1. 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 of semiconductors  Diodes and other electronic devices Some of the lecture materials are from slides prepared by Marder

2. 3/30/2015PHY 752 Spring 2015 -- Lecture 262

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

4. 3/30/2015PHY 752 Spring 2015 -- Lecture 264 Charge and voltage profile near a semiconductor p-n junction Internal voltage:

5. 3/30/2015PHY 752 Spring 2015 -- Lecture 265 Charge and voltage profile near a semiconductor p-n junction Simplified model:

6. 3/30/2015PHY 752 Spring 2015 -- Lecture 266 Charge and voltage profile near a semiconductor p-n junction Simplified model – continued:

7. 3/30/2015PHY 752 Spring 2015 -- Lecture 267 Charge and voltage profile near a semiconductor p-n junction Effects of adding an applied voltage to junction

8. 3/30/2015PHY 752 Spring 2015 -- Lecture 268 Charge and voltage profile near a semiconductor p-n junction V A =0 V A <0 V A >0  (x) V(x)

9. 3/30/2015PHY 752 Spring 2015 -- Lecture 269 Boltzmann equation treatment of current response to diode (relaxation time approximation)

10. 3/30/2015PHY 752 Spring 2015 -- Lecture 2610 Boltzmann equation treatment of current response to diode (relaxation time approximation) electron mobility electron diffusion coefficient; Einstein relation

11. 3/30/2015PHY 752 Spring 2015 -- Lecture 2611 Boltzmann equation treatment of current response to diode (relaxation time approximation) Summary of equations:

12. 3/30/2015PHY 752 Spring 2015 -- 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:

13. 3/30/2015PHY 752 Spring 2015 -- Lecture 2613 -VA-VA p majority n minority n majority p minority Estimation of minority carriers

14. 3/30/2015PHY 752 Spring 2015 -- Lecture 2614 Boltzmann equation treatment of current response to diode Approximate steady state solutions in presence of applied voltage V A = 0 ≈ 0 

15. 3/30/2015PHY 752 Spring 2015 -- 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

16. 3/30/2015PHY 752 Spring 2015 -- Lecture 2616 Boltzmann equation treatment of current response to diode Approximate steady state solutions in presence of applied voltage V A

17. 3/30/2015PHY 752 Spring 2015 -- Lecture 2617 Behavior of diode: j V A <0 V A >0