Electromigration
Encyclopedia
Electromigration is the transport of material caused by the gradual movement of the ion
s in a conductor due to the momentum
transfer between conducting electron
s and diffusing metal atom
s. The effect is important in applications where high direct current densities are used, such as in microelectronics
and related structures. As the structure size in electronics
such as integrated circuit
s (ICs) decreases, the practical significance of this effect increases.
industry. One of the most important engineering studies was performed by Jim Black of Motorola
, after whom Black's equation
is named. At the time, the metal interconnects in ICs were still about 10 micrometre
s wide. Currently interconnects are only hundreds to tens of nanometers in width, making research in electromigration increasingly important.
, military purposes, anti-lock braking system
, medical equipment like Automated External Defibrillator
s and even computers or home entertainment systems, it is an important issue for economic and Human safety/survival reasons.
Due to difficulty of testing under real conditions, Black's equation
is used to predict the life span of integrated circuits.
To use Black's equation
, the component is put through high temperature operating life (HTOL) testing. The component's expected life span under real conditions is extrapolated
from data gathered during the testing.
Although electromigration damage ultimately results in failure of the affected IC, the first symptoms are intermittent glitches, and are quite challenging to diagnose. As some interconnects fail before others, the circuit exhibits seemingly random errors, which may be indistinguishable from other failure mechanisms (such as electrostatic discharge
damage). In a laboratory setting, electromigration failure is readily imaged with an electron microscope, as interconnect erosion leaves telltale visual markers on the metal layers of the IC.
With increasing miniaturization the probability of failure due to electromigration increases in VLSI
and ULSI circuits because both the power density and the current density increase. In advanced semiconductor manufacturing processes, copper
has replaced aluminium
as the interconnect material of choice. Despite its greater fragility in the fabrication process, copper is preferred for its superior conductivity. It is also intrinsically less susceptible to electromigration. However, electromigration (EM) continues to be an ever present challenge to device fabrication, and therefore the EM research for copper interconnects is ongoing (though a relatively new field).
A reduction of the structure (scaling) by a factor k increases the power density proportional to k and the current density increases by k2 whereby EM is clearly strengthened.
In modern consumer electronic devices, ICs rarely fail due to electromigration effects. This is because proper semiconductor design practices incorporate the effects of electromigration into the IC's layout. Nearly all IC design houses use automated EDA
tools to check and correct electromigration problems at the transistor layout-level. When operated within the manufacturer's specified temperature and voltage range, a properly designed IC device is more likely to fail from other (environmental) causes, such as cumulative damage from gamma-ray
bombardment.
Nevertheless, there have been documented cases of product failures due to electromigration. In the late 1980s, one line of Western Digital
's desktop drives suffered widespread, predictable failure 12–18 months after field usage. Using forensic analysis of the returned bad units, engineers identified improper design-rules in a third-party supplier's IC controller. By replacing the bad component with that of a different supplier, WD was able to correct the flaw, but not before significant damage to the company's reputation.
Electromigration can be a cause of degradation in some power semiconductor device
s such as low voltage power MOSFET
s, in which the lateral current through the source contact metallisation (often aluminium) can reach the critical current densities during overload conditions. The degradation of the aluminium layer causes an increase in on-state resistance, and can eventually lead to complete failure.
, characteristics of the passivation
and the interface to other materials also affect the durability of the interconnects. There are also grave differences with time dependent current: direct current
or different alternating current
forms cause different effects.
s affect ionized atom
s in a conductor. The direct electrostatic
force Fe as a result from the electric field therefore having the same direction. The force from the exchange of momentum with other charge carrier
s Fp showing toward the flow of charge carriers. In metallic conductors Fp is caused by a so-called "electron wind" or "Ion wind
".
The resulting force Fres on an activated ion in the electrical field is
Electromigration occurs when some of the momentum
of a moving electron is transferred to a nearby activated ion. This causes the ion to move from its original position. Over time this force knocks a significant number of atoms far from their original positions. A break or gap can develop in the conducting material, preventing the flow of electricity. In narrow interconnect conductors, such as those linking transistors and other components in integrated circuits, this is known as a void or internal failure open circuit
. Electromigration can also cause the atoms of a conductor to pile up and drift toward other nearby conductors, creating an unintended electrical connection known as a hillock failure or whisker failure (short circuit
). Both of these situations can lead to a malfunction of the circuit.
Diffusion processes caused by electromigration can be divided into grain boundary diffusion, bulk diffusion and surface diffusion. In general, grain boundary diffusion is the major electromigration process in aluminum wires, whereas surface diffusion is dominant in copper interconnects.
structure, the electrons moving through it would experience no collisions and electromigration would not occur. In real conductors, defects in the lattice structure and the random thermal vibration of the atoms about their positions causes electrons to collide with the atoms and scatter
, which is the source of electrical resistance (at least in metals; see electrical conduction). Normally, the amount of momentum imparted by the relatively low-mass
electrons is not enough to permanently displace the atoms. However, in high-power situations (such as with the increasing current draw and decreasing wire sizes in modern VLSI microprocessor
s), if many electrons bombard the atoms with enough force to become significant, this will accelerate the process of electromigration by causing the atoms of the conductor to vibrate further from their ideal lattice positions, increasing the amount of electron scattering
. High current density increases the number of electrons scattering against the atoms of the conductor, and hence the speed at which those atoms are displaced.
In integrated circuits, electromigration does not occur in semiconductor
s directly, but in the metal interconnects deposited onto them (see semiconductor device fabrication).
Electromigration is exacerbated by high current densities and the Joule heating
of the conductor (see electrical resistance
), and can lead to eventual failure of electrical components. Localized increase of current density is known as current crowding
.
where
is the atom concentration at the point with a coordinates 
at the moment of time 
, and 
is the total atomic flux at this location. The total atomic flux 
is a combination of the fluxes caused by the different atom migration forces. The major forces are induced by the electric current
, and by the gradients of temperature, mechanical stress
and concentration.
. Define the fluxes mentioned above. 
. Here 
is the electron
charge,
is the effective charge of the migrating atom, 
the resistivity
of the conductor where atom migration takes place,
is the local current density, 
is Boltzmann’s constant, 
is the absolute temperature. 
is the time and position dependent atom diffusivity. 
. We use 
the heat of thermal diffusion. 
here 
is the atomic volume and 
is initial atomic concentration
,
is the hydrostatic stress
and
are the components of principal stress. 
.
Assuming a vacancy mechanism for atom diffusion
we can express
as a function of the hydrostatic stress 
where 
is the effective activation energy
of the thermal diffusion of metal atoms. The vacancy concentration represents availability of empty lattice sites, which might be occupied by a migrating atom.
Here
is a constant based on the cross-sectional area of the interconnect, 
is the current density, 
is the activation energy
(e.g. 0.7 eV for grain boundary diffusion in aluminum),
is the Boltzmann's constant, 
is the temperature and 
a scaling factor (usually set to 2 according to Black). It is clear that current density 
and (less so) the temperature 
are deciding factors in the design process that affect electromigration.
The temperature of the conductor appears in the exponent, i.e. it strongly affects the MTTF of the interconnect. For an interconnect to remain reliable in rising temperatures, the maximum tolerable current density of the conductor must necessarily decrease.
s with silicon. However, it soon appeared that pure aluminium is susceptible to electromigration. Research shown adding 2-4% of copper to aluminium increases resistance to electromigration about 50 times. The effect is attributed to grain boundary segregation of copper, which greatly inhibits the diffusion of aluminium atoms across grain boundaries.
It is known that pure copper used for Cu-metallization is more electromigration-robust than aluminum. Copper wires can withstand approximately five times more current density than aluminum wires while assuming similar reliability requirements. This is mainly due to the higher electromigration activation energy levels of copper, caused by its superior electrical and thermal conductivity as well as its higher melting point. Further improvements can be achieved by alloying copper with about 1% palladium
, which, similar to copper in aluminium, inhibits diffusion of copper atoms along grain boundaries.
However, the maximum wire width possible for a bamboo structure is usually too narrow for signal lines of large-magnitude currents in analog circuits or for power supply lines. In these circumstances, slotted wires are often used, whereby rectangular holes are carved in the wires. Here, the widths of the individual metal structures in between the slots lie within the area of a bamboo structure, while the resulting total width of all the metal structures meets power requirements.
and contact holes, because generally the ampacity of a (tungsten) via is less than that of a metal wire of the same width.The current carrying capacity of a via is much less than a metallic wire of same length. Hence the use of multiple vias with proper geometrical orientation becomes indispensable. Hence multiple vias are often used, whereby the geometry of the via array is very significant: Multiple vias must be organized such that the resulting current is distributed as evenly as possible through all the vias.
Attention must also be paid to bends in interconnects. In particular, 90-degree corner bends must be avoided, since the current density in such bends is significantly higher than that in oblique angles (e.g., 135 degrees).
It causes a net atom transport along the direction of electron flow. The atoms pile up at the anode, voids are generated at the cathode and back stress is induced during electromigration. The typical failure of a solder joint due to electromigration will occur at the cathode side. Due to the current crowding effect, voids form first at the corner of the solder joint. Then the voids extend and cause a failed circuit. Electromigration also influences formation of intermetallic compounds.
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
s in a conductor due to the momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
transfer between conducting electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s and diffusing metal atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s. The effect is important in applications where high direct current densities are used, such as in microelectronics
Microelectronics
Microelectronics is a subfield of electronics. As the name suggests, microelectronics relates to the study and manufacture of very small electronic components. Usually, but not always, this means micrometre-scale or smaller,. These devices are made from semiconductors...
and related structures. As the structure size in electronics
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
such as integrated circuit
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...
s (ICs) decreases, the practical significance of this effect increases.
History
The phenomenon of electromigration has been known for over 100 years, having been discovered by the French scientist Gerardin. The topic first became of practical interest in 1966 when the first integrated circuits became commercially available. Research in this field was pioneered by a number of investigators throughout the fledgling semiconductorSemiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
industry. One of the most important engineering studies was performed by Jim Black of Motorola
Motorola
Motorola, Inc. was an American multinational telecommunications company based in Schaumburg, Illinois, which was eventually divided into two independent public companies, Motorola Mobility and Motorola Solutions on January 4, 2011, after losing $4.3 billion from 2007 to 2009...
, after whom Black's equation
Black's equation
Black's Equation is a mathematical model for the mean time to failure of a semiconductor circuit due to electromigration: a phenomenon of molecular rearrangement in the solid phase caused by an electromagnetic field....
is named. At the time, the metal interconnects in ICs were still about 10 micrometre
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...
s wide. Currently interconnects are only hundreds to tens of nanometers in width, making research in electromigration increasingly important.
Practical implications of electromigration
Electromigration decreases the reliability of chips ( integrated circuits (ICs) ). It can cause the eventual loss of connections or failure of a circuit. Since reliability is important for space travelSpace exploration
Space exploration is the use of space technology to explore outer space. Physical exploration of space is conducted both by human spaceflights and by robotic spacecraft....
, military purposes, anti-lock braking system
Anti-lock braking system
An anti-lock braking system is a safety system that allows the wheels on a motor vehicle to continue interacting tractively with the road surface as directed by driver steering inputs while braking, preventing the wheels from locking up and therefore avoiding skidding.An ABS generally offers...
, medical equipment like Automated External Defibrillator
Automated external defibrillator
An automated external defibrillator or AED is a portable electronic device that automatically diagnoses the potentially life threatening cardiac arrhythmias of ventricular fibrillation and ventricular tachycardia in a patient, and is able to treat them through defibrillation, the application of...
s and even computers or home entertainment systems, it is an important issue for economic and Human safety/survival reasons.
Due to difficulty of testing under real conditions, Black's equation
Black's equation
Black's Equation is a mathematical model for the mean time to failure of a semiconductor circuit due to electromigration: a phenomenon of molecular rearrangement in the solid phase caused by an electromagnetic field....
is used to predict the life span of integrated circuits.
To use Black's equation
Black's equation
Black's Equation is a mathematical model for the mean time to failure of a semiconductor circuit due to electromigration: a phenomenon of molecular rearrangement in the solid phase caused by an electromagnetic field....
, the component is put through high temperature operating life (HTOL) testing. The component's expected life span under real conditions is extrapolated
Extrapolation
In mathematics, extrapolation is the process of constructing new data points. It is similar to the process of interpolation, which constructs new points between known points, but the results of extrapolations are often less meaningful, and are subject to greater uncertainty. It may also mean...
from data gathered during the testing.
Although electromigration damage ultimately results in failure of the affected IC, the first symptoms are intermittent glitches, and are quite challenging to diagnose. As some interconnects fail before others, the circuit exhibits seemingly random errors, which may be indistinguishable from other failure mechanisms (such as electrostatic discharge
Electrostatic discharge
Electrostatic discharge is a serious issue in solid state electronics, such as integrated circuits. Integrated circuits are made from semiconductor materials such as silicon and insulating materials such as silicon dioxide...
damage). In a laboratory setting, electromigration failure is readily imaged with an electron microscope, as interconnect erosion leaves telltale visual markers on the metal layers of the IC.
With increasing miniaturization the probability of failure due to electromigration increases in VLSI
Very-large-scale integration
Very-large-scale integration is the process of creating integrated circuits by combining thousands of transistors into a single chip. VLSI began in the 1970s when complex semiconductor and communication technologies were being developed. The microprocessor is a VLSI device.The first semiconductor...
and ULSI circuits because both the power density and the current density increase. In advanced semiconductor manufacturing processes, copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
has replaced aluminium
Aluminium
Aluminium or aluminum is a silvery white member of the boron group of chemical elements. It has the symbol Al, and its atomic number is 13. It is not soluble in water under normal circumstances....
as the interconnect material of choice. Despite its greater fragility in the fabrication process, copper is preferred for its superior conductivity. It is also intrinsically less susceptible to electromigration. However, electromigration (EM) continues to be an ever present challenge to device fabrication, and therefore the EM research for copper interconnects is ongoing (though a relatively new field).
A reduction of the structure (scaling) by a factor k increases the power density proportional to k and the current density increases by k2 whereby EM is clearly strengthened.
In modern consumer electronic devices, ICs rarely fail due to electromigration effects. This is because proper semiconductor design practices incorporate the effects of electromigration into the IC's layout. Nearly all IC design houses use automated EDA
Electronic design automation
Electronic design automation is a category of software tools for designing electronic systems such as printed circuit boards and integrated circuits...
tools to check and correct electromigration problems at the transistor layout-level. When operated within the manufacturer's specified temperature and voltage range, a properly designed IC device is more likely to fail from other (environmental) causes, such as cumulative damage from gamma-ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
bombardment.
Nevertheless, there have been documented cases of product failures due to electromigration. In the late 1980s, one line of Western Digital
Western Digital
Western Digital Corporation is one of the largest computer hard disk drive manufacturers in the world. It has a long history in the electronics industry as an integrated circuit maker and a storage products company. Western Digital was founded on April 23, 1970 by Alvin B...
's desktop drives suffered widespread, predictable failure 12–18 months after field usage. Using forensic analysis of the returned bad units, engineers identified improper design-rules in a third-party supplier's IC controller. By replacing the bad component with that of a different supplier, WD was able to correct the flaw, but not before significant damage to the company's reputation.
Electromigration can be a cause of degradation in some power semiconductor device
Power semiconductor device
Power semiconductor devices are semiconductor devices used as switches or rectifiers in power electronic circuits . They are also called power devices or when used in integrated circuits, called power ICs....
s such as low voltage power MOSFET
Power MOSFET
A Power MOSFET is a specific type of metal oxide semiconductor field-effect transistor designed to handle significant power levels. Compared to the other power semiconductor devices , its main advantages are high commutation speed and good efficiency at low voltages...
s, in which the lateral current through the source contact metallisation (often aluminium) can reach the critical current densities during overload conditions. The degradation of the aluminium layer causes an increase in on-state resistance, and can eventually lead to complete failure.
Fundamentals
The material properties of the metal interconnects have a strong influence on the life span. The characteristics are predominantly the composition of the metal alloy and the dimensions of the conductor. The shape of the conductor, the crystallographic orientation of the grains in the metal, procedures for the layer deposition, heat treatment or annealingAnnealing (metallurgy)
Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the recrystallization temperature, maintaining a suitable temperature, and...
, characteristics of the passivation
Passivation
Passivation is the process of making a material "passive", and thus less reactive with surrounding air, water, or other gases or liquids. The goal is to inhibit corrosion, whether for structural or cosmetic reasons. Passivation of metals is usually achieved by the deposition of a layer of oxide...
and the interface to other materials also affect the durability of the interconnects. There are also grave differences with time dependent current: direct current
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
or different alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
forms cause different effects.
Forces on ions in an electrical field
Two forceForce
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
s affect ionized atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s in a conductor. The direct electrostatic
Electrostatics
Electrostatics is the branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges....
force Fe as a result from the electric field therefore having the same direction. The force from the exchange of momentum with other charge carrier
Charge carrier
In physics, a charge carrier is a free particle carrying an electric charge, especially the particles that carry electric currents in electrical conductors. Examples are electrons and ions...
s Fp showing toward the flow of charge carriers. In metallic conductors Fp is caused by a so-called "electron wind" or "Ion wind
Ion wind
Ion wind, ionic wind, or coronal wind is a stream of ionized fluid generated by a strong electric field. Francis Hauksbee, curator of instruments for the Royal Society of London, made the earliest report of electric wind in 1709...
".
The resulting force Fres on an activated ion in the electrical field is
Electromigration occurs when some of the momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
of a moving electron is transferred to a nearby activated ion. This causes the ion to move from its original position. Over time this force knocks a significant number of atoms far from their original positions. A break or gap can develop in the conducting material, preventing the flow of electricity. In narrow interconnect conductors, such as those linking transistors and other components in integrated circuits, this is known as a void or internal failure open circuit
Open circuit
The term Open circuit may refer to:*Open-circuit scuba, a type of SCUBA-diving equipment where the user breathes from the set and then exhales to the surroundings without recycling the exhaled air...
. Electromigration can also cause the atoms of a conductor to pile up and drift toward other nearby conductors, creating an unintended electrical connection known as a hillock failure or whisker failure (short circuit
Short circuit
A short circuit in an electrical circuit that allows a current to travel along an unintended path, often where essentially no electrical impedance is encountered....
). Both of these situations can lead to a malfunction of the circuit.
Diffusion mechanisms
In a homogeneous crystalline structure, because of the uniform lattice structure of the metal ions, there is hardly any momentum transfer between the conduction electrons and the metal ions. However, this symmetry does not exist at the grain boundaries and material interfaces, and so here momentum is transferred much more vigorously. Since the metal ions in these regions are bonded more weakly than in a regular crystal lattice, once the electron wind has reached a certain strength, atoms become separated from the grain boundaries and are transported in the direction of the current. This direction is also influenced by the grain boundary itself, because atoms tend to move along grain boundaries.Diffusion processes caused by electromigration can be divided into grain boundary diffusion, bulk diffusion and surface diffusion. In general, grain boundary diffusion is the major electromigration process in aluminum wires, whereas surface diffusion is dominant in copper interconnects.
Thermal effects
In an ideal conductor, where atoms are arranged in a perfect latticeCrystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
structure, the electrons moving through it would experience no collisions and electromigration would not occur. In real conductors, defects in the lattice structure and the random thermal vibration of the atoms about their positions causes electrons to collide with the atoms and scatter
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
, which is the source of electrical resistance (at least in metals; see electrical conduction). Normally, the amount of momentum imparted by the relatively low-mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
electrons is not enough to permanently displace the atoms. However, in high-power situations (such as with the increasing current draw and decreasing wire sizes in modern VLSI microprocessor
Microprocessor
A microprocessor incorporates the functions of a computer's central processing unit on a single integrated circuit, or at most a few integrated circuits. It is a multipurpose, programmable device that accepts digital data as input, processes it according to instructions stored in its memory, and...
s), if many electrons bombard the atoms with enough force to become significant, this will accelerate the process of electromigration by causing the atoms of the conductor to vibrate further from their ideal lattice positions, increasing the amount of electron scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
. High current density increases the number of electrons scattering against the atoms of the conductor, and hence the speed at which those atoms are displaced.
In integrated circuits, electromigration does not occur in semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
s directly, but in the metal interconnects deposited onto them (see semiconductor device fabrication).
Electromigration is exacerbated by high current densities and the Joule heating
Joule heating
Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor releases heat. It was first studied by James Prescott Joule in 1841. Joule immersed a length of wire in a fixed mass of water and measured the temperature...
of the conductor (see electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
), and can lead to eventual failure of electrical components. Localized increase of current density is known as current crowding
Current crowding
Current crowding is a nonhomogenous distribution of current density through a conductor or semiconductor, especially at the vicinity of the contacts and over the PN junctions....
.
Balance of atom concentration
A governing equation which describes the atom concentration evolution throughout some interconnect segment, is the conventional mass balance (continuity) equationwhere
is the atom concentration at the point with a coordinates at the moment of time , and is the total atomic flux at this location. The total atomic flux is a combination of the fluxes caused by the different atom migration forces. The major forces are induced by the electric currentElectric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
, and by the gradients of temperature, mechanical stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
and concentration.
. Define the fluxes mentioned above. . Here is the electronElectron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
charge,
is the effective charge of the migrating atom, the resistivityResistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
of the conductor where atom migration takes place,
is the local current density, is Boltzmann’s constant, is the absolute temperature. is the time and position dependent atom diffusivity. . We use the heat of thermal diffusion. here is the atomic volume and is initial atomic concentrationConcentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...
,
is the hydrostatic stressHydrostatic stress
In continuum mechanics, a hydrostatic stress is an isotropic stress that is given by the weight of water above a certain point. It is often used interchangeably with "pressure" and is also known as confining stress, particularly in the field geomechanics...
and
are the components of principal stress. .Assuming a vacancy mechanism for atom diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
we can express
as a function of the hydrostatic stress where is the effective activation energyActivation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...
of the thermal diffusion of metal atoms. The vacancy concentration represents availability of empty lattice sites, which might be occupied by a migrating atom.
Electromigration reliability of a wire (Black's equation)
At the end of the 1960s J. R. Black developed an empirical model to estimate the MTTF (mean time to failure) of a wire, taking electromigration into consideration:Here
is a constant based on the cross-sectional area of the interconnect, is the current density, is the activation energyActivation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...
(e.g. 0.7 eV for grain boundary diffusion in aluminum),
is the Boltzmann's constant, is the temperature and a scaling factor (usually set to 2 according to Black). It is clear that current density and (less so) the temperature are deciding factors in the design process that affect electromigration.The temperature of the conductor appears in the exponent, i.e. it strongly affects the MTTF of the interconnect. For an interconnect to remain reliable in rising temperatures, the maximum tolerable current density of the conductor must necessarily decrease.
Wire material
The most common conductor used in integrated circuits is aluminium, due to its good adherence to substrate, good conductivity, and formation of ohmic contactOhmic contact
An ohmic contact is a region on a semiconductor device that has been prepared so that the current-voltage curve of the device is linear and symmetric. If the I-V characteristic is non-linear and asymmetric, the contact is not ohmic, but is a blocking or Schottky contact...
s with silicon. However, it soon appeared that pure aluminium is susceptible to electromigration. Research shown adding 2-4% of copper to aluminium increases resistance to electromigration about 50 times. The effect is attributed to grain boundary segregation of copper, which greatly inhibits the diffusion of aluminium atoms across grain boundaries.
It is known that pure copper used for Cu-metallization is more electromigration-robust than aluminum. Copper wires can withstand approximately five times more current density than aluminum wires while assuming similar reliability requirements. This is mainly due to the higher electromigration activation energy levels of copper, caused by its superior electrical and thermal conductivity as well as its higher melting point. Further improvements can be achieved by alloying copper with about 1% palladium
Palladium
Palladium is a chemical element with the chemical symbol Pd and an atomic number of 46. It is a rare and lustrous silvery-white metal discovered in 1803 by William Hyde Wollaston. He named it after the asteroid Pallas, which was itself named after the epithet of the Greek goddess Athena, acquired...
, which, similar to copper in aluminium, inhibits diffusion of copper atoms along grain boundaries.
Bamboo structure and metal slotting
It is obvious that a wider wire results in smaller current density and, hence, less likelihood of electromigration. Also, the metal grain size has influence; the smaller grains, the more grain boundaries and the higher likelihood of electromigration effects. However, if you reduce wire width to below the average grain size of the wire material, the resistance to electromigration increases, despite an increase in current density. This apparent contradiction is caused by the position of the grain boundaries, which in such narrow wires as in a bamboo structure lie perpendicular to the width of the whole wire. Because the grain boundaries in these so-called “bamboo structures” are at right angles to the current, the boundary diffusion factor is excluded, and material transport is correspondingly reduced.However, the maximum wire width possible for a bamboo structure is usually too narrow for signal lines of large-magnitude currents in analog circuits or for power supply lines. In these circumstances, slotted wires are often used, whereby rectangular holes are carved in the wires. Here, the widths of the individual metal structures in between the slots lie within the area of a bamboo structure, while the resulting total width of all the metal structures meets power requirements.
Blech length
There is a lower limit for the length of the interconnect that will allow electromigration to occur. It is known as “Blech length”, and any wire that has a length below this limit will not fail by electromigration. Here, a mechanical stress buildup causes a reversed migration process which reduces or even compensates the effective material flow towards the anode. The Blech length must be considered when designing test structures for electromigration.Via arrangements and corner bends
Particular attention must be paid to viasVia (electronics)
A via is a vertical electrical connection between different layers of conductors in a physical electronic circuit.- In IC :In integrated circuit design, a via is a small opening in an insulating oxide layer that allows a conductive connection between different layers. A via on an integrated circuit...
and contact holes, because generally the ampacity of a (tungsten) via is less than that of a metal wire of the same width.The current carrying capacity of a via is much less than a metallic wire of same length. Hence the use of multiple vias with proper geometrical orientation becomes indispensable. Hence multiple vias are often used, whereby the geometry of the via array is very significant: Multiple vias must be organized such that the resulting current is distributed as evenly as possible through all the vias.
Attention must also be paid to bends in interconnects. In particular, 90-degree corner bends must be avoided, since the current density in such bends is significantly higher than that in oblique angles (e.g., 135 degrees).
Electromigration in Solder Joints
The typical current density at which electromigration occurs in Cu or Al interconnects is 106 to 107 A/cm2. For solder joints (SnPb or SnAgCu lead-free) used in IC chips, however, electromigration occurs at much lower current densities, e.g. 104 A/cm2.It causes a net atom transport along the direction of electron flow. The atoms pile up at the anode, voids are generated at the cathode and back stress is induced during electromigration. The typical failure of a solder joint due to electromigration will occur at the cathode side. Due to the current crowding effect, voids form first at the corner of the solder joint. Then the voids extend and cause a failed circuit. Electromigration also influences formation of intermetallic compounds.
See also
- Integrated circuitIntegrated circuitAn integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...
- SemiconductorSemiconductorA semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
- ElectromagnetismElectromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
- Electrical conduction
- Electromigrated NanogapsElectromigrated nanogapsElectromigrated Nanogaps are gaps formed in metallic bridges formed by the process of electromigration.-Theory:A nanosized contact formed formed by electromigration acts like a waveguide for electrons. The nanocontact essentially acts like a one-dimensional wire with a conductance of G =2e^2/h...
Further reading
- Wiley Encyclopedia of Electrical and Electronics Engineering. Department of Electrical and Computer Engineering University of Wisconsin Madison, 1999.
- Christou, Aris: Electromigration and Electronic Device Degradation. John Wiley & Sons, 1994.
- Ghate, P.B.: Electromigration-Induced Failures in VLSI Interconnects, IEEE Conference Publication, Vol. 20:p 292 299, March 1982.
- H.C. Louie Liu, S.P. Murarka: "Modeling of Temperature Increase Due to Joule Heating During Elektromigration Measurements. Center for Integrated Electronics and Electronics Manufacturing", Materials Research Society Symposium Proceedings Vol. 427:p. 113 119.
- K. Banerjee, A. Mehrotra: Global (Interconnect) Warming. Circuits and Devices, Seiten p 16 32, September 2001.
- J. Lienig, G. Jerke: , Proceedings of the 8th Asia and South Pacific Design Automation Conference (ASP-DAC), 2003, pp. 783–788.
- J. Lienig: , (Download Paper) Proceedings of the International Symposium on Physical Design (ISPD) 2006, pp. 39–46, April 2006.
Reference standards
- EIAElectronic Industries AllianceThe Electronic Industries Alliance was a standards and trade organization composed as an alliance of trade associations for electronics manufacturers in the United States. They developed standards to ensure the equipment of different manufacturers was compatible and interchangeable...
/JEDECJEDECThe JEDEC Solid State Technology Association, formerly known as the Joint Electron Devices Engineering Council , is an independent semiconductor engineering trade organization and standardization body...
Standard EIA/JESD61: Isothermal Electromigration Test Procedure. - EIAElectronic Industries AllianceThe Electronic Industries Alliance was a standards and trade organization composed as an alliance of trade associations for electronics manufacturers in the United States. They developed standards to ensure the equipment of different manufacturers was compatible and interchangeable...
/JEDECJEDECThe JEDEC Solid State Technology Association, formerly known as the Joint Electron Devices Engineering Council , is an independent semiconductor engineering trade organization and standardization body...
Standard EIA/JESD63: Standard method for calculating the electromigration model parameters for current density and temperature.
External links
- http://www.csl.mete.metu.edu.tr/Electromigration/emig.htm What is Electromigration?, Computer Simulation Laboratory, Middle East Technical University.
- http://www.techonline.com/community/ed_resource/feature_article/20421 Electromigration for Designers: An Introduction for the Non-Specialist, J.R. Lloyd, TechOnLine.
- Semiconductor electromigration in-depth at DWPG.Com
- Modeling of electromigration process with void formation at UniPro R&D site
- DoITPoMS Teaching and Learning Package- "Electromigration"