Optimized design of control plans based on risk exposure and resources capabilities

1. Belgacem BETTAYEB PhD Candidate P. Vialletelle*, M. Tollenaere, S. Bassetto G-SCOP Laboratory - Grenoble Institute Of Technology, France * ST microelectronics Crolles, France ISSM PC-O-91 Belgacem.bettayeb@grenoble-inp.fr Optimized design of control plans based on risk exposure and resources capabilities ISSM 2010

2. Problem statement • Quality control and production control policies are usually designed separately • Tools and processes may remain uncontrolled over a long production period  grow up of the uncertainty about products quality • Releasing uncertainty too late may lead to manage a major scrap (thousands of defective products) • An effective monitoring of uncertainty logically leads to the limitation of risk exposure in terms of products loss

3. A 2-stage Control plan design Stage 1 Risk-based allocation Control plan SRimin = nimin / MixProdF(i) nimax = niminniC SRimax = nimax / MixProdF(i) tikmin tikmax • Availability constraints • Target cycle time constraints nimin ; tikmin ; tikmax Actual capacity of control CHRBCP Oper. Criterion Partition Stage 2 Capacity optimization Effective capacity for controls TOTALCAPA 1 C1 n1C RCAPA i niC Ci nCNOP NOP CNOP i  : operation index k  : control index NOP  : number of controlled operations Ci : partition criterion of operation i niC: complementary number of controls nimin  : minimum number of control for operation i tikmin : release date of the kth control of operation i tikmax : due date of the kth control of operation i MixPrdF(i) : planned quantity of the product F(i) F(i) : product index of operation i

4. R0(t) Rn,T(t) R0max RL Rn,T(tk) a T H t1 t2 … tk-1 tk …tn Stage1: Risk based allocation (1/2) Let’s assume • Constant increasing risk • Risk is reset by each control • RL: the limit of risk exposure over which a loss is inadmissible • R0(t): risk evolution without any control plan • Rn,T(t): risk evolution with control plan (n,T) • AVn,T: the added value of control plan (n,T) Rn,T(tk)=a(tk-tk-1) AVn,T=R0max - max Rn,T(t) Objective: remaining below RL

5. Stage1: Risk based allocation (2/2) Optimal control plan should be T* = (t1*,t2*,…,tn*) = argT max AVn,T n* = min n \  T* \ AVn*,T*≥ R0max - RL Solution using precedent assumptions t1* = t2*-t1* =…= tk*-tk-1* =…= H-tn=H/(n+1) n*= ⌈aH/RL - 1⌉  nimin=⌈aHi /RL - 1⌉  i{1,…,NOP}

6. CHRBCP TOTALCAPA TOTALCAPA RCAPA Stage2: Adjustment of initial ctrl plan (1/2) • Case 1. CHRBCP < TOTALCAPA • RCAPA = TOTALCAPA - CHRBCP is distributed among operations according to a repartition criterion Ci i{1,…,NOP} • niC : number of complementary controls to add for each operation i according to Ci • ni = nimin + niC • examples of criterion: Ci= CPMi/CPi ; Ci=(CPMi /CPi.).(Pti/Mti)

7. CHRBCP TOTALCAPA OCHAR Stage2: Adjustment of initial ctrl plan (2/2) • Case 2. CHRBCP > TOTALCAPA • OCHAR = CHRBCP – TOTALCAPAis cancelled by removing some controls on the different operations according to a criterion Ci’=1/ Ci • ni = nimin - niC

8. Numerical Experiments (1/3) • Experimented instance • 3 products : A, B and C • 3 process tools : CMP, CVD and FUR • 1 measurement tool: SATH • Effect of Exposure Limit RL SR=f(RL) ; OBJSAT=75%

9. Numerical Experiments (2/3) • Effect of Measurement capacity SR=f(OBJSAT) RL

10. Numerical Experiments (3/3) • Effect of Measurement capacity and RL SR=f(OBJSAT) RL

11. Summary • An approach based on risk exposure mastering and metrology resources optimization • Need to extend the approach and take into account • multi failure modes • multi layers of control • different capture rates • measurement depths Thank you for your attention ! Questions ?