ECE 875:Electronic Devices

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu

VM Ayres, ECE875, S14

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 junctionExamples

Lecture 16, 14 Feb 14

Jgen = ?

OR

Jrec = ?

Which: are you in forward or reverse bias?What happens to the depletion region WD?

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

g = everything that’s left in U

g is given = 1 x 10-5 sec

If: Assume: Si @ 300 K:

Jgen-rec = q U length

Jgen-rec =

Vext = Vrev = -2 V

VM Ayres, ECE875, S14

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 junctionExamples

Lecture 16, 14 Feb 14

Remember this sequence in real research: find:

1. Charge Q and charge density

2. Electric field E

3. Potential

4. Energy barrier q

5. Depletion region WD or equivalent local region

6. C-V

7. I-V

Q and = Constant values

E (x)

i(x)

q i(x)

Abrupt junction:

For Abrupt junction: find:

1. Charge Q and charge density

2. Electric field E

3. Potential

4. Energy barrier q

Charge density = all relevant concentrations:

VM Ayres, ECE875, S14

For Abrupt junction: find:

1. Charge Q and charge density

2. Electric field E

3. Potential

4. Energy barrier q

Internal electric field E (x): must find separately on p-side and n-side:

VM Ayres, ECE875, S14

Note: Linear:

VM Ayres, ECE875, S14

Internal electric field E (x): must find separately on p-side and n-side:

Internal electric field E (x):

VM Ayres, ECE875, S14

Note: Linear:

Solve for maximum value of E –field:

VM Ayres, ECE875, S14

For Abrupt junction: find:

1. Charge Q and charge density

2. Electric field E

3. Potential

4. Energy barrier q

Find: potential i(x):(Practical: you may be able to measure a potential drop: i(x2) - i(x1) )

+

VM Ayres, ECE875, S14

Can integrate this!

Potential i(x): must find separately on p-side and n-side:

p-side of depletion region:

VM Ayres, ECE875, S14

n-side of depletion region:

VM Ayres, ECE875, S14

Potential i(x): must find separately on p-side and n-side:

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

bi is the potential drop across the whole depletion region – what you mainly measure. Can we say anything

about this factor

VM Ayres, ECE875, S14

bi 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 Nintercept equilibrium potential bi

0

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

V = Vbattery

Example:(a) find the slope and set up the calculation for N(b) find the intercept and set up the calculation for bi

(a)

(b)

Example:

Linearly graded junction: power of x raised by 1:

Q and = linear = Constant x x

E (x)

i(x)

q i(x)

Linearly graded junction: power of x raised by 1:

= linear = Constant “a” x x

An experimental measure for the linearly graded junction: C-V curve:

VM Ayres, ECE875, S14

Missing 2kT/q in (38)

slope

intercept Experimentally sweep this

Example:

Excel (below) or Matlab:

Answer:

Given: abrupt p+n junction