Microelectronic Device Fabrication I (Basic Chemistry and Physics of Semiconductor Device Fabrication) Physics 445/545 David R. Evans
Atomic Orbitals s-orbitals p-orbitals d-orbitals
Chemical Bonding * s,p,d,etc. E B s,p,d,etc. Overlap of half-filled orbitals - bond formation H A H B H A - H B = H 2 Formation of Molecular Hydrogen from Atoms * s,p,d,etc. E B s,p,d,etc. Overlap of filled orbitals - no bonding
Periodic Chart
Crystal Bonding sp 3 antibonding orbitals sp 3 bonding orbitals Conduction Band E C 3p 3s sp 3 E g Si (separated atoms) Si (atoms interact to form tetrahedral bonding geometry) Valence Band Si crystal E V Silicon Crystal Bonding
Semiconductor Band Structures Silicon Germanium Gallium Arsenide
Intrinsic Semiconductor E C N C Conduction Band E F E g E V N V Valence Band Aggregate Band Structure Fermi-Dirac Distribution
n-type Semiconductor E C N C Conduction Band Shallow Donor States E F E i E g E V N V Valence Band Aggregate Band Structure Donor Ionization Fermi-Dirac Distribution
p-type Semiconductor E C N C Conduction Band E i E F E V N V Shallow Acceptor States Valence Band E g Aggregate Band Structure Acceptor Ionization Fermi-Dirac Distribution
Temperature Dependence Fermi level shift in extrinsic silicon Mobile electron concentration (N D = 1.15(10 16 ) cm 3 )
Carrier Mobility No Field Field Present Pictorial representation of carrier trajectory Carrier drift velocity vs applied field in intrinsic silicon
Effect of Dopant Impurities Effect of total dopant concentration on carrier mobility Resistivity of bulk silicon as a function of net dopant concentration
The Seven Crystal Systems
Bravais Lattices
Diamond Cubic Lattice a = lattice parameter; length of cubic unit cell edge Silicon atoms have tetrahedral coordination in a FCC (face centered cubic) Bravais lattice
Miller Indices z O y z x 100 O y 110 x z O y x 111
Diamond Cubic Model 100 110 111
Cleavage Planes Crystals naturally have cleavage planes along which they are easily broken. These correspond to crystal planes of low bond density. 100 110 111 Bonds per unit cell 4 3 3 Plane area per cell a 2 2 a 2 2 a 3 2 4 3 2 2.1 Bond Density a 2 2 2 2a 2 3 3.8 2 2 a a a In the diamond cubic structure, cleavage occurs along 110 planes.
[100] Orientation
[110] Orientation
[111] Orientation
[100] Cleavage
[111] Cleavage
Czochralski Process
Seed Rod (Single Crystal Si) dia. = ~1 cm
Czochralski Process Equipment Image courtesy Microchemicals
Czochralski Factory and Boules
D opant Conce ntration R atio CZ Growth under Rapid Stirring C s C l x=0 dx Distribution Coefficients Dopant K B 0.72 P 0.32 As 0.27 Sb 0.020 Ga 0.0072 Al 0.0018 In 0.00036 10 1 0.9 0.5 0.3 0.2 0.1 0.1 0.05 0.01 0.0 1 0 0.2 0.4 0.6 0.8 1 Le ngth Fractio n CZ Dopant Profiles under Conditions of Rapid Stirring
Enrichment at the Melt Interface
Zone Refining Si Ingot Heater Ingot slowly passes through the needle s eye heater so that the molten zone is swept through the ingot from one end to the other
Dopant Concentration Ratio Single Pass FZ Process L C s C o x=0 dx x 1 0.9 0.5 0.3 0.2 0.1 0.03 0.1 0.01 0.01 0 2 4 6 8 10 Zone Lengths
Dopant Concentration Ratio Multiple Pass FZ Process 1 0.9 0.5 0.3 0.2 0.1 0.03 0.1 0.01 0.01 0 2 4 6 8 10 12 14 16 18 20 Zone Lengths Almost arbitrarily pure silicon can be obtained by multiple pass zone refining.
Vacancy (Schottky Defect) Dangling Bonds
Self-Interstital
Dislocations Edge Dislocation Screw Dislocation
Burgers Vector Edge Dislocation Screw Dislocation Dislocations in Silicon [100] [111]
Stacking Faults Intrinsic Stacking Fault Extrinsic Stacking Fault
Vacancy-Interstitial Equilibrium Formation of a Frenkel defect - vacancy-interstitial pair L V + I Chemical Equilibrium K eq = [ V ][ I]
Thermodynamic Potentials E = Internal Energy H = Enthalpy (heat content) A = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent = internal energy (total system energy) A and G are equivalent = free energy (energy available for work) A = E TS T = Absolute Temperature S = Entropy (disorder) S = k ln W Boltzmann s relation
Vacancy Formation A = ME TS Mv v Mv S Mv = E v S W Mv k Mv = ln W = = ~ 2.3eV k ln W Mv N! ( N M)! M! N! = k ln ( N M )! M! Mv A Mv = ME v NkT ln N + MkT ln M + ( N M) ktln( N M)
Additional Vacancy Formation M A = E + kt ln M kt ln( N M) Mv v M = N exp E kt v Vacancy concentration
Equilibrium Constant Interstitial concentration N N 8 5 = = = kt E N kt E N M i i exp 8 5 exp + = kt E E N K i v eq exp 8 5 2
Internal Gettering Gettering removes harmful impurities from the front side of the wafer rendering them electrically innocuous. O 2 O 2 O 2 O 2 O 2 denuded zone O O O O O O O O O O O O High temperature anneal - denuded zone formation oxygen nuclei Low temperature anneal - nucleation oxide precipitates (with dislocations and stacking faults) Intermediate temperature anneal - precipitate growth
Oxygen Solubility in Silicon 1.0E+19 Interstitial Oxygen Concentration, per cm 3 1.0E+18 1.0E+17 900 1000 1100 1200 1300 Temperature, deg C
Oxygen Outdiffusion
Precipitate Free Energy 3 4r A = ne nts + g SiO + 4 r 2 SiO 2 3 r A = ne nts + g+ 8r 2 4r SiO 2 SiO2 a) - Free energy of formation of a spherical precipitate as a function of radius b) - Saturated solid solution of B (e.g., interstitial oxygen) in A (e.g., silicon crystal) c) - Nucleus formation 2
Critical Radius r 2 = crit ne nts + SiO 2 SiO 2 g a) If critical radius exists, then a larger precipitate grows large b) If critical radius exists, then a smaller percipitate redissolves
Substrate Characterization by XRD q q Constructive Interference Destructive Interference Bragg pattern - [hk0], [h0l], or [0kl]
Wafer Finishing Ingot slicing into raw wafers Spindle Carrier Pad Capture Ring Table Wafer Insert Schematic of chemical mechanical polishing
Vapor-Liquid-Solid (VLS) Growth H 2 H 2 H 2 H 2 catalyst SiH 4 SiH 4 substrate substrate substrate Si nanowires grown by VLS (at IBM)
Gold-Silicon Eutectic liquid A B solid A eutectic melt mixed with solid gold B eutectic melt mixed with solid silicon
Silicon Dioxide Network Non-bridging oxygen SiO 4 tetrahedron Silanol
Thermal Oxidation C C S C G C o F 1 C i F 2 F 3 Si Substrate x Thermal SiO 2 Film Gas One dimensional model of oxide growth Deal-Grove growth kinetics
Steady-state Fluxes F = h ( C C 1 G G S Mass transport flux ) D F = ( C C 2 o i x Diffusion flux ) F 3 =k s C i Reaction flux 1) Diffusion flux is in-diffusion. Any products, e.g., H 2, must out-diffuse. However, out-diffusion is fast and generally not limiting. 2) Mass transport is generally never limiting.
Henry's Law H = C C o S Distribution equilibrium (Henry's Law) Reaction = Mass Transport k s C i = h G C G C o H k C C = s i + G h G C o H
Steady-state Concentrations Reaction = Diffusion ) ( i o i s C C x D C k = Gas phase concentration related to reaction concentration i s o C D x k C + = 1 i s G s G C HD x k H h k C + + = 1
Deal-Grove Model Relationship between thickness and time: + + + + = G s G G s h H k t t ND HC h H k D x 1 ) ( 2 1 0 2 What if an oxide of thickenss, x 0, is already on the wafer? Must calculate equivalent growth time under desired conditions 1 3 1 + + = = D x k h Hk HC k dt dx N F s G s G s + + = 0 2 0 0 1 2 2 x h H k D x DHC N t G s G
Deal-Grove Rate Constants B/A => Linear Rate Constant B => Parabolic Rate Constant + = s h G H k D A 1 2 N DHC B G 2 = + = G s G h Hk N C A B 1 1
Oxidation Kinetics Energy Transition E a Reactant Product E Process Coordinate Rate constants for wet and dry oxidation on [100] and [111] surfaces Process B/A for [100] B/A for [111] B Dry Oxidation 1.03(10 3 kt ) 2. 1.73(10 3 kt ) 2. kt 0.214 1. e 00 e 00 e 23 Steam Oxidation 2.70(10 4 kt ) 2. 4.53(10 4 kt ) 2. kt 0.107 0. e 05 e 05 e 79 Note: Activation energies are in ev s, B/A is in m/sec, B is in m 2 /sec
Linear Rate Constant Orientation dependence for [100] and [111] surfaces affects only the pre-exponential factor and not the activation energy
Parabolic Rate Constant No orientation dependence since the parabolic rate constant describes a diffusion limited process
Pressure Dependence Oxidation rates scale linearly with oxidant pressure or partial pressure
Rapid Initial Oxidation in Pure O 2 This data taken at 700C in dry oxygen to investigate initial rapid oxide growth
Metal-Metal Contact E vac f 1 f 2 y = f 2 f 1 E F1 E F2 E F + + Metal 1 Metal 2
Metal-Silicon Contact E vac f M f Si f Si f M E FM E c E FSi E F + + E v Metal Silicon
Effect of a Metal Contact on Silicon E c E c E i j F j F E F + + Depletion (p-type) E v E F + + Inversion (p-type) E i E v E c E c E F + + j F E i E v E F j F E i E v Accumulation (n-type) Flat Band (n-type) + + E c E F j F E i E v Depletion (n-type)
Metal-Oxide-Silicon Capacitor E vac f Si f M f M f Si f SiO2 E FSi E F + E FM E C E V Metal Silicon Dioxide Silicon
MOS Capacitor on Doped Silicon E C E C E FM j F E i E FSi E FM + E V E V Depletion (p-type) Accumulation (n-type) + j F E FSi E i V g 0 v Schematic of biased MOS capacitor
Biased MOS Capacitors E FM E FM E C E C j F E FSi j F E i E FSi E i Accumulation (p-type) E V Inversion (n-type) E V E C E FM E C E FM j F E i E FSi E V j F E FSi E i Depletion (p-type) Depletion (n-type) E V E C j F E i E FSi E V E C E FSi E FM j F Ei E FM E V Inversion (p-type) Accumulation (n-type)
Capacitance Capacitance CV Response 10 9 8 7 quasistatic 6 5 n-type substrate 4 3 high frequency 2 1 0-100 -50 0 50 100 Bias Voltage depletion approximation 10 9 8 7 quasistatic 6 5 p-type substrate 4 3 2 1 depletion approximation high frequency 0-50 -40-30 -20-10 0 10 20 30 40 50 Bias Voltage
Surface Charge Density Surface Charge Density Surface Charge Density 10000000 1000000 inversion 100000 10000 1000 100 depletion n type substrate 10 accumulation 1-30 -20-10 0 10 20 30 Bias Voltage 10000000 blue: positive surface charge red: negative surface charge 1000000 inversion 100000 10000 1000 100 depletion p type substrate 10 accumulation 1-30 -20-10 0 10 20 30 Bias Voltage
Capacitance, Charge, and Potential 2 d j ( x) = 2 dx Poisson s equation (1-D) s ( x) = q p( x) n( x) + N D N A Charge density for a uniformly doped substrate i = skt 2 2q n Intrinsic Debye Length: a measure of how much an external electric field penetrates pure silicon i
The Depletion Approximation ) ( ) ( 2 2 x N x N q dx d A D s = j Carrier concentrations are negligible in the depletion region = i D A D A s d n N N N N q kt x ln 4 2 max Maximum depletion width D A s D N N q kt = 2 Extrinsic Debye Length: a measure of how much an external electric field penetrates doped silicon
CV vs Doping and Oxide Thickness 10 Capacitance (dimensionless linear scale) 9 8 7 6 5 4 3 2 1 0-100 -50 0 50 100 150 Substrate Doping p-type substrate Capacitance (dimensionless logarithmic scale) 1000 100 10 1 0.1-150 -100-50 0 50 100 Bias Voltage (dimensionless linear scale) Oxide Thickness
CV Measurements C Quasi-static CV C High Frequency CV C ox C ox C min C min V V C C ox Deep Depletion Effect C min slow sweep fast very fast extremely fast V C Flat Band Shift C Fast Interface States C ox Ideal C ox Ideal C FB C FB Actual Actual C min C min V FB V FB V V FB V
Interface States E C E F j F E i E V Interface states caused by broken symmetry at interface E C j F E i E FSi E FM E V Interface states p-type depletion E FM + + + j F E C E FSi E i E V Interface states n-type depletion
Interface State Density Interface state density is always higher on [111] than [100]
IV Response avalanche breakdown log J Fowler-Nordheim tunneling Very T hin T hin T hick 10 MV/cm E Logarithm of current density (J) vs applied electric field (E)
Conduction Mechanisms J = 2 E AFN E exp E o Fowler-Nordheim tunneling J J J J qe = AFP E exp qfb kt ox Frenkel-Poole emission qe = A* T 2 exp qfb kt 4 ox Schottky emission = A E exp e q E ae kt Ohmic (electronic) conduction Ai E = exp q Eai kt Ionic conduction T J = 9 8x ox ox e 3 o V 2 Mobility limited breakdown current
Oxide Reliability 100% Per cent Failed poor reliability good reliability 0% infant mortality time, t, or total charge, Q Each point represents a failed MOS structure - stress is continued until all devices fail QBD - charge to breakdown - constant current stress TDBD - time dependent breakdown - constant voltage stress
Linear Transport Processes Ohm s Law of electrical conduction: j = E = E/ J = electric current density, j (units: A/cm 2 ) J = LX J = Flux, X = Force, L = Transport Coefficient X = electric field, E = V (units: volt/cm) V = electrical potential Fourier s Law of heat transport: q = T L = conductivity, = 1/ (units: mho/cm) = resistivity ( cm) J = heat flux, q (units: W/cm 2 ) X = thermal force, T (units: K/cm) T = temperature Fick s Law of diffusion: F = DC L = thermal conductivity, (units: W/K cm) J = material flux, F (units: /sec cm 2 ) X = diffusion force, C (units: /cm 4 ) C = concentration Newton s Law of viscous fluid flow: F u = u L = diffusivity, D (units: cm 2 /sec) J = velocity flux, F u (units: /sec 2 cm) X = viscous force, u (units: /sec) u = fluid velocity L = viscosity, (units: /sec cm)
Diffusion x A F(x) x F(x ) + Diffusion in a rectangular bar of constant cross section x C t = D 2 C 2 x Fick s Second Law 2 xx0 4Dt C x, t = e 2 N Dt Instantaneous Source - Gaussian profile C N 2 x x 2 Dt 0 0 x, t = erfc Constant Source - error function profile
Instantaneous Source Profile 1.2 1 0.8 0.6 Linear scale 0.4 0.2 0 0 1 2 3 4 5 1.0 Log scale 0.1 0 0.5 1 1.5 2
Constant Source Profile 1.2 1 0.8 0.6 Linear scale 0.4 0.2 0 0 1 2 3 4 5 1.0 Log scale 0.1 0 0.5 1 1.5 2
Surface Probing r r I x f Substrate I T hin Film Substrate Single probe injecting current into a bulk substrate Single probe injecting current into a conductive thin film 1 2 3 4 I I s s s Substrate Four point probe
pn Junction E vac E c E Fn E i E F E Fp E v n type Silicon p type Silicon
Junction Depth 1.2 1 0.8 0.6 0.4 0.2 x J red: background doping black: diffused doping 0 0 1 2 3 4 5 1.00 0.10 x J 0.01 0 0.5 1 1.5 2
Unbiased pn Junctions Band Diagram E F Charge Density E Electric Field V Potential
Biased pn Junctions I IV Characteristics I 0 V 1 C 2 CV Characteristics V pn V
Photovoltaic Effect V OC V I SC I
Solar Cell typical cross section equivalent circuit
Solar Cell IV Curve I I SC I max P V max V OC
Effect of Parasitics, Temperature, etc. effect of R S effect of R SH effect of I 0 effect of n effect of T
Solar Cell Technology Commercial solar cell
LED IV Characteristics
LED Technology Commercial LED s RGB spectrum white spectrum (with phosphor)
Diffusion Mechanisms Vacancy Diffusion - Substitutional impurities, e.g., shallow level dopants (B, P, As, Sb, etc.), Diffusivity is relatively small for vacancy diffusion. Interstitial Diffusion - Interstitial impurities, e.g., small atoms and metals (O, Fe, Cu, etc.), Diffusivity is much larger, hence interstitial diffusion is fast compared to vacancy diffusion. Interstitialcy Mechanism - Enhances the diffusivity of substitutional impurities due to exchange with silicon self-interstitials. This leads to enhanced diffusion in the vicinity of the substrate surface during thermal oxidation (socalled oxidation enhanced diffusion ).
Defect-Carrier Equilibria x + V V + h K = V V V x p = + = V V + h K V = V V = p x + + V V + e K = V V V + x n + ++ ++ V V + e K V = V V ++ + n Vacancies interact with mobile carriers and become charged. In this case, the concentrations are governed by classical mass action equilibria.
Arrhenius Constants for Dopant Atoms Atomic Species I Diffusion Mechanism r V r D oi (cm 2 /sec) r Q I (ev) Si V V V V x = + 0.015 16 10 1180 3.89 4.54 5.1 5.09 As V x V 0.066 12.0 3.44 4.05 B V V x + 0.037 0.76 3.46 3.46 Ga V V x + 0.374 28.5 3.39 3.92 P V V V x = 3.85 4.44 44.2 3.66 4.00 4.37 Sb V V x 0.214 15.0 3.65 4.08 N x V 0.05 3.65
Arrhenius Constants for Other Species Atomic Species Mechanism, Temperature, etc. D oi (cm 2 /sec) Q I (ev) Ge substitutional 6.25(10 5 ) 5.28 Cu (300-700C) (800-1100C) 4.7(10 3 0.04 ) 0.43 1.0 Ag 3 2(10 ) 1.6 Au substitutional interstitial (800-1200C) 2.8(10 2.4(10 1.1(10 3 4 3 ) ) ) 2.04 0.39 1.12 Pt 150-170 2.22-2.15 Fe 3 6.2(10 ) 0.87 Co 9.2(10 4 ) 2.8 C 1.9 3.1 S 0.92 2.2 O 2 0.19 2.54 H 3 2 9.4(10 ) 0.48 He 0.11 1.26
Solid Solubilities
Ion Implantation Dopant species are ionized and accelerated by a very high electric field. The ions then strike the substrate at energies from 10 to 500 kev and penetrate a short distance below the surface. kˆ q vi tangent plane (edge on) v i q i vˆ ^ b c ˆv s vs Elementary hard sphere collision
Co-linear or Centered Collision b=0 c= q=0 tangent plane (edge on) vˆ ^ ˆv v i vi kˆ i s vs mi ms v i = vi mi + ms ; v s 2mi = vi mi + ms Clearly, if m i <m s, then v i is negative. This means that light implanted ions tend to be scattered back toward the surface. Conversely, if m i >m s, then v i is positive and heavy ions tend to be scattered forward into the bulk. Obviously, if m i equals m s, then v i ˆv 0 vanishes. In any case, recoiling silicon atoms are scattered deeper into the substrate.
Stopping Mechanisms Nuclear Stopping - Direct interaction between atomic nuclei; resembles an elementary two body collision and causes most implant damage. Electronic Stopping - Interaction between atomic electron clouds; sort of a viscous drag as in a liquid medium. Causes little damage.
Implant Range Range - Total distance traversed by an ion implanted into the substrate. Projected Range - Average penetration depth of an implanted ion.
Implant Straggle Projected Straggle - Variation in penetration depth. (Corresponds to standard deviation if the implanted profile is Gaussian.)
Channeling Channeling is due to the crystal structure of the substrate.
Implantation Process For a light dose, damage is isolated. As dose is increased, damage sites become more dense and eventually merge to form an amorphous layer. For high dose implants, the amorphous region can reach all the way to the substrate surface.
Point-Contact Transistor
Bipolar Junction Transistor E B C n p n
Junction FET S G D n p n
MOSFET S G D n n p enhancement mode S G D n n p depletion mode
Enhancement Mode FET 7 V 6 V 5 V 4 V