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This paper reviews the real-space multislice method of numerically computing diffracted electron amplitudes and phases. It is found that the number in of terms of propagator expanded is dependent only on the number N of sampling points and the slice thickness epsilon. The practical procedures for accurate use of this method are discussed in detail.

Petrov-Galerkin method is proposed for solving nonlinear reaction-diffusion equations. The concept of ordered pair of supersolution and subsolution is introduced. A monotone iteration is provided for solving the resulting problem. The convergence of the Petrov-Galerkin scheme is discussed. The numerical results show the advantages of such method.

Low-energy protons are able to generate enough energy through direct ionization to cause a high single event upset cross section as the feature size of semiconductor devices shrinks. It poses a large challenge on the present proton single event modeling test technique and the space upset rate prediction method. Experimental study of proton single event effect in three different feature sizes of static random access memory (SRAM) (i.e. 65 nm, 90 nm, and 250 nm) is carried out based on domestic low-energy proton accelerators and also the foreign middle-high proton accelerators. Complete cross section curves of proton single event upset from low energy to high energy are acquired. Test results show that single event upset cross section below 1 MeV proton is up to three orders of magnitude higher than the saturation cross section of high-energy proton in nanometer SRAM. However, single event upset is not observed for protons below 3 MeV in 250 nm SRAM, and no single event multiple-cell upsets occur for protons below 1 MeV in 90 nm and 65 nm SRAM. The accurate geometrical structure model of composite sensitive volume is constructed through the combination of test data with device information, and calibrated further by single event test data of low-LET heavy ion and high-energy proton. Simulation results based on the model and Monte-Carlo calculation can reveal the root cause of low-proton single event upset cross section peak. Proton single event upsets are only caused through direct ionization of protons below 1 MeV. When low-energy protons pass through the multiple metallization and passivation layers of the device, the energy spectrum is broadened near the Bragg peak of the proton direct ionization, and the energy is deposited concentratedly into the sensitive volume through direct ionization. When the proton energy is too high or too low, the energy can not be deposited effectively into the sensitive volume through direct ionization. The energy spectrum straggling of low-energy protons due to the use of degrader has a large influence on the height and width of the single event upset cross section peak. Moreover, the contribution of low protons to the space proton single event upset rate is predicted for GEO orbit environment in the worst day environment. It shows that the direct ionization from low energy dominates the proton single event upset rate in the space in 65 nm SRAM. With the development of device technology, the critical charge of single event upset will be further reduced; and to the single event upset from low proton direct ionization more attention must be paid in the study and evaluation of single event effect.

Single event multiple-cell upsets (MCU) increase sharply with the semiconductor devices scaling. The impacts of several test factors on heavy ion single event MCU in 65 nm SRAM are studied based on the buildup of MCU test data acquiring and processing technique, including the heavy ion LET, the tilt angle, the device orientation, the test pattern and the supply voltage; the MCU physical bitmaps are extracted correspondingly. The dependencies of parameters such as the MCU percentage, MCU mean and topological pattern on these factors are summarized and analyzed. This work is meaningful for developing a more reasonable single event test method and assessing the effectiveness of anti-MCU strategies on nanometer-scale devices.

A dynamical convergence criterion for the real-space multislice method for simulating high-resolution electron microscopy images has been derived. This criterion imposes a practical limitation in determining dynamically the number of terms of the propagation operator P(R) expanded in the subsequent dynamical diffraction calculations concerned with the phase grating selected, the wavefunction and its variation during propagating after choosing the sampling interval Δ and the slice thickness σ. It has been found that, as long as the dynamic criterion is satisfied, much better agreement with the results using a fast Fourier transform multislice method can be obtained.

Single event multiple-cell upsets (MCU) increase sharply as the feature size of semiconductor devices shrinks. MCU poses a large challenge on present radiation hardening technology and modeling test technique. Experimental study of the influence of proton incidence angle on single event multiple-cell upsets in 90 nm static random access memory (SRAM) for middle and high energy proton is carried out. The result shows that MCU percentage and multiplicity increase with increasing proton energy, and the MCU topological pattern presents a certain track-orientation characteristic along the trajectories of the incidence ion when the incidence proton is tilted along the X-direction or Y-direction. Single event upset (SEU) cross section has no evident angular dependence. There is some difference in proton MCU cross section between normal incidence and tilt angle incidence only for 30 MeV proton. Angular effect of proton MCU is associated with proton energy. Due to the lower efficiency of Monte-Carlo method in calculating proton MCU, a fast calculation method for cross section, which aims at single event MCU induced by proton nuclear reaction, is adopted. The binary cascade model in Geant4 toolkit serves as event generators in middle on high proton nuclear reaction. In terms of double differential scattering cross section of secondary particle from proton-material spallation reaction, proton MCU cross section is calculated through integration over the entire space of memory cells array. Based on the distribution of secondary particles, those spallation products with the highest linear energy transfer (LET) and longest range are revealed to emit preferentially in the forward direction, which is the root cause why the angular effect of proton-induced MCU exists. The angular dependence of single event MCU in nanometer SRAM depends strongly on proton energy and critical charge. The higher the proton energy is, the wider the angular distribution of secondary particle is, the greater the energy and LET value of the lateral scattered secondary particle is; and so the angular enhancement effect in MCU cross section for lower energy protons is greater than the higher energy protons. MCU cross section is more isotropic with the increase of the proton energy. Angular effect in MCU cross section becomes stronger with the increase of the critical charge for the same energy proton.

The protons in the secondary beam in the Beijing Electron Positron Collider (BEPC) are first analyzed and a large proportion at the energy of 50–100 MeV supply a source gap of high energy protons. In this study, the proton energy spectrum of the secondary beam was obtained and a model for calculating the proton single event upset (SEU) cross section of a static random access memory (SRAM) cell has been presented in the BEPC secondary beam proton radiation environment. The proton SEU cross section for different characteristic dimensions has been calculated. The test of SRAM SEU cross sections has been designed, and a good linear relation between SEUs in SRAM and the fluence was found, which is evidence that an SEU has taken place in the SRAM. The SEU cross sections were measured in SRAM with different dimensions. The test result shows that the SEU cross section per bit will decrease with the decrease of the characteristic dimensions of the device, while the total SEU cross section still increases upon the increase of device capacity. The test data accords with the calculation results, so the high-energy proton SEU test on the proton beam in the BEPC secondary beam could be conducted.

This paper is a systematic study of the real space dynamical electron diffraction involved in propagation calculation and sets down guidelines based on theoretical analysis for consistent and accurate computation for real space dynamical electron diffraction.

It is shown that the dynamical diffraction calculation using periodic extension of the sampling boundary points leads to serious and artificial errors in the High Resolution Electron Microscope (HREM) image simulation for a non-periodic object in FFT Multi-Slice (FFTMS) method which is now routinely used for the simulation of HREM images from periodic objects.In a systematic study of the problem of induced numerical artifacts, a new method has been proposed for the HREM image simulation of non-periodic objects. It is based on some improvements in the calculation of the phase grating and the propagation operator to the Real Space Multi-Slice (RSMS) method, which are compatible with a non-periodic object.It can be seen from the comparison with the experimental HREM images that much more better agreement can be obtained by using Real Space Multi-Slice method for Non-periodic objects (RSMSN).

This paper reports a study of the quasi-real-space (QRS) method. It is an intermediate procedure between the real-space (RS) and multi-slice (MS) methods. With this technique, most of the numerical calculations are done in RS except that normalization is imposed beyond some threshold value, e.g. σ|φ|2 > 1[sdot]01, where φ is the wavefunction of the electron. It is also numerically shown that truncation of the propagation operator exp (λeδ) to second order in the RS method can lead to computational divergences and how they can be avoided by using the QRS method. Finally, results calculated by the QRS method are compared with those obtained by other existing slice methods. The QRS method gives results similar to the conventional MS calculation with competitive computational speed.

A δ-e criterion in the real-space (RS) method for simulating high-resolution electron microscope images has been derived. This condition imposes a practical limitation in choosing the sampling interval δ and the slice thickness e for the RS method. The validity of the new criterion for the RS image simulation in high-resolution electron microscopy has been rigorously examined. It has been found that when the δ-e condition is satisfied, the RS method gives results similar to the conventional multislice method with a saving in computational time but avoiding the computing divergence which can arise in the RS method.

In a detailed study of the problem of induced numerical artifacts in the Real Space (RS) High Resolution Electron Microscopy (HREM) image simulation, a δ-ε criterion in the RS method for simulating HREM images has been derived. This condition imposes a practical limitation in choosing the sampling interval δ and the slice thickness ε for the RS method. It has been found that when the δ-ε condition is satisfied and a much more accurate formula is used for calculating the propagating factor p(r), the RS method gives results in satisfactory agreement with the conventional FFT multi-slice (FFTMS) method, but saving coputational time and avoiding the computing divergence that may arise in the RS method.

This paper reports a study of the quasi real space (QRS) method. It is an intermediate procedure between the real space (RS) and multislice (MS) methods. With this technique, most of the numerical calculations are done in real space except that the rormalization is imposed beyond some threshold value, for example ∑|Φ|2>1.01 where Φ is the wave function of the electron. It is also shown why truncation of the propagation operator eλε△ to second order in the RS method can lead to computational divergencies and how they can be avoided by using the QRS method. Finally, results calculated by the QRS method are compared with other existing slice methods. The QRS method gives results similar to the conventional MS calculation with competitive computational speed.