30794082 semiconductor thermal design

Semiconductor Device Thermal Characterization and System DesignRoger Stout, PE Research Scientist Corporate R&D: Technology DevelopmentRPS 2010 April

Corporate Research & Development Packaging Technology

Course outline Part I: Characterization (75 minutes) Why Everything you Thought You Knew (about device thermal characteristics) is Wrong Characterization Techniques Miscellaneous Measurement Techniques

Part II: Linear Superposition (120 minutes) Basic Theory The Reciprocity Theorem A Detailed Example and its Implications Building a System Model Time Varying Heat Sources

Part III: Thermal Runaway (45 minutes) Theory Datasheet example High-Temperature Reverse Bias qual example1 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Part I Characterization

2

Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

Corporate R&D : Packaging Technology

Can this device handle 2 W?

3



Why is ONs SOT-23 thermal number so much worse than the other guys? ON SOT-23 package 60x60 die Solder D/A Copper leadframe Min-pad board Still air

some other guy SOT-23 package 20x20 die Epoxy D/A Alloy 42 leadframe 1 x 2oz spreader Big fan

4



Fundamental ideas Heat flows from higher temperature to lower temperature The bigger the temperature difference, the more heat that flows Three modes of heat transfer Conduction (solids, fluids with no motion) Convection (fluids in motion) Radiation (it just happens)

5



Thermal-electrical analogytemperature power temp/power voltage current resistance

energy/degree

capacitance

6



Junction temperature?Historically, for discrete devices, the junction was literally the essential pn junction of the device. This is still true for basic rectifiers, bipolar transistors, and many other devices. More generally, however, by junction these days we mean the hottest place in the device, which will be somewhere on the silicon (2nd Law of Thermodynamics).

This gets to be somewhat tricky to identify as we move to complex devices where different parts of the silicon do different jobs at different times.7 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Whats wrong with theta-JA?

2

JA

TJ Ta PdJA

TJJtab

Ttab Pd

TJ8

Pd

Ta

TJCorporate R&D : Packaging Technology

Jtab

Pd

Ttab


Theta-JA vs. copper area

9



Typical thermal test board types

Min-pad board

1-inch-pad board

Minimum metal area to attach device (plus traces to get signals and power in and out)

Device at center of 1x1 metal area (typically 1-oz Cu); divided into sections based on lead count

10



Theta ( ) vs.. Psi ( ) JEDEC terminology Z JX , R JA older terms ref JESD23-3, 23-4 JA ref JESD 51, 51-1 JMA ref JESD 51-6 JT, TA ref JESD 51-2 JB, BA ref JESD 51-6, 51-8 R JB ref JESD 51-8 Great overview, all terms: JESD 51-12

11



Theta (Greek letterWe know actual heat flowing along path of interest

Txxy

Ty

qpath

TyTx

true thermal resistance12 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Psi (Greek letterWe dont know actual heat flowing along path of interest

Txxy

Ty

qtotal

??Tx all we know is total heat input13 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

Ty

a reference number onlyCorporate R&D : Packaging Technology

Facts and fallacies Basic idea: thermal resistance is an intrinsic property of a package Flaws in idea: there is no isothermal surface, so you cant define a case temperature Plastic body (especially) has big gradients

different leads are at different temperatures multiple, parallel thermal paths out of package

14



An example of a device with two different Max Power ratings Suppose a datasheet says: Tjmax = 150C But it also says: JA = 100C/W JL = 25C/W Pd = 1.25W (Tamb=25C) Pd = 3.0W (TL=75C)

25 100 *1.25 25 125 150

75 25 * 3 75 75 150

Wheres the inconsistency?15 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Wheres the inconsistency?TJ =150C25C/W ( JL) 100C/W ( JA)Whats TL? Not 75C !!

(try about 119C)

TA =25C

of the way from ambient to Tj

16



Back in the good old days ...metal can -fair approximation of isothermal surface axial leaded device -only two leads, heat path fairly well defined

17



Which lead? Where on case?

18



Archetypal package10%

convection case

wire/clip

silicondie attach

flag/leadframe10%

20%

60%

circuit boardCorporate R&D : Packaging Technology

19


Then we change things add an external heatsink optional heatsink

flip the die over optional heatsink

40%

60%

mold compound/ case wire/clip silicondie attach

optional case

die attach pads/ balls optional underfill

silicon

flag/leadframe

20%

40%application board

20%

application board

20%

20



A bare flip chip10%silicon pads/ balls underfill application board

90%

21



Same ref, different valuesJ tab

1.2 C/WJ tab

Pd Tc

50 W 25 C

0.8 C/W

Pd Tc

1.5W 25 C

1 GPM of H 2 O

still air

22



Even when its constant, its not!TjR1 (path down to board) constant at 20package environment

R3 (path through case top) constant at 80

TL

TCR4 (case to air path resistance) constant at 500, or 20x R2

1000 900 800 700 600 500 400 300 200 100 0 1

thetaJA - var brd only thetaJA - var airflow

JA

TJ Tamb Q total

1 1 R1 R 2board

1 R3 R 41000

R2 (board resistance) vary from 1 to 1000

10 rstnc. [C/W] 100

theta-JA

Tamb25 psi-JL - var brd only psi-JL - var airflow 60 50 40 15 20

psi-JTpsi-JC - var brd only psi-JC - var airflow

psi-JLJL

T J TL Q total

R1 10 R1 R 2 1 5 R3 R 40 1 10board rstnc. [C/W]

30 20 10 0 100 1000 1

JT

TJ TC Q total

10

R3 R3 R 4 1 board R1 R 2 rstnc. [C/W] 100

1000

23



TjJA

Ta

24



Fallacies recap: Package resistance isnt fixed: multiple heat paths exiting package boundary conditions dictate heat flow Heat sinks Neighboring devices/power dissipation Single vs.. double-sided boards Local convection vs.. board-edge cooling Multiple layers/power/ground planes

Therefore, different application environments will see different package resistanceSemiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

25


Characterization TechniquesTypical TSP behaviorcalibrate forward voltage at controlled, small (say 1mA) sense current

Characterization Techniques125C sense current

T

Vf

25C

0.5 V

Vf

0.7 V

26



How to measure Tjtrue const. current supply(1 mA typical)

approximate const. current supply

10K DUT

OR

10.7V DUT If V f-0.7V, then I-1mA

27



How to heatsample current is off while heating current on sample current is always on

10K heating power supply


10.7VDUT

10.7V

OR

DUT

28



The importance of 4-wire measurements+(1.00 V) Power Output = 1 W supply -(0 V) 0.18 V 0.64 W 0.70 W 0.05 V29 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

1A

0.82 V 0.90 W 0.85 V

0.15 V

0.95 V


Which raises an interesting question:+(1.00 V) Power Output = 3 W supply -(0 V) 0.45 V 1.3 W 0.02 V 0.55 V

3A

1.3 W 0.3 W 0.98 V

Is this a fair characterization of a low-Rds-on device?30 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Bipolar transistor TSP is Vce at designated constant current Heating is through Vce Choose a base current that permits adequate heatingbias resistor TSP supply

10K

switch

TSP=Vcebias supply heating supply

31



Schottky diode TSP is forward voltage at low current Voltages are typically very small (especially as temperature goes up) Highly non-linear, though maybe better as TSP current increases; because voltage is low, higher TSP current may be acceptable Heating current will be large

32



MOSFET / TMOS Typically, use reverse bias back body diode for both TSP and for heating May need to tie gate to source (or drain) for reliable TSP characteristicTSP supply

10K

switch

TSP=Vsd

heating supply +

33



MOSFET / TMOS method 2 If you have fast switches and stable supplies Forward bias everything and use two different gate voltages

TSP supply

10Kclose switch to heat

close switch to heat

close switch to measure

+ V-gate for heating -

+ V-gate for measure -

TSP=Vds

+ heating supply -

34



RF MOS They exist to amplify high frequencies (i.e. noise)! Feedback resistors may keep them in DCTSP supply

10Kclose switch to heat

TSP supply + + heating supply -

close switch to heat

close switch to measure

+ V-gate for heating -

TSP = body diode

35



IGBT Drain-source channel used for both TSP and heating Find a gate voltage which turns on the drain-source channel enough for heating purposes Use same gate voltage, but typically low TSP current for temperature measurementTSP supply

10K

switch

TSP=Vdsgate voltage heating supply

36



Thyristor Anode--to-cathode voltage path TSP supply used both for TSP and for heating 10K typical TSP current probably lower switch than holding current, so gate must be turned on for TSP anode gate readings; try tying it to the anode (even so, we used 20mA to test SCR2146) TSP=Vac Hopefully, with anode tied to gate, cathode enough power can be dissipated to heat device without exceeding gate voltage limit37 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

heating supply

Logic and analog Find any TSP you can ESD diodes on inputs or outputs Body diodes somewhere Heat wherever you can High voltage limits on Vcc, Vee, whatever Body diodes or output drivers Live loads on outputs (be very careful how you measure power!)

38



Heating curve method vs.. cooling curve method

39



Quick review: Basic Tj measurementfirst we heat then we measure



10.7V DUT

10.7V DUT

40



Question What happens when you switch from heat to measure?

Answer: stuff changes More specifically, the junction starts to cool down

41



Basic heating curve transient methodVfcalibrate forward voltage @ 1mA sense current convert cooling volts to temperature.5V

measurementsvoltage current

1 ma power-off cooling power-off cooling power-off cooling power-off coolingsteady state reached

highcurrent heating

highcurrent heating

highcurrent heating

highcurrent heating

T25C

Temperature

125C

measured temperatures Time

Vf

.7V

42



Heating curve method #2voltage

1 ma

highcurrent heating

highcurrent heating

highcurrent heating

highcurrent heating

Temperature

power-off cooling

power-off cooling

power-off cooling

power-off cooling

Time

measured temperatures43 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Time

current

measurementsvoltagecurrent

Basic cooling curve transient methodVfcalibrate forward voltage @ 1mA sense current Temperature.5V

1 ma

highcurrent heating

power-off cooling convert cooling volts to temperature

125C

T25C

steady state reached

Temperature

Vf

.7V

Time (from start of cooling)

Time transient cooling period (data taken)

heating period

subtract cooling curve from peak temperature to obtain heating curve equivalent

44



Whoa! that last step there Heating vs.. cooling Physics is symmetric, as long as the material and system properties are independent of temperature

45



Heating vs.. cooling symmetry

Start of constant power input (step heating)

Start of (constant) power offjunction flag

lead

(all the same curves, flipped vertically)

back of board edge of board

46



For a theoretically valid cooling curve, you must begin at true thermal equilibrium (not uniform temperature, but steady state) So whatever your JA, max power is limited to:power47 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

T j max

TambientJA


By the way Steady-state vs.. transient ? Since you must have the device at steady state in order to make a full transient cooling-curve measurement, steady-state JA is a freebie. (given that you account for the slight cooling which took place before your first good measurement occurred)

48



Effect of power on heating curve24x steadystate power 6x steadystate power 3x steadystate power 2x steady-state power

Tj-maxjunction temperature

steady-state max power

< steady-state max power

Tamb49 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

timeCorporate R&D : Packaging Technology

Some initial uncertaintya few initial points may be uncertain

high-current heating Temperature steady state reached

but once were past the uncertain range, all the rest of the points are goodpower-off coolingtransient cooling period (data taken)

heating period Time

50



Heating vs.. cooling tradeoffsHEATING starting temperature ambient limited by tester closer to ambient all points similar errorCorporate R&D : Packaging Technology

COOLING ? limited to steady-state closer to Tj-max error limited to first few points

heating powertemperature of fastest data error control51 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

Still air vs.. moving air Varying the air speed is mainly varying the heat loss from the test board surface area, not from the package itself You just keep re-measuring your boards characteristics

52



100

total system thermal resistance90

8070 60 50 40 30 20

little package

package resistance

theta-JA [C/W]

mediumsized package

board resistance10 0 0.1

big package

1

10

air speed [m/s]

53



Different boards Min-pad board 1 heat spreader board Youre mainly characterizing how copper area affects every package and board, not how a particular package depends on copper area

54



1" pad vs min-pad350

Roger Stout 5/25/2000

300

Source: Un-derated thermal data from old PPD database

SOD-323

250TSOP-6

SOT-23

1" pad thetaJA (C/W)

SOT-23

200SOD-123 SOD-123 TSOP-6(AL42) SOT-23

150Micro 8

TSOP-6

SO-8

SOD-123 SMA & Pow ermite

100SMB Dpak D2pak & TO220 Top Can Top Can SMC SOT-223 SO-8

50

overall linear fit is: 1" value = [0.51*(min-pad value) - 7]

0 0 100 200 300 400 500 600 700 min pad thetaJA (C/W)

55



Standard coldplate testing infinite heatsink (that really isnt) for measuring thetaJC on high-power devices If both power and coldplate temperature are independently controlled, two parameter compact models may be created

56



Standard coldplate testing Detailed design and placement of case TC can have significant effect on measured value

57



2-parameter data reductionQheat up, Q1

Q1 Q2

T1

QR1

1 T j T1 R1

(

)

1 T j T2 R2

(

)

This has the form of a two-variable linear equation: heat in, Q Tj R2

y

m1 x1 m2 x2 b

where:

m1T2 heat down, Q2Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

m2

1 R1 1 R2

x1 x2

(T

j

T1 )j

(T

T2 )

b

0

58


A single coldplate testambient Ta Rja80.0 0 120. 00 100. 00

Tj

Ta

Tjc ( C)

Tc

coldplate

Tj Rjc Tc coldplate

60.0 0 40.0 0 20.0 0 Incr easing Power, Chuck H eld Cold No P ower, Chuck T emper ature Incr eased 20.0 0 40.0 0 60.0 0 80.0 0 100. 00

0.00 -20. 00 0.00 -20. 00

Tja (C)

59



ambient Ta Rba Tb Rjb Tj Rjc Tc coldplateTjc ( C)

A single coldplate test, package down120. 00 100. 00 80.0 0 60.0 0 40.0 0 20.0 0 0.00 -10. 00 0.00 -20. 00 Incr easing Power, Chuck H eld Cold No P ower, Chuck T emper ature Incr eased 10.0 0 20.0 0 30.0 0 Tjb (C) 40.0 0 50.0 0 60.0 0

Tj

Ta

Tb

Tc coldplate

60



Miscellaneous Measurement Topics

Thermocouple Theory 101 Infrared Theory 202

61



Thermocouple Theory 101

62



Thermocouple Theoryregion B - 20cm of wire length between the junction and the door of the temperature chamber region C 10cm of TC wire length passing from inside of chamber door to outside of chamber door

TC junction B Aperfectly uniform temperature chamber at 100C

C D

TC scanner

perfectly uniform ambient temperature of 25C

region A - a 1cc box around the junction

region D 100cm of TC wire length from outside of chamber to TC measuring instrument

63



Thermocouple Theory Question #1: where is the temperature actually being sensed? or to put it another way, which region of the four defined above (A, B, C, D), is the one that matters, as far as generating the EMF being measured by the TC scanner? Why?The emf is generated where there is a temperature gradientB C D

TC junction Aperfectly uniform temperature chamber at 100C

perfectly uniform ambient at 25C

64



Thermocouple Theory Question #2: if the purpose of the TC scanner is to measure an EMF, theoretically how much current has to flow in the wire to make the correct measurement?

None. Ideally, a galvanometer circuit balances the EMF at the scanner until no current flows.

Corollary: wire size, and therefore resistance, may affect how long it takes the galvanometer circuit to stabilize.65 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Thermocouple Theory Question #3: what do the two wires in the TC actually do, and why do they have to be made of different materials?100C V=0.0025V

100C

Different materials have different Seebeck coefficients, i.e., V/C. So if you have two different materials, the same temperature gradient appearing in along both wires will result in two different EMFs.V=0.0037V

25C

25C

66



Thermocouple Theory Question #4: what does the junction in a TC actually do?25C

V=0.0025V

100C

Provides the common electrical point that relates the EMFs in the two wires to each other, hence the net difference appears at the open end of the circuit.

Net V=0.0012V

V=0.0037V

The junction DOES NOT measure the temperature; the wires do!25C

Corollary: if the junction itself is isothermal, it can be made of any material whatsoever!67 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Thermocouple Theory Question #5: if you really wanted to calibrate this thermocouple, where would you need to apply the test conditions?

TC junction B A C

Everywhere along its length!D

68



Infrared Theory 202

69



Infrared TheoryA opaque surface radiates thermal energy in proportion to its absolute temperature (to the fourth power), and some other things

q70 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

AT

4


Infrared TheoryIts also absorbing infrared energy from everything else around it (since everything else has a temperature and is therefore emitting)

It turns out that the absorptivity equals the emissivity.71 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Infrared TheoryThere is thus a net energy transfer which, in the simplest situations, may be described by:

q

obj

Aobj (Tobj

4

Tencl

4

)

(typically applies to a small, isothermal object in a big, isothermal enclosure)72 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Infrared TheoryBut it quickly gets more complicated when there are multiple objects (or temperatures) hanging around. Each object has a view factor of every other object Each object has its own emissivity (usually NOT unity)

73



Infrared TheoryThe emissivity, , is also related to the reflectivity, , as follows:

1So the worse something emits, the better it reflects, and vice-versa.

74



Infrared Theory

In other words, unless youre looking at a perfect emitter (aka a blackbody), you dont simply see less radiation than you would for a blackbody, you see some of the radiation of whats behind you!

75



Infrared TheoryIn even the simplest real-life situation, you usually have four objects, and their associated temperatures, to consider: The test specimen (130C) The surrounding room (25C) You (33C) The detector (-195C)

76



Infrared Theory

(the room) The target(the detector itself)

(you)

(the room)Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

77


Infrared TheorySo if youre looking at a shiny, low emissivity specimen, youll see a combination of these four temperatures (that is, the radiation representing these four temperatures) all bouncing into the detector! Depending on the angles involved, therefore, it is quite possible to see vastly higher temperatures than are really there, or vastly lower temperatures are really there.78 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Hot water loop

Footprints

79



Direct view

In mirror

80



Reflection

Emissivity

81



View at 10 am

View at 10 pm

82



83



Infrared TheoryMoral:

For accurate temperature measurements, you must account for the emissivity of the target, and you must control the background!

84



Infrared TheoryHeres one way to approach it:isothermal enclosure, high emissivity, opaque to infrared

IR camera

DUT

85



Infrared TheoryGoverning equationTwo reference scans

I

I back a T 41

I1I2

I back a T14I back a T2 4

Solve for Temperature

Solve for the unknowns

T

I

I back a

4

a

I2 T24

I1 T14

I back

T2 4 I1 T14 I 2 T2 4 T14

In terms of the reference scan quantities:

T

T2 (I4

I1 ) T1 (I I 2 I14

I2 )

1

4

86



Part II Linear Superposition

87



Linear superposition what is it? The total response of a point within the system, to excitations at all points of the system, is the sum of the individual responses to each excitation taken independently.Tsource 2

Tcomposite

Tsource1

Tsource n

88



Linear superposition when does it apply? The system must be linear in brief, all individual responses must be proportional to all individual excitations.

Tnet ATA89 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

TA

B

TA

C

TA

D

2 qB

3 qCCorporate R&D : Packaging Technology

1.2 qD

Linear superposition doesnt apply if the system isnt linear.

T

a(T , q1 ) q1 b(T , q2 ) q2

T

a q1

n1

b q2

n2

90



Linear superposition how do you use it?Tamb

Tref5Tj6 Tj5

Tj3Tref3

Tj2

Tref1 Tj4 TB91 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Tj1

Linear superposition when would you use it?

When you have multiple heat sources (that is, all the time!)

92



junction temperature vector

theta matrix assembled from simplified subsystems

power input vector

T j1 Tj2 T jn93

J 1A 21

12 J 2A

1n 2n

n1 n2

JnA

q1 q2 qn

Ta

self-heating termsSemiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

board interactionsCorporate R&D : Packaging Technology

junction temperature vector

theta matrix assembled from simplified subsystems

power input vector

T j1 Tj2 T jn

JB1 21

BA1 JB 2

12 BA2

1n 2n

n1 n2

JBn BAn

q1 q2 qn

Ta

device resistance94 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

board resistanceCorporate R&D : Packaging Technology

visualizing theta and psiheat in here measurements here are s

J1A J1B(idle heat source x)

measurements here are s (idle heat source y)

xA

BA

yA

thermal ground95 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

theta matrix doesnt have to be squarejunction temperature vector one column for each heat sourceJA1 12 x1 L1 1 B1 12 JA 2 x2 L1 2 B2 13 23 x3 L1 3 B3

power input vector

T j1 Tj2 TxA TL1 A TBA

q1 q2 q3(why is this and not ?)

one row for each heat source

one row for each temperature location of interest96 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010


Electrical reciprocity

+ 5V -

+ -

+ ?V -

+

0.3 V V-

I 0.3A 2 V

97



Thermal reciprocityheat input here

response here

same response here

98



Another thermal reciprocity example

(r)response here

heat input here same response here

(s)

(s)

(r)

99



When does reciprocity NOT Apply? Upwind and downwind in forced-convection dominated applications

B

Cairflow A D Heat in at A will raise temperature of C more than heat in at C will raise temperature of A B and D may still be roughly reciprocal

100



(square part of) matrix is symmetriccolumns are the heat sources J1 J2 J3 J4 rows are the response locations J5 J6 75 65 55 60 22 10 73 65 71 60 55 25 11 65 55 60 65 61 21 15 55 60 55 61 73 18 11 59 22 25 21 18 125 14 22 10 11 15 11 14 180 10

R1R3 R5 BSemiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

5520 65

6024 63

6314 62

6119 63

2195 21

1515 12

101


Superposition exampleTamb=25 Tref5=47.0 Tj6=36.0 Tj5=49.2

Tj3=85.5 Tref3=85.5

Tj2=96.5

Device 1 heated, 1.1 W

Tref1=105.3 Tj4=91.0 Tj1=107.5 TB=96.5

102



Reduce the dataTj1 Tambj1Aj1A

75 65 55

q1Tj2 Tamb q1

107.5 25 1.196.5 25 1.1

75

j2A j3A

j2 A

65

j4A j5A

6022 10 73 55 20 65

TBBA

j6A r1A

Tamb q1

96.5 25 1 .1

65

r3A r5A BA

103



Device 2 heated, 1.2 Wj1A j2A

65 71

Tamb=25 Tref5=53.8 Tj6=38.2 Tj5=55.0

j3Aj4A j5A j6A r1A

6055 25 11

6560 24 63

Tj3=97.0 Tref3=97.0

Tj2=110.2r3A r5A

Tref1=103.0 Tj4=91.0 Tj1=103.0 TB=100.6104 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

BA

Device 3 heated, 1.3 Wj1A

55 60

Tamb=25j2A

Tref5=43.2 Tj6=44.5

j3A

6561 21 15

Tj5=52.3

j4A j5A j6A

Tj3=109.5 Tref3=106.9

Tj2=103.0r1A r3A

5563 14 62

Tref1=96.5

Tj4=104.3

Tj1=96.5TB=105.6

r5A BA

105




60 55

Tamb=25j2A

Tref5=45.9 Tj6=37.1

j3A

6173 18 11

Tj5=44.8

j4A j5A j6A

Tj3=92.1 Tref3=92.1

Tj2=85.5r1A r3A

5961 19 63

Tref1=89.9

Tj4=105.3

Tj1=91.0TB=94.3

r5A BA

106




22 25

Tamb=25j2A

Tref5=91.5 Tj6=34.8

j3A

2118 125 14

Tj5=112.5

j4A j5A j6A

Tj3=39.7 Tref3=39.7

Tj2=42.5r1A r3A

2221 95 21

Tref1=40.4

Tj4=37.6

Tj1=40.4TB=39.7

r5A BA

107




10 11

Tamb=25j2A

Tref5=32.5 Tj6=115.0

j3A

1511 14 180

Tj5=32.0

j4A j5A j6A

Tj3=32.5 Tref3=32.5

Tj2=30.5r1A r3A

1015 15 12

Tref1=30.0

Tj4=30.5

Tj1=30.0TB=31.0

r5A BA

108



Collect the /J1 J2 J3 75 65 55 60 22 10 65 71 60 55 25 11 55 60 65 61 21 15

values60 55 61 73 18 11 22 25 21 18 125 14 10 11 15 11 14 180

columns are the heat sources

J4rows are the response locations J5 J6 R1 R3 R5 BSemiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

7355 20 65

6560 24 63

5563 14 62

5961 19 63

2221 95 21

1015 15 12

109


Now apply actual power

Tamb=25Tref5=106.3

Actual power in applicationTj5=124.7

Tj6=139.1

Qj1

.4

Q j2Tj3=134.9 Tj2=140.1

.4.4 .4 .5 .2

Q j3 Q j4 Q j5 Q j6

Tref3=134.1Tref1=138.8 Tj4=135.8 Tj1=140.0 TB=139.1110 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Compute some effective /

values

Take Tj1, for instance. Remember when it was heated all alone, we calculated its self-heating theta-JA like this:

Tj1 Tambj1A

q1

107.5 25 1.1

75

Now lets see:

Tj1 Tambj1A

q1

140 25 0.4

288

111



And thats not just a single aberration!Junction to ReferenceSelf heatingj1A j2A j3A j4A j5A j6A j1-R1

3.0 2.0 36.8

vs. 1.5x vs. 1.0x vs. 1.2x

2.0 2.0 30.0

288288 274 277 199 309

vs. 3.8x vs. 4.1x vs. 4.2x vs. 3.8x

7571 65 73

j3-R3 j5-R5

Junction to Boardj1-B

2.2

vs. 0.2x

10.0

vs. 125 1.6x vs. 180 1.7x

j2-Bj3-B j4-B

2.5-10.5 -8.3

vs. 0.3xvs. -3.5x vs. -0.8x

8.03.0 10.0

112



Is the moral clear? You simply cannot use published theta-JA values for devices in your real system, even if those values are perfectly accurate and correct as reported on the datasheet and you know the exact specifications of the test conditions. Not unless your actual application is identical to the manufacturers test board and uses just that one device all by itself.

113



So is it really this bad?Only sort-of. Lets revisit the math for one device

Tj1 Tj2 Tjn

J1A 12

12 J2 A

12 q2n

1n 2n

1nTj1Tj1

JnA1n qn

2nJ1A q1

q1 q2 qnTaTa

Ta

1nqn

J1A q1 2

effective ambient

114



A graphical viewIsolated deviceTj1J1A q1

power, q

1

TaTa

J1A

junction temperature , TJ1

Device in a systemn

shift in effective ambient

Tj1

J1A q1 2 J1A q1

1n qn

TaTa

1J1A

still the same slope

Ta

Ta

junction temperature , TJ1

115



What about that system theta we saw earlier that was so different?power q1 the system theta-JA 1J1A J1A

device #1 power/temperature perturbations will fall on this line

NOT this one

1n

Ta116

1n qn 2

Ta

the isolated-device theta-JA TJ1

junction temperature



How does effective ambient relate to board temperature?system slope for isolated deviceif any of these are non-zero, Ta will be higher than Tan

Tj1

j1a

Q1i 2B1a

(

i1

Qi ) Ta

(

j1B

)QB1a

1

effective Ta ambient

j1B

Q1

Q1TB1a

TaTa

Tj1Btemperature rise, board to J1117 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

when Q1 is not zero, both zero, both of of these be these willwill be non-zero zero

temperature rise, ambient to boardCorporate R&D : Packaging Technology

Predicting the temperature of high power components The device and system are equally important to get right

Predicting the temperature of low power components The system is probably more important than the deviceSemiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

118


Using the previous board example theta arrayJ1 J2 J3

75 65 55 60 22

65 71 60 55 25

55 60 65 61 21

60 55 61 73 18

22 25 21 18 125

10 11 15 11 14 Qj1

power vector0.5

J4J5 J6 R1 R3 R5 B

Q j2 0.5Q j3 0.5 Q j4 0.5 Q j5 0.2 Q j6 0.02

1073 55 20

1165 60 24

1555 63 14

1159 61 19

1422 21 95

18010 15 15

65

63

62

63

21

12Corporate R&D : Packaging Technology

119


Observe the relative contributionsFor junction 1 (a high power component) we have: the device itself the other devices = (75 x 0.5) + (65 x 0.5) + (55 x 0.5) + (60 x 0.5) + (22 x 0.2) + (10 x 0.02) + 25

=

37.5

+ 32.5 + 27.5 + 30 + 4.4 + 0.2

+

25

= 37.5 +120 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

94.6

+

25


Graphically, a high-power device looks like this:power q1=0.5 W note the embedded theta-JA looks like 264 C/W decreasing power

increasing power

1264 C/W

175 C/W

=94.6 Cn

25 C

1n qn 2

=37.5 C (J1Aq1)

157 C TJ1


121



Relative contributions to TJ6the other devices = (10 x 0.5) + (11 x 0.5) + (15 x 0.5) + (11 x 0.5) + (14 x 0.2) + (180 x 0.02) + 25 the device itself = 5.0 + 5.5 + 7.5 + 5.5 + 2.8 + 3.6 = 26.3 + 3.6 + 25 + 25

122



Graphically, low-power device #6 looks like this:

power and just in case you were wondering, the embedded theta-JA looks like 1495 C/W !1 =3.6 C

q6=0.02 W=26.3 C

180 C/W

25 C

54 C TJ6


123



Controlling the matrix

How to harness this math in Excel

124



3x3 theta matrix, 3x1 power vector Excel mathMatrix MULTiply obtained by using multi-cell placement Ctrl-Shift-Enter rather {=array formula notation} than ordinary Enter of array formula

theta matrix

power vector

array reference to theta matrix

array reference to power vector

125



7x3 theta matrix, 3x1 power vector Excel mathdont forget to use theta matrix is no longer square Ctrl-Shift-Enter # of columns still must equal # of rows of power vector to invoke array formula notation array formula now occupies 7 cells

126



7x3 theta matrix, 3x2 power vector Excel mathpower vector is now a 3x2 array each column is a different power scenario, yet both are still processed using a single array (MMULT) formula the single MMULT array formula now occupies 7 rows and 2 columns (one column for each independent power scenario result)

127



Temperature direct contributions and totals120

120

80

temperature rise [C] sum of sourcesJ1 J2 J3 J4 J5 J6 R1 R3 R5 B

temperature rise [C], each source

100

100

80

60

60

40

40

20

20

0 result location

0 J1 J2 J3 J4 J5 J6 R1 R3 R5 J3 at 0.4 W J6 at 0.2 W B result location J3 at 0.4 W J6 at 0.2 W J1 at 0.4 W J4 at 0.4 W J2 at 0.4 W J5 at 0.5 W

J1 at 0.4 W J4 at 0.4 W

J2 at 0.4 W J5 at 0.5 W

128



Normalized responses at each location due to each source200

normalized response [C/W], each source

180 160 140 120 100 80 60 40 20 0 J1 J2 J3 J4 J5 J6 R1 response location R3 R5 B J1 at 1 W J2 at 1 W J3 at 1 W J4 at 1 W J5 at 1 W J6 at 1 W

129



Filling in the theta-matrix

Handy formulas for quick estimates Utilizing symmetry

130



Conduction resistancebasic heat transfer relationship for 1-D conductionq dT k A dx k A T L

if we defineR T q

thenR L k ACorporate R&D : Packaging Technology

131


Convection resistancebasic heat transfer relationship for surface coolingq h A T

if we defineR T q

thenR 1 hACorporate R&D : Packaging Technology

132


Radiation resistancebasic heat transfer relationship for surface radiationq F A (T 4 Ta4 ) F A (T 2 Ta2 )(T Ta )(T Ta ) F A (T 2 Ta2 )(T Ta ) T

if we defineR T q

thenR 1 FA (T 2 Ta2 )(T Ta )

temperatures must be expressed in degrees absolute!

133



Thermal capacitance and time constantCapacitance is ability to store energy specific heat is energy storage/mass Based on simple RC concept, relate rate of storage to rate of flux, result is

Cso if

cp Vand if

= RC

Rthen

L and C k Ac pL2 k L2

c p (L A )

Rthen

1 and C h Ac pL h

c p (L A )

134



Some useful formulas conduction resistance.. R convection resistance... RL k A 1 h A c pV c pL2 k c pL T h Q A 2 cp k t

thermal capacitance..... C characteristic time... (dominated by 1-D conduction) characteristic time... (dominated by 1-D convection) short-time 1-D transient response...

135



Terms used in preceding formulas L - thermal path length A - thermal path cross-sectional area k - thermal conductivity k - density cp cp - heat capacity - thermal diffusivity cpk - thermal effusivity h - convection heat-transfer film coefficient) T - junction temperature rise Q - heating power t - time since heat was first applied

136



When do these effects enter?hundreds of seconds tens of seconds a second or so


mainly environmental convection and radiation effects

mainly local application board conduction effects

typical heating curve for device on FR-4 board in still-airtime

mainly package

materials/conduction effects137 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

if

R

then

and

2R

4R138 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Cylindrical and spherical conduction (through radial thickness) resistance formulasro ln ri k L[solid angle]

Half-cylinder

R

R

1 ri 2 1 ri 4

1 ro k 1 ro k

Hemisphere

[included angle]

Full cylinder

R

r ln o ri 2 k L

R

Full sphere

where

L cylinder length ri inner radius ro outer radius

139



Package-shrink gotchaRemember how much of theta-JA depends on what isnt the package?

Well, what if your cooling depends significantly on convection from the board surface (whether free or forced air)?

q

h A

T

A

q h T

So never mind the package resistance, the board can only transfer a certain amount of heat to the air:*Special thanks to Dave Billings for the idea behind this slide140 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Package-shrink gotcha1000 A 2 mm

1.0q WW 1E-5 mm2 C

h

100C TSo if 4 SOT23s each have 0.25 W, then T=0.25*200=50C PROBLEM: No problem! 4 SOT23s on a 1000 mm2 board, effective JA=400C/W

1 SOT23 on a 250 mm2 spreader, JA=200C/W

Fortunately, 0.25 W each x 400C/W100C*Special thanks to Dave Billings for the idea behind this slide141 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Whew!

Package-shrink gotchaNOW your favorite supplier comes out with the next generation version (much smaller) of the same component.SOT23 4 SOT723s on a 1000 mm2 SOT23s board, JA=400C/W, T=100C, power = 1 W total, power = 1 W total, 0.25 W each each

Decrease size (but not power and reduce power dissipation dissipation) (RDSON or other electrical performance)

How many SOT723s can you put in that same 1000 mm2? ANSWER: 4 88 SOT723s on a 1000 mm2 board, JA=800C/W, T=100C, power = 1 W total, 0.125 W each

SOT723*Special thanks to Dave Billings for the idea behind this slide142 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010


PERIODIC and NON-PERIODIC POWER INPUT

Duty-cycle curves Normalized and non-normalized Linear superposition applied to time domain

143



Square-wave duty cycles (aka ratios) What the heck are they? show peak junction temperature as a function of duty cycle and pulse width

Where do they come from? heating curve is equivalent to the limiting case of a 0% duty-cycle, where once the pulse width is over, theres never another cycle linear superposition allows you to generate the whole family from the heating curve

144



Representative duty cycle response chart2.5 R(t), Thermal Resistance [C/W]

2

1.5

d=0.5

1

0.2 0.10.05 Single pulse

0.5

0 0.00001

0.0001

0.001

0.01 t, time (s)

0.1

1

10

145



It begins with one of these:100

transient thermal response for axial lead rectifier Junction-to-Lead, 1/4" lead length

10

R(t)JL [C/W]

1

0.1 0.0001

0.001

0.01

0.1

1

time [s]

10

100

1000

A single-pulse response is the same as a 0% duty cycle - if you think in terms of a 0% duty cycle meaning you have only one pulse (however long it lasts), but once you turn if off, you never turn it back on again. So any finite on time is zero percent of infinitely long off.146 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

published formulasNon-dimensionalized versionsr(t , d ) dr(t , d ) d

dimensionalized versionsR(t , d ) d R

(1(1

d ) * r(t )d ) * r(t p) r(t ) r( p)

(1

d ) R(t )

r (t , d ) d

(1

d)*r t

t d

r (t ) r

t d

R(t , d ) d R

(1

d) R t

t d

R(t ) R

t d

lim R(t , d ) d Rt 0

lim R(t , d )t

R

147



A normalized curve:1JL=27.4C/W

r(t)JL [normalized]

0.1

normalized transient thermal response for axial lead rectifier Junction-to-Lead, 1/4" lead length

0.01 0.0001

0.001

0.01

0.1

1

time [s]

10

100

1000

Is this really such a bright idea?

148



Consider this family of non-normalized curves:100

Transient thermal response for axial lead rectifier Junction-to-Lead, varying lead length

10

R(t)JL [C/W]

R(t)-1" R(t)-3/8" 1 R(t)-1/32"

0.1 0.0001

0.001

0.01

0.1

time [s]

1

10

100

149



The danger!100


10

r(t)JL [normalized]

See what happens to the shorttime response when you normalize!

R(t)JL [C/W]

R(t)-1" R(t)-3/8" 1 R(t)-1/32"

0.1 0.0001 1

0.001

0.01

0.1

time [s]

1

10

100

JL-1/32"=20.0C/W JL-3/8"=34.9C/W

0.1

JL-1"=54.9C/W

0.01

r(t)-1/32" r(t)-3/8" r(t)-1"

normalized transient thermal response for axial lead rectifier, Junction-to-Lead varying lead length

0.001 0.0001

0.001

0.01

0.1

time [s]

1

10

100

150



Compare the families of curves:100

R(t)JL [C/W]

Different steady states

square-wave duty cycles for 1/32" lead length

10

single pulse 1% duty cycle 2% duty cycle 5% duty cycle

1

10% duty cycle 20% duty cycle 50% duty cycle

Same shorttime 0% (single-pulse)

0.1 0.0001

0.001

0.01

0.1

time [s]

1

10

100

100

square-wave duty cycles for 1" lead length

R(t)JL [C/W]

Different everything between !!

10

single pulse 1% duty cycle 2% duty cycle 5% duty cycle

1

10% duty cycle 20% duty cycle 50% duty cycle

0.1 0.0001

0.001

0.01

0.1

time [s]

1

10

100

151



What to do if youre given a normalized curve Find out what reference value it was normalized from Undo it

If you cant find out Throw the curve away

152



Linear Superposition Applied to Time Domain

153



Basic heating curve - a single pulseR(t)

t

Q

t

power input corresponding to single pulse heating curve154 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Single pulse (actually turned off)Finite pulse, decomposed into two infinite stepsQ

equalsa t

Q

plust

Q a t

Temperature response of a finite pulse (constructed from superposition of two single pulse responses)R(t) R(t) R(t) a t

plust

equalsa t

155



Two differing pulsesTwo finite pulses decomposed into infinite stepsQ1 a Q2 b c Q1 t a -Q1 Q2 b c -Q2 t

is made up of

Temperature response constructed for two finite pulses (constructed from superposition of four single pulse responses)R(t)R(t)

results in this

156



An arbitrary pulse train Temperature at end of nth pulsen

Tni 1

Pi R(t2 n

[

1

t 2i

2

)

R(t2n

1

t 2i

1

)]

Notes: times and pulses must be in strictly increasing chronological orderP1 Pn P2

When there is no off period between two consecutive pulses, set t 2i 2 t 2i 3 (i.e. do not combine them into a single value)t2n-1

Powert0 t1 t2

t3 time

t2n-2

For temperature at the beginning of the nth pulse, set t 2n 1 t 2n 2

157



An exampleItem P1 P2 P3 t1 t3 t3-1 t3-2 t5 t5-1 t5-2 t5-3 t5-4t0 t6 t4

Junction Temperarure

Value 80 40 70 0.0001 0.0013 0.0012 0.0010 0.0035 0.0034 0.0032 0.0022 0.0002Item

unit W W W s s s s s s s s sunit

P(PK) Peak Power (Watts)

100 80 60 40 20 0 t0 t1 t2 1 t3 2 t, Time (ms) 3 t4 t5 4 P1 P2 P3

T1T2

P R(t1 ) 1P R(t3 ) R(t3 t1 ) 1 P2 R(t3 t 2 )

[

]

T3 T1 T2

Value

T33 t4 t5 4

P R(t5 ) R(t5 t1 ) 1

[

] ]

0.0000 s 0.0003 s 0.0012 s

t0 t1 t2

1 t3 2 t, Time (ms)

P2 R(t5 t 2 ) R(t5 t3 ) P3 R(t5 t 4 )

[

158



How to read the curve For small time differences, and on a low resolution log-log plot, what can you do?100


10

1

0.1 0.0001

0.001

Item P1 P2 P3 t1 t3 t3-1 t3-2 t5 t5-1 0.01 t5-2 t5-3 t5-4

Value 80 40 70 0.0001 0.0013 0.0012 0.0010 0.0035 0.0034 0.0032 0.0022 0.0002

unit W W W s s s s s s 0.1 s s s

R(t)JL [C/W]

R(t)-1" R(t)-3/8" R(t)-1/32"

time [s]

1

10

100

159



Assume power law (straight line on log-log plot)R(t ) a tn

t2

t1

t1 ta R(t1 ) t1n

R(t 2 ) t2n

R(t

) R(t )R(t

t t

n

n

R(t ) 1

log n

R(t 2 ) log t2

t

R(t1 ) t1

)

R(t )

R(t )n

t

160



How to read the curve #2 For small time differences, and on a low resolution log-log plot, what can you do?100

anchors R(.0001) 0.22 R(.02) 3.3


10

1

0.1 0.0001

0.001

0.01

0.1

time [s]

1

interpolate R(t1) 0.22 R(t3) 0.82 R(t3-1) 0.79 R(t3-2) 0.72 R(t5) 1.36 R(t5-1) 1.34 10 R(t5-2) 1.30 R(t5-3) 1.08 R(t5-4) 0.32

R(t)JL [C/W]

R(t)-1" R(t)-3/8" R(t)-1/32"

100

161



ResultsP(PK) Peak Power (Watts)100 80 60 40 20 0 t0 t1 t2 1 t3 2 t, Time (ms) 3 t4 t5 4 P1 P2 P3

T1 T2

P R(t1 ) 80 0.22 17 .6 C 1 P [ R(t3 ) R(t3 t1 )] P2 R(t3 t 2 ) 1 80 (0.82 0.79 ) 40 0.72 2.4 28 .8 31 .2 C

Junction Temperarure

T3 T1 T2

T3

P [ R(t5 ) R(t5 t1 )] 1 P2[ R(t5 t 2 ) R(t5 t3 )] P3 R(t5 t 4 ) 80 (1.36 1.34 ) 40 (1.30 1.08) 70 0.32 1.6 8.8 22 .4 32 .8 C

t0 t1 t2

1 t3 2 t, Time (ms)

3 t4

t5

4

162



Another transient analysis examplepower

1825.2W

23

Heres our power input scenario:power 20 pulses 25.2W

repeat 20 times, then stop for 6800 microsecondstime

20 pulses

time 802 last of 20 pulses ends 7600

163



equivalence of non-zero average response with (constant average) + (zero-average disturbance)Actual duty cycle and responsepeak Tavg valley Tavg due to Qavg

Superposition of average and disturbance

Power shifted to average zero

Q0Qavg= d Q

(1-d) Q

0-dQ

164



Another example, contHow do we analyze it? Over three time scales:power

1825.2W

instantaneous excursions based on local duty cycle

23power

average Tj based on local avg power

average excursions based on global duty cycle

repeat 20 times

time

25.2W

burst

timepower 25.2W

7600

15200

average Tj based on global avg power20 pulses time 802 last of 20 pulses ends 7600

165



Endless Possibilities

166



A rampA finite ramp decomposed into several infinite stepsPt a

P

is made up of

a

t

Temperature response constructed for finite ramp (constructed from superposition of many single pulse responses)Q t a Q

results in thisa

t

167



An arbitrary pulseAn arbitrary pulse decomposed into several infinite stepsQ t a Q

is made up of

Temperature response constructed for this arbitrary pulseQ Q

t

results in thist

168



Multiple Time-Varying Heat Sources

169



Basically the same theta-matrix idea, only now everything is a function of time as welljunction temperature vectorT j1 (t ) T j 2 (t ) TxA (t ) TL1 A (t ) TBA (t )

one column for each heat source(t ) 12 (t ) x1 (t ) L1 1 (t ) B1 (t ) (t ) JA 2 (t ) x 2 (t ) L1 2 (t ) B 2 (t )12

power input vector

JA1

(t ) 23 (t ) x 3 (t ) L1 3 (t ) B 3 (t )13

q1 (t ) q2 (t ) q3 (t )

one row for each heat source

one row for each temperature location of interest170 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Each heat source needs to be independently heated.

Each temperature needs to be measured whether heating itself or being heated by another.

Time (sec) thermal system boundary

Measurement cycle(s)Time (sec)

*Special thanks to Dave Billings for this slide171 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010


Temperature (C)

Power input (W)

but first, some words about

Thermal RC networks Grounded (Cauer) vs.. non-grounded (Foster) Orders of magnitude, rungs Pulses and periodic waveforms Short-time behavior, limits, and limitations

172



Thermal capacitance (grounded vs.. non-grounded) In electrical circuit, voltage on a capacitor is difference between its two terminals, and you have physical access to both A lumped parameter thermal model is predicated on energy storage being determined entirely by one temperature Therefore, in a thermal circuit, you only have access to one terminal of each capacitor, namely the one where you identify the temperature. The other terminal is ground.173 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Models: grounded vs.. non-groundedCauer ladders Foster ladders

Physical significance: if thermal capacitors are grounded, they bear some relationship to a physical system; not so for non-grounded Cs Mathematical convenience: certain non-grounded networks are mathematically trivial Interchangeability: single-input thermal systems can be represented as either grounded or non-grounded; multiple-input thermal systems are easy to model as grounded-C networks; it can be done, though with some intricate bookkeeping, using non-grounded-C networks174 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Actual thermal RC networksNon-grounded CFoster ladder1.7004 C/W 2.6627 3.9740 10.0255 11.7747 35.3008 33.1212 Tj

vs..

grounded C comparisonCauer ladderTj

7.02E-04 W-sec/C 2.3207 C/W 4.41E-03 5.89E-02 1.55E-01 6.03E-01 1.46E+00 4.16E+002.7397 8.3551 14.6949 21.0538 39.637 9.7581 Ta

5.96E-04 W-s ec/C 4.20E-03 3.67E-02 1.01E-01 4.13E-01 9.20E-01 1.14E+01

Ta175 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010


2-rung Foster model

R1

C1

R1

1 sC1

1 sC1 1 R1

R1 R1C1 s 1

R2 R2 C2 s 1

R2

C2

R2

1 sC2

R2 R2 C2 s 1

176



2-rung Cauer modelC1 R11 sC2

R1

1 sC1

R1R2 R2 C2 s 1

1 sC1

R2

C2

R2

R1

R2 R2 C2 s 1

1 sC1

1 sC1 1 R1 R2 R2 C2 s 1

R1 R2 C2 s R1 R2 R1C1 R2 C2 s R1C1 R2 C1 R2 C2 s 12

177



2-rung models compared Time constants are roots of denominators "tau" is not RC product when capacitors are grounded !

non-grounded capacitors:(Foster)R1 R1C1 s 1 1 1 C1 s 112

grounded-capacitors:R1 R2 C2 s R1 R2 R1C1 R2 C2 s R1C1 R2 C1 R2 C2 s 1where time constants are 2 R1 C11

(Cauer)s s R1 R2 R1 R2 C 2 11

can be written

1 C1

s

12

R2 R2 C2 s 1 1 1 C2 s 12

can be written

1

c r

c

1

c r

2

c

c 4 r

r 100 10 3 1 1

c 0.01 0.1 1 /3 0.1 1

1

2

R1C1

R2C2

2 R2 C22

where time constants are1

r 1 c

rr

r 1 cR2 R1 c

2

rC1 C2

4

r c

R1C1

2

R2 C2

and defining

0.99 0.91 0.73 0.90 0.38

1.01 1.10 1.36 1.11 2.62

178



Interesting (and important) implicationsFoster ladderRungs can be in any order and Tj has identical behavior! So where do you split it?Tj

Cauer ladderOrder matters, so a split can make good physical sense. Tj2.3207 C/W 5.96E-04 W-s ec/C 4.20E-03 3.67E-02 1.01E-01 4.13E-01 9.20E-01 1.14E+01 Ta

1.7004 C/W 2.6627 3.9740 10.0255 11.7747 35.3008 33.1212

7.02E-04 W-sec/C 4.41E-03 5.89E-02 1.55E-01 6.03E-01 1.46E+00 4.16E+00

package

2.7397 8.3551

??

14.6949 21.0538 39.637 9.7581

environment

Ta

179



Orders of magnitude and rungs It is a rare transient curve that cannot be followed very accurately with time constants no closer than about 1 order of magnitude apart. This means that you need only about one rung per decade of transient response.

180



For what its worth ...Every Cauer (grounded-capacitor) ladder has a mathematical solution. By definition, its mathematical solution represents a corresponding Foster (non-grounded-capacitor) ladder. Every Foster (non-grounded-capacitor) ladder having distinct (i.e. non-repeated) time constants, has a corresponding Cauer (grounded-capacitor) equivalent. (However, there is no a priori guarantee that all Rs and Cs will be positive!)Ref: L. Weinberg, Network Analysis and Synthesis, McGraw Hill Book Company, Inc., 1962

181



RC network mathCauer ladder continued fraction:Z sC1 R1 sC 2 1 1 1 1 R2 ... 1 ...

with some algebra, both may be written:Z Nn s Dn 1 s

Foster ladder, sum of simple fractions:Z R1 R1C1s 1 R2 ... R2 C 2 s 1 Ri ... Ri Ci s 1

182



Arbitrary repetitive pulse

Q

t p 2p

p period of waveform

183



Generalized periodic square waveSo consider a general rectangular pulse positioned arbitrarily within a

repetitive cycle of period p. We can derive expressions for theinfinite sum of responses in three regions :Q t arbitrary time of interestm t a

R(t )i 1

Ri 1 e Fi (t )j 1

i

t a jp

Ri 1 em

i

t

R(t )i 1

Ri 1 e

i

p b pulse turns off a pulse turns on

2p

t measured from edge of power stepm t b

R(t )i 1

Ri 1 et b jp

i

0 t184

a

a t

b

b t

p

Fi (t )j 1

Ri 1 e

i



Infinite summationUtilizing the identitiesj 0

zj

1 1 z

andj 1

z

j

1 z 1

and doing some algebra, we can show these results:

0 tb t p

aa t p

a ti

bb t p a ti

b tepi i

pb t a t

Fi (t )

Ri

e

i

epi

Fi (t )

Ri 1

e

Fi (t )

Ri

e

i

epi

i

1 e

1 e

1 em

In each domain, we then sum over all rungs of the Foster model:

F (t )i 1

Fi (t )

185



RCEnd result for arbitrary periodic power Model for Multiple Square Waves in One Cycle

An important point of this example is that for complex power inputs, absolute peak temperatures do not always correspond to the ends of the highest power pulse!Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

186


Short-time limits What do RC models do at shortest time? roll off linearly with timet t

R(t )

R1 1 e

1

R2 1 e t1

2

t2

R1 1 R1 t1

1

t2 2 21

R2 1 R1 t1

1

t2 2 2 2

t2 2 21

t2 2 21

R(t )

R11

R22

t

R12 1

R22 2

t2 2

So for small t: R(t ) (const) t

187



RC models and Surface Heating It turns out that if Rs and Cs grow at a uniform ratio, a sqrt(t) behavior ( b t ) is approached in the limit If ratio is 1:3 (increasing with distance from junction node), rung-to-rung time constant ratio will be about

one order of magnitude, and the network will follow theoretical sqrt(t) within a few percent

188



Rungs vs.. sqrt(t) behavior1.0E+0

Exact sqrt(t) model1.0E-1

1.0E-2

1 rung 1.0E-3 2 rungs @ 3.0:1 3 rungs @ 3.0:1 4 rungs @ 3.0:1 1.0E-4 1.0E-8 5 rungs @ 3.0:1 1.0E-7 1.0E-6 1.0E-5 1.0E-4 1.0E-3 1.0E-2 1.0E-1 1.0E+0 1.0E+1

189



Where does that leave us with respect to the applicability of RC networks? We need to pay attention to silicon thickness vs.. device technology if surface heating is a good model, be sure your RC network has time constants short enough to land within the silicon within the silicon timescaleL2

, if surface heating is a good

model, you have to extend the RC network into that region on the other hand, if surface heating is not a good model (implying that volumetric heating is better), the fastest rung of your RC network can be set to the actual R&C corresponding to the volume being heated190 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

Multiple heat-source RC networks You need data (experiment or simulation) Fit an RC network (or networks) to the data Foster networks, well see an Excel-based approach Cauer networks, beyond the scope of this tutorial

Using SPICE: directly input your RC networks Foster networks can be complicated Cauer networks are straightforward

Using Excel: Foster networks, well see an Excel-based approach Cauer networks are not practical

191



Typical 2-input heating/response curves250q1 self avg q2 self avg interact

200

q1R(t) [C/W]150

q1 RC-fit q2 RC-fit q1q2 fit

100

q2

50

0 1E-4

1E-3

1E-2

1E-1

1E+0

1E+1

1E+2

1E+3

heating time [s]Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

192


Fitting Foster ladders in Excel

193



Using RMSE as fitting parameterA 1 B C D E F G H I J K L

RMSE test pow er [W] Time

1.9 1.00

1.3 1.00

0.5 1.00 TABLE 1: Foster model taus 1.0E-4 1.0E-3 1.0E-2 1.0E-1 1.0E+0 1.0E+1 1.0E+2 q1 R's 11.2 7.6 12.5 76.6 70.0 2.3 41.0 q2 R's 0.8 2.9 2.3 45.6 67.5 2.2 37.7 interact R's -0.1 0.3 -0.7 -2.3 38.4 4.0 34.1

23

q1 self q2 self q1 RC- q2 RC- q1q2 fit 8.48 9.68 10.59 11.82 14.14 14.64 15.37 15.87 16.37 16.98 18.45 18.58 20.29 1.16 1.32 1.50 1.67 1.84 2.02 2.21 2.42 2.65 2.89 3.14 3.17 3.76 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9.18 10.51 11.67 12.63 13.45 14.14 14.80 15.46 16.16 16.86 17.60 18.39 19.21 1.01 1.20 1.40 1.59 1.79 1.98 2.19 2.41 2.67 2.92 3.20 3.50 3.80 -0.03 -0.03 -0.03 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.04 0.05

4 5 6 7 8 9

1.26E-4 1.64E-4 2.09E-4 2.60E-4 3.18E-4 3.82E-4 4.58E-4 5.48E-4 6.57E-4 7.78E-4 9.19E-4 1.09E-3 1.28E-3

1011 12 13

{=SQRT(SUMSQ(E4:E100TABLE 5: results at arbitrary times B4:B100)/COUNT(E4:E100))} 120.5 100.70.00 25.0 {=$G$2*SUM(interact_Rs 25.0 *(1-EXP(-A4/taus)))} 30.0 0.01 59.6 0.05 90.0 39.1

1415 16

194



Excels SolverUse Excels solver to minimize the error between the input data and the RC model.1000 0.6 0.4 100 0.2 0

-0.2 10 -0.4 -0.6 1 Simlation data R-C model Fit Error -0.8 -1 -1.2 100 1000

0.1 1E06

1E05

1E- 0.001 0.01 04

Simulation data0.1

1

10

Time (sec)

After optimization

195



Fit error (C/W)

R(t) (C/W)

Using SPICE to exercise the models

196



Using Foster RC models in SPICETself1 (volts) Tself2 (volts)

Q1 (amps)+ + Tj1 Tpos1 Tj2 -

Tpos2 time

Tneg2

Tneg1

Q2 (amps)

time

different networks of self heating elementsSemiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

identical networks of positive interaction elementsCorporate R&D : Packaging Technology

identical networks of negative interaction elements

197

1/4th of a 4-input Foster RC SPICE modelPiecewise linear current source for power input from each source generating heat.Summing tool to add voltages from the separate interaction networks with the self heating network Thermal equivalent Foster RC networks (note that all these Rs are positive) The output port (OUT1) will be where you want to monitor the temperature response Each heat source will require a similar block in order to simulate the temperature response of the self heating effect as well as the interactions. Thermal ground by adding a voltage potential to the ground point ambient temperature can be added.

*Special thanks to Dave Billings for this slide198 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010 Corporate R&D : Packaging Technology

A 2-input Cauer network modelTj1 C11 R11 R12 C12 C22 R22 C23 R23 C24 time R21 Tj2 Apply q1 to Tj1 node

C21

q1 (watts)

C13

R33 R13 C14 R14 C5 R44

R24R5 C6 R6 q2 (watts) Apply q2 to Tj2 node

C7 R7 time

199



Using Excel to exercise Foster models

200



Setting up a 2-input Excel modelI1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

J

K

L

M

Nambient

O25

P

Q

R

S

T

U

V

W

X

Y

Z

TABLE 1: Foster model taus 1.0E-4 1.0E-3 1.0E-2 1.0E-1 1.0E+0 1.0E+1 1.0E+2 q1 R's 11.2 7.6 12.5 76.6 70.0 2.3 41.0 q2 R's 0.8 2.9 2.3 45.6 67.5 2.2 37.7 interact R's -0.1 0.3 -0.7 -2.3 38.4 4.0 34.1

TABLE 2: pow er input vs time t0 change_at q1_pow er q2_pow er delta q1 delta q2 time 0.5 0.00 1.0 0.5 1.0 0.5 t1 0.10 1.0 0.0 0.0 -0.5 t2 0.25 0.0 1.3 -1.0 1.3 t3 0.40 0.8 0.9 0.8 -0.4 t4 1.00 0.8 0.0 0.0 -0.9 t5 1.10 0.0 0.0 -0.8 0.0 t6 1.50 0.0 1.0 0.0 1.0 t7 2.00 0.0 0.0 0.0 -1.0 t8 2.60 0.0 0.4 0.0 0.4 t9 3.00 0.6 0.4 0.6 0.0 t10 0.6 0.7 0.0 0.3 t11 0.0 0.7 -0.6 0.0

5.00 10.00

TABLE 3: unit step relative to chosen time 0.50 141.5 51.7 0.40 0.25 0.10 68.4 -15.1 0.00 0.0 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0.00 0.0 0.0 1.4 0.00 0.0 0.0

TABLE 5: results at arbitrary times 120.5 0.00 0.01 0.05 0.10 0.25 0.26 0.26 0.27 0.29 25.0 59.6 90.0 112.2 143.6 116.5 110.0 101.0 89.2 100.7 25.0 30.0 39.1 47.4 37.1 46.3 50.3 56.9 67.4

TABLE 4: sum of terms T1_terms T2_terms -5.1 -109.3 -36.6 75.7

Tj1 =SUM(T2_terms)+ambient 180 Tj2 160 140 120 100 q1_pow er q2_pow er

{=IF(time>change_at,time-change_at,0)} {=SUM((S7*q1_Rs+S8*interact_Rs)* (1-EXP(-time/taus)))} 1.21

{=SUM((R7*interact_Rs+R8*q2_Rs)*(1-EXP(-time/taus)))}{=TABLE(,time)}0.8Corporate R&D : Packaging Technology

=SUM(T1_terms)+ambientperature [C]

201


80

Results from a 2-input Excel Foster model180.0 160.0 140.0 1.00 120.0 Tj1 Tj2 q1_pow er q2_pow er 1.20 1.40

temperature [C]

100.0 80.0 60.0

0.80

0.60

0.40 40.0 20.0 0.0 0 1 2 3 tim e [s] 4 5 6 0.20

0.00

202



power [W]

Organizing the sheet for transient solutionA cell for keeping track of the overall time progression of ALL blocks.

=IF(Master_Time>Row_Time,Master_time-Row_time,0)

Self heating column (each cell is a separate array formula) {=dP-D#*SUM(R1:R10*(1-EXP(-dtime/Tau1:Tau10)))}

Interaction heated columns (each cell is a separate array formula) {=dP-D#*SUM(R5:R10*(1-EXP(-dtime/Tau5:Tau10)))}

A section for power input to the heat sources*Special thanks to Dave Billings for this slide203 Semiconductor Device Thermal Characterization and System Analysis (RPS) April 2010

A section for Time changes

A section for power changes

A section for Temperature response calculation


Table for plotting temperature output=SUM(D1:D1_by_D4) +T_ambient

Note!

Time in this column can be independent of the time values in the power input sectionNext, Select this whole region Apply a Data > Table option


Results from a 4-input Excel Foster modelTemperature (C)1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.05 0.1 0.15 Time (Sec) 0.2 0.05 0.1 0.15 Time (Sec) 0.2 0.05 0.05 0.1 0.15 Time (Sec) 0.2 D13 2.5 2 1.5 1 0.5 0 0 0.05 0.1 Time (Sec) 0.15 T_D1 T_D2 T_D3 T_D4

Power (W)

0.25 D2

0.2

0.25

0.3

Last power input0.1 0.15 Time (Sec) 0.2

0.25 D3

Temperature (C)

3 2.5 2 1.5 1 0.5 0 0 0.05 0.1 Time (Sec) 0.15 0.2 0.25 0.3

Power (W)

0.25

Temperature (C)

3 2.5 2 1.5 1 0.5 0 0 0.05 0.1 Time (Sec) 0.15 0.2 0.25 0.3

Power (W)

0.25

Temperature (C)

D4

3 2.5 2 1.5 1 0.5 0 0 0.05 0.1

Power (W)

Time (Sec) 0.15

0.2

0.25

0.3


Recap With the right tools, a thermal RC n

30794082 semiconductor thermal design

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