Block-Based Compact hermal Modelg of Semcoductor Itegrated Crcuts Master s hess Defese Caddate: Jg Ba Commttee Members: Dr. Mg-Cheg Cheg Dr. Daqg Hou Dr. Robert Schllg July 27, 2009
Outle Itroducto Backgroud hermal Modelg Curret Researches o hermal Modelg Geeral Cocepts Least Squares Method ad hermal Modelg Cocept hermal Crcut Model Developmet Geeral Procedure of Developg Compact Model Selectg Boudary Nodes for Compact hermal Model Applcato to a SOI Iverter Smulato Results of Each Block Heat Flux ad emperature Ifluece o Boudary hermal Cotuty Cocluso
Itroducto hermal ssue of the devce ad crcut Degrade the devce performace ad lfe tme Affect the dra curret he fluece of the thermal ssue to crcut desg Prolog the desg cycle tme ad crease the workload he mportace for cluso of thermal aalyss the desg process Shorte the desg cycle tme
Curret Research I Sgle-emperature (S) ode model for SOI devce A smplfed thermal crcut model wdely used dustry Itegrated to the IC desg process Lmtato Ca ot represet the realstc temperature gradet alog the devce chael Erroeous heat flux to the termals ad a urealstc temperature estmato of tercoects Gate Chael Isulator Substrate
Curret Research II Compact hermal Model for Electroc System A model wth much smaller umber of parameters tha the umber of parameters descrbg a detaled model. Based o the cocept of thermal crcut equatos Its am s to buld a Boudary Codto Idepedet (BCI) thermal compact model Lmtato Ca oly be appled to a sgle IC package Not a real BCI model he boudary codtos used to smulate the model are chose by log experece
Objectves of Work Fd a mathematcal method to apply the boudary codtos stead of experece selecto Buld a block-based compact thermal model whch s costruct by several stadard blocks A 2D SOI semcoductor crcut s take as a example Approve the fluece of the heat flux ad temperature o the boudary ode selecto
Geeral Cocepts Least Squares Method hermal Modelg Cocept
Least Squares Method A commoly used method to solve a overdetermed system o obta the best but ot the uque soluto for the system For a set of data (x,y ), (x 2,y 2 ),, (x,y ), where x s a depedet varable ad y s a depedet varable. he fucto of ths model could be wrtte as, he least squares method s to fd the parameter values, whe the sum, S, of squared resduals s the mmum, he equato could be trasformed to matrx form, ( ) ( ) ( ) ( ) ( ) = 2 2 = + + + =, ˆ = m j j j m m x φ β x φ β x φ β x β φ β x f y m j j j x y r S 2 2 m j X X y S j m k k k j,, 0, 2 y X Xβ X y X X X
hermal Modelg Cocept hermal Crcut Equato s derved from Heat Coducto Equato Δ C th = + Ps, t Rth Steady state A aalogy ca be made betwee the Electrc Crcut Model ad hermal Crcut Model k, k k R k P =,,
hermal Crcut Model Developmet Geeral Procedure of Developg Compact Model wo Dfferet Approaches to Select Boudary Nodes for Compact hermal Model
Basc Cocept he cocept of block-based he mportat thermal formato he devce jucto he juctos of metal ad devces he juctos ad corers of metal tercoects Areas of hgh temperature gradet Every materal eeds to have at least oe ode the teror or o the boudary
Resstace Network Dervato hermal crcut equato for the steady state s a lear equato: hus, for odes, - equatos ca be wrtte dow: where s a matrx, G s a matrx ad P s a matrx k k k k P R,,, = G = P 2 2 s th th P R t C, + Δ =, 2, 2, 2 2, 2 2,3 2 3,2 2,,3 3,2 2 P R R R P R R R P R R R
Resstace Network Dervato (Cotue) Whe m s large eough, ths s a overdetermed system m 2 G P m P m [ ] [ ] G = P Solved by least squares method G = - [ ] [ ] [ ] [ ] P
Data Collecto ANSYS s used to apply the boudary codto ad geerate temperature data Radom umbers are used to be the value of power desty, heat flux ad temperature. wo codtos should be satsfed to obta the good qualty data R 3 3,4 4 Heat flux through the resstace must be large eough durg the smulato to collect temperature data P 3 R 2,3 2 R 2,4 R,3 P 4 R,2 R,4 P 2, 2,, m geerated from smulatos should be depedet
Resstace Network Optmzato Resstace Network Optmzato s eeded to crease the processg speed ad stable the resstace etwork Redudat resstors. Resstors betwee two far odes. Resstors across two dfferet materals.
Selectg Boudary Nodes for Compact hermal Model Boudary Nodes Represeted by Small Areas Boudary Nodes Represeted by Les x 4 -x =325m x 3 -x 2 =90m x 2 -x =x 4 -x 3 =7.5m y 4 -y =480m y 3 -y 2 =200m y 2 -y =00m y 4 -y 3 =80m
Boudary Nodes Represeted by Small areas as odes wth adabatc boudary Small Areas Apply proper powers o each ode ad make oe of the odes as the thermal groud Export the temperature ad power of each ode he locato of the thermal groud ca be chaged
Resstace Network Usg the Frst Approach 36 resstors are reduced to 4 resstors he dffereces of the detcal par resstors are less tha 4%
he Sgle Itercoect Structure Powers are appled to Nodes 4 ad 6, ad Node 8 s the thermal groud Dffereces as large as 25% ad 8% are observed at Nodes 7 ad 3. he average dfferece s however below 0%.
he Mult-Block Itercoect Structure he structure cossts of sx -shape tercoect blocks. he average error for the 6-block structure s about 5% he left sde has larger errors tha the rght sde.
Boudary Nodes Represeted by Les Le segmets as odes wth marg outsde Apply powers o the outsde boudares ad make oe boudary as the thermal groud Export the temperature of each ode segmet ad power of each dvso Iclude as much heat flow codtos as possble
Resstace Network 78 resstors for 3 odes are reduced to 28 resstors he dffereces of the detcal par resstors are stll less tha 4%
he Mult-Block Itercoect Structure he average temperature errors are decreased to 6% he thermal cotuty problem o the terfaces s solved
Applcato to a SOI Iverter Smulato Results of Each Block he verter layout s dvded to several stadard blocks he thermal crcut model for each stadard block s costructed Heat Flux Ifluece o Boudary hermal Cotuty Equal boudary dvso Uequal boudary dvso
Structure ad Dvsos of Iverter he verter usg SOI techology wth gate oxde thckess 2m ad gate legth 65m he 2D structure s dvded to 6 blocks wth 7 dfferet buldg blocks
Substrate 20 thermal resstors are reduced to 29 resstors he maxmum dfferece detcal pars s less tha 2%
Metal--Cotact Itercoect 20 thermal resstors are reduced to 30 resstors he maxmum dfferece for each detcal resstor par s less tha.5%
Metal-2 05 thermal resstors are reduced to 30 resstors he maxmum dfferece for each detcal resstor par s less tha %
Oxde- 05 thermal resstors are reduced to 36 resstors he maxmum dfferece for each detcal resstor par s less tha 4.5%
Oxde-2 05 thermal resstors are reduced to 32 resstors he maxmum dfferece for each detcal resstor par s less tha 2.2%
Heat Flux Ifluece o Boudary hermal Cotuty Equal Boudary Dvsos For most blocks, heat fluxes alog terfaces may chage subtly. Uequal Boudary Dvsos For certa blocks, such as devce blocks, the heat flux alog the terface(s) may chage dramatcally. Small dvsos ear strog flux regos are eeded. Devce block wll take as a example to make a comparso of two method
Equal Boudary Dvsos Node selecto: Four equal dvso o two sdes Fve odes alog the chael he optmzato leads to a reducto the umber of resstors from 23 to 50
Smulato Results Powers ad thermal groud he result errors betwee the block-based thermal crcut ad ANSYS smulato are aroud %
Heat Flux ad emperature Ifluece he dfferece betwee two results ear the slco flm s about 6% Both the strog heat flux ad large temperature gradet o the boudary may affect the accuracy of the thermal compact crcut More odes may eed to be added
Uequal Boudary Dvsos Node selecto: Fve uequal dvso o two sdes he optmzato leads to a reducto the umber of resstors from 23 to 54 for devce block ad from 36 to 42 for oxde- block
Smulato Results Powers ad thermal groud he result errors betwee the block-based thermal crcut ad ANSYS smulato are less tha %
Cocluso ad Future Work Locatos ad shapes of jucto odes are mportat factors to costruct a accurate model. he power appled to the ode should clude the total power over the boudary dvso for that ode, whle the ode temperature s the average temperature of the cetered ode segmet. Iclude as may cases as possble to guaratee that the heat fluxes ca cover all drectos ad provde eough heat flow to every sgle resstace. I the future, 2D structure should be further exteded to 3D structure more realstc structure. he block-based thermal crcut ca be mplemeted Spce smulato ad provde a useful tool for electro-thermal smulato.
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