3/30/2015PHY 752 Spring 2015 -- Lecture 261 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 26:  Chap. 19 in Marder  Properties.

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Presentation transcript:

3/30/2015PHY 752 Spring Lecture 261 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 26:  Chap. 19 in Marder  Properties of semiconductors  Diodes and other electronic devices Some of the lecture materials are from slides prepared by Marder

3/30/2015PHY 752 Spring Lecture 262

3/30/2015PHY 752 Spring Lecture 263 Charge and voltage profile near a semiconductor p-n junction Equilibrium distributions

3/30/2015PHY 752 Spring Lecture 264 Charge and voltage profile near a semiconductor p-n junction Internal voltage:

3/30/2015PHY 752 Spring Lecture 265 Charge and voltage profile near a semiconductor p-n junction Simplified model:

3/30/2015PHY 752 Spring Lecture 266 Charge and voltage profile near a semiconductor p-n junction Simplified model – continued:

3/30/2015PHY 752 Spring Lecture 267 Charge and voltage profile near a semiconductor p-n junction Effects of adding an applied voltage to junction

3/30/2015PHY 752 Spring Lecture 268 Charge and voltage profile near a semiconductor p-n junction V A =0 V A <0 V A >0  (x) V(x)

3/30/2015PHY 752 Spring Lecture 269 Boltzmann equation treatment of current response to diode (relaxation time approximation)

3/30/2015PHY 752 Spring Lecture 2610 Boltzmann equation treatment of current response to diode (relaxation time approximation) electron mobility electron diffusion coefficient; Einstein relation

3/30/2015PHY 752 Spring Lecture 2611 Boltzmann equation treatment of current response to diode (relaxation time approximation) Summary of equations:

3/30/2015PHY 752 Spring Lecture 2612 Boltzmann equation treatment of current response to diode Approximate solution ignoring “minority” carriers and assuming spatially constant currents j n and j p For HW, you will show that the above solutions are consistent with the equations:

3/30/2015PHY 752 Spring Lecture VA-VA p majority n minority n majority p minority Estimation of minority carriers

3/30/2015PHY 752 Spring Lecture 2614 Boltzmann equation treatment of current response to diode Approximate steady state solutions in presence of applied voltage V A = 0 ≈ 0 

3/30/2015PHY 752 Spring Lecture 2615 Boltzmann equation treatment of current response to diode Approximate steady state solutions in presence of applied voltage V A Solution to diffusion equations: for x>x n for x<x p

3/30/2015PHY 752 Spring Lecture 2616 Boltzmann equation treatment of current response to diode Approximate steady state solutions in presence of applied voltage V A

3/30/2015PHY 752 Spring Lecture 2617 Behavior of diode: j V A <0 V A >0