Microelectronic Device Fabrication I. Physics 445/545. David R. Evans

Transcription

1 Microelectronic Device Fabrication I (Basic Chemistry and Physics of Semiconductor Device Fabrication) Physics 445/545 David R. Evans

2 Atomic Orbitals s-orbitals p-orbitals d-orbitals

3 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

4 Periodic Chart

5 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

6 Semiconductor Band Structures Silicon Germanium Gallium Arsenide

7 Intrinsic Semiconductor E C N C Conduction Band E F E g E V N V Valence Band Aggregate Band Structure Fermi-Dirac Distribution

8 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

9 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

10 Temperature Dependence Fermi level shift in extrinsic silicon Mobile electron concentration (N D = 1.15(10 16 ) cm 3 )

11 Carrier Mobility No Field Field Present Pictorial representation of carrier trajectory Carrier drift velocity vs applied field in intrinsic silicon

12 Effect of Dopant Impurities Effect of total dopant concentration on carrier mobility Resistivity of bulk silicon as a function of net dopant concentration

13 The Seven Crystal Systems

14 Bravais Lattices

15 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

16 Miller Indices z O y z x 100 O y 110 x z O y x 111

17 Diamond Cubic Model

18 Cleavage Planes Crystals naturally have cleavage planes along which they are easily broken. These correspond to crystal planes of low bond density Bonds per unit cell Plane area per cell a 2 2 a 2 2 a Bond Density a a a a a In the diamond cubic structure, cleavage occurs along 110 planes.

19 [100] Orientation

20 [110] Orientation

21 [111] Orientation

22 [100] Cleavage

23 [111] Cleavage

24 Czochralski Process

25 Seed Rod (Single Crystal Si) dia. = ~1 cm

26 Czochralski Process Equipment Image courtesy Microchemicals

27 Czochralski Factory and Boules

28 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 Ga Al In Le ngth Fractio n CZ Dopant Profiles under Conditions of Rapid Stirring

29 Enrichment at the Melt Interface

30 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

31 Dopant Concentration Ratio Single Pass FZ Process L C s C o x=0 dx x Zone Lengths

32 Dopant Concentration Ratio Multiple Pass FZ Process Zone Lengths Almost arbitrarily pure silicon can be obtained by multiple pass zone refining.

33 Vacancy (Schottky Defect) Dangling Bonds

34 Self-Interstital

35 Dislocations Edge Dislocation Screw Dislocation

36 Burgers Vector Edge Dislocation Screw Dislocation Dislocations in Silicon [100] [111]

37 Stacking Faults Intrinsic Stacking Fault Extrinsic Stacking Fault

38 Vacancy-Interstitial Equilibrium Formation of a Frenkel defect - vacancy-interstitial pair L V + I Chemical Equilibrium K eq = [ V ][ I]

39 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

40 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)

41 Additional Vacancy Formation M A = E + kt ln M kt ln( N M) Mv v M = N exp E kt v Vacancy concentration

42 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

43 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

44 Oxygen Solubility in Silicon 1.0E+19 Interstitial Oxygen Concentration, per cm 3 1.0E E Temperature, deg C

45 Oxygen Outdiffusion

46 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

47 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

48 Substrate Characterization by XRD q q Constructive Interference Destructive Interference Bragg pattern - [hk0], [h0l], or [0kl]

49 Wafer Finishing Ingot slicing into raw wafers Spindle Carrier Pad Capture Ring Table Wafer Insert Schematic of chemical mechanical polishing

50 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)

51 Gold-Silicon Eutectic liquid A B solid A eutectic melt mixed with solid gold B eutectic melt mixed with solid silicon

52 Silicon Dioxide Network Non-bridging oxygen SiO 4 tetrahedron Silanol

53 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

54 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.

55 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

56 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

57 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 ) ( What if an oxide of thickenss, x 0, is already on the wafer? Must calculate equivalent growth time under desired conditions = = D x k h Hk HC k dt dx N F s G s G s + + = x h H k D x DHC N t G s G

58 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

59 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 ) (10 3 kt ) 2. kt e 00 e 00 e 23 Steam Oxidation 2.70(10 4 kt ) (10 4 kt ) 2. kt 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

60 Linear Rate Constant Orientation dependence for [100] and [111] surfaces affects only the pre-exponential factor and not the activation energy

61 Parabolic Rate Constant No orientation dependence since the parabolic rate constant describes a diffusion limited process

62 Pressure Dependence Oxidation rates scale linearly with oxidant pressure or partial pressure

63 Rapid Initial Oxidation in Pure O 2 This data taken at 700C in dry oxygen to investigate initial rapid oxide growth

64 Metal-Metal Contact E vac f 1 f 2 y = f 2 f 1 E F1 E F2 E F + + Metal 1 Metal 2

65 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

66 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)

67 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

68 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

69 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)

70 Capacitance Capacitance CV Response quasistatic 6 5 n-type substrate 4 3 high frequency Bias Voltage depletion approximation quasistatic 6 5 p-type substrate depletion approximation high frequency Bias Voltage

71 Surface Charge Density Surface Charge Density Surface Charge Density inversion depletion n type substrate 10 accumulation Bias Voltage blue: positive surface charge red: negative surface charge inversion depletion p type substrate 10 accumulation Bias Voltage

72 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

73 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

74 CV vs Doping and Oxide Thickness 10 Capacitance (dimensionless linear scale) Substrate Doping p-type substrate Capacitance (dimensionless logarithmic scale) Bias Voltage (dimensionless linear scale) Oxide Thickness

75 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

76 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

77 Interface State Density Interface state density is always higher on [111] than [100]

78 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)

79 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

80 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

81 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)

82 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

83 Instantaneous Source Profile Linear scale Log scale

84 Constant Source Profile Linear scale Log scale

85 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 I I s s s Substrate Four point probe

86 pn Junction E vac E c E Fn E i E F E Fp E v n type Silicon p type Silicon

87 Junction Depth x J red: background doping black: diffused doping x J

88 Unbiased pn Junctions Band Diagram E F Charge Density E Electric Field V Potential

89 Biased pn Junctions I IV Characteristics I 0 V 1 C 2 CV Characteristics V pn V

90 Photovoltaic Effect V OC V I SC I

91 Solar Cell typical cross section equivalent circuit

92 Solar Cell IV Curve I I SC I max P V max V OC

93 Effect of Parasitics, Temperature, etc. effect of R S effect of R SH effect of I 0 effect of n effect of T

94 Solar Cell Technology Commercial solar cell

95 LED IV Characteristics

96 LED Technology Commercial LED s RGB spectrum white spectrum (with phosphor)

97 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 ).

98 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.

99 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 = As V x V B V V x Ga V V x P V V V x = Sb V V x N x V

100 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 ( C) ( C) 4.7( ) Ag 3 2(10 ) 1.6 Au substitutional interstitial ( C) 2.8(10 2.4(10 1.1( ) ) ) Pt Fe 3 6.2(10 ) 0.87 Co 9.2(10 4 ) 2.8 C S O H (10 ) 0.48 He

101 Solid Solubilities

102 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

103 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.

104 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.

105 Implant Range Range - Total distance traversed by an ion implanted into the substrate. Projected Range - Average penetration depth of an implanted ion.

106 Implant Straggle Projected Straggle - Variation in penetration depth. (Corresponds to standard deviation if the implanted profile is Gaussian.)

107 Channeling Channeling is due to the crystal structure of the substrate.

108 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.

109 Point-Contact Transistor

110 Bipolar Junction Transistor E B C n p n

111 Junction FET S G D n p n

112 MOSFET S G D n n p enhancement mode S G D n n p depletion mode

113 Enhancement Mode FET 7 V 6 V 5 V 4 V