Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
2000-10-25
2004-09-21
Paladini, Albert W. (Department: 2125)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C700S030000, C700S031000, C703S007000
Reexamination Certificate
active
06795800
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a process of designing an integrated circuit, and more particularly, to a method for extracting a plurality of model parameters required for simulating the operation and the performance of a circuit design and a method for simulating the operation and the performance of the circuit.
2. Description of the Related Art
It is essential to determine whether integrated circuit designs will operate as desired, how the performance of the integrated circuit will be, and how the statistical distribution and deviation of the performances will be, and to feed back the simulation results into the design process. Such a simulation is performed using a widely known program, which is referred to as SPICE. The SPICE program requires information on the layout of devices such as the sizes of the circuit devices, the length of signal paths therebetween and various model parameters showing the characteristic performance of the devices and the overall interconnected circuit. Model parameters may have physical meaning such as the length X
l
and the width X
w
of a channel, the thickness t
ox
of a gate insulating layer, and the change &Dgr;V
th
in a threshold voltage according to the change in the doping concentration of a channel region. Other model parameters may indicate simple coefficients of a SPICE model equation. The process of extracting model parameters for a circuit is a complicated and time-consuming task, with many measurements and much trial and error. The general process of extracting model parameters will be described as follows, taking a transistor device as an example.
Drain currents with respect to gate-source voltages V
GS
and drain-source voltages V
DS
are measured and an I-V characteristic curve is prepared. The I-V characteristic curve can be measured, while changing the operating voltage V
CC
, the substrate bias voltage V
BB
, the length and the width of a channel, and device temperature. As a result, various I-V characteristic curves are created.
In the I-V characteristic curves shown in
FIG. 1
, results of measuring drain current I
D
according to the change in the gate-source voltage V
GS
, the drain-source voltage V
DS
, the substrate bias voltage V
BB
and the operating voltage V
CC
, are shown. In
FIG. 1
, I-V characteristic curves with respect to predetermined length and width of a channel and a predetermined temperature are shown. Various I-V characteristic curves which are similar to the I-V characteristic curves shown in
FIG. 1
are created as the length and the width of the channel and the temperature are changed. Because of all the variables, the number of times that a drain current value is measured can be several hundreds through several thousands. Typically, the transistor devices for measuring the current value according to the change in a voltage are referred to as a test element group (TEG) formed in an unused area, e.g., a scribe line between one chip and another chip, of a wafer on which mass-produced integrated circuit chips are formed.
The process of extracting model parameters includes 1) substituting initial values into the model parameters for the I-V calculating equation of the SPICE program; 2) performing the needed calculations based on such initial values; and 3) changing the initial values until the calculation results converge on actual (measured) I-V characteristic curves. These steps are repeated until convergence is within a predetermined tolerance. Values obtained when the calculation results converge on the actually measured I-V characteristic curves become the model parameters. The model parameters of a previously known device having the characteristics closest to those of the currently designed device are typically used as initial values. The model parameters are preferably a set which converges on the measured I-V characteristic curves, while changes to the length and the width of the channel, the temperature during measurement, an operating voltage, and a substrate bias voltage concurrently are made.
The model parameter set obtained as described above is substituted for the input variable to the SPICE model equation, and device and circuit performance characteristics, e.g. speed, are calculated.
In order to determine the degree and deviation to which the performance of a circuit may vary according to the position of the circuit on a wafer or the position of a wafer in a wafer cassette, simulation is performed not on only one device but on plural devices variously positioned on one or more wafers (refer to U.S. Pat. No. U.S. 5,790,436). In this case, the above mentioned process of extracting the model parameter set must be repeated with respect to each device and wafer position to create a plurality of model parameter sets. Those of skill will appreciate that this is a complicated and time-consuming task.
A method of extracting the model parameter set using electrical test (ET) data instead of I-V characteristic curves has been proposed. See James C. Chen et al “E-T Based Statistical Modeling and Compact Statistical Circuit Simulation Methodologies”, IEDM, 1996, pp. 635-638. That article describes a method of directly measuring parameters such as the change amount &Dgr;L in the length of the channel, the change amount &Dgr;W in the width of the channel, the thickness T
ox
of a gate insulating layer, and the drain-source resistance R
d5
among the model parameters, and extracting the remaining parameters using ET data such as drain saturation current I
dsat
. However, it is more difficult to directly measure physical parameters than it is to measure the I-V characteristics. For example, it is very difficult to measure such parameters by a physical technique involving the use of a scanning electronic microscope. Accordingly, such parameters are usually measured by an indirect method by which the parameters are derived from electrical measurement. It is not possible to guarantee the reliability of such derived parameter values.
Of interest to integrated circuit designers is what influence do changes in specific characteristics of an elementary device of an integrated circuit design have on the performance of the entire integrated circuit. Also of interest are which characteristics of the device most greatly affect the performance of the integrated circuit. However, conventional techniques for extracting model parameters and evaluating integrated circuit designs do not adequately meet such needs.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a method of simply extracting model parameter sets when two or more model parameter sets are required in order to statistically simulate the performance of a circuit design.
It is another object of the present invention to provide a method of estimating sensitivity, i.e. determine the influence that changes in elementary device characteristics have on the performance of the entire circuit.
Accordingly, to achieve the first object, there is provided a method of extracting n (n being an integer greater than or equal to 2) model parameter sets in order to statistically simulate the operation and performance of an integrated circuit design, wherein a first model parameter set is extracted by a conventional method and the remaining n−1 model parameter sets are extracted using not an I-V characteristic curve but instead the main characteristic data of an elementary device as a target function.
In a method of extracting model parameter sets according to the present invention, n points are designated in one or more wafers and an elementary device of the integrated circuit is formed at each of the n points. An I-V characteristic curve is created by measuring the I-V characteristic of the elementary device formed at one point among the n points and a first model parameter set is extracted which converges on the I-V characteristic curve within a predetermined error range. With respect to the second through nth model parameter sets, the second through nth main characteristic data value
Marger & Johnson & McCollom, P.C.
Paladini Albert W.
Samsung Electronics Co,. Ltd.
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