Measuring Joule heating and strain induced by electrical current with ...
JOURNAL OF APPLIED PHYSICS 109, 074908 (2011)
Measuring Joule heating and strain induced by electrical current with Moire´ interferometry Bicheng Chen and Cemal Basarana) Electronic Packaging Laboratory, State University of New York at Buffalo, 102 Ketter Hall, Buffalo, New York 14260, USA
(Received 22 October 2010; accepted 16 February 2011; published online 7 April 2011) This study proposes a new method to locate and measure the temperature of the hot spots caused by Joule Heating by measuring the free thermal expansion in-plane strain. It is demonstrated that the hotspot caused by the Joule heating in a thin metal film/plate structure can be measured by Phase shifting Moire´ interferometry with continuous wavelet transform (PSMI/CWT) at the microscopic scale. A demonstration on a copper film is conducted to verify the theory under different current densities. A correlation between the current density and strain in two orthogonal directions (one in the direction of the current flow) is proposed. The method can also be used for the measurement of the Joule heating in the microscopic solid structures in the electronic packaging devices. It is shown that a linear relationship exists between current density squared and C 2011 American Institute of Physics. [doi:10.1063/1.3565045] normal strains. V
I. INTRODUCTION
The insatiate demand for the miniaturization of the electronics imposes stringent requirements on the thermal and mechanical reliability of the electronic packaging. Interconnect and solder bumps are required to carry higher current densities because of the shrinking sizes of the devices. The Joule heating in the microelectronic packaging causes localized hot spots, which can be the precursor for damage initiation processes.1–3 Electromigration induced damage is accelerated due to the combined effects of the hot spot caused by the Joule heating and the current crowding.4–6 The current crowding is nonuniform distribution of current density, which leads to localized hotspot. The hot spots caused by the Joule heating can further introduce large temperature gradients causing thermomigration.5,7–10 Successfully identifying the hotspots in the interconnects can be critical to extending the lifetime of electronic devices, while enhancing the reliability of electronic packaging. At a microscopic scale, Joule heating involves an energy transfer from the moving electrons to the ions of metals. This is caused by scattering of the electrons and exacerbated by imperfections within the lattice structure (i.e., impurity atoms, vacancies, dislocations, grain boundaries, and lattice vibrations).11 The energy transferred to the ions is called Joule’s heating. The hotspot is generally caused by an irregularity of the electric field distribution, which can be identified by measuring the temperature difference before and after the change in the electric field. Since the hot spot-caused Joule Heating is a localized effect, it requires a microscopic fullfield temperature measurement instead of a macroscopic point probing method (for example, thermocouple or resistance temperature detection).12,13 Although several microscopic thermal imaging and measurement techniques were developed for measuring the temperature field (e.g., Liquid a)
Electronic mail: [email protected].
0021-8979/2011/109(7)/074908/7/$30.00
Crystal Thermography, Fluorescence Microthermography), only Infrared (IR) emission microscopy, Scanning Thermal Microscopy (SThM), and the PSMI/CWT based method (proposed in this study) show enough potential to identify the hotspot in the electronic packages.14–17 IR emission microscopy is one of the optical methods that is based on detecting the emitted radiation, reflected radiation, or stimulated radiation from the specimen.18 The researchers have successfully applied IR emission microscopy to study the localized hot spot induced by Joule heating.1,3,9,19 The resolution of IR emission microscopy is restricted by the diffraction limit of the emitted wave, which is typically k/2. The typical wavelength of the emitted wave for the solid material is around 10lm. The accurate emissivity of the material is required for the calculation of absolute temperature distribution. On the other hand, the contact methods based on Atomic Force Microscopy (AFM) are also available as SThM by replacing the tips of the AFM with a thermocouple, or thermister. SThM offers high resolutions and temporal responses.15,16,20,21 The scanning time for 50 by 50 lm2 is reported in the order of 3 mins, with 200 lines/ 50lm resolution. Scanning Joule Expansion Microscopy (SJEM) was proposed to use AFM to map the change of topology of a surface with a polymer coating.22–24 Since the deformation of the polymer coating is caused by the temperature difference, the surface temperature can therefore be inferred. Compared with SThM, no temperature sensing tips are required in SJEM. Nevertheless, all of the methods introduced above measure physical variables in order to infer the temperature, while the temperature difference can be used to determine the Joule heating effect. The objective of the paper is to establish a new method to identify the hot spots caused by Joule Heating by measuring the free thermal expansion in-plane strains. Strainbased temperature sensing has been applied before using fiber-optics,25,26 and the Moire´ interferometry has been widely used for full field strain analysis of microelectronic
109, 074908-1
C 2011 American Institute of Physics V
Downloaded 11 Apr 2011 to 128.205.114.91. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
074908-2
B. Chen and C. Basaran
J. Appl. Phys. 109, 074908 (2011)
packaging.11,27–30 The operational theory and methodology for full-field in-plane strain measurement of Phase Shifting Moire´ Interferometry with Continuous Wavelet Transform (PSMI/CWT) are explained in the Ref. 31. In principle, the Joule heating leads to nonuniform temperature field which creates a nonuniform strain field. Because PSMI/CWT is only sensitive to the in-plane strain, the hot spots in the thin metal film/plate can be identified by strain patterns. PSMI/CWT can identify the hot spots with a resolution of 50lm. This theory is also verified by a finite element study on a thin metallic film/plate. The experimental demonstration was carried out on a copper film because copper is the most common metal for electronics. ABAQUSV finite element software was used for validation. The strain distributions were measured under different electrical current levels (i.e., 20A, 22A, and 24A). A regression model was built to find a relationship between the current density and the in-plane strain distribution. R
II. THEORETICAL BASIS OF THE MEASUREMENT TECHNIQUE
The formulation in this section establishes a relationship among current crowding, Joule heating, and the strain caused by these two effects. Poynting’s theorem states the conservation of energy for the electromagnetic field,32 as shown in Eq. (1): @U ~ ~ ~ ~ þ r S þ Jf E ¼ 0; @t
(1)
~ is the electrical field, S~ is where J~f is the current density, E the Poynting vector, and U is the energy density. Considering low frequency direct current (DC) cases, Poynting vector S~ contributes no change to the energy density; we can define Joule heating from Eq. (1): @U ~ ~ ¼ Jf E: Qj ¼ @t
(2)
Considering the linear relationship between the electric field ~ and the current density J~f , Eq. (2) can be rewritten in terms E of the current density, as shown in Qj ¼ J~f
J~f ¼ q0 J~f J~f ; r0
(3)
~ r0 is the electrical conductivity and r0 where J~f ¼ r0 E, ¼ 1=q0 , q0 is the electrical resistivity. The heat conduction equation with heat generation is given by cq
@T ¼ kr2 T þ Q; @t
(4)
where c is the specific heat, q is the density, k is the thermal conductivity, T is the temperature field, and Q is the internal heat generation. The heat conduction equation Eq. (4) shows that the internal heat generation will cause the temperature gradient and the formation of a hot spot. The hot spot is defined as a
location with nonuniform elevated temperature, as compared with surrounding locations. The shape and range of the hot spot depends on several factors. Heat conduction equation due to an electric field is given by, cq
@T ¼ kr2 T þ q0 J~f J~f : @t
(5)
Most of the time, the surface of the solid is in contact with the environment. The boundary condition of the environmental convection33 is given by k
@T þ qb ¼ hc ðT HÞ; @~ n
(6)
where H is the ambient temperature, hc is the heat transfer coefficient, @=@~ n is the directional derivative of a scalar function along the normal direction, and qb is the heat generation on the boundary (which is the Joule heating in the scope of this paper). The temperature field inside the body of a solid caused by internal Joule heating, can be determined by solving the partial differential equation Eq. (5) with the boundary condition given in Eq. (6). The temperature field with a current crowding will exhibit elevated temperature around the area, which can be targeted as the hot spot. While the infrared microscopy uses the surface radiation to measure the temperature, the proposed method uses the strain field as a reference to measure the temperature field. The constitutive equation of thermoelasticity, building a relation between the temperature change and the strain distribution,33,34 is given by, (for a homogeneous, isotropic body.) 1 m rij rkk dij þ aDTdij ði; j ¼ 1; 2; 3Þ; eij ¼ 2G 1þm
(7)
where G is the shear modulus, m is the Poisson’s ratio, a is the coefficient of thermal expansion, DT is the temperature change, dij is the Kronecker’s symbol, rij , and eij are the stress and strain in the index notation, respectively. In order to make the in-plane strain reflect the temperature field, in-plane normal strain in Eq. (7) can be rewritten in the form as shown in Eq. (8). The normal strain can be used to identify the hot spots created by the Joule heating, as long as error given by Eq. (9) is very small. ei ¼ aDT þ ri ði ¼ 1; 2Þ
(8)
Ri ¼ ri =aDT
Measuring Joule heating and strain induced by electrical current with Moire´ interferometry Bicheng Chen and Cemal Basarana) Electronic Packaging Laboratory, State University of New York at Buffalo, 102 Ketter Hall, Buffalo, New York 14260, USA
(Received 22 October 2010; accepted 16 February 2011; published online 7 April 2011) This study proposes a new method to locate and measure the temperature of the hot spots caused by Joule Heating by measuring the free thermal expansion in-plane strain. It is demonstrated that the hotspot caused by the Joule heating in a thin metal film/plate structure can be measured by Phase shifting Moire´ interferometry with continuous wavelet transform (PSMI/CWT) at the microscopic scale. A demonstration on a copper film is conducted to verify the theory under different current densities. A correlation between the current density and strain in two orthogonal directions (one in the direction of the current flow) is proposed. The method can also be used for the measurement of the Joule heating in the microscopic solid structures in the electronic packaging devices. It is shown that a linear relationship exists between current density squared and C 2011 American Institute of Physics. [doi:10.1063/1.3565045] normal strains. V
I. INTRODUCTION
The insatiate demand for the miniaturization of the electronics imposes stringent requirements on the thermal and mechanical reliability of the electronic packaging. Interconnect and solder bumps are required to carry higher current densities because of the shrinking sizes of the devices. The Joule heating in the microelectronic packaging causes localized hot spots, which can be the precursor for damage initiation processes.1–3 Electromigration induced damage is accelerated due to the combined effects of the hot spot caused by the Joule heating and the current crowding.4–6 The current crowding is nonuniform distribution of current density, which leads to localized hotspot. The hot spots caused by the Joule heating can further introduce large temperature gradients causing thermomigration.5,7–10 Successfully identifying the hotspots in the interconnects can be critical to extending the lifetime of electronic devices, while enhancing the reliability of electronic packaging. At a microscopic scale, Joule heating involves an energy transfer from the moving electrons to the ions of metals. This is caused by scattering of the electrons and exacerbated by imperfections within the lattice structure (i.e., impurity atoms, vacancies, dislocations, grain boundaries, and lattice vibrations).11 The energy transferred to the ions is called Joule’s heating. The hotspot is generally caused by an irregularity of the electric field distribution, which can be identified by measuring the temperature difference before and after the change in the electric field. Since the hot spot-caused Joule Heating is a localized effect, it requires a microscopic fullfield temperature measurement instead of a macroscopic point probing method (for example, thermocouple or resistance temperature detection).12,13 Although several microscopic thermal imaging and measurement techniques were developed for measuring the temperature field (e.g., Liquid a)
Electronic mail: [email protected].
0021-8979/2011/109(7)/074908/7/$30.00
Crystal Thermography, Fluorescence Microthermography), only Infrared (IR) emission microscopy, Scanning Thermal Microscopy (SThM), and the PSMI/CWT based method (proposed in this study) show enough potential to identify the hotspot in the electronic packages.14–17 IR emission microscopy is one of the optical methods that is based on detecting the emitted radiation, reflected radiation, or stimulated radiation from the specimen.18 The researchers have successfully applied IR emission microscopy to study the localized hot spot induced by Joule heating.1,3,9,19 The resolution of IR emission microscopy is restricted by the diffraction limit of the emitted wave, which is typically k/2. The typical wavelength of the emitted wave for the solid material is around 10lm. The accurate emissivity of the material is required for the calculation of absolute temperature distribution. On the other hand, the contact methods based on Atomic Force Microscopy (AFM) are also available as SThM by replacing the tips of the AFM with a thermocouple, or thermister. SThM offers high resolutions and temporal responses.15,16,20,21 The scanning time for 50 by 50 lm2 is reported in the order of 3 mins, with 200 lines/ 50lm resolution. Scanning Joule Expansion Microscopy (SJEM) was proposed to use AFM to map the change of topology of a surface with a polymer coating.22–24 Since the deformation of the polymer coating is caused by the temperature difference, the surface temperature can therefore be inferred. Compared with SThM, no temperature sensing tips are required in SJEM. Nevertheless, all of the methods introduced above measure physical variables in order to infer the temperature, while the temperature difference can be used to determine the Joule heating effect. The objective of the paper is to establish a new method to identify the hot spots caused by Joule Heating by measuring the free thermal expansion in-plane strains. Strainbased temperature sensing has been applied before using fiber-optics,25,26 and the Moire´ interferometry has been widely used for full field strain analysis of microelectronic
109, 074908-1
C 2011 American Institute of Physics V
Downloaded 11 Apr 2011 to 128.205.114.91. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
074908-2
B. Chen and C. Basaran
J. Appl. Phys. 109, 074908 (2011)
packaging.11,27–30 The operational theory and methodology for full-field in-plane strain measurement of Phase Shifting Moire´ Interferometry with Continuous Wavelet Transform (PSMI/CWT) are explained in the Ref. 31. In principle, the Joule heating leads to nonuniform temperature field which creates a nonuniform strain field. Because PSMI/CWT is only sensitive to the in-plane strain, the hot spots in the thin metal film/plate can be identified by strain patterns. PSMI/CWT can identify the hot spots with a resolution of 50lm. This theory is also verified by a finite element study on a thin metallic film/plate. The experimental demonstration was carried out on a copper film because copper is the most common metal for electronics. ABAQUSV finite element software was used for validation. The strain distributions were measured under different electrical current levels (i.e., 20A, 22A, and 24A). A regression model was built to find a relationship between the current density and the in-plane strain distribution. R
II. THEORETICAL BASIS OF THE MEASUREMENT TECHNIQUE
The formulation in this section establishes a relationship among current crowding, Joule heating, and the strain caused by these two effects. Poynting’s theorem states the conservation of energy for the electromagnetic field,32 as shown in Eq. (1): @U ~ ~ ~ ~ þ r S þ Jf E ¼ 0; @t
(1)
~ is the electrical field, S~ is where J~f is the current density, E the Poynting vector, and U is the energy density. Considering low frequency direct current (DC) cases, Poynting vector S~ contributes no change to the energy density; we can define Joule heating from Eq. (1): @U ~ ~ ¼ Jf E: Qj ¼ @t
(2)
Considering the linear relationship between the electric field ~ and the current density J~f , Eq. (2) can be rewritten in terms E of the current density, as shown in Qj ¼ J~f
J~f ¼ q0 J~f J~f ; r0
(3)
~ r0 is the electrical conductivity and r0 where J~f ¼ r0 E, ¼ 1=q0 , q0 is the electrical resistivity. The heat conduction equation with heat generation is given by cq
@T ¼ kr2 T þ Q; @t
(4)
where c is the specific heat, q is the density, k is the thermal conductivity, T is the temperature field, and Q is the internal heat generation. The heat conduction equation Eq. (4) shows that the internal heat generation will cause the temperature gradient and the formation of a hot spot. The hot spot is defined as a
location with nonuniform elevated temperature, as compared with surrounding locations. The shape and range of the hot spot depends on several factors. Heat conduction equation due to an electric field is given by, cq
@T ¼ kr2 T þ q0 J~f J~f : @t
(5)
Most of the time, the surface of the solid is in contact with the environment. The boundary condition of the environmental convection33 is given by k
@T þ qb ¼ hc ðT HÞ; @~ n
(6)
where H is the ambient temperature, hc is the heat transfer coefficient, @=@~ n is the directional derivative of a scalar function along the normal direction, and qb is the heat generation on the boundary (which is the Joule heating in the scope of this paper). The temperature field inside the body of a solid caused by internal Joule heating, can be determined by solving the partial differential equation Eq. (5) with the boundary condition given in Eq. (6). The temperature field with a current crowding will exhibit elevated temperature around the area, which can be targeted as the hot spot. While the infrared microscopy uses the surface radiation to measure the temperature, the proposed method uses the strain field as a reference to measure the temperature field. The constitutive equation of thermoelasticity, building a relation between the temperature change and the strain distribution,33,34 is given by, (for a homogeneous, isotropic body.) 1 m rij rkk dij þ aDTdij ði; j ¼ 1; 2; 3Þ; eij ¼ 2G 1þm
(7)
where G is the shear modulus, m is the Poisson’s ratio, a is the coefficient of thermal expansion, DT is the temperature change, dij is the Kronecker’s symbol, rij , and eij are the stress and strain in the index notation, respectively. In order to make the in-plane strain reflect the temperature field, in-plane normal strain in Eq. (7) can be rewritten in the form as shown in Eq. (8). The normal strain can be used to identify the hot spots created by the Joule heating, as long as error given by Eq. (9) is very small. ei ¼ aDT þ ri ði ¼ 1; 2Þ
(8)
Ri ¼ ri =aDT
