Morris Shatzkes

A model for conductor failure considering diffusion concurrently with electromigration resulting in a current exponent of 2

A model was constructed for electromigration failure where both Fickian diffusion and mass transport due to the electromigration driving force are considered concurrently. The solution to the resulting diffusion equation yields a current exponent of 2 and an activation energy consistent with grain‐boundary self‐diffusion. A modification of the standard median time to failure equation first proposed by Black is suggested.

Impact ionization model for dielectric instability and breakdown

A mechanism describing the incipient stages of intrinsic dielectric breakdown is formulated for the case of a wide‐band‐gap insulator with a low hole mobility. Dielectric instability results from the tunnel injection of electrons from the cathode contact and the subsequent impact ionization and field distortion which lead to dielectric breakdown. The model, evaluated for the parameters of SiO2, predicts an intrinsic breakdown voltage which approaches a lower limit of V=9+φ for very thin films, where φ is the cathode contact barrier in volts. As a result, both the electric field at breakdown and the critical current density increase rapidly as the film thickness is reduced below 200 A.

Impact ionization and positive charge in thin SiO2 films

The magnitude and the centroid of the positive charge induced in the SiO2 layer of an MOS capacitor have been determined from measurements of deviations of the fields at the electrodes from the average field in the oxide. The field at the metal electron‐injecting electrode is found from the current density, which deviates from a Fowler‐Nordheim characteristic with respect to the average field at high fields; the field at the SiO2‐Si interface is found from the shift of the high‐frequency capacitance‐voltage curve. For cathode fields ≳10 MV/cm, the charge is linearly related to the cathode field and is the same for both of the film thicknesses used, 494 and 263 A. The centroid, measured from the injecting electrode, is a decreasing function of the cathode field. From these results, the average field can be derived as a function of the cathode field and the film thickness, even for cathode fields beyond breakdown. A maximum average field is found to exist, which is identified as the average field at breakdo...

On the nature of conduction and switching in SiO2

Further experimental results are presented concerning high conduction and switching in Al–SiO2–Si sandwich structures. The high‐conduction state is filamentary and is governed mainly by the voltage across the sandwich. It is relatively insensitive to variations in device geometry. Periodic current oscillations are observed for certain combinations of series load resistance and applied voltage. Once the high‐conduction state is achieved, it can be maintained at applied voltages below the one required to cause the transition but larger than a minimum voltage, which may be related to the minimum ionization energy in SiO2. Fluctuations are observed that depend on external circuit configuration, i.e., the load line, and on the ambient temperature. It is shown that a two‐branched current‐voltage characteristic can account for the observed behavior. A physical model is presented in an attempt to provide a qualitative explanation of the origin of this form of characteristic. Local damage is evident whenever the h...

Electron tunneling at Al‐SiO2 interfaces

The Murphy‐Good tunneling theory, modified with a Franz‐type two‐band dispersion relation, accurately represents emission of electrons from metals into SiO2 using parameters that are invariant with temperature and that agree with independent measurements. Parameters related to properties of the SiO2 do not change when different metal electrodes are used. Deviations of the measured I‐V characteristic from the model calculation which occur at low field can be explained in terms of interfacial inhomogeneities in the effective barrier height. For thin dry SiO2 grown on boron‐dope silicon, the effective size of the inhomogeneities increases with decreasing oxidation temperature.

Kinetic study of electromigration failure in Cr/Al-Cu thin film conductors covered with polyimide and the problem of the stress dependent activation energy

The electromigration lifetime of Cr/Al-Cu conductors covered with polyimide passivation was studied as a function of temperature and current density. The activation energy for failure was found to be substantially higher than that found in studies of similar metals without polyimide. A current exponent of 2 was determined in the absence of temperature gradient failure. An improved method for calculating the activation energy for temperature gradient failure is described. The problem of the apparent stress-dependent activation energies is discussed. >

Determination of breakdown rates and defect densities in SiO2

Abstract Breakdowns in SiO 2 have been classified as defect related, due to wear-out and intrinsic. However, techniques to ascertain defect densities and breakdown rates at defects have not been available, nor has the distinction between wear-out and defect- related or intrinsic breakdowns been clearly demonstrated. A particular problem has been the inability to distinguish defect types, i.e. defects having different breakdown rates. Another source of confusion has been the tacit assumption that breakdown field histograms obtained from ramp breakdown tests are independent of the ramp rate, which cannot be valid for finite breakdown rates. We obtained relationships specifying the statistics of breakdown, including the effect of defects. These actually derive from results describing a Markov death process and depend on the time integrals of breakdown rates in defect-free regions and at defects and on parameters describing the defect distributions. For Poisson distributions of the defect, these parameters are the mean number of defects per device for each defect type. Any breakdown test is described by the same relations since the nature of the test enters only through the time integral of the breakdown rates. If a wear-out mechanism is operative, then the breakdown rates will depend on the time explicitly, i.e. not only via the time dependences of the applied field and temperature. procedures for obtaining defect densities and breakdown rates follow from the derived dependence on these quantities of the expectation value of the fraction of devices broken down. Ramp tests at various ramp rates are advantageous for this purpose. The field dependence of the breakdown rates can be extracted directly from the experimental data and no a priori form for this dependence need be assumed. Experimental results obtained from multiple ramp breakdown tests will be presented. The field dependence of the breakdown rates is found to vary significantly from a simple exponential dependence. Following Klein, the effect of fluctuations on the breakdown rates will be considered qualitatively to rationalize their observed field dependence. No explicit time dependence of the breakdown rates is indicated over the range of field covered by the data, implying the absence of wear-out.

Characteristic length and time in electromigration

A characteristic length can be defined as the distance a vacancy moves under an electromigration force to do thermal work KT. The times for a vacancy to drift and diffuse this characteristic length are equal and thus define a characteristic time. The diffusion coefficient and the drift velocity are unity when these characteristic values are used as units of length and time. Therefore, when these units are used in the absence of vacancy sources and sinks, the vacancy continuity equation contains no parameters. These considerations are used to estimate the length current density threshold, the electromigration failure times, the edge‐displacement velocity, and the incubation time. These estimates are consistent with published experimental results.

Electromigration‐induced compressive stresses in encapsulated thin‐film conductors with and without the presence of drift velocity

Electromigration‐induced compressive stresses in encapsulated thin‐film conductors were studied by using NPN transistors as pressure sensors. If the current exits at the midpoint of a conductor through an ideal blocking boundary, an emitter of an NPN transistor, then the compressive‐stress gradient with and without the presence of the drift velocity can be studied. Based on the observed compressive‐stress gradients, estimates for the diffusion constant, D=8.0×10−13 cm2/s, and the drift velocity, V=1.4×10−11 cm/s, were made for a temperature‐bias condition of 1470 kA/cm2 and 180 °C. The time‐dependent buildup of the concentration for different boundary conditions was consistent among the experiments and the models presented.

Distribution of dopant in SiO2‐Si

The distribution of dopant in SiO2‐Si during dry thermal oxidation and postoxidation anneal is studied. Analytical expressions for the distribution functions are derived, on the assumptions that the oxide film grows in accordance with the t1/2 law and that before oxidation the dopant is uniformly distributed in the silicon. Cases in which tn≠t1/2 are discussed, with particular attention to the effect of n≳1/2 on the distribution of the dopant in the oxide. Calculations are provided for boron, describing its distribution in the oxide and in the silicon as a function of postoxidation anneal. Some experimental results concerning the distribution of boron in the silicon are provided for various oxide thicknesses, oxidation temperatures, and anneal times. These results were obtained from spreading‐resistance measurements.