EE 5340
Semiconductor Device Theory
Lecture 08 – Spring 2011
Professor Ronald L. Carter
ronc@uta.edu
http://www.uta.edu/ronc
Second Assignment
• Submit a signed copy of the document
posted at
www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf
©rlc L08-15Feb2011
2
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
http://www.uta.edu/ronc/5340/tests/.
©rlc L08-15Feb2011
3
Diffused or Implanted
IC Resistor (Fig 2.451)
©rlc L08-15Feb2011
4
An IC Resistor with
L = 8W (M&K)1
©rlc L08-15Feb2011
5
Typical IC doping
profile (M&K Fig. 2.441)
©rlc L08-15Feb2011
6
Mobilities**
©rlc L08-15Feb2011
7
IC Resistor
Conductance
W
dG  qn x nx  dx
L
xj
W
G
q  n x nx dx
L 0
xj
1
g  q  n x nx dx, Rs 
g
0
©rlc L08-15Feb2011
8
An IC Resistor with
Ns = 8, R = 8Rs (M&K)1
©rlc L08-15Feb2011
9
The effect of lateral
diffusion (M&K1)
©rlc L08-15Feb2011
10
A serpentine pattern
IC Resistor (M&K1)
R = NSRS + 0.65NCRS
note: RC = 0.65RS
©rlc L08-15Feb2011
11
Fermi Energy
• The equilibrium carrier concentration
ahd the Fermi energy are related as
 no 
 Ef  Efi 
no

Ef  Efi  kT ln   , and
 exp 
ni
 kT 
 ni 
• The potential
f = (Ef-Efi)/q
• If not in equilibrium,
a quasi-Fermi level
(imref) is used
©rlc L08-15Feb2011
12
Electron quasi-Fermi
Energy (n = no + n)
The Quasi - Fermi level (Imref) is defined :
 no  n 
 ,
Efn  Efi  kT ln 
 ni 
and the carrier density is :
 Efn  Efi 
no  n

 exp 
ni
 kT 
©rlc L08-15Feb2011
13
Hole quasi-Fermi
Energy (p = po + p)
For holes, the Imref is defined as :
 po  p 
 ,
Efi  Efp  kT ln 
 ni 
and the carrier density is :
 Efi  Efp
po  p
 exp 
ni
 kT
©rlc L08-15Feb2011




14
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
15
Si and Al and model
(approx. to scale)
metal
n-type s/c
Eo
Eo
qfm,Al ~
4.1 eV
EFm Ec
EFi
Ev
©rlc L08-15Feb2011
p-type s/c
Eo
qcsi~
4.05 eV
qcsi~
4.05 eV
qfs,n
qfs,p
EFn
EFp
Ec
EFi
Ev
16
Making contact between metal & s/c
• Equate the EF in
Eo
the metal and s/c
qc (electron
materials far from
affinity)
the junction
qf
• Eo(the free level),
(work function)
must be continuous
across the jctn.
Ec
E
N.B.: qc = 4.05 eV (Si), F
E
Fi
qf F
and qf = qc  Ec - EF
Ev
©rlc L08-15Feb2011
17
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
18
Ideal metal to n-type
barrier diode (fm>fs,Va=0)
metal
n-type s/c
qcs
qfm
qfBn
qfi
qfs,n
EFm
Depl reg
©rlc L08-15Feb2011
qf’n
Eo
Ec
EFn
EFi
Ev
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
19
Metal to n-type
non-rect cont (fm<fs)
n-type s/c
metal
qcs
qfm
qfB,nqfi
qfs,n
EFm
Acc reg
©rlc L08-15Feb2011
qfn
Eo
No disc in Eo
Ex=0 in metal
==> Eo flat
fB,n=fm - cs
= elec mtl to
s/c barr
Ec
EFn f = f -f < 0
i
Bn n
EFi
Ev Accumulation
region
20
Ideal metal to p-type
barrier diode (fm<fs)
metal
p-type s/c
No disc in Eo
Ex=0 in metal ==>
E
o
qfs,p
Eoflat
qcs
qfm
fBn= fm- cs = elec
qf i
mtl to s/c barr.
qfBn
Ec fBp= fm- (cs + Eg)=
EFi
hole m to s barr.
EFm
EFp fi = fm-fs,p = hole
qfBp
Ev
s/c to mtl barr.
Depl reg
©rlc L08-15Feb2011
qfi qf <0
p
21
Metal to p-type
non-rect cont (fm>fs)
metal
n-type s/c
qcs
qfm
qfBn
q(fi)
qfs,n
EFm
qfBp qfi
Accum reg
©rlc L08-15Feb2011
qf p
Eo
Ec
EFi
EfP
Ev
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.
22
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
23
References
1 and M&KDevice
Electronics for Integrated
Circuits, 2 ed., by Muller and Kamins, Wiley,
New York, 1986. See Semiconductor Device
Fundamentals, by Pierret, Addison-Wesley,
1996, for another treatment of the  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
24