ELEC2104!–!SEMESTER&2"
Microelectronic*Circuit*Elements*
Diodes"and"Transistors"are"nonlinear"devices"and"form"the"basic"microelectronic"circuit"elements.""
Circuit*Element*
Description*
Diodes*
•
Allows"current"to"flow"only"in"one"direction"
•
Forms"basis"of"voltage"limiters,"voltage"doublers,"half=
wave"and"full=wave"rectification"
•
Forms"basis"of"most"digital"and"analogue"
microelectronic"circuits""
•
Either:"Bipolar(Junction(Transistors((BJT)("and"
Complementary(metal–oxide–semiconductor((CMOS)(
Transistors"
*
Transistors*
•
Equation*
BJT$Equation:$
Used"in:"switches,(logic(gates,(flipAflops,(amplifiers,(
opamps"
$
$
CMOS$Equation:$
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BJT*
"
*
*
CMOS*
"
Domains*of*Processing*and*Circuit*Analysis*Review*
Information"is"stored"in"terms"of"voltage"and"current"in"electric"circuits:"
•
Digital*circuits:"voltage"or"current"is"either"ON"or"OFF"==>"Information"is"represented"as"1s"and"0s""
•
Analog*circuits:"voltage"or"current"is"present"at"continuous"levels""
"
Continuous"Amplitude"(CA)"versus"Discrete"Amplitude"(DA)"
Continuous"Time"(CT)"versus"Discrete"Time"(DT)"
DTDA:"Digital"signal"
processors"and"computers""
•
Digitization"of"amplitude"makes"circuit"insensitive"to"analogue"imperfections"
such"as"tolerance,"matching,"and"noise.""
•
Requires"sampling"in"the"time"domain"leading"to"aliasing"
CTCA:"Amplifiers,"RF"front=
end"of"mobile"phone"
•
Does*NOT"require"time"sampling"and"does"not"suffer"from"aliasing,""
•
SENSITIVE"to"tolerance,"matching,"and"noise"
DTCA:"Digital"camera"and"
switched=capacitor"filters"
•
Suffers"from"both"aliasing"and"sensitivity"to"tolerance,"matching"and"noise"
CTDA:"Spike=based"signal"
processing"(human"brain)""
•
Eliminates"aliasing"and"maintains"advantages"of"amplitude"quantization"
•
Research"area"for"electronic"devices"
"
Circuit*Elements:*
Passive*Elements:*
!
Unable"to"amplify"or"generate"energy"""
!
e.g."resistors,"inductors,"capacitors"&"diodes"
!
Able"amplify"or"generate"energy"
!
Allow"us"to"amplify"or"switch"the"information"stored"in"voltage"or"current"
!
e.g."independent"voltage/current"sources,"dependent"voltage/current"
sources,"transistors"&"rectifiers""
*
Active*Elements:*
*
"
Linear*Versus*NonJLinear*Networks*
Linear$circuit$elements"are"components"that"have"a"linear"relationship"between"current"voltage."(i.e."do"not"change"with"
the"level"of"voltage"or"current)"
Non:linear$circuit$elements"do"not"have"a"proportional"output."[A(light(bulb(filament(is(a(nonAlinear(resistor.((Increasing(
the(voltage(applied(to(a(light(bulb(past(a(certain(point(will(not(make(the(light(any(brighter.((This(also(prevents(the(light(
bulb(from(burning(out(too(quickly.]
Example:"Compute"the"input"impedance"for"the"circuit"shown"below:""
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Semiconductor*Physics*
Solid=state"electronics:"Circuits"and"devices"are"built"out"of"solid"materials"(rather"than"vacuum"tubes)""
Physics*Overview:*
The"electrons"in"an"atom"have"different"energy"levels,"called"atomic"
orbitals"""
The"energy"levels"are"really"waves,"represented"by"a"wavefunction,"which"
indicates"where"electrons"are"allowed"to"be."""
"
"
Put"electrons"in"a"solid"and"you"get"
gaps"in"the"quantized"energy"levels:"
called"a"‘Band"Gap’.""
"
"
Conductor*(metal)*
SemiJMetal*
SemiJconductor*
Insulator*
*
*
*
Overlap*between*
conduction*and*valence*
band*
*
Small*Band*Energy*Gap*
*We(can(dope(both(materials(to(change(their(properties.(As(well,(with(semiAmetals(putting(them(under(pressure(can(
change(the(band(overlap.((
"
Semiconductors:*
Difference(between(metals(and(semiconductors:(
A"semiconductor"will:(
•
"increase"in"conductivity"with"an"increase"in"temperature"or"electric"field"strength"since"more"electrons"have"
more"energy"to"cross"bandgap"to"enter"the"conduction"band""
•
have"the"number"of"free"electrons"increase"exponentially"with"temperature,"overriding"the"effect"of"the"
scattering"
A"metal"will:"
•
decrease"in"conductivity"with"an"increase"in"temperature"since"the"lattice"structure"of"the"metal"vibrates"and"
scatters"the"electrons."These"vibrations"are"called"phonons.""
"
!
*
*
Silicon*Covalent*Bond*Model*
•
Near"absolute"zero,"all"bonds"are"complete."All"electrons"are"sitting"in"the"valence"band"and"no"electrons"are"in"the"
conduction"band""
"
Electron"Hole"Pairs:"
•
Increasing"temperature"adds"energy"to"the"system"and"breaks"bonds"in"the"lattice."For"each"bond"that"is"broken,"an"
electron"enters"the"conduction"band."This"leaves"a"hole"in"the"valence"band.""
•
When"an"electron"leaves"a"hole"in"a"bond,"another"electron"can"leave"a"bond"to"fill"that"vacancy""
•
Hole"propagates"and"charge"is"moved"across"the"silicon""
"
"
Free"electrons"in"the"conduction"band"and"empty"holes"in"the"valence"band"are"called"charge"carriers.""
Intrinsic*Carrier*Concentration:*
Fermi*Level*of*Semiconductor:*No."of"electrons"in"conduction"band"="No."of"holes"in"the"valence"band"since"the"electrons"
have"to"leave"the"valence"band"to"enter"the"conduction"band.*
"
Since"the"No."of"electrons"in"conduction"band"="No."of"holes"in"the"valence"band,""we"can"equate"n"="p,"hence:"
"
Note:*
•
Number"of"intrinsic"carriers"is"a"semiconductor"is"exponentially"related"to"the"band=gap"energy."
•
A"smaller"band=gap"means"more"carriers.""
Carrier*Drift/Drift*Current*
•
An"electric"field"is"directional:"positive"charges"===>"negative"charges""
•
When"an"electric"field"applied"on"a"semi=conductor,"a"force"is"exerted"on"electrically"charged"objects"given"by:"
"
•
Drift"current"is"the"result"of"the"movement"of"charged"particles"when"an"electric"field"is"applied"on"a"semiconductor""
"
• At"low"E"fields,"carrier"drift"velocity"v"(cm/s)"is"proportional"to"electric"field"E"(V/cm)"by"the"mobility"m"""
• Mobility"(µ)"is"a"measure"of"how"quickly"a"carrier"can"move"through"a"material"when"under"the"force"of"an"electric"
field"and"is"determined"by"scattering"
Hole"mobility"<"electron"mobility"
• Hole"current"is"the"result"of"multiple"covalent"bond"hops."
• Electrons"can"move"freely"about"the"crystal."""
Mathematically,"we"write:""
•
"
•
vn and"vp ="electron"and"hole"velocity"(cm/s),""
"
"
µn"and" µp"="electron"and"hole"mobility"(cm2/V.s)""
"
•
Carrier"velocity"cannot"increase"indefinitely.""
•
At"high"fields,"carrier"velocity"saturates"because"of"
scattering"and"this"effect"places"upper"limits"on"the"
speed"of"solid=state"devices.""
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Resistivity$and$Conductivity$
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Formulas*To*Remember:*
Electron*Drift:*
Hole*Drift:*"
"
"
Resistance:*(R)"
Resistivity:*(ρ)*
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Conductivity:*(σ)*
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"
"
"
*Note:"n"="p"for"semi=conductors"
Resistivity*
"
EXAMPLE:"Find"the"resistivity"of"intrinsic"silicon"at"room"temperature"and"classify"it"as"an"insulator,"semiconductor,"or"
conductor."You"are"given:""
10
3"
• ni ="10 /cm at"room"temperature""
"
2
• µm ="1350"cm /Vs""
"
2
• µp ="500"cm /Vs""
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*
EXAMPLE:"We"have"a"bar"of"pure"silicon"with"the"following"dimensions:"
1( µm(wide(x(1(µm(thick(x(1(cm(long(
If"we"apply"a"6V"electric"field,"what"drift"current"will"be"present"in"the"
material?""
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More*Semiconductors:*
Intrinsic/Extrinsic*Semiconductors*
In"pure"silicon,"a"weak"insulator,"every"electron"that"is"excited"into"the"conduction"band"leaves"one"hole"in"the"valence"
band"""
no.$of$electrons$(n)(in(conduction(band(=(no.$of$holes$(p)(in(valence(band(
To"increase"carrier"concentration"(i.e."make"it"a"better"conductor),"we"can:"
1)
Increase*temperature"to"excite"more"electrons"into"conduction"band"
2)
Use"light*energy*
3)
Doping"==>"Adding"small"and"well=controlled"amounts"of"impurities"into"semiconductor"to"release"more"carriers,"
either"more(free(electrons"(donors)"or"more(free(holes"(acceptors)"whereby"the"semiconductor"material"remains"
neutral"(no."of"protons"="no."of"electrons)"
Doping"enables"us"to"vary"the"charge"carrier"density"to"change"the"resistivity"and"other"properties"of"the"
semiconductor"
"
Semiconductor*Doping*
NJType*
Semiconductor*
•
Dope"with"Group"V"element"(e.g."P,"As)"with"5"
valence"electrons"into"a"Si"lattice,"4"of"its"electrons"
will"form"covalent"bonds"with"the"surrounding"Si"
atoms""
•
5 "valence"electron"is"weakly"bound"
•
Energy"of"level"of"extra"donor"electron"(ED)"is"closer"
to"conduction"band"(Ec)"than"valence"band"(about"
0.045"eV"for"phosphorous)"
n">"p"
Majority carrier =
electrons
•
th
"
Result:"donor"electrons"move"up"to"conduction"
band"more"easily"
"
PJType*
Semiconductor*
•
Dope"with"Group"III"element"(e.g."B)"with"3"valence"
electrons"into"a"Si"lattice,"its"electrons"will"form"
covalent"bonds"with"3"of"the"surrounding"Si"atoms"
•
4 "Si"atom,"there"will"be"a"hole"where"no"electron"is"
bound""
•
Donor"atoms"have"unfilled"covalent"bonds"with"
energy"state"EA,"which"is"closer"to"EV"(about"0.044"
eV"for"boron)"
•
Result:"valence"band"electrons"move"up"to"acceptor"
sites"more"easily"to"form"covalent"bond"pairs"
n"<"p"
Majority carrier =
holes
th
Note:$$
"
•
Majority"carrier"="carrier"with"the"larger"concentration"
•
Minority"carrier"="carrier"with"the"smaller"concentration"
"
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Compensated*
Semiconductor*
•
Semiconductors"doped"with"both"n=type"and"p=type"
dopants"
•
If"ND >"NA,"there"are"more"ND donor"levels."The"
"
"
donor"electrons"fill"the"acceptor"sites.""
•
The"remaining"ND ="NA"electrons"are"available"for"
"
promotion"to"the"conduction"band"
"
"
•
Acceptors"and"donors"can"fill"energy"levels"
introduced"by"doping"
•
Compensation"decreases"mobility""
Important*to*Remember:*
For"both"intrinsic"and"extrinsic"(doped)"semiconductors,"the"mass*action*law"always"holds:"
pn = ni2
Also,"the"sum"of"all"charges"is"zero:""
p"+"ND ="n"+"NA"
"
Semiconductor*
Equation*
Practical*Doping*Level*
NJType*Semiconductor*
n"≈""(ND"="NA)"
ND large"means"n"≈"ND"
"
true only if: ND >> NA and n >> p
PJType*Semiconductor*
p"≈"(NA"="ND)"
NA large"means"p"≈"NA"
"
true only if: NA >> ND and p >> n
14
3(
21
3
*Typical(doping(ranges(are(10 /cm to(10 /(cm (
•
Majority"carrier"concentrations:"independent*of*
temperature"(over"practical"temp."ranges).""
•
Minority"carrier"concentrations:"dependent*on*temperature"
2
since"proportional"to"ni "
•
Mobility"of"carriers"degrades"with"doping"because"the"
impurities"can"cause"electrons"and"holes"to"scatter"as"they"
move"through"the"semiconductor""
"
"
Diffusion*Current*
•
Diffusion"current"can"be"generated"by"varying"the"doping"concentration"and/or"the"doping"type"across"a"region"of"
semiconductor"allowing"carriers"to"move"from"high"concentration"regions"to"low"concentration"regions"
•
It"is:"
•
o
negligible"in"metals"due"to"their"high"conductivity"
o
dependent"on"diffusion"constant"and"concentration"profile"
o
the"movement"of"either"electrons"or"holes"
"
Einstein’s*Relation:"Links"diffusion"constant"+"mobility"through"thermal"
voltage"(moves"carriers"without"E"field)"
"
"
•
Carriers"move"in"a"direction"towards"regions"of"lower"concentration"until"it"
crashes"into"another"carrier"whereby"the"diffusion"current"densities"are"
proportional"to"the"carrier"gradient"
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"
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Semiconductor*
NJType*
Semiconductor*
Equation*for*Drift*
Equation*for*Diffusion*
"
"
Dn ≡ electron diffusion constant (cm2/s)
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PJType*
Semiconductor*
"
"
Diffusion currents in the presence
of a concentration gradient
2
Dp ≡ hole diffusion constant (cm /s)
"
Total*current,"due"to"each*carrier*component*(holes*&*electrons),"is"the*sum*of*the*drift*and*diffusion*current:"
"
Hence,"the"total*current"in"semiconductor,"which"accounts*for*both*hole*and*electron*components,"is:"
"
*
*
15"
3
EXAMPLE:"Pure"silicon"is"doped"with"2"×"10 arsenic"atoms/cm ."What"is"its"resistivity"at"room"temperature?"You"are"
given:""
•
•
µm ="1320"cm2/Vs""
"
µp ="460"cm2/Vs""
"
*
*
*
*
*
*
DIFFUSION*CURRENT:*EXAMPLE*#1*
What"is"the"electron"diffusion"current"density"at"room"temperature"for"
the"following"region"of"silicon"if"the"electron"mobility"is"350"cm2/Vis"and"
WB ="0.5"cm?""
"
"
*
*
*
*
DIFFUSION*CURRENT:*EXAMPLE*#2*
What"will"the"total"current"be"at"x=0"if"we"apply"a"20V/cm"electric"field"to"this"same"
material?""
The"electric"field"is"oriented"so"that"it"is"pointing"towards"x=0.""
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