# New Curve Tracing Algorithm in ATLAS

Introduction

The new curve tracing feature in Version 3.0 of
**ATLAS** overcomes the problems associated with the simulation
of devices with arbitrarily shaped I-V curves.

Obtaining I-V curves for such complex phenomena as strong breakdown, snap-back and latchup is made very difficult because of the possible multi-value character of the resulting I-V curves. This requires that switching from voltage to current boundary conditions and vice versa be performed during the simulation.

If no special algorithm is used such simulation requires an expert knowledge of the shape of the I-V curve, and a clear understanding of when to switch from one type of boundary condition to another. Performing such simulations is problematic and time consuming as it usually takes several attempts to get the final results.

In the previous version of **ATLAS** the simple
switching algorithm from voltage to current boundary conditions
was based on the estimate of the value of the ionization integral.
If the value of this integral is close to unity the program automatically
switches from voltage to current boundary conditions.

The shortcomings of this algorithm are due to the lack of an automatic selection of the voltage and current step sizes, and no automatic backward switching from current to voltage boundary conditions. On the other hand, two powerful algorithms which handle a fully automated tracing of complex I-V curves without any user intervention are described in the literature [1, 2].

The algorithm developed in [2] is now implemented
in **ATLAS** and will be available in the next release. This
algorithm, based on the dynamic load line technique, provides an
optimal choice of boundary conditions for each bias point, and a
gradual transition from voltage to current conditions, and vice
versa. The simulation of complex I-V curves can now be performed
using only one SOLVE statement. Tracing complex I-V curves in **ATLAS**
is now a routine task.

Examples

The following two examples demonstrate the capabilities of the new curve tracing algorithm. The first example is a breakdown simulation of a one-dimensional pn diode. The non-isothermal drift diffusion model, where Poisson's equation, the two carrier continuity equations, and the lattice heating equation are solved self-consistently, is used for this simulation. Figure 1 shows the I-V curve obtained with the curve tracing algorithm. The sharp second breakdown around 50V is easily calculated with the reasonable bias stepping and resolution.

Figure 1.

The second example is a breakdown simulation of
a LDD MOSFET with 0.8µm channel length. The energy balance
model, where Poisson's equation, the two carrier continuity equations,
and the two energy balance equations are solved self-consistently,
is used for this calculation. Figure 2 shows the Id-Vd characteristics
for Vg=1V. Again, the curve tracing algorithm produces the results
for this complicated problem without any difficulties, even in the
vicinity of the snap-back point. These two examples illustrate that
the new algorithm implemented in **ATLAS** allows reliable automatic
simulation of complex device phenomena with arbitrarily shaped I-V
curves.

Figure 2.

References

[1] W.M. Coughran, M.R. Pinto, and R.K. Smith,

"Computation of Steady-State CMOS Latchup Characteristics,"

IEEE Trans. Computer Aided Design, vol.7, pp. 307-323, 1986. [2] R.J.G. Goosens, S. Beebe, Z. Yu, and R.W. Dutton,

"An Automatic Biasing Scheme for Tracing Arbitrarily Shaped I-V Curves,"IEEE Trans. Computer Aided Design, vol.13, pp. 310-317, 1994.