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Lasers Defect Correction in DRAM's • Problem: very hard to make memory chips with no defects • Memory chips have maximum density of devices • Repeated structures all substitutable • Create spare rows and columns of memory • After testing locates defective bit cut off that column • Substitute in working column/row for defects • Use laser cutting program in that column address in spare • Typically have 4 spares in each half a DRAM • Started with 64K DRAM's in 1979 • Difficult to build DRAM's without this • Now also important for embedded SRAM/DRAM • Embedded rams typically > 256K • Very Important for Systems on a Chip (SoC)
Poly Silicon Cuts (Fuses) • Use laser to cut polysilicon lines • Melts back the poly • Some damage to coverglass • Each die test, defects determined, and laser cut • Commercial machines >$750- 2,000K do this (e.g. ESI)
Yield Improvement on DRAM’s With Laser Repair • New DRAM’s uses highest density Microfab process available • Currently generation using 0.13 micron 5/6 level metal • Typical new DRAM design has low yield ~ 1-3% • Cost of production independent of yield • Hence if can increase yield by 100% drastically cut costs • Yield follows Negative Binomial Statistics (defects cluster) has a “Culster Coefficient” that measures this • Average defects may be 2-5 per chip but a few have only 0-1 • Can get 2-4 times improved yield
Vertical Laser Silicon Nitride Links • Vertical laser links used to make permanent connections • Metal 1 over metal 2 with silicon rich Silicon Nitride SNx between • Laser melts top metal creates Al Si short 1st to 2nd metal • Unconnected R > 1GΩ, Laser Linked ~1-2Ω • Argon laser focused on pad top ~ 1 μm spot, 1 msec at 1 W • Structure allows cutting of lines & removal of the link if needed • Could carry > 1 mA current to power cells • Designed to route signal interconnecting circuit blocks • Developed MIT Lincoln Lab 1981: Chapman, Raphel, Herdon • Used to create worlds first wafer scale device DSP integrator on 5x5 cm substrate 1983
Laterial Laser Diffused Link • Designed to use Standard CMOS process • Two doped areas separate by min allowed gap • Laser pulse melts silicon, causes dopant to cross gap • Creates permanent connections • Can see dopant across gap using Scanning Ion Microscopy • Made in structures from 5 micron to 0.5 micron CMOS • Developed at MIT Lincoln Lab 1986: Chapman, Raphel, Canter • Makes ~50-100 ohm resistance connection • Implemented in wafer scale projects at Lincoln Lab and SFU
2nd Metal:22.4 x 3.3 um
1st Metal:18.2 x 3.3 um
Link gap: 2 um
Tongue Cut Points
1st Metal Cut Point
Linking Points
+
+
2nd Metal Cut Point
N+ N+
Contact cut
Via
Connected Link Unformed Link
Laser Diode Linked Structures
Large Area/Wafer Scale Silicon Systems • Large area structures: problem is yield declines with square of area • Break system into repeated circuit blocks cells with buss • Many cells some defective use laser links to make connections • Laser links make permanent connections – very fast • Important for combinations of Transducers & links • Several Designs of Wafer Scale Devices at MIT Lincoln Labs • At SFU made Laser area Transducer Arrays • Combine micromachining and WSI techniques
SignalBus
SignalBus
Signal Bus Signal BusSignal Bus
I/O Processors
I/OProcessors
Defect Avoidance Switches
(b)
(a)FPGACell
SRAMCell
FPGACell
SRAMCell
Laser Linking/Microsurgery Table • Table moves circuit under focused laser spot • Position done by laser interferometry: 0.02 micron positing • Microscope/TV system shows circuit • Electro-optical shutter gives control of laser pulse duration
Laser Direct Write Photomasks • Photomasks create the patterns used in microfabrication (IC’s) • Patterns projected on wafer to make circuits • Creation of regular masks expensive • Requires several exposure, development and etching steps • Created a direct laser write photomask • Put down ~15-100 nm film of Bismuth & Indium • When hit with laser turns transparent: change from 3OD to 0.2 OD • When laser hits Bi/In or Sn/In film creates transparent oxide
Quartz
BiIn
(a)
Converted
UnexposedArea
Converted
(b)
Exposure Illumination
(c)
Sputtered Bilayer
Laser Raster-Scanned
BiIn
ConvertedConverted
Bitmap file
X-Y Table X
Y
Laser BeamObjective Lens
Optical Shutter
input
output to control shutter
output to control X-Y table
0
0.5
1
1.5
2
2.5
3
3.5
1 10 100 1000 10000Laser Power (mW)
OD
(Sn/
In &
Bi/I
n @
365
nm)
Sn/In
Bi/In
Bimetallic Grayscale Photomasks Grayscale masks contain many gray levels When hits photoresist developed thickness function of exposure Can create 3D microfabricated devices (eg. Microoptics, MEMS) Better OD range and cheaper than existing grayscales
UnexposedArea
Converted
(d)
Exposure Illuminat ionLaser Exposure with Different Power
SnIn
SnIn
SnIn
(a)
Con verted
UnexposedArea
Converted
(b)
Exposure Illumination
(c)
Sputtered Bilayer
Laser Raster-Scanned
SnIn
ConvertedConverted
Quartz
(e) (f)
Wafer
Photor esist
3D struct ure on photoresist
0
0.5
1
1.5
2
2.5
3
3.5
0 50 100 150 200Laser Power (mW)
OD
(Sn/
In @
365
nm)
0
2000
4000
6000
8000
10000
12000
14000
25 75 125 175 225X (um)
Y (A
)
Low Power Laser Applications: Alignment & Measeurement Circularizing Laser Diodes
• Laser diodes are important for low power applications • But laser diodes have high divergence & asymmetric beams • Get 5-30o beam divergence • Start with collimator: high power converging lens: stops expansion • Then compensate for asymmetry • Use cylindrical lens beam expander • Cylindrical lenses: curved in one axis only unlike circular lenses • Expands/focuses light in one direction only (along curved axis) • Results in circular collimating beam
Quadrature Detectors for Alignment • Often put detector on object being aligned to laser • Use 4 quadrant detector Silicon photodiode detector • Expand beam so some light in each quadrant • Amount of photocurrent in each quadrant proportional to light • Detect current difference of right/left & top bottom • Higher current side has more beam • Perfect alignment null current for both sides
Laser Leveling • Lasers used to project lines of light • Accuracy is set by the level of the beam source • Used in construction projects: lines and cross lines • Get vertical and horizonal • Laser diodes give low cost levels now • More complex: reflect light back from object • Make certain light is reflected along the same path • Called Autocolation
Laser Size Gauging • Gauging is measuring the size of objects in the beam • Simplest expand beam the refocus • Object (eg sphere) in beam reduces power • Estimate size based on power reduction • More accurate: scanning systems • Scan beam with moving mirror (focused to point) • Then measure time beam is blocked by object • Knowing scan range then measure size of object
Laser & Linear Detector Array • Use laser diode to illuminate a linear or 2D detector array • Laser diode because creates collimated beam • Expand beam to fill area • Image is magnified or shrunk by lens • Use pixel positions to determine object profile • Low cost pixel arrays makes this less costly to gage scanners
Laser Scanner to Detect Surface Defects • Laser beam scanned across surface of reflective (eg metal) sheets • Detect reflected light • Flaws result in reduce or increase light • Timing (when scanning) determines defect size • Instead of spot use cylindrical expander to beam line of light • Moving sheet (eg metal, glass, paper) crosses beam • Use line or 2D images to detect changes • Use both reflection and transmission depending on material • Transmission can detect changes in thickness or quality
Bar Code Scanners • Diode laser now widely used in Bar code scanners • Typically use two axis scanner • Laser beam reflected from mirror on detector lens • Bar code reflected light comes back along same path • Detect rising and falling edge of the pattern • Note: have the laser beam & return light on same path • Use small mirror or beam splitter to put beam in path
Laser Triangulation • Lasers aimed at precise angles depth/profiles using triangulation • Single spot for depth measurement • Laser spot focused by lens onto detector array • Change in laser spot depth position Δz • Gives change in position Δz’ at detector • Change set by magnification caused by lens • θ laser to lens angle • φ angle between detector an lens axis • Resulting equations
zsinsinmz Δ
φθΔ ⎟
⎠
⎞⎜⎝
⎛=′
• Get real time measurement of distance changes
Laser Profileometry • Use cylindrical lens to create line of laser light • Use 2D detector array (imager) & lens to observe line • If object is moving get continuous scan of profile • Problems: Background light eg sunlight • Changes in surface reflectance makes signal noisy • Eg log profileometry for precise cutting of logs • Problem is log surface changes eg dark knots, holes
Lidar • Laser equivalent of Radar (RAdio Detection And Ranging) • LIDAR: LIght Detection And Ranging • Can use pulses & measure time of flight (like radar) • But only hard to measure <10-10 sec or 3 cm • Better phase method • Modulate the laser diode current with frequency fm • Then detector compares phase of laser to detector signal • Phase shift for distance R is
( ) mmm
fcandR22 λλπφ ==
• Then the distance is
φπ mf4cR =
• If > modulation wavelength λm need to get number of cycles • In extreme phase changes in the laser light • That requires a very stable (coherent) laser: HeNe not diode
Laser Heat Processing: Advantages • Laser radiation very "clean" no containments with other materials • Working atmosphere can be controlled as needed • Lasers can be focused to small spots very localized heating at very high power • Careful control of heating power • Beam easy to direct into hard to access points Can pass beam through glass to isolated areas • Energy generally deposited near the surface
General Heat Flow • Laser heating is just like other heat flow problems • For the time being assume heat source note that this is not always possible for laser • Heat flows by Fourier Law of Heat Conduction
TkAxTkAQ ∇−=
∂∂
−=
where Q = heat generated: Watts (some books use H) k = Thermal conductivity W/moC or W/cmoC heat flow per unite area per unite distance A = cross sectional area T = temperature in oC z = depth into the material • This is actually the definition of thermal conductivity • Note this assumes steady state conditions • laser heating stabilizes in 10-12 to 10-13 sec Thus assume steady state conditions
Thermal Values of Materials • Thermal Conductivity changes with temperature Hence k may change with position Specific Heat • When heat enters a volume temperature change depends Specific Heat C of material, J/kg/oK • Specific Heat determine how much heat needed to raise temperature of unit mass one degree C. Density • Density of material ρ Kg/m3 Latent Heats • Latent heats give the energy required for a phase change unites of J/kg • Lf Latent Heat of Fusion: energy for melting • Lv Latent Heat of Vaporization: energy to vaporize
Basic Heat Flow Differential Equations • let q. be the energy deposited per unit volume (use H in some books) W/m3 • Consider heat flowing through a volume • Then: energy at left face = change in internal energy + energy out right face • Then energy per unit time in left face (Fourier’s law)
xTkAqx ∂
∂−=
• Thermal Conductivity k W/m/oK • If uniform k, steady state get Newton’s Law of Cooling
xTkAqx Δ
Δ−=
• Hence can calculate heat loss if know thermal conductivity
Thermal Values of Materials • Thermal Conductivity changes significantly with materials • Inverse of thermal conductivity like resistance in electric circuit • Newton heat flow means slope of conductive varies as 1/k
kAq
xT x−=
ΔΔ
• In construction use R values, which are 1/k but in British units hr-ftoF/BTU • Higher the R the less heat flow
Basic Heat Flow Differential Equations • Now consider heat flowing through a volume • In the general case there q deposited and q generated within • Then: energy at left face + heat generated = change in internal energy + energy out right face • Energy per unit time in left face
xTkAqx ∂
∂−=
• Energy out of right face of x+dx is
⎥⎦⎤
⎢⎣⎡
⎟⎠⎞
⎜⎝⎛
∂∂
∂∂
+∂∂
−=∂
∂+=+ dx
xTk
xxTkAdx
xqqq x
xdxx
• Energy generated within the element per unite volume & time
Adxqqgen &=
• Change (loss) in internal energy due to heating of material
dxtTCAq ernalint ∂
∂= ρ
Basic Heat Flow Differential Equations • Thus writing the energy balance
dxxernalintgenx qqqq ++=+
⎥⎦⎤
⎢⎣⎡
⎟⎠⎞
⎜⎝⎛
∂∂
∂∂
+∂∂
−∂∂
=+∂∂
− dxxTk
xxTkAdx
tTCAAdxq
xTkA ρ&
• Combining gives heat flow DE
tTCq
xTk
x ∂∂
=+⎟⎠⎞
⎜⎝⎛
∂∂
∂∂ ρ&
• If assume thermal conductivity constant with position then
tT1
kq
xT2
2
∂∂
=+∂∂
α&
• where α Thermal Diffusivity in m2/s
Ck
ρα =
α Thermal Diffusivity • Thermal Diffusivity gives T rise caused by an applied heat pulse or how rapidly heat diffuses through the material • High thermal diffusivity: low surface temperature rise deep penetration of heat pulse • Low thermal diffusivity: high surface temperature rise
• In three dimensional the heat flow DE becomes
tT1
kqT2
∂∂
=+∇α
&
• Use ∇2 for coordinate system that notes symmetry of problem • For Cartesian
2
2
2
2
2
22
zT
yT
xTT
∂∂
+∂∂
+∂∂
=∇
• Often useful to use cylindrical coordinates for laser • Example laser spots are circularly symmetric • As angle is often uniform reduces from 3D to 2D problem values • Reduces to a problem in radius and depth • But must use proper cylindrical polar equations to get right
2
2
22
2
2
22 11
θ∂∂
+∂∂
+∂∂
+∂∂
=∇T
rzT
rT
rrTT
Temperature Change for Uniform Illumination • Assume that the surface is uniformly illuminated by the laser • Energy absorbed at the surface in a very small depth
H=I(1-R)
where R = reflectivity I = light intensity • The heat DE has been solved for depth z and time t (by Carslaw & Jaeger, 1959)
⎥⎦
⎤⎢⎣
⎡=Δ
t2zierfct
kH2)t,z(T
αα
• The ierfc is the integral of the complementary error function
Error Function Related Equations • Heat flow equations are related to the Error Function erf
dse2)x(erfx
0
s2
∫ −=π
• This is the integral of a Gaussian between 0 and x • The Complementary Error Function erfc
( ) ( )xerf1xerfc −=
• erfc is the error function but integred from x to infinity • The ierfc is related to the error function by
( ) ( ) ( ) ( )[ ]xerf1xxexp1dsserfcxierfc 2x
−−−== ∫∞ π
• ierfc(1) = 0.05 and is falling rapidly
Useful Error Function Approximations • Error function erf(x), Complementry Error Function erfc(x) are
dse2)x(erfx
0
s2
∫ −=π
dse2)x(erf1)x(erfcx
s2
∫∞
−=−=π
• erf(x) hard to find but easy to approximate with
( ) 232
2211)( xetatataxerf −++−=
47047.01
1=
+= pwhere
pxt
a1 = 0.3480242, a2 = -0.0958798, a3 = 0.7478556 • See Abramowitz & Segun (Handbook of Mathematical Functions) • Error on this is < 2.5x10-5 for all x • We are using complementary error function
erfc(x) = 1 - erf(x) erfc(0) = 1 erfc(∞) = 0
• Approximation has <2% error for x << 5.5 • For x > 5.5 use asymptotic approximation
∞→⎥⎦⎤
⎢⎣⎡ −→
−
xasx211
xe)x(erfc 2
x2
π
• Excel & Quatropro spreadsheet have erf() and erfc() built in. Must activate analysis toolpack & solver first but become inaccurate for x>5.4 – then use asymptotic • For x > 5.4 then ierfc(x) becomes
∞→→−
xasx2e)x(ierfc 2
x2
π
Temperature Rise for Uniform Illumination • From DE solution since ierfc is small for x>1 • Thus find that T rise is small when
1t2
z>
α
• Hence small rise when t4z2 α>
• Heat will diffuse a depth L in time of order
α4Lt
2
=
• Change in surface temperature with time substitute z = 0 and note
( )π10ierfc =
• Thus surface temperature change is:
[ ]π
αα tkH20ierfct
kH2)t,0(T ==Δ
• Thus temp increases with tα
Temperature Change with Finite Time Laser Pulse • If have a square pulse of duration tp • The for t < tp follow the previous formula • For Time greater than the pulse
( ) ( ) ( )ptt tt,zTt,zTt,zTp
−−=Δ > δδ
• eg. Consider Cooper with H = 1010 W/m2 for tp = 10-6 sec • From table α = 1.16x10-4 m2/s • T rises highest at surface (z=0) and changes fastest • At pulse end heat has diffused about L
m10x15.2)10)(10x16.1(4t4L 564 −−− =≈≈ α • At depth peak T occurs much later, and lower values
Laser Focused into a Spot • If laser focused into uniform spot radius a then formula changes to (by Carslaw & Jaeger, 1959)
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡ +−⎥
⎦
⎤⎢⎣
⎡=Δ
t2azierfc
t2zierfct
kH2)t,z(T
22
ααα
• Term on right caused by sideways diffusion • At the centre of the spot (z = 0 )
⎭⎬⎫
⎩⎨⎧
⎥⎦
⎤⎢⎣
⎡−=Δ
t2aierfc1t
kH2)t,z(T
απα
• This gives same as uniform heating if
1t2
aierfc <<⎥⎦
⎤⎢⎣
⎡α
• This is true for ierfc(>1) thus
α4at
2
<
• eg for Copper with a = 1 mm and α = 1.16x10-4 m2/s, ( )
( ) s10x16.2tor10x16.14
10t 34
23−
−
−
<<
Laser Focused into a Spot • As t goes to infinity (very long times) it can be shown
( ) [ ]zazkHt,zT 22 −+=Δ
• Thus for finite spot temperature reaches a limit • Highest surface temp
( )k
Ha,0T =∞Δ
• Effects of beam Gaussian distribution is not that different • In practice as thermal conductivity k, reflectance R, thermal diffusivity α all vary with temperature • Thus tend to use numerical simulations for real details
Example Focused Laser Spot Calculation
Phase Changes and Energy Balance • Energy Balance: Energy in = Energy to raise temp + heat flow
• Note: a rough rule of thumb if near steady state half the energy goes into heat flow so energy required is twice that to raise temperature • As heating increase will get melting of the surface • Eventually also get vaporization point • All requires energy to heat • In general the specific heat of the material changes Cs = specific heat of solid Cl = specific heat of liquid phase Lf = Latent Heat of Fusion: energy for melting Lv = Latent Heat of Vaporization: energy to vaporize • Energy required to melt a unite volume of material
( )[ ]fmsm LTTCE +−= ρ where Tm is the melting point, T the starting temp. ρ = density of material • Note: this does not include energy lost to heat flow
Phase Changes and Energy Balance • When vaporization occurs
( ) ( )[ ]vfmvvmsv LLTTCTTCE ++−+−= ρ
• Generally true that heat capacity does not change much with T
CCC vm ≈≈
• Generally Latent heat of vapourization >heat of fusion vf LL <
• Vapourization temperature is much > base or melting T<Tm<Tv
• Energy input required is approximately
( )vvv LCTE +≈ ρ