1. ECE 875: Electronic Devices
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University

2. Lecture 15, 12 Feb 14 Hw 04: FRI: Pr. 2.07 Chp. 02: pn junction:
Experimental measurements for concentration:
Hall effect – Chp. 01: material:
measure VAB, and I, choose dimensions and Bext
C-V – Chp. 02: pn junction
Two realistic configurations beyond abrupt linear pn junction:
Linearly graded junction
Double layer junction: important, develops at interfaces
VM Ayres, ECE875, S14

3. Lecture 15, 12 Feb 14 Hw 04: FRI: Pr. 2.07 Chp. 02: pn junction:
Experimental measurements for concentration:
Hall effect – Chp. 01: material:
measure VAB, and I, choose dimensions and Bext
C-V – Chp. 02: pn junction
Two realistic configurations beyond abrupt linear pn junction:
Linearly graded junction
Double layer junction: important, develops at interfaces
VM Ayres, ECE875, S14

4. Example:
Sweep the voltage
Instrument reads out C typically in Farads

5. Example: Sze Fig:
V = Vbattery

6. Where is C: depletion region of a pn junction:
Can show equivalence to parallel plate capacitor:
- Qtotal es
+ Qtotal

7. Where is C: depletion region of a pn junction:

8. Where you measure: C-V = same as I-V:
= SMU
+Vext-
Sweep the voltage p+ n WD
= WDp + WDn

9. Lecture 15, 12 Feb 14 Hw 04: FRI: Pr. 2.07 Chp. 02: pn junction:
Experimental measurements for concentration:
Hall effect – Chp. 01: material:
measure VAB, and I, choose dimensions and Bext
C-V – Chp. 02: pn junction
VM Ayres, ECE875, S14

10. pn junction at equilibrium: ECE 474: Streetman & Bannerjee
VM Ayres, ECE875, S14

11. pn junction at equilibrium: ECE 474: Streetman & Bannerjee
Q = charge density r x Vol
r = q with sign (ND+ or NA-)
Poisson equation relates charge to electric field E :
dE /dx = r/ese0
(material is not polarized or magnetic)
VM Ayres, ECE875, S14

12. Abrupt pn junction at equilibrium: ECE 875: Sze:
Q = charge density r x Vol
r = q with sign (ND+ or NA-) p n
Poisson equation
dE /dx = r/ese0
Solve for E
Solve for built in potential ybi  V0
Any potential:
= Area
VM Ayres, ECE875, S14

13. Abrupt pn junction at equilibrium: Sze: names:
Potential V0  ybi
Potential barrier qV0  qybi
p-side: Ei – EF  qyBp
n-side: EF – Ei  qyBn
p-side: EF – EV  qfp
n-side: EC – EF  qfn
Potential drop across depletion region WD=
Pot’l drop across p-side of WD + pot’l drop across n-side of WD : ybi = yp + |yn|
Potential drop from 0 to x in WD: yi(x)
VM Ayres, ECE875, S14

14. Important questions are:
What is the magnitude and direction of the internal electric field?
What are the values of the various potential drops that matter?
Can I get an experimental measure of anything?
VM Ayres, ECE875, S14

15. What is the magnitude and direction of the internal electric field
What is the magnitude and direction of the internal electric field? Can I get an experimental measure of anything?
An antenna probe won’t work inside a solid
-no direct experimental measure of E (x) -x
E direction
-WDp =
= WDn
VM Ayres, ECE875, S14

16. E direction E magnitude: f(x)
What is the magnitude and direction of the internal electric field? Can I get an experimental measure of anything? -x
E direction
About the directions:
E (x) direction = -x
dx from/to direction = +x
x is + from 0 to WDn
x is – from –WDp to 0
E magnitude: f(x)
-WDp =
= WDn

17. What are the values of the various potential drops that matter
What are the values of the various potential drops that matter? Can I get an experimental measure of anything?
Yes: can get an experimental measure of potential. The loop will include the built-in potential ybi and Vext and any IR drops.
Total potential drop Vp-to-n is mainly across W
ybi
Vext
VM Ayres, ECE875, S14
= SMU

18. Potential energy barrier and built-in potential in terms of dopants:
But what if doping concentrations are not what you think?
VM Ayres, ECE875, S14

19. Internal electric field E (x): in WD:
VM Ayres, ECE875, S14

20. Internal electric field E (x):
Note: Linear:
VM Ayres, ECE875, S14

21. Internal electric field E (x):
Can solve for maximum value of E -field:
VM Ayres, ECE875, S14

22. Internal electric field E (x):
VM Ayres, ECE875, S14

23. Internal electric field E (x):
Note: Linear:
VM Ayres, ECE875, S14

24. Go from electric field E (x) to potential yi(x)
Go from electric field E (x) to potential yi(x). Why: you may be able to measure a potential drop. +
Can integrate this!
= E 0 x + C
VM Ayres, ECE875, S14

25. Must separate this into p-side and n-side of depletion region answers:
p-side of depletion region:
VM Ayres, ECE875, S14