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MIT6_012F09_lec03

# MIT6_012F09_lec03 - 6.012 Electronic Devices and Circuits...

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6.012 - Electronic Devices and Circuits Lecture 3 - Solving The Five Equations - Outline Announcements Handouts - 1. Lecture; 2. Photoconductivity; 3. Solving the 5 eqs. See website for Items 2 and 3. Review 5 unknowns: n(x,t), p(x,t), J e (x,t), J h (x,t), E(x,t) 5 equations: Gauss's law (1), Currents (2), Continuity (2) What isn't covered: Thermoelectric effects; Peltier cooling Special cases we can solve (approximately) by hand Carrier concentrations in uniformly doped material (Lect. 1) Uniform electric field in uniform material (drift) (Lect. 1) Low level uniform optical injection (LLI, τ min ) (Lect. 2) Photoconductivity (Lect. 2) Doping profile problems (depletion approximation) (Lects. 3,4) Non-uniform injection (QNR diffusion/flow) (Lect. 5) Doping profile problems Electrostatic potential Poisson's equation Clif Fonstad, 9/17/09 Lecture 3 - Slide 1

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Non-uniform doping/excitation: Summary What we have so far: Five things we care about (i.e. want to know): Hole and electron concentrations: Hole and electron currents: Electric field: p ( x , t ) and n ( x , t ) J hx ( x , t ) and J ex ( x , t ) E x ( x , t ) And, amazingly, we already have five equations relating them: Hole continuity: Electron continuity: Hole current density: Electron current density: Charge conservation: " p ( x , t ) " t + 1 q " J h ( x , t ) " x = G # R \$ G ext ( x , t ) # n ( x , t ) p ( x , t ) # n i 2 [ ] r ( t ) " n ( x , t ) " t # 1 q " J e ( x , t ) " x = G # R \$ G ext ( x , t ) # n ( x , t ) p ( x , t ) # n i 2 [ ] r ( t ) J h ( x , t ) = q μ h p ( x , t ) E ( x , t ) # qD h " p ( x , t ) " x J e ( x , t ) = q μ e n ( x , t ) E ( x , t ) + qD e " n ( x , t ) " x % ( x , t ) = " & ( x ) E x ( x , t ) [ ] " x \$ q p ( x , t ) # n ( x , t ) + N d ( x ) # N a ( x ) [ ] So...we're all set, right? No, and yes ..... Clif Fonstad, 9/17/09 Lecture 3 - Slide 2 We'll see today that it isn't easy to get a general solution, but we can prevail.
Thermoelectric effects * - the Seebeck and Peltier effects (current fluxes caused by temperature gradients, and visa versa) Hole current density, isothermal conditions: Drift Diffusion J h = μ h p " d q # [ ] dx \$ % & ( ) + qD h " dp dx \$ % & ( ) Hole potential Concentration energy gradient gradient Hole current density, non- isothermal conditions: Drift Diffusion Seebeck Effect J h = μ h p " d q # [ ] dx \$ % & ( ) + qD h " dp dx \$ % & ( ) + qS h p " dT dx \$ % & ( ) Temperature gradient Seebeck Effect: temperature gradient current Generator Peltier Effect: current temperature gradient Cooler/heater * A cultural item; we will only consider isothermal Clif Fonstad, 9/17/09 Lecture 3 - Slide 3 situations on 6.012 exams and problem sets.

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Thermoelectric effects - the Seebeck and Peltier effects Two examples: Right - The hot point probe, an apparatus for determining the carrier type of semiconductor samples. Below - A thermoelectric array like those in thermoelectric generators and solid-state refrigerators. (current fluxes caused by temperature gradients, and visa versa) Clif Fonstad, 9/17/09 Ref.: Appendix B in the course text. Lecture 3 - Slide 4
Thermoelectric Generators and Coolers - Cooling/heating for the necessities of life Image of thermoelectric wine cooler removed due to copyright restrictions.

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