Hidden defects in printed circuit bare boardsare exposed by heat diffusion performance

International Journal of Electronics and Communication Engineering AND COMMUNICATION0976 –
INTERNATIONAL JOURNAL OF ELECTRONICS & Technology (IJECET), ISSN
6464(Print), ISSN 0976 – 6472(Online) Volume& Issue 3, October- December (2012), © IAEME
ENGINEERING 3, TECHNOLOGY (IJECET)

ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 3, Issue 3, October- December (2012), pp. 08-13 IJECET
© IAEME: www.iaeme.com/ijecet.asp
Journal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEME
www.jifactor.com

HIDDEN DEFECTS IN PRINTED CIRCUIT BARE BOARDS
ARE EXPOSED BY HEAT DIFFUSION PERFORMANCE

Yair Dankner
Industrial Engineering and Management department,
Shenkar College of Engineering and Design, 12 Anna Frank Street, Ramat Gan 52526,
Israel e-mail: yairdan@ shenkar.ac.il; yairdan@zahav.net.il.

Manuscript received September 3, 2012 and Accepted on October 22nd, 2012

ABSTRACT

A light source or an oven is used for several seconds to force a heat gradient along a buried
channel in printed circuit board. Then, it is let to cool while we analyze the emitted heat through
end points to expose the hidden defects. The heat diffusion equation is used numerically for a
common defect to predict the electric current flow by means of thermal current flow. This
patented method is a novel non contact optical inspection, to challenge the market demand for
miniaturization with efficiency.

Index Terms-Diffusion processes, Circuit analysis, Circuit faults, Printed circuits.

I. INTRODUCTION

Printed circuit boards (PCBs) contain copper channels buried in an insulating reinforced resin
[1]. The manufacturing process, based on chemical and pressing activities creates defects and
impurities [2]. The frequent defects are: (i) "open circuit” where a zone was over etched and the
gap was filled by the resin (cut type). (ii) Short-circuit between two channels and (iii) current
leakage to adjacent channel.

One of the testing methods is the long time preparation 'bed of nails' [3] which fails if pads are

.

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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME

too close to each other. 'Flying probe' method uses just two nails and closer spatial distance [4].
'Automated optical inspection' combined with infrared and X-ray image processing, can examine
the channels from underneath but, before pressing. Defects occurred after pressing adversely
affects the method.

II. THE IDEA AND PRIMARY DISCUSSION
Patented innovative non contact testing method [5] is introduced to analyze the bare PCB. Bed
of nails and flying probe techniques operate according to Ohms law,
A ∆V
I= (V 2 - V1 ) = (1)
ρl R

Where I is the current of electrons, A is the cross-sectional area, ρ is the resistivity, ℓ is the
length, R is the resistance and ∆V is the voltage gradient across the channel.
Newton’s law of cooling,
A
H= (T 2 - T1 ) (2)
rl

Has similar behavior. H is the current of heat, A is the cross-sectional area, ‫ ݎ‬is the thermal
resistivity, ℓ is the length and ∆T is the temperature gradient across the channel. The
thermoelectric effect links between those two. The one dimensional heat diffusion equation
(developed from eq. 2) with no additional heat source or heat sink is,
α 2 T xx = Tt (3)

ߙଶ is the thermal diffusivity coefficient along the channel and varies whenever a defect is
present. ܶ௫௫ is the second partial derivative of the temperature with respect to ‫ ݔ‬coordinate along
the channel and ܶ௧ is the first partial derivative of temperature with respect to time. ߙ ଶ=݇/‫ߩݏ‬
where ݇ is the thermal conductivity, ‫ ݏ‬is the specific heat and ߩ is the density.
We create a thermal current across the channel, analyze it, and predict the appropriate electric
current. Defects will affect the heat flow along the channel. This article displays basic
simulations produced by solving numerically the one and two dimensional heat diffusion
equations for homogeneous copper channel with a cut type defect only (over etching). The two
and three dimensions can handle as well: (i) the leakage of heat to the insulating resin, (ii) a
channel that has one entrance but few outlets, (iii) a channel with varying dimensions, (iv) a heat
sink. Other questions and possible solutions are: (i) if one end point does not reach the PCB’s
surface, we can attach an adequate “wire leg” to conduct the heat to the surface, (ii) if exposed
channels loose heat rapidly, we can force a heat from above or contrary, create a “thermal
blanket” via some insulating foam to be removed after measurement.

III. CHARACTERIZING THE CUT TYPE DEFECT ZONE – "DEFECT"
How does the defect behave with respect to electric and heat currents? What is its estimated
diffusivity coefficient value? A rectangular shaped copper channel 100 mm long and 0.1 mm2
cross sectional area with no defect will yield negligible resistance (0.01 Ω). If we consider that
the defect carries less than 10 Ω resistance, beyond which the channel is out of order, then the
defect looks like two resistors, resin and copper, connected in parallel or in series. Its length

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along the channel (‫ )ݔ‬can be less than 1 µm or more than 1 mm. For example, if this zone has a
length of 1 mm and it behaves like two resistors connected in parallel then the equivalent
resistance is that of the squeezed etched copper film whose cross sectional area decreases to
about 1 µm over 1 µm. Electrons migrate via the metallic film but phonons via the resin which
occupies almost the whole cross sectional area of the deformed zone. Thermal diffusivity
coefficient in that zone is expected to be 0.001-0.01 cm2/sec which is in the range of the
insulating materials. Why? hot electrons, which carry most of the thermal heat along the copper
channel (free of defects), find themselves bumping on each other when penetrating the thin
metallic film (defect) thus, loosing crucial part of their thermal energy to the surrounding resin
(electric current however, is not influenced by the overwhelmed hot electrons as their charge is
thermal independent). If the zone behaves like two resistors connected in series then resin or
adhesive had contaminated the zone and created tiny impurity balls. For example, a tiny impurity
ball whose radius is 30 Å distributed along 1 µm or 1 mm zone yields the 10 Ω resistance.

IV. THE SIMULATION SET-UP
Modulated light is focused on a pad for several seconds creating a heat pulse that will
propagate and will be emitted at the other side. The heat transfer function of the channel is
created. An oven is another way to simultaneously absorb rapidly heat inside the channels
(copper and resin thermal resistivities differ by about 4 orders of magnitude). After several
seconds, the channels are allowed to cool.

V. NUMERICAL RESULTS
A one-dimensional 10 cm long channel was heated by an oven from 20°C to 60°C for 5
seconds. Then, it was let to cool while emitting its extra heat through its end sides for 2 seconds.
Fig. 1 shows the temperature versus time for the left end (line) and the right end (line with
circles). It possesses a cut type defect zone of 60 µm length located 9 cm from left end. The
diffusivity coefficients of the copper and the cut type zone were taken as 1.14 and 0.01 cm2/sec
respectively. The plots are linked after 0.9 seconds. Linkage time depends on defect size and
location.
A one dimensional 1 cm long channel was heated at its left side by a laser to 120°C for 0.1 sec
(Fig. 2). The temperature behavior at the right end side was analyzed twice: once without any
defect (line) and once with a 60 µm length cut type defect zone located at the center of the
channel (line with squares). The plots are linked after 0.45 sec. Linkage time depends on defect
size and location. If the input temperature is modulated to a sinusoidal form with frequency les
then 0.1 Hz (centered at 80°C with amplitude of 25°C), the emitted heat will have a sinusoidal
form as well. Enlarging the channel length results in decreasing the modulated frequency. The
heat current velocity along the channel depends upon the temperature gradient across the
channel, its duration at the entrance and the existence of defects and impurities. 100°C input
temperature for 0.5-2 seconds duration on a channel with no defects will yield a velocity of 4-10
cm/sec. This behavior can be explained by the fact that thermal conductivity (݇) increases with
increasing temperature since the average velocity of hot electrons increases and therefore the
forward transport of heat increases. However, it adversely affects the electrical conductivity (σ)
because collisions divert the electrons from forward transport of charge. ݇/σ is proportional to the

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temperature according to Wiedemann-Franz law [6].

A two-dimensional channel: 0.02 cm width and 10 cm long, embedded in between substrate
layers of 0.2 cm, was heated by an oven to 60°C for 5 seconds and then was let to cool for 10
seconds. It possesses a cut type defect zone of 100 µm length located 8 cm from left side. The
diffusivity coefficient in the defect zone as well in the substrate was taken as 0.001 cm2/sec. Fig.
3 shows the temperature distribution along the channel after 5 seconds of heating (line) and after
10 seconds of cooling (dots) where the temperature difference between end points is ∆T=2°C.
∆T depends linearly on oven's temperature and channel's width. The cooling rate depends on
defect size and location.

Fig. 1. Temperature (°C) versus cooling time (sec) analyzed at both end sides of a 10 cm long
one dimensional channel with a cut type defect length of 60 µm located 9 cm from left side.

Fig. 2. Temperature versus time analyzed at the right end side of a 1 cm long one dimensional
channel with and without a defect. The cut type defect zone has a length of 60 µm located at the
center. The left end side was heated with a laser to 120°C for 0.1 sec.

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Fig. 3. Temperature distribution along a 10 cm long two dimensional channel whose width is
0.02 cm. A cut type defect zone of 100 µm length is located 8 cm from left side. The channel
was heated by an oven to 60°C for 5 sec (line) and then it was left to cool down for 10 sec (dots).

VI. EXPERIMENTAL RESULTS
An insulated copper cable 2.5 mm diameter and 236 cm length, made of 77 narrower 0.25 mm
diameter wires, was used. Both of its end sides were immersed in a cup filled with boiled water
for 1 minute. Then, the cup was removed and the temperature measurement at both end sides
almost coincide as expected. We repeat the process where now a defect zone was created by
cutting all the wires except one, along a 6.5 cm length located 9.5 cm from end side. The defect
tries to imitate an over etched channel. The temperature measurement at both end sides behaves
the same as shown for the one dimensional case in Fig. 1. One should notice the fact that electric
current resistance is negligible but the heat current is almost blocked therefore, a defect that
cannot be detected by means of electricity: Bed of nails or Flying probe.

VII. CONCLUSION
This method reveals defects by: (i) Comparing the heat flow rate at both end-sides with each
other with respect to different input heating criteria. (ii) Analyzing the channel's heat transfer
function. (iii) Comparing the heat current in a specified channel to that of a perfect one. (iv)
Spectral analysis of the emitted heat: (a) The emissivity of the coated pad depends on
temperature and wavelength. The temperature along the channel depends on phonons too
because heat in metals is carried by electrons (major) and phonons (minor). In addition, phonon
scattering by impurities and defects alter their wavelength. (b) Phonons create infrared radiation
around 10 µm (Wien’s law: λmaxT ≈3000 µm⋅K). With miniaturization demands, the channel's
width will gradually decrease to that range and it will behave like a waveguide, whose metallic
optical constants are wavelength dependent [7].

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REFERENCES
[1] R. S. Khandpur, Printed circuit boards: design, fabrication, assembly and testing, Tata-
McGraw Hill Education, New-Delhi, 2005.
[2] A. Kusiak and C. Kurasek, “Data mining of printed-circuit board defects”, IEEE Trans.
Robot. Autom., Vol. 91, pp. 191-196, Apr. 2001.
[3] Clyde F. Coombs, Printed Circuits Handbook, McGraw-Hill Handbooks, New York, 2007.
[4] M. Deaves, “On test (electronic device testing)”, IET Manuf. Eng., Vol. 82, pp.40-43, Oct.
2003.
[5] Yair Dankner, “Electric ultimate defects analyzer detecting all defects in PCB/MCM,” U.S.
Patent 7 877 217 B2, January 25, 2011.
[6] C. Kittel, Introduction to Solid State Physics, 5th Ed., John-Wiley, New York, 1976.
[7] Yair Dankner and A. Katzir, “Evanescent wave spectroscopy for the determination of the
optical constants of thin silver films deposited on a silver-halide fiber,” Appl. Opt. 36, 873
(1997).

Author Profile

Yair Dankner born in Haifa, Israel 15 August 1960. First, second and third degrees in Physics
in the Technion – Israel High Institute for Technology, Haifa, Israel. M.Sc in 1987 in the field of
fiber optic interferometer for measuring adsorption of hazardous gases. D.Sc in 1993 in the field
of optical gain in Multiple Quantum Wells. Post doc in Tel Aviv University, Tel-Aviv, Israel, in
the field of Silver-Halide fibers for industrial applications.

Yair was working in the field of optics in the Israeli Industry while teaching students in the
Israeli academy. Among his published articles are, (i) Yair Dankner, “Losses from single mode
fiber considered as a perturbation problem”, Applied Optics, vol. 34 (6), pp.1015-1018, 1995. (ii)
Yair Dankner, “Optical gain and saturation of photoexcited type-II superlattice”, Solid State
Communications, Vol. 93, No. 8, pp.707-712, 1995. (iii) Yair Dankner, O. Eyal and A. Katzir,
“Two bandpass fiberoptic radiometry for monitoring temperature of photoresist during dry
etching”, Appl. Phys. Lett., 68, pp.2583-85, Apr. 1996. Among his published patents are, (i) US
6481856 and (ii) US 7877217.

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Hidden defects in printed circuit bare boardsare exposed by heat diffusion performance

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