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Institute of Radio Physics and Electronics
University of Calcutta
A Diamond Jubilee Celebration program
Organized byRadio Physics and Electronics Association (1960)
CAS in Radio Physics and Electronics (1963)
S. K. Mitra Centre for Space weather (2004)Centre fur TeleInFrastructur (CTIF) -India (2007)UGC Networking Resource Centre in Physical Sciences (2008)
Centre for Research & Training in Microwave & Millimeterwave Technolog
National MEMS Design Centre (2009)
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Workshop onFrontiers of Electronics and Communication
atNorth Eastern Regional Institute of Science andTechnology
(NERIST),Nirjuli, Arunachal Pradesh
August 08, 2007
Modern Semiconductor Materials And Devices Physics, Technology and Challenges
P. K. Basu
Director, UGC Networking Resource Centre for Physical Science Institute of Radio Physics and Electronics
University of Calcutta
A Lecture under IEEE National Distinguished LectureProgramme
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DEVICE PHYSICS
NanoDev - 1
P. K. Basu
Institute of Radio Physics and Electronics92 Acharya Prafulla Chandra Road
Kolkata 700 009
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Current Voltage Relation
J
Current density J = Charge crossing unit area per sec.
Consider a bar of cross section area = 1 cm2, length =v cm = velocity of electrons. Electrons in volumev x 1 cm3 will cross unit area per unit time.Total no of electrons =n x v x 1; Total charge =nev
J = nev = neE; v = E; = mobility of electrons , E = Electric field =V/length. I = J xA = neE x A= neV(A/L)
V = (1 / ne )( L/A ) I = RI : Ohms law R = L/A ; =(1/)= specific resistance; = conductivity = ne.
v
LA
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What is a Semiconductor?
Has conductivity between metal(10 7 ) and insulator(10 -7
) A band gap separates the conduction and valencebands
Band gap varies from 0.1 3.0 eV; higher gapscorresponds to insulators
Typical Semiconductors :
Ge : 0.7 eV : Elemental
Si : 1.1 eV : Elemental
GaAs: 1.43 eV : III-V compound
ZnS : 2.6 : II-VI Compound
In x Ga 1-x As : III-V alloy
Si is the most widely used material in electronics/ VLSI
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Semiconductor
III-V II-VI IV-VI IV-IV
AlAs,AlPAlSbAlN
BAsBNBPBSb
GaAsGaPGaSbGaN
ZnSZnSeZnTeZnO
HgSHgSeHgTe
CdSCdTeCdSe
MISC
InAsInPInSbInN
MgSMgSeMnSeMnTe
SnTeEuTeYbTeSnTe
PbTePbSePbS
GeTe
SiGeC
SiC
TeGaSeCuCl
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Semiconductor Alloys
Binary Alloy: Si1-xGex (0 < x
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Amorphous Polycrystals Single crystal
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Growth of single crystalof Si
View of finished wafer of Si
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Hydrogen bond Si: Atomic No. 14 : 2 + 8+ 4electrons. Covalent bonding in Si.4 outermost electrons shared by 4nearest neighbours
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Pure Si crystal at T > 0K. A bond is broken by thermal energy.An EHP is created. An el goes from VB to CB. An emptystate(hole) is created in Si crystal.ni = p i = Intrinsic carrier
concentration.
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What is a Semiconductor?
Has conductivity between metal(10 7) and insulator(10 -7)
A band gap separates the conduction and valence bands
Band gap varies from 0.1 3.0 eV; higher gaps corresponds to insulators
The upper band, the CB is empty at 0K and VB is full at 0K.
Electric field > no e in CB > no flow of e > no current. Similarly at VB all states are full. No ecan gain energy from E-field> no movement of charge> no current. Semiconductor is aninsulator at 0k.
At higher temperature electrons go from VB to CB. There is an EHP. Now e and h areaccelerated by E-field and current flows.
J = e(n n +p p )E = E Ohms law > Current is proportional to electric field = mobilityconductivity.
Intrinsic (pure) semiconductor: n =p; n ~ exp(-E g /k BT).
Intrinsic n or p increases with decrease in gap, increase in T
N =1.5 x 10 10cm -3 at 300 K. No control on n or p or conductivity.
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Current Flow and Conductivity
Current density J = E
To calculate conductivity of intrinsic Si atroom temperature
Conductivity = e(n i n + p i p ) ; n = 1500 n = 500;
n = 1.5 x 10 10 ; conductivity = 4.8 x 10 -6 mho/cm very low and cannot be controlled.
HOW TO INCREASE AND CONTROLCONDUCTIVITY?
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Doped /Extrinsic Semiconductors
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Donor and Donor Binding EnergyConsider pure Si doped with Gr. V atom like P, As etc.
P atom substitutes a Si atom. 4 electrons out of 5 take part inbonding process.
Extra 5 th electron rotates around parent nucleus. H atomproblem Bohr theory needed.
Electron mass = effective mass; material permittivity inCoulomb force.
Binding energy = 13.6 ( m*/m 0 ) (eps 0 /eps) 2 eV.
m* = 0.12 m 0 ; eps = 16 eps 0
Binding energy ~ 6 meV. < kT at 300 (26 meV)
P atom easily ionised P + ions + 1 electron overall chargeneutrality
The e goes to CB > one e per P atom
If P atom = 10 15 cm -3 , same number of free electrons.
Conductivity increases by 5 orders!
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Carrier Concentration
n = N C exp[- ( E C E F )/k BT ]
N C = [42 (m*k BT)3/2]/h3 : Effective Density of States p = N v exp[- ( E F E V )/k BT ]
N V = [42 (m*k B T)3/2 ]/h3 : Effective Density of States
np = n i2
Whenn (or N D ) = N C , Fermi level touches CB edge: conditionfor degeneracy
dE E E m
dE E S dN cc
c2/1
2/3
22)(
2
2
1)(
==
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Band Structure Calculation Kronig Penney model Tight binding approximation Nearly free electron model Pseudopotential method
k.p perturbation (useful near the bandextrema of semiconductors)
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X1
X4
25
15
2L3
L1
L3
0 (100)(111)
0
-2
24
6
HHLH
k=(000)X5
X1X3
L3
L3
L1 15 1
15
E(eV)
-2
2
4
k=/a(111) k=2/a(100)SO
k x
k y
k z
Band Structure of Si
Band Structure of GaAs
Constant energy surfaces inCB of Si
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E E
Eg Eg
q
k k 00
Conduction band
Valence band
Direct and Indirect Gap Semiconductors
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Scattering MechanismsBulk: Impurity, Phonons, Defects (Alloy Disorder)
QW: Remote Impurity Scattering in MD structures,Surface Roughness
QWR: Reduced scattering rate for 1 DEG
QD: Phonon bottleneck
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Hot Carrier Phenomena
Velocity saturation, ndr, velocity overshoot and ballistic transport
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DEVICE PHYSICS: Fundamentals
P. K. Basu
Institute of Radio Physics and Electronics92 Acharya Prafulla Chandra Road
Kolkata 700 009
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p-n junction
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METAL OXIDE SEMICONDUCTOR FIELD
EFFECT TRANISTORS
MOSFETs
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Classification
Enhancement mode : n channel , p channel
Depletion mode: n channel, p channel
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CMOS INVERTER
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I sub = 0 C ox (W/L)(m-1)(V T )2
exp[(V G V T )/mkT] x [ 1 exp(- V ds /kT)] m = 1 + (C dm /C ox )
Lower V T increases subthreshold leakage current. V ds has little effect onsubthreshold current.
T d f l lt g f CMOS
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Trends of power supply voltage of CMOS
MOSFET: The Leaky Switch
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y
Subthreshold leakage (I sub )Dominant when device isOFF.Enhanced by reduced V T due to process scaling
Gate tunneling leakage (I gate )Due to aggressive scalingof the gate oxide layer
thickness (Tox)A super exponentialfunction of ToxComparable to I sub at 90nmtechnology
Power consumption vs supply for a CMOS
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Power consumption vs supply for a CMOSgate using bulk and SOI CMOS devices
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Power Explosion
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Power Explosion
IEDM 2003
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Leakage Power
Leakage power limits Vt scalingLeakage power limits Vt scaling
A. Grove, IEDM 2002
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Leakage Current Components
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Leakage Current Components
I1 = pn reverse bias current
I2 = Weak Inversion
I3 = Gate oxide tunneling
I4 = Hot carrier injection
I5 = GIDL
I6 = DIBL
Cross section of bulk and SOI MOS
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Cross section of bulk and SOI MOSdevices
Quantum SizeEff
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Q Effect Free Electron, ~ e ikx
Let us take E ~ 10 meVDe Broglie Wavelength,
m2
1h
m2
k E 2
222
=
mE2h=
~ 500 m = 0.067 m o
(2) Confine the electron
(Particle in a boxL
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Band bending and subbands at Si-SiO 2 interface
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High gate voltage triangular potential e motion quantized predicted bySchrieffer verified in Si MOSFET byIBM in 1966
To CB of SiO2
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Different Tunneling Processes through ThinGate
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Different Forms of FETs
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(a) MOSFET (b) FIN FET (c ) Nano Wire FET (d) Vertical NWFET: completeuniform wrap-around gate (e) Array of Vertical NWFETs as in (d).
C. Thelander, Materials Today, vol. 9, no. 10, p. 28 (2006)
High Electron Mobility Transistors (HEMTs)
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High Electron Mobility Transistors (HEMTs)
The 2DEG in GaN is separated from impurity ions in AlGaN. Reduced Couscattering leads to mobility enhancement. The text-book examples deal withAlGaAs/GaAs modulation doped single heterojunction.
Modulation doped
Or AlGaAs
or GaAs
Resonant Tunneling Diodes
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QCA The Four Dot DeviceQCA The Four Dot Device
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Uses electrons in cells tostoreandtransmitdata Electrons move between different positions via
electron tunneling Logic functionsperformed byCoulombic interactions
Carbon Nanotubes between Metal Electrodes
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References (contd)
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M Balkanski and R F Wallis (2000)Semiconductor Physics and Applications, OxfordUniv Presss, Oxford UK.
P K Basu (2003)Theory of Optical Processes in Semiconductors: Bulk and Microstructures, Clarendon Press, Oxford, UK.
G Bastard (1988)Wave mechanics Applied to Semiconductor Heterostructures, LesEditions de Physique, Les Ulis.
C Weisbuch and B Vinter (1991)Quantum Semiconductor Structures, Academic, SanDiego
V Mitin, M A Strocio and Kochelap (1999)Quantum Heterostructures , John Wiley,
NY. B K Ridley (2000)Quantum Processes in Semiconductors, 5th edition, ClarendonPress, Oxford,
Paul Harrison (2000)Quantum Wells, Wires and Dots: Theoretical and Computational Physics, John Wiley & Sons, Ltd, Chichester, UK.
Omar Manasreh (2005).Semiconductor Heterojunctions and Nanostructures, McGrawHill, NY.
John H. Davies (1998)The Physics of Low-Dimensional Semiconductors: An Introduction, Cambridge Univ Press , Cambridge, UK.
Jasprit Singh (2003) Electronic and optoelectronic properties of semiconductor structures , Cambridge Univ. Press, Cambridge, New York.
R A Smith (1964)S i d t Cambridge Univ Press Cambridge UK
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