Semiconductor Device Modeling and
Characterization – EE5342 Lecture 6 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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First Assignment
• e-mail to [email protected]– In the body of the message include
subscribe EE5342 • This will subscribe you to the
EE5342 list. Will receive all EE5342 messages
• If you have any questions, send to [email protected], with EE5342 in subject line.
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Second Assignment
• Submit a signed copy of the document that is posted at
www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf
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Drift Current• The drift current density
(amp/cm2) is given by the point form of Ohm LawJ = (nqmn+pqmp)(Exi+ Eyj+ Ezk), so
J = (sn + sp)E = sE, wheres = nqmn+pqmp defines the
conductivity• The net current is SdJI
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Drift currentresistance• Given: a semiconductor resistor
with length, l, and cross-section, A. What is the resistance?
• As stated previously, the conductivity,
s = nqmn + pqmp
• So the resistivity, r = 1/s = 1/(nqmn +
pqmp)
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Drift currentresistance (cont.)• Consequently, since
R = rl/AR = (nqmn + pqmp)-1(l/A)
• For n >> p, (an n-type extrinsic s/c)
R = l/(nqmnA)• For p >> n, (a p-type extrinsic s/c)
R = l/(pqmpA)
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Drift currentresistance (cont.)• Note: for an extrinsic
semiconductor and multiple scattering mechanisms, since
R = l/(nqmnA) or l/(pqmpA), and
(mn or p total)-1 = S mi-1, then
Rtotal = S Ri (series Rs)• The individual scattering
mechanisms are: Lattice, ionized impurity, etc.
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Exp. mobility modelfunction for Si1
Parameter As P Bmmin 52.2 68.5 44.9mmax 1417 1414
470.5Nref 9.68e16 9.20e16
2.23e17a 0.680 0.711
0.719
a
mmmm
refa,d
minpn,maxpn,minpn,pn,
NN1
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Exp. mobility modelfor P, As and B in Si
0
500
1000
1500
1.E+13 1.E+15 1.E+17 1.E+19
Doping Concentration (cm̂ -3)
Mob
ility
(cm̂
2/V-
sec)
PAsB
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Carrier mobilityfunctions (cont.)• The parameter mmax models 1/tlattice
the thermal collision rate• The parameters mmin, Nref and a
model 1/timpur the impurity collision rate
• The function is approximately of the ideal theoretical form:
1/mtotal = 1/mthermal + 1/mimpurity
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Carrier mobilityfunctions (ex.)• Let Nd
= 1.78E17/cm3 of phosphorous, so mmin = 68.5, mmax = 1414, Nref = 9.20e16 and a = 0.711. Thus mn = 586 cm2/V-s
• Let Na = 5.62E17/cm3 of boron, so
mmin = 44.9, mmax = 470.5, Nref = 9.68e16 and a = 0.680. Thus mn = 189 cm2/V-s
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Lattice mobility
• The mlattice is the lattice scattering mobility due to thermal vibrations
• Simple theory gives mlattice ~ T-3/2
• Experimentally mn,lattice ~ T-n where n = 2.42 for electrons and 2.2 for holes
• Consequently, the model equation is mlattice(T) = mlattice(300)(T/300)-n
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Ionized impuritymobility function• The mimpur is the scattering mobility
due to ionized impurities• Simple theory gives mimpur ~
T3/2/Nimpur• Consequently, the model equation
is mimpur(T) = mimpur(300)(T/300)3/2
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Mobility Summary
• The concept of mobility introduced as a response function to the electric field in establishing a drift current
• Resistivity and conductivity defined
• Model equation def for m(Nd,Na,T)• Resistivity models developed for
extrinsic and compensated materials
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Net silicon (ex-trinsic) resistivity• Since
r = s-1 = (nqmn + pqmp)-1
• The net conductivity can be obtained by using the model equation for the mobilities as functions of doping concentrations.
• The model function gives agreement with the measured s(Nimpur)
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Net silicon extrresistivity (cont.)
1.00E-021.00E-011.00E+001.00E+011.00E+021.00E+03
1.E+13 1.E+15 1.E+17 1.E+19
Doping Concentration (cm̂ -3)
Resis
tivity
(ohm
-cm)
PAsB
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Net silicon extrresistivity (cont.)• Since
r = (nqmn + pqmp)-1, and mn > mp, (m = qt/m*) we
have rp > rn
• Note that since1.6(high conc.) < rp/rn < 3(low
conc.), so1.6(high conc.) < mn/mp < 3(low
conc.)
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Net silicon (com-pensated) res.• For an n-type (n >> p)
compensated semiconductor, r = (nqmn)-1
• But now n = N = Nd - Na, and the mobility must be considered to be determined by the total ionized impurity scattering Nd + Na = NI
• Consequently, a good estimate isr = (nqmn)-1 = [Nqmn(NI)]-1
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Equipartitiontheorem• The thermodynamic energy per
degree of freedom is kT/2Consequently,
sec/cm10*mkT3v
and ,kT23vm2
1
7rms
thermal2
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Carrier velocitysaturation1• The mobility relationship v = mE is
limited to “low” fields• v < vth = (3kT/m*)1/2 defines “low”• v = moE[1+(E/Ec)b]-1/b, mo = v1/Ec for
Si parameter electrons holes v1 (cm/s) 1.53E9 T-0.87 1.62E8 T-
0.52
Ec (V/cm) 1.01 T1.55 1.24 T1.68
b 2.57E-2 T0.66 0.46 T0.17
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vdrift [cm/s] vs. E [V/cm] (Sze2, fig. 29a)
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References *Fundamentals of Semiconductor Theory and
Device Physics, by Shyh Wang, Prentice Hall, 1989.
**Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago.
M&K = Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, 2003.
• 1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986.
• 2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981.