ECE 875: Electronic Devices

ECE 875:Electronic Devices

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State [email protected]

VM Ayres, ECE875, S14

Chp. 01

Crystals:HW01 solutions

Energy levels: E-k Effective mass mij*vgroup

Egap is a function of temperature T

Lecture 05, 17 Jan 14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

R’ ≠ R

VM Ayres, ECE875, S14

math except 0

physically: to describe |R’|: Z = a whole number ≠ 0

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

Pr. 1.04 and 1.05: Useful for electron on x-ray diffraction:

k-spaceSAED diffraction pattern

VM Ayres, ECE875, S14

Electronics: Transport: e-’s moving in an environment

Correct e- wave function in a crystal environment: Bloch function:Sze:r,k) = exp(jk.r)Ub(r,k) = (r + R,k)

Correct E-k energy levels versus direction of the environment: minimum = Egap

Correct concentrations of carriers n and p

Correct current and current density J: moving carriersI-V measurementJ: Vext direction versus internal E-k: Egap direction

Fixed e-’s and holes:C-V measurement

x Probability f0 that energy level is occupied

q n, p velocity Area

(KE + PE) (r,k) = E (r,k)

Pr. 1.05: Useful for (r,k):

VM Ayres, ECE875, S14

HW01:

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

Why assigned:fcc

bcc

Start:

Find a*, b*, c*:

Get similar

VM Ayres, ECE875, S14

This Wigner-Sietz cell of bcc reciprocal space ‘structure’ = is the 1st Brillouin zone for all fcc primitive cell-based crystals:

The fcc a*, b*, c* looks likea bcc arrangement.

Take ┴ bisector planes midway between the atoms

VM Ayres, ECE875, S14

fcc-type Wigner Seitz cell is useful for HW02 Pr. 1.08: Si:

VM Ayres, ECE875, S14

Chp. 01

Crystals:HW01 solutions

Energy levels: E-k Effective mass mij*vgroup

Egap is a function of temperature T

Lecture 05, 17 Jan 14

VM Ayres, ECE875, S14

E

k

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

Given:

Can you find an effective mass? A group velocity?

VM Ayres, ECE875, S14

Egap as a function of temperature T:

Sze, p. 15: Stated without proof:This approximation in eq’n (12) works well in Si and GaAs:

T

TKETE gapgap

2

0

VM Ayres, ECE875, S14

Egap as a function of temperature T:

Sze, p. 15: Stated without proof:This approximation in eq’n (12) works well in most cases:

T

TKETE gapgap

2

0

VM Ayres, ECE875, S14

Egap as a function of temperature T:

Sze, p. 15: Stated without proof:This approximation in eq’n (12) works well in most cases:

T

TKETE gapgap

2

0

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

Egap (0 K) is in Appendix F; an are not

Note that everything is 300 K except Egap (0 K) Note differences between Egap (300 K) and Egap (0 K)

VM Ayres, ECE875, S14

and for Si and GaAs are given in Sze Fig. 06

Literature

Ioffe

Extrapolated Egap (0 K)

VM Ayres, ECE875, S14

Example problem:

A satellite in low earth orbit experiences a temperature swing of +200oC sun side to – 200oC dark side. Its electronics are Si-based. Find the range of Egap and compare it to operation on earth.

VM Ayres, ECE875, S14

Example problem:

A satellite in low earth orbit has a temperature swing of +200oC sun side to – 200oC dark side over 24 h. Its electronic are Si-based. Find the range of Egap and compare it to operation on earth.

T = 200oC = 473 K

T = - 200oC = 73 K

Egap (73 K): graph estimate: 1.16 eVEgap (300 K): on graph: 1.12 eVEgap (473 K): graph estimate: 1.08 eV

Calculated solution or graphical solution

VM Ayres, ECE875, S14

Will explore further in photodetector sensitivities in Chp. 13