Simulating 3D OHMIC Heating Effects in Metal

 

Introduction

A new feature has been added to Silvaco's device simulator ATLAS, which allows the simulation of ohmic heating effects in metals using the Giga or Giga3D modules. The feature has been included in response to metal heating problems that increasingly occur in interconnects for very aggressive technologies.

Normally metals in device simulators are treated as either ohmic or Schottky contacts with little regard for their bulk resistivity, since this is usually insignificant compared to the resistivity of the underlying semiconductor.

The new feature now allows the ohmic resistance, and the heating it causes, to be taken into account for both 2D and 3D arbitrary device structures. The steady state simulations allow temperature dependent thermal resistivities and conductivities to be defined by the user, so any arbitrary metal could be defined.

Heating effects can also be investigated in time domain by applying a transient pulse to the structure. For such simulations, the temperature dependent specific heat capacities for the materials can also be defined by the user.

The simulation of ohmic resistance in a metal is activated using the new key word "conductor" on the region statement containing the metal. For example, the following region statement defines a 10um long aluminum interconnect that is 0.5um wide and 0.6um thick:

region number=1 material=Aluminum \
conductor x.min=0 x.max=0.5 \
y.min=0 y.max=0.6 z.min=0 z.max=10

The temperature dependent resistivity coefficient can be specified using the "drhodt" parameter in the material statement. An example is shown below:

material material=Aluminum drhodt=0.00429

Thermal resistivity coefficients for a number of known metals have been included as default parameters. These values were taken from reference 1.

Aside from these two new parameters, all aspects of simulating self heating effects using Giga and Giga3D remain as before, so the user may reference the manual and the many DeckBuild examples for further information.

 

Steady State Example

A simple "dogbone" type structure was constructed using the ATLAS Device3D simulator. One electrical contact was defined at each end of the dogbone and these contacts were held at 300K (room temperature).

In order to simulate radiation from the top of the device through the surrounding oxide to the air, a thermal contact was defined covering the entire top surface and a further thermal contact was defined on the bottom of the structure to simulate conduction through to the substrate.

The resulting structure in Figure 1 shows a TonyPlot3D image of the surface and side temperature contours of the surrounding oxide following the application of a suitable voltage across the two contacts. Figure 2 shows the same structure but with the surrounding oxide hidden, a standard features of TonyPlot3D, so that the temperature contours of the aluminum conductor can be seen.

Figure 1. Temperature plot at the surface of the passivation oxide
due to thermal heating of a buried interconnect aluminum line.

 

Figure 2. The same plot as Figure 1, but with the underlying
conductor revealed with the TonyPlot3D “hide” feature.

 

 

Transient Example

In this example, the same structure was used, but instead of applying a steady state voltage across the conductor to dissipate power, a voltage pulse with a rise time of 1ns was applied for 10us, then turned off again at the same ramp rate. The relevant solve statements are reproduced below:

solve vanode=0.1 endramp=1e-9 tstop=1e-5 dt=1e-11

solve vanode=0 endramp=1e-9 tstop=2e-5 dt=1e-11

Thermal specific heat capacities are defined using the material statement in the normal way. Several temperature dependent models are available to the user. The resulting temperature rise waveform from what was effectively a square wave voltage pulse is shown in Figure 3, giving the expected result.

Figure 3. Transient heating at the center of a metal line as a
result of a square waved voltage pulse applied to it’s end.

 

Conclusion

A new ATLAS Giga and Giga3D capability has been demonstrated and examples given as to a typical use. The new capability will be available to existing customers who have the Giga or Giga3D modules as no new module will be required. If you are interested in this new feature and currently do not have a Giga or Giga3D license, please contact your account manager for further details.

 

References

  1. Handbook of Chemistry and Physics, 56th Edition, 1975-76, CRC Press.