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

Lecture 17, 17 Feb 14 Chp. 02: pn junction: Abrupt pn junction Linearly graded pn junction Both: Experimental measurements: C-V curves Examples VM Ayres, ECE875, S14

Remember this sequence in real research: find: Charge Q and charge density r Electric field E Potential y Energy barrier q y Depletion region WD or equivalent local region C-V I-V

Abrupt junction: Q and r = Constant values E (x) yi(x) q yi(x)

An experimental measure for the Abrupt junction: C-V curve: VM Ayres, ECE875, S14

Example: HW05: Sze Pr. 2.02 (a) find the slope and set up the calculation for N (b) find the intercept and set up the calculation for ybi Slope ~ 1/N: V = Vbattery

Realistic experimental result: VM Ayres, ECE875, S14

Example:

Linearly graded junction: power of x raised by 1: Achieve by co-doping Q and r = linear = Constant x x = a x E (x) yi(x) q yi(x)

Linearly graded junction: power of x raised by 1: r = linear = Constant “a” x x

An experimental measure for the linearly graded junction: C-V curve: Missing 2kT/q in (38) intercept Experimentally sweep this slope VM Ayres, ECE875, S14

Example:

Excel (below) or Matlab:

Answer: And given: it is an abrupt p+n junction

Example:

Slope Intercept

Slope:

Given: p+n: N =

Intercept

Answer: 6 properties:

Given: p+n: WD

What is LD: the Debye length:

Debye length:

Debye length: 1. working definition of a good abrupt junction 2. watch out for circumstances that can create a small depletion width WD < LD

In Example: ✔

Lecture 17, 17 Feb 14 Chp. 02: pn junction: Abrupt pn junction Linearly graded pn junction Both: Experimental measurements: C-V curves Examples VM Ayres, ECE875, S14

Linearly graded junction: power of x raised by 1: Achieve by co-doping Q and r = linear = Constant x x = a x E (x) yi(x) q yi(x)

Steps 1-3:

E –field = E (x), and E max:

Potential yi(x), and ybi:

An experimental measure for the linearly graded junction: C-V curve: Missing 2kT/q in (38) intercept Experimentally sweep this slope VM Ayres, ECE875, S14