Course Administration

• Schedule change: Supreme 4 process simulator lecture moved later
  • Need to cover Transit Enhanced Diffusion (TED) first
  • Today covering ion implantation instead (4 lectures total)
• Homework #4 delayed due to Red Sox game
• Handout #20 distributed: Term project topics and requirements
  • ~15 potential topics listed (not exhaustive)
  • Topics include: dopant diffusion in SiGe, laser annealing, selective epitaxial growth
  • Requires instructor approval
  • Choice between 20-page written report or 15-17 minute oral presentation
  • Must research multiple papers, not just regurgitate one source
  • Oral presentations require handouts for class

Ion Implantation Introduction

• Chapter 8 coverage over next 4 lectures
• Only semiconductor process modelable from first principles
  • Based on fundamental physics vs empirical models
  • Fewer free parameters than other processes
• Dominant method for introducing dopants despite lattice damage
• Replaced traditional predeposition/drive-in methods

Historical Context and VT Control

• Introduced to manufacturing late 1970s as enabling technology
• Primary driver: accurate threshold voltage (VT) control in MOSFETs
• VT equation includes ion implant term: Q×φ/Cox
  • φ = implant dose (atoms/cm²)
  • Precise dose control enables precise VT adjustment
• Traditional predeposition method limitations:
  • Poor dose control (temperature/time sensitive)
  • 1 second at 1000°C gives 10¹⁴ atoms/cm² (too high for VT adjust)
  • Ion implant can achieve 10¹² atoms/cm² with excellent control

Dose Control Mechanism

• Dose = (1/Area) × ∫(I/q)dt
  • I = beam current (measurable with ammeter)
  • q = electronic charge
  • Integration over time provides precise charge counting
• Example calculation: 0.1 μA beam, 20×20 cm² area
  • Dose rate = 1.6×10⁹ atoms/cm²/sec
  • Excellent dynamic range (0.01 μA to mA beam currents)

Ion Implanter Design

• Vacuum system with ion source and mass analyzer
• Ion source: ionizes species (e.g., BF₂ gas → B⁺, F⁻, BF₂⁺)
• Extraction voltage (0-30 kV) sets initial ion energy
• E×B filter for mass selection
  • Centrifugal force = magnetic force (mv²/r = qvB)
  • Only desired mass passes through resolving slit
• High voltage accelerator (50-200 kV) for final energy
• X-Y scan plates for beam rastering across wafer
• Current integrator for dose monitoring

Ion Distribution Physics

• Random collision process with silicon atoms
• Two energy loss mechanisms:
  • Nuclear collisions (billiard ball-like)
  • Electronic drag forces
• Key parameters:
  • Total range: sum of all path segments
  • Projected range (Rp): depth projection (more important)
• Statistical process creates distribution of final positions

Profile Characteristics by Ion Mass

• Light ions (Boron): travel deeper, broader distributions
  • At 200 keV: Rp ≈ 0.55 μm, very broad profile
• Heavy ions (Antimony): shallow, narrow distributions
  • At 200 keV: much shallower than Boron, tight distribution
• Intermediate ions (Phosphorus, Arsenic): between extremes

Gaussian Approximation

• First-order model: N(x) = Npeak × exp[-(x-Rp)²/(2ΔRp²)]
• Two parameters: Rp (projected range), ΔRp (standard deviation)
• Integrated dose Q = √(2π) × ΔRp × Npeak
• Works well for heavy ions, less accurate for light ions
• Tabulated values available in textbooks and literature

Lateral Distribution and Masking

• 3D ion distribution: elongated ellipse in beam direction
• Lateral straggle: ΔRp⊥ (perpendicular to beam)
• Point response function approach for modeling
• Mask edge effects critical for device dimensions
  • Lateral straggle under gate determines channel length
  • Important for short channel effects

Masking Calculations

• Mask thickness requirement: Xm = Rp* + M×ΔRp*
  • * denotes parameters in mask material
  • M typically ~5 standard deviations
• Penetrating dose: complementary error function
• Tilted implants create shadowing effects
  • Often require symmetric tilts for device uniformity

Profile Evolution During Annealing

• Simple case: Gaussian preserved during diffusion
• Final standard deviation: √(ΔRp² + 4Dt)
• Peak concentration decreases as profile broadens
• More complex behavior in real systems due to TED

Advanced Profile Modeling

• Real profiles show skewness (non-Gaussian behavior)
• Light ions: skewed toward surface (backscattering)
• Heavy ions: skewed deeper (forward momentum)

Pearson IV Distribution

• Four-moment description: Rp, ΔRp, skewness (γ), kurtosis (β)
• Differential equation solution for accurate profiles
• Peak location: Rp + a (offset from Rp)
• Skewness effects:
  • γ < 0 (Boron): peak deeper than Rp
  • γ > 0 (heavy ions): peak shallower than Rp
• Tabulated parameters available for common dopants

Ion Channeling Effects

• Single crystal silicon has open channels along crystal axes
• Ions can travel much deeper via channeling
• Critical angle (ψc): maximum misalignment for channeling
  • Boron <111>: ~3°, Arsenic <111>: ~4.4°
• Dose-dependent effects:
  • Low dose: maintains crystal structure, deep channeling tails
  • High dose: amorphizes crystal, eliminates channeling

Channeling Control Methods

• Controlled misalignment: 7° tilt + rotation
• Amorphous overlayers (limited effectiveness)
• Residual channeling still occurs at end-of-range
  • Critical angle increases as ions slow down
  • Creates exponential tail in profiles

Modeling Complexity Hierarchy

• Gaussian (2 parameters): basic approximation
• Pearson IV (4 parameters): accurate for amorphous
• Pearson IV + exponential tail (6 parameters): includes channeling
• Dual Pearson (9 parameters): complex channeling cases
• Monte Carlo: most accurate but computationally intensive
• Boltzmann Transport Equation (BTE): compromise approach

Monte Carlo Simulation

• Follow individual ion trajectories from surface to rest
• Statistical accuracy: error ∝ 1/√N
• Requires ~10⁵ ions for 10% accuracy over 3 decades
• Computationally expensive (hours to days)
• Most accurate for complex geometries and channeling

Key Process Parameters

• Beam energy: determines Rp and profile shape
• Dose: total atoms implanted per unit area
• Tilt angle: controls channeling
• Rotation: randomizes crystal orientation
• Masking materials: defines implant regions
• Wafer temperature: affects damage accumulation
• Dose rate: influences heating and damage kinetics