FieldsSemiconductors and electronic assembly
Experiments here usually have about 5 factors and 16 runs. Fractional factorials and full factorials are the most common.
- Full factorial
- Fractional factorial or screening
- Central composite or Box-Behnken
- Other designs
Show the numbers
| Kind of design | Experiments | Factors | Runs |
|---|---|---|---|
| Full factorial | 15 | 4 | 16 |
| Fractional factorial or screening | 16 | 6 | 16 |
| Central composite or Box-Behnken | 5 | 2 | 12 |
| Other designs | 4 | 4.5 | 24 |
Factors and runs are the medians of each kind.
Full factorial
Every combination of the factor levels.
- Base current of polysilicon at two doping levels and three anneal temperatures, run twice (Problem 5.25)Montgomery (2013) · 2 factors, 12 runs
- Epitaxial layer thickness on silicon wafers: arsenic flow rate by deposition time, a 2^2 run four times (Table P6.1) (Problem 6.12)Montgomery (2013) · 2 factors, 4 runs
- Etch rate of silicon nitride: gap, C2F6 gas flow and RF power, a 2^3 factorial run twiceMontgomery (2013) · 6 factors, 8 runs
- Mean and standard deviation of the coating thickness on a wafer against speed, pressure and distance in a 3^3 (adapted from Box and Draper 2007) (Problem 12.11)Montgomery (2013) · 3 factors, 27 runs
- Oxide thickness of wafers in a vertical oxidation furnace: temperature, time, pressure and gas flow, a 2^4 with four wafers measured in each runMontgomery (2013) · 4 factors, 16 runs
Show the rest
- Resistivity of Problem 6.36 with four centre runs (Problem 6.37)Montgomery (2013) · 4 factors, 20 runs
- Resistivity of a silicon wafer after a critical processing step, a single replicate of a 2^4 (Table P6.10) (Problem 6.36)Montgomery (2013) · 4 factors, 16 runs
- The plasma etch 2^3 of Example 6.1 run in two replicates of two shifts each, ABC confounded in replicate I and AB in replicate IIMontgomery (2013) · 3 factors, 16 runs
- Unused error correction of Problem 6.22 with four centre runs (Problem 6.23)Montgomery (2013) · 4 factors, 20 runs
- Unused error correction of a 2d-matrix laser mark: laser power, pulse frequency, cell size and writing speed in a 2^4 (Table P6.5) (Problem 6.22)Montgomery (2013) · 4 factors, 16 runs
- Yield of a semiconductor process: aperture, exposure time, development time, mask dimension and etch time in a single replicate of a 2^5 (Problem 6.26)Montgomery (2013) · 5 factors, 32 runs
- Yield of the semiconductor process of Problem 6.26 with four centre runs (Problem 6.27)Montgomery (2013) · 5 factors, 36 runs
- Bottom electrode film stress after layer B is deposited: a 2^3 full factorial (Ramtron)Schmidt and Launsby (2000) · 3 factors, 8 runs
- Bottom electrode film stress and resistance: thickness of layer A by the presence of layer C, two readings a run (Ramtron)Schmidt and Launsby (2000) · 2 factors, 4 runs
- Coating thickness in a 2^2 of time and temperature, four wafers from each of three lots a run: wafer-to-wafer, lot-to-lot and within-wafer variationSchmidt and Launsby (2000) · 2 factors, 4 runs
Fractional factorial or screening
A planned part of the combinations, to find the factors that matter.
- Camber of semiconductor substrates: lamination temperature, time and pressure and firing temperature, cycle time and dew point in 16 runs (Problem 8.28)Montgomery (2013) · 6 factors, 16 runs
- Photoresist thickness in the spin coating experiment, simulated on the six-factor no-confounding design and analysed by forward stepwise regressionMontgomery (2013) · 6 factors, 16 runs
- Photoresist thickness on a spin coater: a 2^(6-2) resolution IV design and its single-factor fold over on spin speed, in two blocksMontgomery (2013) · 6 factors, 32 runs
- Photoresist thickness on a spin coater: the 2^(6-2) with a partial fold over, the eight fold-over runs with spin speed lowMontgomery (2013) · 6 factors, 24 runs
- Resist thickness on a spin coater: volume, batch, spin time, spin speed, acceleration and cover in a 2^(6-1), three readings per wafer (Problem 8.29)Montgomery (2013) · 6 factors, 32 runs
Show the rest
- Si/SiGe selective epitaxial growth: SiH2Cl2, GeH4, HCl, B2H6 and temperature in a 2^(5-1) with two centre runs, three responses (Problem 8.36)Montgomery (2013) · 5 factors, 18 runs
- Transistor gain: six factors in a 2^(6-2) resolution IV design (Problem 8.52)Montgomery (2013) · 6 factors, 16 runs
- Yield of an integrated circuit process: aperture, exposure time, develop time, mask dimension and etch time in a 2^(5-1)Montgomery (2013) · 5 factors, 16 runs
- A circuit board etching process: seven factors in an L8 (Problem 3 of chapter 5)Schmidt and Launsby (2000) · 7 factors, 8 runs
- Bonding gold wire to GaAs wafers: five bonder settings in an L8, 24 bonds a run scored bond or no bond (Cray Research)Schmidt and Launsby (2000) · 5 factors, 8 runs
- Silicon doping level of GaAs: arsine, TMGa and silane flows in a duplicated L4Schmidt and Launsby (2000) · 3 factors, 4 runs
- Solder defects of a wave solder process: five control factors in an L8 inner array, three noise factors in an L4 outer arraySchmidt and Launsby (2000) · 5 factors, 8 runs
- Solder defects on printed wiring assemblies: four board design and two flow solder parameters in an L18, three boards a run (Texas Instruments)Schmidt and Launsby (2000) · 8 factors, 18 runs
- A 2^(8-4) screening design on a photolithography process (critical dimension of CMOS III gates)Schmidt and Launsby (2000) · 8 factors, 17 runs
- The L18 of the solderability case study, its INT column as the array has it before its level 3 is set to 2Schmidt and Launsby (2000) · 6 factors, 18 runs
- The outer array of the wave solder example: three noise factors in an L4Schmidt and Launsby (2000) · 3 factors, 4 runs
Central composite or Box-Behnken
Extra runs that fit curvature, to find an optimum.
- The CVD tungsten experiment of 5.4.7.3 as its R code fits it: pressure and H2/WF6 in natural unitsNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 2 factors, 11 runs
- Uniformity and stress of a CVD tungsten layer against pressure and the H2/WF6 ratio: an 11-run central composite inscribed designNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 2 factors, 11 runs
- A semiconductor process with two controllable and three noise variables: a 23-run combined array from a CCD in five factors, and its mean and variance modelsMontgomery (2013) · 5 factors, 23 runs
- Mean and variance of the thickness of four wafers processed together in a chemical vapor deposition CCD (Problem 11.14)Montgomery (2013) · 2 factors, 12 runs
- A plasma etch process window: pressure, power and etchant flow in a 20-run central composite design (Honeywell)Schmidt and Launsby (2000) · 3 factors, 20 runs
Other designs
Optimal, blocked, split-plot and other designs made for the problem.
- Uniformity of a single-wafer plasma etch: a 2^(5-1) split-plot with electrode gap, gas flow and pressure (hard to change) in eight whole plots, time and RF power in the subplotsMontgomery (2013) · 5 factors, 16 runs
- Wafer implant dosage (4 levels) blocked by furnace run (3 levels): a randomized block designNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 1 factor, 12 runs
- JMP's default split-plot design for the plasma etching experiment: a 2^5 in eight whole plots of A, B and C, four subplots of D and E in eachMontgomery (2013) · 5 factors, 32 runs
- Oxide growth on silicon wafers: a 2^4 in two replicates, temperature and gas flow (hard to change) in the whole plots, time and wafer position in the subplotsMontgomery (2013) · 4 factors, 32 runs