EE 5340Semiconductor Device TheoryLecture 07 – Spring 2011

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc

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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• 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 ofcarriers• 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)

kji

kji

zn

yn

xn

qDnqDJ

zp

yp

xp

qDpqDJ

nnn

ppp

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Diffusion ofcarriers (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 ofCarriers (cont.)

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Current densitycomponents

nqDJ

pqDJ

VnqEnqEJ

VpqEpqEJ

VE since Note,

ndiffusion,n

pdiffusion,p

nnndrift,n

pppdrift,p

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Total currentdensity

nqDpqDVJ

JJJJJ

gradient

potential the and gradients carrier the

by driven is density current total The

npnptotal

.diff,n.diff,pdrift,ndrift,ptotal

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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 Einsteinrelationship• For Ex = - Vt (1/no)dno/dx, and

• Jn,x = nqmnEx + qDn(dn/dx) = 0• This requires that

nqmn[Vt (1/n)dn/dx] = qDn(dn/dx)

• Which is satisfied ift

pt

n

n Vp

D likewise ,V

qkTD

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Silicon Planar Process1

• 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• 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) stress-relief oxide and Si3N4 removed by etching, (d) scanning electron micrograph (5000 X) showing LOCOS-processed wafer at (b).

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Al Interconnects1

• 1Figure 2.33 (p. 104) A thin layer of aluminum can be used to connect various doped regions of a semiconductor device. 1

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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 devia-tion DRp for implantation of phosphorus into Si, SiO2, Si3N4, and Al [M&K ref 11].

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.2 DtL

Implant andDiffusion Profiles

Figure 2.211 Complementary-error-function and Gaussian distribu-tions; the vertical axis is normalized to the peak con-centration Cs, while the horizon-tal axis is normal-ized to the char-acteristic length

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References1 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 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.