxGAdxxJAxJ qt n Adx nnnn 緒 )()( 1 Continuity Equation TEC-101
  • 6. Summary: Continuity Equations The continuity equations are established based on conservation of carriers, and therefore hold generally: The minority carrier diffusion equations are derived from the continuity equations, specifically for minority carriers under certain conditions (small E-field, low-level injection, uniform doping profile): Lp n Ln n GR x xJ qt p GR x xJ qt n )(1)(1 Lp n P n Ln p N p GR x p D t p GR x n D t n 2 2 2 2 TEC-101Continuity Equation