ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

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

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

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

Example: Sze Fig: V = Vbattery

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

Where is C: depletion region of a pn junction:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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