ELEC2104!–!SEMESTER&2"
Microelectronic*Circuit*Elements*
Diodes"and"Transistors"are"nonlinear"devices"and"form"the"basic"microelectronic"circuit"elements.""
Circuit*Element* Description* Equation*
Diodes* • Allows"current"to"flow"only"in"one"direction"
• Forms"basis"of"voltage"limiters,"voltage"doublers,"half=
wave"and"full=wave"rectification"
*
Transistors* • Forms"basis"of"most"digital"and"analogue" BJT$Equation:$
microelectronic"circuits""
• Either:"Bipolar(Junction(Transistors((BJT)("and"
Complementary(metal–oxide–semiconductor((CMOS)( $
Transistors"
$
• Used"in:"switches,(logic(gates,(flipAflops,(amplifiers,(
CMOS$Equation:$
opamps"
"
*
*
"
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" • Digitization"of"amplitude"makes"circuit"insensitive"to"analogue"imperfections"
processors"and"computers"" such"as"tolerance,"matching,"and"noise.""
• Requires"sampling"in"the"time"domain"leading"to"aliasing"
CTCA:"Amplifiers,"RF"front= • Does*NOT"require"time"sampling"and"does"not"suffer"from"aliasing,""
end"of"mobile"phone"
• SENSITIVE"to"tolerance,"matching,"and"noise"
DTCA:"Digital"camera"and" • Suffers"from"both"aliasing"and"sensitivity"to"tolerance,"matching"and"noise"
switched=capacitor"filters"
CTDA:"Spike=based"signal" • Eliminates"aliasing"and"maintains"advantages"of"amplitude"quantization"
processing"(human"brain)""
• Research"area"for"electronic"devices"
"
,Circuit*Elements:*
Passive*Elements:* ! Unable"to"amplify"or"generate"energy"""
! e.g."resistors,"inductors,"capacitors"&"diodes"
*
Active*Elements:* ! 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""
"
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:""
"
"
"
"
"
"
"
"
" "
, 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* Small*Band*Energy*Gap*
band* *
*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.""
"
Resistivity$and$Conductivity$
"
Microelectronic*Circuit*Elements*
Diodes"and"Transistors"are"nonlinear"devices"and"form"the"basic"microelectronic"circuit"elements.""
Circuit*Element* Description* Equation*
Diodes* • Allows"current"to"flow"only"in"one"direction"
• Forms"basis"of"voltage"limiters,"voltage"doublers,"half=
wave"and"full=wave"rectification"
*
Transistors* • Forms"basis"of"most"digital"and"analogue" BJT$Equation:$
microelectronic"circuits""
• Either:"Bipolar(Junction(Transistors((BJT)("and"
Complementary(metal–oxide–semiconductor((CMOS)( $
Transistors"
$
• Used"in:"switches,(logic(gates,(flipAflops,(amplifiers,(
CMOS$Equation:$
opamps"
"
*
*
"
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" • Digitization"of"amplitude"makes"circuit"insensitive"to"analogue"imperfections"
processors"and"computers"" such"as"tolerance,"matching,"and"noise.""
• Requires"sampling"in"the"time"domain"leading"to"aliasing"
CTCA:"Amplifiers,"RF"front= • Does*NOT"require"time"sampling"and"does"not"suffer"from"aliasing,""
end"of"mobile"phone"
• SENSITIVE"to"tolerance,"matching,"and"noise"
DTCA:"Digital"camera"and" • Suffers"from"both"aliasing"and"sensitivity"to"tolerance,"matching"and"noise"
switched=capacitor"filters"
CTDA:"Spike=based"signal" • Eliminates"aliasing"and"maintains"advantages"of"amplitude"quantization"
processing"(human"brain)""
• Research"area"for"electronic"devices"
"
,Circuit*Elements:*
Passive*Elements:* ! Unable"to"amplify"or"generate"energy"""
! e.g."resistors,"inductors,"capacitors"&"diodes"
*
Active*Elements:* ! 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""
"
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:""
"
"
"
"
"
"
"
"
" "
, 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* Small*Band*Energy*Gap*
band* *
*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.""
"
Resistivity$and$Conductivity$
"
