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ECE162-Lecture-06-Principles-Device-Analysis

# ECE162-Lecture-06-Principles-Device-Analysis - ECE 162...

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ECE 162 FUNDAMENTALS OF MICROELECTRONIC DEVICES Lecture 06 PRINCIPLES OF SEMICONDUCTOR DEVICE ANALYSIS Professor Hisham Z. Massoud Department of Electrical and Computer Engineering Fitzpatrick Building, Room 3521 Duke University, Durham, NC 27708–0291 [email protected] https://courses.duke.edu/webapps/portal/frameset.jsp ECE 162 Chapter 05 – Principles of Semiconductor Device Analysis Lecture 06.1

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LECTURE 06 - TOPICS 1. The Net-Charge Concentration 2. Charge Neutrality and Quasi-neutrality 3. Relationship Between the Electric Field and the Electrostatic Potential 4. Relationship Between the Net-Charge Concentration and the Electric Field 5. Relationship Between the Net-Charge Concentration and the Electrostatic Potential 6. The Current-Density Equations 7. The Carrier-Continuity Equations 8. Relationship Between the Electrostatic Potential and the Thermal-Equilibrium Carrier Concentrations 9. Interface Conditions ECE 162 Chapter 05 – Principles of Semiconductor Device Analysis Lecture 06.2
1. THE NET-CHARGE CONCENTRATION The constituents of the net-charge concentrations are electrons, holes, and ionized donor and acceptor atoms. In general, it is given by % ( ~ r, t ) q h p ( ~ r, t ) - n ( ~ r, t ) + N + d ( ~ r ) - N - a ( ~ r ) i . In static one-dimensional problems, it is given by % ( x ) q h p ( x ) - n ( x ) + N + d ( x ) - N - a ( x ) i . This definition of the net-charge concentration does not include the con- centrations of charges trapped on structural, chemical, and electrical-stress- induced defects in semiconductors or dielectrics. ECE 162 Chapter 05 – Principles of Semiconductor Device Analysis Lecture 06.3

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2. CHARGE NEUTRALITY AND QUASI-NEUTRALITY In a uniformly doped semiconductor region at thermal equilibrium, charge neutrality is satisfied. The charge-neutrality condition is expressed as p + N + d = n + N - a . where n and p are the thermal-equilibrium concentrations of electrons and holes, respectively. In non-equilibrium conditions, majority carriers readily move and change their concentration with time in order to reduce and, ultimately, eliminate any deviations from charge neutrality. Time-dependent deviations from charge neutrality decrease with a characteristic time constant on the order of the dielectric relaxation time τ diel , given by τ diel = Si σ , where σ is the silicon conductivity. ECE 162 Chapter 05 – Principles of Semiconductor Device Analysis Lecture 06.4
2. CHARGE NEUTRALITY AND QUASI-NEUTRALITY Position-dependent deviations from charge neutrality disappear within a few extrinsic Debye lengths L D , given by L D,P = q D p,P τ diel,P or L D,N = q D n,N τ diel,N , where D p,P and D n,N are the majority-carrier diffusion coefficients, and τ diel,P and τ diel,N the dielectric relaxation times in p -type and n -type silicon, respec- tively. In non-equilibrium conditions where quasi-neutrality can be assumed to be valid, i.e., where charge deviations from neutrality are assumed to be small, the concentrations of electrons and holes are given by p ( x, t ) p ( x ) + Δ p ( x, t ) and n ( x, t ) n ( x ) + Δ n ( x, t ) , where Δ n ( x, t ) Δ p ( x, t ) and Δ n ( x, t ) ∂x Δ

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ECE162-Lecture-06-Principles-Device-Analysis - ECE 162...

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