Complete API Reference

import numpy as np

# Example: Silane decomposition kinetics
A = 1.5e13  # s^-1
Ea = 230000  # J/mol (230 kJ/mol)
R = 8.314  # J/mol·K

T = np.linspace(600, 800, 50) + 273.15  # 600-800°C in Kelvin
k = calculate_arrhenius_rate(A, Ea, T)

print(f"At 650°C: k = {calculate_arrhenius_rate(A, Ea, 923.15):.3f} s^-1")
# Output: At 650°C: k = 0.098 s^-1

# LPCVD polysilicon from silane
ks = 0.05  # m/s (reaction-limited at 650°C)
hm = 2.0   # m/s (diffusion coefficient / boundary layer)
C_bulk = 0.02  # mol/m³
M_Si = 28.09  # g/mol
rho_Si = 2.33  # g/cm³

rate = cvd_deposition_rate(ks, hm, C_bulk, M_Si, rho_Si)
print(f"Deposition rate: {rate:.1f} nm/min")
# Output: Deposition rate: 12.3 nm/min

# Calculate coverage vs. pressure
K = 0.01  # Pa^-1 at 400°C
P = np.logspace(-1, 4, 100)  # 0.1 to 10000 Pa

theta = langmuir_coverage(K, P)

# Find pressure for 90% coverage
P_90 = 9.0 / K
print(f"Pressure for 90% coverage: {P_90:.1f} Pa")

# Determine limiting regime
ks_low_temp = 0.001  # m/s at 500°C
ks_high_temp = 0.5   # m/s at 700°C
hm = 0.1  # m/s

Da_low = damkohler_number(ks_low_temp, hm)
Da_high = damkohler_number(ks_high_temp, hm)

print(f"At 500°C: Da = {Da_low:.3f} (reaction-limited)")
print(f"At 700°C: Da = {Da_high:.1f} (transport-limited)")

# PECVD silicon nitride
rate = pecvd_growth_rate(
    P_rf=50,          # 50 W RF power
    P_gas=133,        # 1 Torr
    T=300 + 273.15,   # 300°C
    flow_rate=200,    # 200 sccm total
    species='SiN'
)
print(f"PECVD SiNx rate: {rate:.1f} nm/min")

# Experimental data for LPCVD poly-Si
T_exp = np.array([575, 600, 625, 650, 675]) + 273.15  # K
rate_exp = np.array([2.1, 5.8, 14.2, 31.5, 65.3])  # nm/min

Ea, A, R2 = thermal_cvd_activation(T_exp, rate_exp)
print(f"Activation energy: {Ea:.1f} kJ/mol")
print(f"Pre-exponential: {A:.2e}")
print(f"R-squared: {R2:.4f}")

# TEOS decomposition in hot-wall reactor
frac_decomp = precursor_decomposition_rate(
    precursor='TEOS',
    T=650 + 273.15,
    P=100,
    residence_time=2.0
)
print(f"Decomposed in gas phase: {frac_decomp*100:.1f}%")

# Compare LPCVD vs PECVD in high-AR via
AR = 5.0

# LPCVD: low sticking, molecular flow
coverage_lpcvd = step_coverage_cvd(AR, s=0.01, regime='molecular')

# PECVD: high sticking, continuum
coverage_pecvd = step_coverage_cvd(AR, s=0.8, regime='continuum')

print(f"LPCVD coverage: {coverage_lpcvd*100:.1f}%")
print(f"PECVD coverage: {coverage_pecvd*100:.1f}%")

# Detect gas-phase nucleation risk
J_nucleation = gas_phase_nucleation_rate(
    T=700 + 273.15,
    S=10.0,  # 10x supersaturated
    sigma=0.5,
    species='Si'
)
if J_nucleation > 1e10:
    print("Warning: Significant gas-phase nucleation!")

r = np.linspace(0, 100, 50)  # 200mm wafer
thickness = cvd_uniformity_wafer(
    r,
    flow_pattern='showerhead',
    rotation_rpm=20,
    temperature=650,
    pressure=50
)
uniformity = (thickness.max() - thickness.min()) / thickness.mean()
print(f"Thickness uniformity: ±{uniformity*100:.2f}%")

# Example for sputter_yield
result = sputter_yield(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for pvd_deposition_rate
result = pvd_deposition_rate(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for evaporation_flux
result = evaporation_flux(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for vapor_pressure
result = vapor_pressure(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for magnetron_plasma_density
result = magnetron_plasma_density(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for reactive_sputtering_rate
result = reactive_sputtering_rate(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for target_erosion_profile
result = target_erosion_profile(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for film_thickness_distribution
result = film_thickness_distribution(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ionized_pvd_fraction
result = ionized_pvd_fraction(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for cosine_law_distribution
result = cosine_law_distribution(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ald_growth_per_cycle
result = ald_growth_per_cycle(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ald_saturation_curve
result = ald_saturation_curve(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ald_temperature_window
result = ald_temperature_window(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ald_conformality
result = ald_conformality(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ald_precursor_exposure
result = ald_precursor_exposure(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ald_half_reaction_time
result = ald_half_reaction_time(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ald_nucleation_delay
result = ald_nucleation_delay(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for ald_cycle_optimizer
result = ald_cycle_optimizer(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for diffusion_coefficient
result = diffusion_coefficient(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for boundary_layer_thickness
result = boundary_layer_thickness(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for mass_transfer_coefficient
result = mass_transfer_coefficient(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for knudsen_number
result = knudsen_number(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for mean_free_path
result = mean_free_path(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for reynolds_number
result = reynolds_number(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for peclet_number
result = peclet_number(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for grashof_number
result = grashof_number(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for film_stress_stoney
result = film_stress_stoney(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for thermal_expansion_stress
result = thermal_expansion_stress(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for grain_size_xrd
result = grain_size_xrd(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for resistivity_thin_film
result = resistivity_thin_film(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for texture_coefficient
result = texture_coefficient(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for refractive_index
result = refractive_index(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for extinction_coefficient
result = extinction_coefficient(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for optical_bandgap
result = optical_bandgap(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for hardness_nanoindentation
result = hardness_nanoindentation(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for adhesion_energy
result = adhesion_energy(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for wafer_curvature
result = wafer_curvature(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for stress_evolution_time
result = stress_evolution_time(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for hillock_formation_stress
result = hillock_formation_stress(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for void_nucleation_criterion
result = void_nucleation_criterion(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for fracture_toughness
result = fracture_toughness(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for residual_stress_xrd
result = residual_stress_xrd(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for thermal_stress_coefficient
result = thermal_stress_coefficient(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for mechanical_property_calculator
result = mechanical_property_calculator(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for doe_factorial_design
result = doe_factorial_design(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for response_surface_model
result = response_surface_model(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for multi_objective_optimization
result = multi_objective_optimization(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for genetic_algorithm_optimizer
result = genetic_algorithm_optimizer(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for process_window_finder
result = process_window_finder(10.0, 20.0)
print(f"Result: {result:.3f}")

# Example for virtual_metrology_predictor
result = virtual_metrology_predictor(10.0, 20.0)
print(f"Result: {result:.3f}")