Semiconductor engineering calculators

Yield, quality and reliability (8)

• Process capability (Cp and Cpk) calculator
  Calculate Cp, Cpk and Cpm from specification limits and the mean and standard deviation, or paste measurement data. Shows the estimated out-of-spec rate in ppm and a Cpk-to-defect-rate table.
• Die per wafer (DPW) calculator
  Calculate how many dies fit on a wafer from the wafer diameter and die size, with scribe line width and edge exclusion. Compares 200 mm and 300 mm wafers.
• Die yield calculator (defect density models)
  Estimate die yield from defect density (D0) and die area with the Poisson, Murphy and Seeds models, and compare the yield of one large die with chiplets.
• Reliability test sample size and LTPD calculator
  Find the sample size needed to demonstrate a reliability at a given confidence level, the LTPD from test results, and the test size needed to show a FIT target with acceleration.
• Wafer weight, area and thickness calculator
  Calculate the weight, area, usable area and volume of wafers from 2 inch to 450 mm in silicon, SiC, GaAs, GaN, sapphire and glass, with SEMI nominal thicknesses.
• Acceleration factor and failure rate (FIT) calculator
  Calculate acceleration factors with the Arrhenius, Peck, Coffin-Manson and Black models, and the failure rate in FIT and MTTF from test size, duration and failures.
• Weibull analysis calculator (β, η, B-life)
  Fit a Weibull distribution to failure times by median rank regression to get the shape β, scale η, reliability at any time, B-life and MTTF, with a probability plot.
• Fault coverage and shipped defect rate (DPPM) calculator
  Calculate the shipped defect rate in DPPM from yield and fault coverage, the coverage needed for a DPPM target, test pass rate and expected escapes.

Fab economics and operations (6)

• Chip cost calculator (wafer price ÷ good dies)
  Estimate the cost per good chip from wafer price, die size, defect density and wafer size, and compare a monolithic die with the same area split into chiplets.
• Wafer capacity converter (8-inch and 12-inch equivalent)
  Convert fab capacity between 6-inch, 8-inch and 12-inch equivalent wafers per month, week or year, and estimate good chips per month from die size and defect density.
• Transistor density (MTr/mm²) calculator
  Estimate logic transistor density in MTr/mm² from contacted gate pitch, metal pitch and cell height, and extrapolate it with Moore's law.
• Overall equipment efficiency (OEE) calculator
  Calculate overall equipment efficiency from SEMI E10 time categories: availability, operational, rate and quality efficiency, plus MTBF, MTTR and a breakdown of losses.
• Cycle time and WIP calculator (Little's law)
  Calculate fab cycle time from WIP and throughput with Little's law, the X-factor and days per mask layer, and queue time at a tool from utilization with Kingman's formula.
• Oxygen concentration in silicon (Oi) converter
  Convert interstitial oxygen concentration in CZ silicon between atoms/cm³, ppma, ppmw and FTIR absorption coefficient under New ASTM, Old ASTM, JEIDA, IOC-88 and DIN.

Device physics and crystals (14)

• MOSFET threshold voltage (Vth) calculator
  Calculate MOSFET threshold voltage, flat-band voltage and body effect coefficient from substrate doping, EOT, gate work function, fixed charge and body bias, for nMOS and pMOS.
• Miller index, d-spacing and plane angle calculator
  Calculate interplanar spacing, Bragg angle 2θ, selection rules and the angle between planes for Si, Ge, GaAs, InP, SiC, Cu and Al, with common silicon plane angles.
• Sheet resistance and resistivity calculator (four-point probe, doping)
  Calculate sheet resistance and resistivity from four-point probe readings with geometry and thickness corrections, and convert between silicon doping concentration and resistivity.
• Depletion width, built-in potential and junction capacitance calculator
  Calculate depletion width, built-in potential, maximum field and junction capacitance of an abrupt pn junction in Si, Ge, GaAs, SiC or GaN under reverse bias.
• Intrinsic carrier concentration and Fermi level calculator
  Calculate intrinsic carrier concentration, electron and hole densities and the Fermi level position in Si, Ge, GaAs, 4H-SiC and GaN versus temperature and doping.
• MOSFET drain current (I–V characteristics) calculator
  Calculate MOSFET drain current in the linear and saturation regions, transconductance, output resistance, intrinsic gain and off-state current, with ID–VDS curves.
• Diode I–V characteristics and forward voltage calculator
  Calculate diode forward voltage, temperature coefficient and differential resistance with the Shockley equation and series resistance, using SPICE-style parameters for common diodes.
• Carrier mobility, diffusion coefficient and diffusion length calculator (silicon)
  Calculate electron and hole mobility in silicon versus doping and temperature with the Arora model, plus diffusion coefficient, diffusion length and velocity saturation.
• EOT and MOS capacitor (C–V) calculator
  Calculate equivalent oxide thickness for high-k gate stacks such as HfO₂ on interfacial SiO₂, gate capacitance and the low- and high-frequency C-V curves of a MOS capacitor.
• Hall effect measurement (van der Pauw) calculator
  Analyze van der Pauw resistivity and Hall effect measurements to get sheet resistance, carrier concentration, conductivity type, sheet carrier density and Hall mobility.
• Silicon absorption coefficient and penetration depth calculator
  Look up the absorption coefficient and penetration depth of light in crystalline silicon from 250 to 1150 nm, and the fraction absorbed or transmitted by a layer.
• Solar cell conversion efficiency calculator
  Calculate solar cell efficiency from Jsc, Voc and fill factor, estimate Voc and FF from saturation current, and see the detailed-balance efficiency limit versus band gap.
• Responsivity and quantum efficiency converter (photodiodes and image sensors)
  Convert between quantum efficiency and responsivity in A/W, calculate photocurrent and photon flux, and estimate image sensor pixel signal, noise and dynamic range.
• Lattice mismatch and critical thickness calculator
  Calculate lattice mismatch for SiGe, Ge, GaAs, InP, GaN and AlN on common substrates, and the critical thickness of SiGe on Si with the Matthews-Blakeslee and People-Bean models.

Power devices and thermal design (6)

• Junction temperature and thermal resistance calculator
  Calculate junction temperature from power loss and thermal resistances, the maximum allowable loss, the heat sink you need and Tj from a measured case temperature with ψjt.
• Power semiconductor loss calculator (MOSFET, IGBT)
  Calculate conduction, switching and reverse recovery losses of a power MOSFET or IGBT from Rds(on), Eon/Eoff or rise and fall times, and see how loss changes with switching frequency.
• Breakdown voltage and on-resistance limit (unipolar limit) calculator
  Calculate the drift layer doping, thickness and specific on-resistance limit for a target breakdown voltage in Si, GaAs, SiC, GaN and Ga₂O₃, with Baliga's figure of merit.
• Gate drive power and gate resistance calculator
  Calculate gate drive power, driver peak current, Miller plateau transition times and bootstrap capacitance for Si MOSFET, SiC MOSFET, GaN HEMT and IGBT gates.
• DC-DC converter (buck, boost) inductor calculator
  Calculate duty cycle, inductance, peak inductor current, output ripple, required output capacitance and input ripple current for buck and boost DC-DC converters in continuous mode.
• LED current-limiting resistor calculator
  Calculate the current-limiting resistor for one or more LEDs in series, pick the nearest E12 or E24 value, and see resistor power, LED power and typical forward voltage by color.

Plasma, vacuum, films and facilities (24)

• Plasma parameter calculator (Debye length and sheath)
  Calculate Debye length, Child-law sheath thickness, plasma frequencies, Bohm velocity, ion current density and floating potential for etch and CVD plasmas.
• Paschen's law (breakdown voltage) calculator
  Calculate DC breakdown voltage from gas, pressure, electrode gap and secondary electron coefficient with Paschen's law, and plot Paschen curves for air, Ar, He and N₂.
• Mean free path (vacuum) calculator
  Calculate the mean free path, Knudsen number, flow regime, number density, impingement rate and monolayer formation time from gas, pressure and temperature.
• Thin film stress and wafer bow calculator (Stoney equation)
  Calculate thin film stress from wafer bow or radius of curvature with the Stoney equation, thermal stress from expansion mismatch, and bow of 200 mm and 300 mm wafers.
• Dew point ⇔ moisture concentration (ppm) converter
  Convert between dew point and moisture concentration (ppmv, ppbv) at any pressure, and see the dew points of typical semiconductor process gases.
• Cleanroom class calculator (ISO 14644-1)
  Calculate maximum particle concentrations for ISO 14644-1 classes, find the class from a measured count, and get the minimum number of sampling locations and sample volume.
• Lithography resolution and depth of focus calculator (Rayleigh criterion)
  Calculate lithography resolution R = k₁λ/NA and depth of focus DOF = k₂λ/NA² for KrF, ArF dry, ArF immersion, EUV and High-NA EUV, or any wavelength and NA.
• Thermal oxide thickness calculator (Deal-Grove model)
  Calculate silicon dioxide thickness from dry or wet oxidation temperature and time with the Deal-Grove model, solve for the time to reach a target thickness, and see silicon consumed.
• Ion implantation profile calculator (Rp, peak concentration, junction depth)
  Estimate projected range, straggle, peak concentration and junction depth for boron, BF₂, phosphorus and arsenic implants in silicon, with a Gaussian profile plot.
• Interconnect RC delay calculator (Cu, Co, Ru, Mo)
  Estimate resistance, capacitance and RC delay of fine interconnects with size-effect resistivity, barrier thickness and low-k dielectrics, and compare copper with cobalt, ruthenium and molybdenum.
• CMP removal rate calculator (Preston equation)
  Calculate CMP removal rate with the Preston equation from pressure and relative velocity, the polish time with overpolish, and the radial removal profile from platen and head speeds.
• Dopant diffusion (diffusion coefficient, junction depth) calculator
  Calculate dopant diffusion profiles and junction depth for boron, phosphorus, arsenic and antimony in silicon for predeposition (erfc), drive-in (Gaussian) and two-step diffusion.
• Spin coating thickness and spin speed calculator
  Estimate resist or coating thickness at any spin speed from one point on the spin curve, solve for the speed that gives a target thickness, and correct for viscosity.
• Electroplating thickness and time calculator (Faraday's law)
  Calculate plated thickness, deposition rate, plating time, current and charge for copper, nickel, gold, silver, tin, cobalt and palladium using Faraday's law.
• Etch time, overetch and selectivity calculator
  Calculate total etch time with overetch, the minimum overetch to clear the wafer, worst-case underlayer loss, the selectivity needed and remaining mask thickness.
• Overlay and edge placement error (EPE) budget calculator
  Combine overlay contributors from scanner, process, mask and metrology by root sum of squares, add CD uniformity to get edge placement error, and check the remaining margin.
• ALD cycle count and deposition time calculator
  Calculate the number of ALD cycles, cycle time, deposition time, throughput and effective deposition rate for Al₂O₃, HfO₂, ZrO₂, SiO₂, SiN, TiN and ZnO.
• Vacuum pump-down time and conductance calculator
  Calculate chamber pump-down time, pipe conductance in viscous and molecular flow, effective pumping speed and the base pressure set by gas load.
• MFC gas conversion factor (GCF) calculator
  Convert thermal mass flow controller readings between calibration gas and process gas, calculate setpoints and full scale, gas mixture factors and estimates from physical properties.
• Oxide film color and thickness calculator (interference colors)
  See the interference color and reflectance spectrum of SiO₂ or Si₃N₄ films on silicon for any thickness, and estimate thickness from adjacent reflectance maxima.
• Cleaning chemical mixing and concentration calculator
  Calculate the wt% and mol/L of SC1, SC2, SPM, DHF, BHF and other cleaning and etching mixtures from volume ratios, and the volume of each stock chemical.
• dBm, W and V converter (RF power, VSWR)
  Convert between dBm, dBW, W, mW, volts and dBµV at any impedance, calculate VSWR, return loss and reflected power, and add up gains and losses in dB.
• ALD step coverage and exposure calculator
  Calculate the precursor exposure and pulse time needed for ALD to coat the bottom of high-aspect-ratio holes and trenches, using the Gordon kinetic model.
• ALD throughput comparison by tool architecture
  Compare the throughput and depreciation per wafer of single-wafer, spatial (rotary) and batch ALD tools for a given film thickness and growth per cycle.

Circuit design and memory (7)

• Setup and hold timing slack calculator
  Calculate setup and hold slack, maximum frequency and data arrival times for a flip-flop to flip-flop path from clock period, clock-to-Q, logic delay, skew and uncertainty.
• Memory bandwidth calculator (DDR, LPDDR, GDDR)
  Calculate peak and effective memory bandwidth from transfer rate, bus width and channel count for DDR4, DDR5, LPDDR5, LPDDR5X, GDDR6, GDDR6X and GDDR7.
• HBM bandwidth calculator (GPU memory bandwidth and capacity)
  Calculate HBM bandwidth and capacity per stack and per GPU for HBM2E, HBM3, HBM3E and HBM4, and the theoretical token rate of LLM inference from model size.
• CMOS power consumption (αCV²f) calculator
  Calculate CMOS dynamic, short-circuit and leakage power, energy per cycle and power density, and see how voltage and frequency scaling (DVFS) change power.
• PCIe and CXL bandwidth calculator
  Calculate PCIe and CXL link bandwidth by generation and lane count, including encoding efficiency, TLP overhead and transfer time.
• ADC SNR and ENOB calculator
  Estimate ADC SNR and effective number of bits from resolution, clock jitter, thermal noise and oversampling, and convert measured SINAD to ENOB.
• 3D NAND capacity and bit density calculator
  Estimate 3D NAND die capacity and bit density from layer count, bits per cell, string footprint and array efficiency, and SSD capacity from the number of dies.

Further reading

For the equipment behind these calculations, see Japanese semiconductor equipment by category; for the makers, see Japanese semiconductor companies.