Reliability Models for Failure Mechanisms

Electromigration 

Electromigration is the movement of metal atoms of a metal line in the direction of the current flow through that metal line. This mechanism is similar to pebbles in a stream, which are picked up and transported by the water in the direction of the water currents.  As such, during electromigration, metal atoms are removed from the starting end of the metal line and accumulates at the other end, forming voids at the entrance and hillocks at the exit of the metal line.  Thus, electromigration can result in open circuits (due to the voids) or line-to-line short circuits (due to the hillocks).  

Electromigration is accelerated by temperature and current density, and is modeled as follows:

tf = CJ^-ne^(Ea/kT)                                                                           

AF = tf_use / tf_test

AF = (J_test/J_use)ⁿ e^{(Ea/k) (1/Tuse-1/Ttest)}       

where:    

C = a constant based on metal line properties                      

n = integer constant from 1 to 7                                                  

Tuse, Ttest = temperature during use and under test, respectively

Juse, Jtest = current density during use and under test, respectively

Ea = 0.5 - 0.7 eV for pure Al

Corrosion

Corrosion is metal degradation due to chemical or electrolytic reactions in the presence of moisture, contaminants, and bias.

Corrosion rate is a function of temperature (T), relative humidity (RH), and bias (V).

Let AF = tf_use / tf_test

and

tf   = C(RH)^-3e^(0.9/kT).

With no applied voltage:          

AF = (RH_test/RH_use)³ e^{(0.9/k) (1/Tuse-1/Ttest)}         

With voltage V applied:              

AF = (V) (RH_test/RH_use)³ e^{(0.9/k) (1/Tuse-1/Ttest)}         

where:

C = a constant                    

RHuse, RHtest = relative humidity during use and under test, respectively

Tuse, Ttest = temperature during use and under test, respectively

Time-dependent Dielectric Breakdown (TDDB)

Time-dependent Dielectric Breakdown, or TDDB, is the destruction of dielectric layers occurring over time.

R = A₁e^(-Ea/kT+CV)

AF = tf_use / tf_test  = R_test /R_use

AF =  e^{([-Ea/k] [1/Ttest-1/Tuse] + C [Vtest-Vuse])}     

where:   A₁,  C = constants                                                     

Ea = 0.8 - 0.9 eV

Vuse, Vtest = voltage applied during use and under test, respectively

<Back to Page 1 - Intro to Reliability Modeling>

<Proceed to Page 3 - Rel Models for Hot Carrier, Bonding, Fatigue Failures>

See also:  Reliability Engineering;  Failure Analysis;  Process Qualification; 

Package Failures;  Die Failures

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