Semiconductors
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$Equation:$ "
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:""
" " " " " " " " "
"
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""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"
"
" " Semiconductor* NJType* Semiconductor*
Equation*for*Drift*
Equation*for*Diffusion*
"
"
Dn ≡ electron diffusion constant (cm2/s)
" 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."" " " " " " " "
"
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$Equation:$ "
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:""
" " " " " " " " "
"
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""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"
"
" " Semiconductor* NJType* Semiconductor*
Equation*for*Drift*
Equation*for*Diffusion*
"
"
Dn ≡ electron diffusion constant (cm2/s)
" 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."" " " " " " " "
"
