Patent Application
20090299706
The present invention relates to a simulator technique using a computer and, more particularly, to a method, a device and a program for simulating nano substance in an electric field.
Aiming to more sufficiently describe the current technical level relating to the present invention, all of the patents, patent applications, patent publications, scientific articles and so on, which are cited or specified herein, are hereby incorporated by reference in their entirety.
As indicated in the International Technology Roadmap for Semiconductors, a next-generation semiconductor having a semiconductor gate length of 30 nm of shorter is expected to be put to practical use after 2010.
Further, researches have been actively conducted for practical application of new-generation electronic devices based on new nano substance as typified by a carbon nanotube.
Promotion of such researches strongly requires accurate prediction of the electronic property and the electric conduction in a case where a nano structure is actually in an electric field, and some advantageous effects are expected such as reduction in cost and time for trial and errors during repeated creation of a nano structure and a device-operation property.
Conventional simulation technologies for device operation were performed based on the classical Boltzmann transport equation by way of: extracting a necessary parameter from a band structure when executing a macro simulation with the simulation including dielectric constant, effective mass and relaxation time; and calculating, based on the classical electrodynamics, the field distribution relative to the assumed device structure.
In the case of Si material, improved accuracy was successfully achieved of the aforementioned effective mass approximation and relaxation time.
Non-patent Document 1: E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984)
Non-patent Document 2: J. Ihm, A. Zunger, and M. L. Cohen, J. Phys. C: Solid State Physics, Vol. 12, 4409 (1979) Non-patent Document: O. Sugino and Y. Miyamoto, Phys. Rev. B59, 2579 (1999); Phys. Rev. B66, 89901(E) (2002)
However, the aforementioned prior arts contained the following problems.
The first problem is that since the channel length is in the nanoscale order, electronic transportation could not described by way of the classical Boltzmann transport equation.
This is because when the channel length is of nanoscale, the electronic transportation is shifted to ballistic transportation, and because accuracy could not improve unless the electronic transportation chases the real time evolution of the wave function of electrons when passing through portion of channel from the electrode.
The second problem is that the aforementioned prior arts make it difficult to accurately predict the advantageous effect of the electric field application.
This is because in the case of nano-scale substance, changes in the electronic state itself caused by electric field application cannot be ignored.
The third problem is that one cannot accurately predict the response time of electrons.
This is because the motion of electrons, when a strong electronic field is applied to a nano substance, is far from the state of equilibrium.
As could be understood from the foregoing, conventional simulators correspond to a structure of micron-order size, the operating characteristic of which is simulated by combining the classical electrodynamics with the transport equation. Besides, a “fitting parameter”, having little physical basis, is applied for prediction of the operation so that an experiment can be reproduced. Such a conventional approach is problematic when applied to nano-scale materials. This is because in the case of nanoscale material, quantum effect can be detected in electronic conduction. Further, information is required including: atomic-scale information such as a defective configuration of a channel layer, a configuration of the contact zone between a semiconductor material and an electrode; and information on change in the electronic state caused by electric field application, thus resulting in limitation of “fitting” by a parameter.
Meanwhile, ab initio calculation, effective for atomic-scale calculation, can now be applied to nacoscale material, too.
However, there is no method for calculating an electronic state under an applied field distribution in response to a nano structure, and for combining with a calculation approach in which is calculated a device operating characteristic, leading to a problem of calculation accuracy under an applied electric field.
Hence, there is a need for assuming a feasible equivalent circuit in order to conduct an operating prediction of a nanoscale material. The operating prediction of a nanoscale material can be obtained only by executing a quantum-mechanical static calculation under a condition where a parameter necessary for an equivalent circuit (contact resistance and parasitic capacitance, and so on) is uniform due to the parallel flat plate even if a state is assumed where no electric field of a nano substance is applied or even if an electric field is assumed. Accurate prediction of operation of a device is thus painstaking.
Accordingly, the present invention is created in view of the above-described problems, and the invention is intended to provide a simulation method, a system and a program that calculates the dynamical response in an electric field, and that enables accurate simulation without using a “fitting parameter” or the like.
The invention disclosed in the present application substantially comprises the following configuration in order to solve the above-described problems.
The first method (system, program) of the present invention simulates a nano substance in an electric field by way of a Fourier transform process by virtually applying a model on which a three-dimensional periodic boundary condition is imposed.
The second method (system, program) of the present invention arranges a virtual charge distribution on a space mesh such that an optional field distribution is simulated.
The third method (system, program) of the present invention applies the virtual charge distribution such that an initial condition is virtually set in which electrons are bound to a position away from a substance.
The fourth method (system, program) of the present invention combines the first to third methods (systems, programs) with an approach to simultaneously simulate, by way of ab initio calculation, the dynamics of electrons and atomic nuclei in a nano substance, such that the electric conduction in the nano substance and the electron irradiation thereto are simulated.
According to the present invention, the dynamical response of electrons is calculated in an electric field, and the motion of atomic nuclei can thus be solved together.
According to the present invention, in case where a device comprises, for example, nano material, the time response of electrons in an electric field is a simulation of the specific group velocity, electron-lattice scattering and electron-electron scattering, all of which the electrons themselves retain, and thus, accurate simulation can be achieved even without any “fitting parameter”.
This is because in the present invention, density distribution of electrons can be calculated based on an electronic wave function that is changing over time under an electric field by way of precise calculation according to ab initio calculation; and because a potential caused by the density distribution of electrons, a potential caused by an electric field, as well as a potential from a lattice, are all precisely introduced in the calculation.
According to the present invention, the simulation technology allows automatic introduction of the change of electronic state generated by electric field application.
This is because in the present invention, the electronic state in a nanotube, which state gradually changes in the presence of an electric field, is calculated based on the ab initio calculation and on the time-dependent density functional theory.
The present invention models a device structure by means of ab initio calculation according to periodic boundary condition, and optionally assumes a virtual charge distribution around a device structure, so that a uniform electric field generated by a parallel plate, as well as a spatially non-uniform electric field, can be freely produced in accordance with an assumed condition of the virtual charge density.
The present invention having such a configuration is appropriate for simulating an electric characteristics of nano material under three electrodes consisting of source, drain and gate of a FET.
In order to calculate the dynamical response of electrons, the present invention solves a time-dependent Schrödinger equation at the ab initio calculation level while the motions of atoms are classically treated reproduced, so that the effect of electric field application is directly included in the motion of electrons and atoms.
This enables real-time simulation of the electronic response in a device material, and of the interaction caused thereby between lattice and electrons.
In this way, the present invention can simulate the dynamical operating characteristic of an electronic device on the basis of a nanometer-scale material without using any arbitrary parameter.
Combination of a method for electric field calculation according to classical electrodynamics with a method for calculation of the time-dependent Schrödinger equation based on ab initio principles allows inspection of the device operation dependent on time.
Besides, the present invention, according to the similar principles, allows for dynamical simulation of structural change by electron irradiation to nano substance, and of structural displacement in a strong electric field. The present invention will be explained as follows in accordance with the Embodiments.
Referring to
The virtual charge distribution 1 can be optionally generated on a real-space mesh, and the charge distribution can be calculated by solving a Poisson equation. The simulation system according to the present Embodiment simulates a device either under a vacuum region condition or under a periodic boundary condition in which is assumed existence of a continuum dielectric, so that a potential distribution is calculated by way of Fourier-transforming a charge distribution into a reciprocal lattice space. The electric field strength distribution is equivalent to space derivative of the potential distribution. Meanwhile, in the present Embodiment, a Poisson equation is solved under the virtual charge distribution and the charge distribution in a substance so that a potential is evaluated. Using this potential, a plurality of wave functions relative to electrons and so on are solved so that a new electronic density is evaluated.
The substance (material model) 2 is formed in a periodic boundary similar to that of the virtual charge distribution 1. Hence, the electronic state can be calculated using a band calculation on a planar wave basis according to the Bloch theorem.
Further, the plane wave basis is also used for solving the time-dependent Schrödinger equation of electrons.
Following is a detailed explanation of the operation of the present Embodiment with reference to
In
A frame 3 in
The merit of the periodic boundary condition is that the electric potential and electric field according to the virtual charge distribution 1 indicated in
Besides, under the existence condition of the virtual charge distribution 1 and the substance (material model) 2, the time evolution of electrons can be calculated according to the time-dependent density functional theory (Non-patent Document 1: E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984)).
In this case, the virtual charge distribution 1 and the charge distribution of electrons in the substance (material model) 2 are added, and the added charge distributions are Fourier-transformed into a reciprocal lattice space (momentum space), so that the entire energy of a system can be calculated. Further, the energy (the entire energy of a system) is differentiated with respect to atomic coordinates so that the classical force field applied to atoms can be calculated.
Accordingly, when solving the motion of electrons and atomic nuclei, the sum of potential energy of atomic nuclei (the entire energy of density functional theory (Non-patent Document 2: J. Ihm, A. Zunger, and M. L. Cohen, J. Phys. C: Solid State Physics, Vol. 12, 4409 (1979)) and the kinetic energy of atomic nuclei is conserved.
A merit of the simulation in which a periodic boundary condition is imposed is that confirmation of whether or not this law of conservation is numerically satisfied allows for easy confirmation of the calculation accuracy.
Adopting the already-published technology of calculating the time evolution of electrons (Non-patent Document 3: O. Sugino and Y. Miyamoto, Phys. Rev. B59, 2579 (1999); Phys. Rev. B66, 89901(E) (2002)), the calculation accuracy can be ensured for up to a simulation time of 1 picosecond order even when a simulation is conducted in which the motion of atomic nuclei is combined.
Following is the explanation of operation of the present Embodiment with reference to specific embodiments.
In
Here, in order to present a visually clear explanation of the effect of the electric field application,
The electric field strength is at 0.37V/angstrom, which is on the same order of the electric field strength when measured by a typical scanning tunneling electron microscope.
A contraption is provided at both ends of
Similar to
The most apparent point one can see by comparing
Such screening phenomenon can be widely seen in metallic substance, and the simulation according to the present application enables calculation of the time for the screening.
This is a simulation technology effective for estimating the upper limit of the operating frequency of an element that is switched by electric field application, e.g. FET (Field Effective Transistor).
According to the present Embodiment, the dynamical response of electrons is calculated in an electric field, and the motion of atomic nuclei can thus be solved simultaneously.
In case where a device comprises, for example, nano material, the time response of electrons in an electric field is a simulation of the specific group velocity, electron-lattice scattering and electron-electron scattering, all of which electrons themselves retain, and thus, accurate simulation can be achieved even without any “fitting parameter”.
This is because in the present invention, density distribution of electrons can be calculated based on electronic wave functions that are changing over time under an electric field by way of precise calculation according to ah initio principles; and because a potential caused by the calculation, a potential due to an electric field, as well as a potential from a lattice, are all precisely introduced in the calculation.
According to the present Embodiment, change in the electronic state (electronic structure) caused by electric field application is also automatically introduced.
This is because in the present Embodiment, this calculation is based on ab initio calculation, and because the electronic states in a nanotube, gradually changing in the presence of an electric field, are calculated by time-dependent density functional theory.
Following is a detailed explanation of another Embodiment of the present invention with reference to the drawings.
The lower part of
Such a calculation model can be applied to a simulation of operation of an electric field effect transistor.
When time t>0, the virtual charge 7 is dislocated to the position shown in
Each of the simulation systems according to the above-described Embodiments can be executed on an optional data processing device (computer) provided with a central processing unit (CPU), a memory device, a display device and so on (not shown). Loading a simulation program according to the present invention from the memory device of a data processing device to the main memory in the central processing unit and executing the program, the simulation results of
The present invention can be applied to anything that relates to a simulator technology using a computer and, more particularly, to a method, a device and a program for simulating nano substance in an electric field; and is not limited in terms of the possibilities of use thereof.
The invention has been described in detail with reference to certain preferred Embodiments thereof, but it will be understood that these Embodiments are intended just for describing the invention with specific examples thereof and not for limiting the invention. It should be clear that any skilled person, after reading the present specification, could make modifications or substitutions using equivalent components and technologies. However, it should also be clear that such modifications or substitutions would still be covered by the true scope and spirit of the appended Claims.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2006-209766 | Aug 2006 | JP | national |
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/JP2007/060646 | 5/24/2007 | WO | 00 | 3/10/2009 |
