Updated 2014-11-29 11:34:23 by gold

Semiconductor Chip Yield and eTCL Slot Calculator Demo Example , numerical analysis edit

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gold Here is some eTCL starter code for calculating semiconductor chip yield. Most of the testcases involve replicas or models, using assumptions and rules of thumb.

The 2 given numbers are expected number of failures on chip and alpha constant. The formula for semiconductor chip yield is (1+(defects/alpha))**alpha. All entries and results in positive domain. The eTCL calculator offers change of constant2 (1.0), but that constant2 is not expected to change in most calculations. The eTCL calculator can calculate the number of defects from the product of chip defect density or defect errors per sq mm times the chip surface area in sq mm. If the failures calculated from density*area are non zero, the number of failures from chip density will superceed the first entry. The number of failures is not a quantity tied to metric units, so the product of compatible units can be entered like defects per square inch times surface area in square inches.

In planning any software, it is advisable to gather a number of testcases to check the results of the program. The results of the testcases are estimated using the hand calculator and then checked in the eTCL slot calculator. Pseudocode and equations are developed from the hand calculations and theory. Small console programs are written to check or proof the alternate subroutines or procedures, rather than keeping the unblessed code and comment lines in the main slot calculator. Finally the improved or alternate subroutines are loaded into the slot calculator. The eTCL slot calculator is effectively a shell program to input entries, host calculation routines, and display results. Additional significant figures are used to check the eTCL calculator, not to infer the accuracy of inputs and product reports.

*Push Button Operation**

For the push buttons in the eTCL slot calculator, the recommended procedure is push testcase to fill entry frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console. For testcases in a computer session, the eTCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared on the next solve button. The calculator display has a caution flag subroutine for negative numbers, unrecognizable text characters, and operation outside expected operation range. On a degrading scale, the calculator will post warning flags to the console report, issue degraded accuracy notices, and may reset some negative and offscale numbers to positive defaults. Errors pass through the warning flag routine once on the same testcase and multiple error calls on the same fault are possible. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the functions (subroutines).

Pseudocode and Equations

     #pseudocode can be developed from rules of thumb.
     #pseudocode: some problems can be solved by proportions (rule of three), to some order of magnitude
     #pseudocode: enter quantity1,  quantity2, quantity3 and expected output (quantity4) for testcases.
     #pseudocode: enter time in years, number of remaining items
     #pseudocode: output fraction of (remaining items) over (items at time zero)
     #pseudocode: ouput remaining items as fraction or percent
     #pseudocode: output fraction of (quantity4 ) over ( quantity1 at time zero)
     #pseudocode: output fraction of (quantity2) * (quantity3 ) over (quantity1 at time zero)
     #pseudocode: outputs should be in compatible units.
     #pseudocode: rules of thumb can be 3 to 15 percent off, partly since g..in g..out.
     #pseudocode: need test cases > small,medium, giant
     #pseudocode: need testcases within range of expected operation.
     #pseudocode: are there any cases too small or large to be solved?

Testcases Section

Testcase 1

table 1printed in tcl wiki format
quantity value comment, if any
testcase number:1
1.0 :fatal defects on chip
0.5 :alpha constant (ranges from .3 to 5.)
1.0 :constant2 (optional, usually 1.)
0.0 :expected number of fatal defects per square mm (optional)
0.0 :chip surface area square mm (optional)
0.0 :answers: product of defects/sq mm * sq mm, superceeds if area not zero above
57.735026918962575 :semiconductor chip yield percent
0.5773502691896257 :semiconductor chip yield (0<factor<1)


Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
testcase number:2
10.0 :fatal defects on chip
0.5 :alpha constant (ranges from .3 to 5.)
1.0 :constant2 (optional, usually 1.)
0.0 :expected number of fatal defects per square mm (optional)
0.0 :chip surface area square mm (optional)
0.0 :answers:product of defects/sq mm * sq mm, superceeds if area not zero above
21.82178902359924 :semiconductor chip yield percent
0.2182178902359924 :semiconductor chip yield (0<factor<1)


Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
testcase number:3
1.0 :fatal defects on chip
0.5 :alpha constant (ranges from .3 to 5.)
1.0 :constant2 (optional, usually 1.)
0.3 :expected number of fatal defects per square mm (optional)
4.0 :chip surface area square mm (optional)
1.2 :answers: product of defects/sq mm * sq mm, superceeds if area not zero above
54.23261445466404 :semiconductor chip yield percent
0.5423261445466404 :semiconductor chip yield (0<factor<1)


References:

  • Introduction to IC Yield - University of California, Berkeley [www-inst.eecs.berkeley.edu/ ~ee290h/ fa05/ Lectures/ PDF/ lecture%201%20intro%20IC%20Yield]
  • Semiconductor Manufacturing - Process Yields,[www.semiconductor-manufacturing.net/Process-Yields.htm]

Screenshots Section:

Semiconductor_Chip_Yield

[Semiconductor_Chip_Yield]

[Semiconductor_Chip_Yield]

Appendix Code edit

*appendix TCL programs and scripts

        # pretty print from autoindent and ased editor
        # Semiconductor Yield Calculator 
        # written on Windows XP on eTCL
        # working under TCL version 8.6.x and eTCL 1.0.1
        # gold on TCL WIKI, 10nov 2014
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {fatal defects on chip:} }
        lappend names {alpha constant (ranges from .3 to 5.):}
        lappend names {constant2 (optional, usually 1.): }
        lappend names {expected number of fatal defects per square mm (optional):}
        lappend names {chip surface area square mm (optional):}
        lappend names {answers: product of defects/sq mm * sq mm, superceeds if area not zero above: }
        lappend names {semiconductor chip yield percent : }
        lappend names {semiconductor chip yield (0<factor<1) :}
        foreach i {1 2 3 4 5 6 7 8} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
      proc about {} {
            set msg "Calculator for Semiconductor Yield 
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg }   
      proc break_flag_routine {     } {
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global spares 
            global testcase_number
            set t9 $testcase_number
            set product_entries [* $side1 $side2 $side3 $side4 $side5 $side6 $side7 $side8] 
            if { $product_entries < 0.0 } { puts " warning flag! negative numbers detected in product entries ref. tc$t9" }
            foreach item { 1 2 3 4 5 6 7 8 9 10 } {
            set error$item 0 }
            #{-?\d*(\.\d+)?}  regsub -all -- {[^0-9.-]} $input "" number 
            if { $side1 < 0.0 } { set side1 .000001 ; set error1 1  }
            if { $side2 < 0.0 } { set side2 .000001 ; set error1 1  }
            if { $side3 < 0.0 } { set side3 .000001 ; set error1 1  }
            if { $side4 < 0.0 } { set side4 .000001 ; set error1 1  } 
            if { $side5 < 0.0 } { set side5 .000001 ; set error1 1  }
            if { $side6 < 0.0 } { set side6 .000001 ; set error1 1  }
            if { $side7 < 0.0 } { set side7 .000001 ; set error1 1  }
            if { $side8 < 0.0 } { set side8 .000001 ; set error1 1  } 
            if { $error1 == 1 } { puts " warning flag! negative numbers detected, defaulted to positive entries ref. tc$t9" }
            foreach item { 1 2 3 4 5 6 7 8 9 10 } {
            set error$item 0 }
            return 1 }    
       proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number
            incr testcase_number 
            #{-?\d*(\.\d+)?}  regsub -all -- {[^0-9.-]} $input "" number 
            #set side1 [* $side1 1. ]
            regsub -all --  {-?\d*(\.\d+)?} $side1 "" numbers  
            puts " $numbers   " 
            set input {$1.23, $-5.00, $15.99} 
            regsub -all {[^0-9.-]} $input " " numbers ; puts " $numbers "
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ] 
            break_flag_routine
            set constant 1.0
            set ad_rated 1.0
            set alpha 0.5           
            set yield1 0.
            set alpha  $side2  
            set ad_rated $side1
            set defect_area_density $side4
            set surface_area $side5
            set fatal_defects_fm_area [* $defect_area_density $surface_area 1. ]
            if { $fatal_defects_fm_area > 0. } { set ad_rated $fatal_defects_fm_area }
            set constant [* $side3 1. ]
            set term1  [+ 1. [/ $ad_rated $alpha ] ]
            set term5 [* $alpha -1.0 ]
            set yield1 [* [pow $term1 $term5  ] ]
            set yield_percent [* $yield1 1.E2 1. ]
            set side6 $fatal_defects_fm_area
            set side7 $yield_percent
            set side8 $yield1
                  }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff" 
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh" 
             }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global testcase_number
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| testcase number:|$testcase_number | |&"           
            puts "&| $side1 :|fatal defects on chip |   |&"
            puts "&| $side2 :|alpha constant (ranges from .3 to 5.)| |& "
            puts "&| $side3 :|constant2 (optional, usually 1.)| |& "
            puts "&| $side4 :|expected number of fatal defects per square mm (optional) |  |&"
            puts "&| $side5 :|chip surface area square mm (optional)  |  |&"
            puts "&| $side6 :|answers:product of defects/sq mm * sq mm, superceeds if area not zero above  |  |&"
            puts "&| $side7 :|semiconductor chip yield percent |  |&"
            puts "&| $side8 :|semiconductor chip yield  (0<factor<1) |  |&"
         }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1.0 0.5 1.0 0.0 0.0 0.0 58.0 0.58}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 10.0 0.5 1.0 0.0 0.0 0.0 21.8 0.218 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 1.0 0.5 1.0 0.3 4.0 1.0 54.0 0.54 }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command about
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
        . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Semiconductor Chip Yield Calculator"


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Comments Section edit

[Semiconductor_Chip_Yield]

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