1. EE 5340 Semiconductor Device Theory Lecture 06 – Spring 2011
Professor Ronald L. Carter

2. Review the Following R. L. Carter’s web page:
EE 5340 web page and syllabus. (Refresh all EE 5340 pages when downloading to assure the latest version.) All links at:
University and College Ethics Policies
Makeup lecture at noon Friday (1/28) in 108 Nedderman Hall. This will be available on the web.
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3. First Assignment Send e-mail to ronc@uta.edu
On the subject line, put “5340 ”
In the body of message include
address: ______________________
Your Name*: _______________________
Last four digits of your Student ID: _____
* Your name as it appears in the UTA Record - no more, no less
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4. Second Assignment Submit a signed copy of the document posted at
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5. Schedule Changes Due to University Weather Closings
Make-up class will be held Friday, February 11 at 12 noon in 108 Nedderman Hall.
Additional changes will be announced as necessary.
Syllabus and lecture dates postings have been updated.
Project Assignment has been posted in the initial version.
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6. Drift Current
The drift current density (amp/cm2) is given by the point form of Ohm Law
J = (nqmn+pqmp)(Exi+ Eyj+ Ezk), so
J = (sn + sp)E = sE, where
s = nqmn+pqmp defines the conductivity
The net current is
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7. Drift current resistance
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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8. Drift current resistance (cont.)
Consequently, since
R = rl/A
R = (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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9. Drift current resistance (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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10. Net intrinsic mobility
Considering only lattice scattering
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11. 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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12. Net extrinsic mobility
Considering only lattice and impurity scattering
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13. Net silicon extr resistivity (cont.)
Since
r = (nqmn + pqmp)-1, and
mn > mp, (m = qt/m*) we have
rp > rn
Note that since
1.6(high conc.) < rp/rn < 3(low conc.), so
1.6(high conc.) < mn/mp < 3(low conc.)
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14. Ionized impurity mobility 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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15. Figure (p. 32 in M&K1) Low-field mobility in silicon as a function of temperature for electrons (a), and for holes (b). The solid lines represent the theoretical predictions for pure lattice scattering [5].
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16. Exp. m(T=300K) model for P, As and B in Si1
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17. Exp. mobility model function for Si1
Parameter As P B
mmin
mmax
Nref e e e17 a
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18. Carrier mobility functions (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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19. Carrier mobility functions (ex.)
Let Nd = 1.78E17/cm3 of phosphorous, so mmin = 68.5, mmax = 1414, Nref = 9.20e16 and a =
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 =
Thus mp = 189 cm2/V-s
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20. 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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21. Figure (p. 29) M&K Dopant density versus resistivity at 23°C (296 K) for silicon doped with phosphorus and with boron. The curves can be used with little error to represent conditions at 300 K. [W. R. Thurber, R. L. Mattis, and Y. M. Liu, National Bureau of Standards Special Publication 400–64, 42 (May 1981).]
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22. Net silicon extr resistivity (cont.)
Since
r = (nqmn + pqmp)-1, and
mn > mp, (m = qt/m*) we have
rp > rn, for the same NI
Note that since
1.6(high conc.) < rp/rn < 3(low conc.), so
1.6(high conc.) < mn/mp < 3(low conc.)
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23. 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 is r = (nqmn)-1 = [Nqmn(NI)]-1
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24. Figure (p. 31 M&K) Electron and hole mobilities in silicon at 300 K as functions of the total dopant concentration. The values plotted are the results of curve fitting measurements from several sources. The mobility curves can be generated using Equation with the following values of the parameters [3] (see table on next slide).
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25. 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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26. Equipartition theorem
The thermodynamic energy per degree of freedom is kT/2
Consequently,
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27. Carrier velocity saturation1
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) E9 T E8 T-0.52
Ec (V/cm) T T1.68
b E-2 T T0.17
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28. Carrier velocity2 carrier velocity vs E for Si, Ge, and GaAs (after
Sze2)
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29. Carrier velocity saturation (cont.)
At 300K, for electrons, mo = v1/Ec = 1.53E9(300)-0.87/1.01(300) = 1504 cm2/V-s, the low-field mobility
The maximum velocity (300K) is vsat = moEc = v1 = 1.53E9 (300) = 1.07E7 cm/s
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30. References
M&K and 1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986.
See Semiconductor Device Fundamen-tals, by Pierret, Addison-Wesley, 1996, for another treatment of the m model.
2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981.
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31. 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.
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