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

Lecture 16, 14 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 Examples VM Ayres, ECE875, S14

Which: are you in forward or reverse bias? Jgen = ? OR Jrec = ? Which: are you in forward or reverse bias? What happens to the depletion region WD? VM Ayres, ECE875, S14

1/tg = everything that’s left in U VM Ayres, ECE875, S14

Jgen-rec = q U length Jgen-rec = tg is given = 1 x 10-5 sec If: Assume: Si @ 300 K:

Vext = Vrev = -2 V

Lecture 16, 14 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 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)

For Abrupt junction: find: Charge Q and charge density r Electric field E Potential y Energy barrier q y

Charge density r = all relevant concentrations: VM Ayres, ECE875, S14

For Abrupt junction: find: Charge Q and charge density r Electric field E Potential y Energy barrier q y

Internal electric field E (x): must find separately on p-side and n-side: Note: Linear: VM Ayres, ECE875, S14

Internal electric field E (x): must find separately on p-side and n-side: VM Ayres, ECE875, S14

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

Solve for maximum value of E –field: VM Ayres, ECE875, S14

For Abrupt junction: find: Charge Q and charge density r Electric field E Potential y Energy barrier q y

Find: potential yi(x): (Practical: you may be able to measure a potential drop: yi(x2) - yi(x1) ) + Can integrate this! VM Ayres, ECE875, S14

Potential yi(x): must find separately on p-side and n-side: p-side of depletion region: VM Ayres, ECE875, S14

Potential yi(x): must find separately on p-side and n-side: n-side of depletion region: VM Ayres, ECE875, S14

Example: find the potential drop across the p-side of the depletion region VM Ayres, ECE875, S14

Answer: potential DROP: Eq’n (15a) VM Ayres, ECE875, S14

At least have an experimental estimate of E max ybi is the potential drop across the whole depletion region – what you mainly measure. At least have an experimental estimate of E max Can we say anything about this factor VM Ayres, ECE875, S14

ybi is the potential drop across the whole depletion region – what you mainly measure. You know how you doped NA and ND – but could have hidden impurities or a bad doping process WD = VM Ayres, ECE875, S14

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

Useful parts on C-V graph: slope  concentration N intercept  equilibrium potential ybi V = Vbattery VM Ayres, ECE875, S14

The 2 x kT/q correction factor: Shielding by neutral region electrons Shielding by neutral region holes VM Ayres, ECE875, S14

Example: (a) find the slope and set up the calculation for N (b) find the intercept and set up the calculation for ybi V = Vbattery

(a)

(b)

Example:

Linearly graded junction: power of x raised by 1: Q and r = linear = Constant x 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: Given: abrupt p+n junction