EE 5340
Semiconductor Device Theory
Lecture 07 – 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
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Test 1 – Tuesday 22Feb11
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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/.
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Diffusion of
carriers
• In a gradient of electrons or holes,
p and n are not zero
• Diffusion current,`J =`Jp +`Jn (note
Dp and Dn are diffusion coefficients)

 p p
p 
Jp   qDpp   qDp  i 
j  k 
z 
 x y

 n
n
n 
Jn   qDn n   qDn  i 
j  k 
x y
z 

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Diffusion of
carriers (cont.)
• Note (p)x has the magnitude of
dp/dx and points in the direction of
increasing p (uphill)
• The diffusion current points in the
direction of decreasing p or n
(downhill) and hence the - sign in the
definition of`Jp and the + sign in the
definition of`Jn
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Diffusion of
Carriers (cont.)
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Current density
components

Note, since E  V



Jp,drift   pE  pq pE  pq pV



Jn,drift  nE  nqnE  nqnV

Jp,diffusion   qDpp

Jn,diffusion   qDnn
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Total current
density
The total current density is driven by
the carrier gradients and the potential
gradient





Jtotal  Jp,drift  Jn,drift  Jp,diff.  Jn,diff.

Jtotal    p  n V  qDpp  qDnn

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
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Doping gradient
induced E-field
•
•
•
•
•
If N = Nd-Na = N(x), then so is Ef-Efi
Define f = (Ef-Efi)/q = (kT/q)ln(no/ni)
For equilibrium, Efi = constant, but
for dN/dx not equal to zero,
Ex = -df/dx =- [d(Ef-Efi)/dx](kT/q)
= -(kT/q) d[ln(no/ni)]/dx
= -(kT/q) (1/no)[dno/dx]
= -(kT/q) (1/N)[dN/dx], N > 0
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Induced E-field
(continued)
• Let Vt = kT/q, then since
• nopo = ni2 gives no/ni = ni/po
• Ex = - Vt d[ln(no/ni)]/dx
= - Vt d[ln(ni/po)]/dx
= - Vt d[ln(ni/|N|)]/dx, N = -Na < 0
• Ex = - Vt (-1/po)dpo/dx
= Vt(1/po)dpo/dx
= Vt(1/Na)dNa/dx
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The Einstein
relationship
• For Ex = - Vt (1/no)dno/dx, and
• Jn,x = nqnEx + qDn(dn/dx) = 0
• This requires that
nqn[Vt (1/n)dn/dx] = qDn(dn/dx)
• Which is satisfied if
Dp
Dn kT

 Vt , likewise
 Vt
n
q
p
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Silicon Planar Process1
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• M&K1 Fig. 2.1 Basic
fabrication steps in
the silicon planar
process:
• (a) oxide formation,
• (b) oxide removal,
• (c) deposition of
dopant atoms,
• (d) diffusion of
dopant atoms into
exposed regions of
silicon.
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LOCOS Process1
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•
1Fig
2.26 LOCal
Oxidation of Silicon
(LOCOS). (a) Defined
pattern consisting of
stress-relief oxide and
Si3N4 where further
oxidation is not desired,
(b) thick oxide layer
grown over the bare
silicon region, (c) stressrelief oxide and Si3N4
removed by etching, (d)
scanning electron
micrograph (5000 X)
showing LOCOSprocessed wafer at (b).
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Al
1
Interconnects
• 1Figure 2.33 (p. 104) A thin layer of
aluminum can be used to connect various
doped regions of a semiconductor device.
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Ion Implantation1
•
1Figure
2.15 (p. 80) In ion implantation, a beam of
high-energy ions strikes selected regions of the
semiconductor surface, penetrating into these
exposed regions.
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Phosphorous
implant Range
(M&K1 Figure
2.17) Projected
range Rp and its
standard deviation DRp for
implantation of
phosphorus into
Si, SiO2, Si3N4,
and Al [M&K ref
11].
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Implant and
Diffusion Profiles
L  2 Dt .
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Figure 2.211
Complementaryerror-function and
Gaussian distributions; the vertical
axis is normalized
to the peak concentration Cs,
while the horizontal axis is normalized to the characteristic length
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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.
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