1. EE 5340 Semiconductor Device Theory Lecture 08 – Spring 2011
Professor Ronald L. Carter

2. Second Assignment Submit a signed copy of the document posted at
©rlc L08-15Feb2011

3. Test 1 – Tuesday 22Feb11 11 AM Room 129 ERB
Covering Lectures 1 through 9
Open book - 1 legal text or ref., only.
You may write notes in your book.
Calculator allowed
A cover sheet will be included with full instructions. For examples see
©rlc L08-15Feb2011

4. Diffused or Implanted IC Resistor (Fig 2.451)
©rlc L08-15Feb2011

5. An IC Resistor with L = 8W (M&K)1
©rlc L08-15Feb2011

6. Typical IC doping profile (M&K Fig. 2.441)
©rlc L08-15Feb2011

7. Mobilities**
©rlc L08-15Feb2011

8. IC Resistor Conductance
©rlc L08-15Feb2011

9. An IC Resistor with Ns = 8, R = 8Rs (M&K)1
©rlc L08-15Feb2011

10. The effect of lateral diffusion (M&K1)
©rlc L08-15Feb2011

11. A serpentine pattern IC Resistor (M&K1)
R = NSRS NCRS
note: RC = 0.65RS
©rlc L08-15Feb2011

12. Fermi Energy
The equilibrium carrier concentration ahd the Fermi energy are related as
The potential f = (Ef-Efi)/q
If not in equilibrium, a quasi-Fermi level (imref) is used
©rlc L08-15Feb2011

13. Electron quasi-Fermi Energy (n = no + n)
©rlc L08-15Feb2011

14. Hole quasi-Fermi Energy (p = po + p)
©rlc L08-15Feb2011

15. Ex-field when Ef - Efi not constant
Since f = (Ef - Efi)/q = Vt ln(no/ni)
When Ef - Efi = is position dependent,
Ex = -df/dx = -[d(Ef-Efi)/dx] = - Vt d[ln(no/ni)]/dx
If non-equilibrium fn = (Efn-Efi)/q = Vt ln(n/ni), etc
Exn = -[dfn/dx] = -Vt d[ln(n/ni)]/dx
©rlc L08-15Feb2011

16. Si and Al and model (approx. to scale)
metal
n-type s/c
p-type s/c Eo Eo Eo
qcsi~ 4.05 eV
qcsi~ 4.05 eV
qfm,Al ~ 4.1 eV
qfs,n
qfs,p Ec Ec
EFm
EFn
EFi
EFi
EFp Ev Ev
©rlc L08-15Feb2011

17. Making contact be- tween metal & s/c
Equate the EF in the metal and s/c materials far from the junction
Eo(the free level), must be continuous across the jctn.
N.B.: qc = 4.05 eV (Si),
and qf = qc + Ec - EF Eo
qc (electron affinity) qf
(work function) Ec EF
EFi
qfF Ev
©rlc L08-15Feb2011

18. Equilibrium Boundary Conditions w/ contact
No discontinuity in the free level, Eo at the metal/semiconductor interface.
EF,metal = EF,semiconductor to bring the electron populations in the metal and semiconductor to thermal equilibrium.
Eo - EC = qcsemiconductor in all of the s/c.
Eo - EF,metal = qfmetal throughout metal.
©rlc L08-15Feb2011

19. Ideal metal to n-type barrier diode (fm>fs,Va=0)
n-type s/c
No disc in Eo
Ex=0 in metal ==> Eoflat
fBn=fm- cs = elec mtl to s/c barr
fi=fBn-fn= fm-fs elect s/c to mtl barr Eo
qfm
qcs
qfi
qfBn
qfs,n Ec
EFm
EFn
EFi
Depl reg Ev
qf’n
©rlc L08-15Feb2011

20. Metal to n-type non-rect cont (fm<fs)
n-type s/c
No disc in Eo
Ex=0 in metal ==> Eo flat
fB,n=fm - cs = elec mtl to s/c barr
fi= fBn-fn< 0
Accumulation region Eo
qcs
qfm
qfs,n
qfi
qfB,n Ec
EFm
EFn
EFi Ev
qfn
Acc reg
©rlc L08-15Feb2011

21. Ideal metal to p-type barrier diode (fm<fs)
EFp Eo Ec Ev
EFi
qfs,p
qcs
p-type s/c
qfm
EFm
metal
qfBn
qfi
qfp<0
Depl reg
qfBp
No disc in Eo
Ex=0 in metal ==> Eoflat
fBn= fm- cs = elec mtl to s/c barr.
fBp= fm- (cs + Eg)= hole m to s barr.
fi = fm-fs,p = hole s/c to mtl barr.
©rlc L08-15Feb2011

22. Metal to p-type non-rect cont (fm>fs)
EFi Eo Ec Ev
EfP
qfs,n
qcs
n-type s/c
qfm
EFm
metal
qfBn
q(fi)
qfp
Accum reg
qfBp
qfi
No disc in Eo
Ex=0 in metal ==> Eo flat
fB,n = fm - cs = elec mtl to s/c barr
fBp= fm- (cs + Eg) = hole m to s
fi = fm-fs,n = s/c to mtl barr.
©rlc L08-15Feb2011

23. Metal/semiconductor system types
n-type semiconductor
Schottky diode - blocking for fm > fs
contact - conducting for fm < fs
p-type semiconductor
contact - conducting for fm > fs
Schottky diode - blocking for fm < fs
©rlc L08-15Feb2011

24. References
1 and M&KDevice Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, See Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996, for another treatment of the m model.
2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981.
3 and **Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997.
Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989.
©rlc L08-15Feb2011