A simulation method for ionization damage effects in oxide layers of microelectronic devices

Abstract

The application discloses a simulation method of ionization damage effect of an oxide layer of a microelectronic device, and comprises the following steps: (1) establishing an initial state model of a simulation system; (2) constructing an event table; (3) calculating transition frequencies of all possible event combinations of particle transition and reaction in the simulation system according to the constructed event table and the state of the simulation system; (4) determining an event combination to be occurred before a next simulation time step and determining a system state after the event combination based on a first random number and the calculated transition frequencies of the various event combinations of the simulation system; (5) determining a time length of the simulation time step based on a second random number and updating a simulation time of the simulation system; (6) injecting event simulation radiation; (7) iteratively circulating; and (8) representing simulation results of the ionization damage effect in one or more defect area or concentration changes and outputting.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology of radiation effects, and in particular to a method for simulating the ionization damage effect of oxide layers in microelectronic devices. Background Technology

[0002] The space radiation environment contains various charged particles such as protons, electrons, and heavy ions. These charged particles interact with the semiconductor materials of aerospace equipment and devices, causing various types of damage.

[0003] The total dose effect of ionizing radiation is one of the space radiation effects, and it is closely related to the oxide layer (such as silicon dioxide) materials widely used in microelectronics processes. When charged particles (such as electrons, protons, etc.), gamma rays, and X-rays act on the oxide layer of a device to generate excess electron-hole pairs, a series of physical processes such as recombination, transport, and trapping will occur at different locations inside the device, affecting the electrical properties of the electronic device.

[0004] Numerical simulation is the primary technique for studying the physical mechanisms of ionization damage effects on oxide layers. Extensive research on numerical simulation of ionization damage effects has already been conducted in this field.

[0005] However, the main drawback of existing technologies lies in the differing understandings among researchers regarding the formation mechanism of ionization damage effects. This often leads to the simplification or neglect of certain important physical processes in the formation of radiation-sensitive products, potentially resulting in an incomplete or inaccurate understanding of the physical mechanisms of ionization damage effects. Existing related models can be broadly categorized into space charge models, bimolecular models, competition models, and binary reaction rate models. Due to the incomplete background mechanisms upon which these models are based, their simulation results are not entirely accurate.

[0006] Another problem with existing technologies is that numerical simulation methods are based on the finite element numerical solution of mean field theory. This method has the limitation of large errors when the sample is small and the dose rate is extremely low. In addition, it cannot calculate the case of non-uniformity of electron-hole pairs in time and space. Summary of the Invention

[0007] To address the aforementioned problems, the present invention aims to propose a simulation method for the ionization damage effect of oxide layers in microelectronic devices. This method is based on a specially designed kinetic Monte Carlo (KMC) simulation method, which constructs an event table of all relevant particles and defects in the oxide layer during the radiation process based on a more comprehensive mechanism of ionization damage. Radiation is simulated using injection events, and the simulation time step is continuously updated during the simulation of selected events. Therefore, compared with existing simulation methods based on incomplete physical mechanisms, the accuracy of the simulation results can be improved.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, this application provides a method for simulating the ionization damage effect of oxide layers in microelectronic devices, comprising: Step (1): Based on the oxide layer structure of the microelectronic device to be simulated, establish an initial state model of the simulation system. The initial state model includes the spatial range and boundary of the system, the set types of mobile particles and their concentrations within the spatial range, and the preset types of defects and their regions and concentrations within the spatial range. Step (2): Construct an event table, which includes migration events and reaction events. The migration events define the transition modes of various mobile particles, and the reaction events include the reactions between mobile particles and the reactions between mobile particles and defects. Step (3): Based on the constructed event table and the state of the simulation system, calculate the transition frequencies of all possible event combinations of particle transitions and reactions in the simulation system; Step (4): Based on the first random number and the transition frequencies of various event combinations of the simulated system, determine the event combinations to occur before the next simulation time step, and determine the system state after the event combinations. Step (5): Based on the second random number, determine the duration of the simulation time step and update the simulation time of the simulation system; Step (6): Based on the set conditions, simulate radiation with injection events, and update the state of the simulated system after the injection events; Step (7): Repeat the iterative loop from step (3) to step (6) until the set simulation termination condition is met; Step (8) is to characterize and output the simulation results of one or more defects in terms of regional or concentration changes when the simulation ends, thus achieving the simulation termination conditions.

[0009] In one implementation, in step (1), the mobile particle includes: electrons, holes, protons, and hydrogen molecules; The defects include deep-level defects and shallow-level defects; the deep-level defects are distributed at a set concentration within a set depth range from the contact surface; the shallow-level defects are uniformly distributed in the remaining area of ​​the oxide layer.

[0010] In one implementation, the boundary includes the boundary of the contact surface between the metal and semiconductor in the microelectronic device, as well as the boundary of other non-contact surfaces. For the boundary of the contact surface, a barrier is preset to prevent the movement of a certain type of movable particle. For other boundaries, periodic boundary conditions are applied to movable particles of a given type.

[0011] In one implementation, in step (2), during a migration event, each type of mobile particle corresponds to a diffusion coefficient, a migration barrier, and a migration step size; In a simulated time step, the movable particle migrates randomly in six directions.

[0012] In one implementation, the specific types of defects include: Neutral deep-level defects and their hydrogenation defects include: ; Charged deep-level defects and their hydrogenation defects include: ; Neutral shallow-level defects and their hydrogenation defects include: ; Charged shallow-level defects and their hydrogenation defects include:

[0013] Dangling Si-H bonds and interface trap charges N it .

[0014] Reactions between mobile particles include: High-energy photons interact with amorphous SiO2, ionizing it to generate electron-hole pairs. Some of these electron-hole pairs recombine after a period of time. (1) The interaction between mobile particles and defects includes: (1) The interaction between holes and defects; (2) The interaction between electrons and defects; (3) Defects decompose hydrogen molecules to release protons; (4) The defect decomposes directly, releasing protons; (5) Formation of interface trap charges.

[0015] In one implementation, in step (6), the injection event occurs at fixed time steps.

[0016] In one implementation, during the injection event, multiple movable particles of a set type are generated at multiple random locations within the spatial range of the system.

[0017] In one implementation, if the calculated simulation time step is longer than a fixed time step in each iteration, the event combination selected based on the first random number will not occur.

[0018] The present invention has the following advantages due to the adoption of the above technical solutions: Current simulations of ionization damage primarily rely on numerical solutions using the finite element method (FEM) based on the continuity assumption. This method has significant limitations. When applied to scenarios with extremely small device sizes or extremely low dose rates, the continuity assumption may no longer be applicable. Furthermore, the computational difficulty of the FEM increases significantly when dealing with three-dimensional cases, resulting in most current FEM simulations being limited to one-dimensional and two-dimensional models. In addition, the temporal and spatial locality and pulsed nature of ion irradiation are difficult to describe using the FEM method. Our proposed method effectively addresses these issues.

[0019] Compared to the finite element method, the simulation method provided in this invention takes a particle transport perspective, tracking the motion of individual particles, which facilitates more accurate analysis of specific physical processes. This method is applicable to oxide layers of arbitrary thickness, and its computational complexity is almost unaffected by dimensionality, making the simulation of three-dimensional devices relatively simple. Furthermore, the simulation can set the initial defect distribution as needed and can simulate irradiation conditions that are non-uniform in time and space, such as pulsed irradiation and ion irradiation. These characteristics make this method more adaptable and accurate than the finite element method in simulating the irradiation effects of electronic devices, especially when considering complex irradiation conditions. Attached Figure Description

[0020] Figure 1 This is a graph showing the relationship between the statistical approximation of the electron diffusion coefficient and the electron free diffusion time in one embodiment of the present invention. Figure 2 This is a graph showing the relationship between mobility statistics and the magnitude of the external electric field in an embodiment of the present invention. Figure 3 This is a schematic diagram of the program flow in a detailed embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0022] This application provides a method for simulating the ionization damage effect of oxide layers in microelectronic devices, including: Step (1): Based on the oxide layer structure of the microelectronic device to be simulated, establish an initial state model of the simulation system. The initial state model includes the spatial range and boundary of the system, the set types of mobile particles and their concentrations within the spatial range, and the preset types of defects and their regions and concentrations within the spatial range. Step (2): Construct an event table, which includes migration events and reaction events. The migration events define the transition modes of various mobile particles, and the reaction events include the reactions between mobile particles and the reactions between mobile particles and defects. Step (3): Based on the constructed event table and the state of the simulation system, calculate the transition frequencies of all possible event combinations of particle transitions and reactions in the simulation system; Step (4): Based on the first random number and the transition frequencies of various event combinations of the simulated system, determine the event combinations to occur before the next simulation time step, and determine the system state after the event combinations. Step (5): Based on the second random number, determine the duration of the simulation time step and update the simulation time of the simulation system; Step (6): Based on the set conditions, simulate radiation with injection events, and update the state of the simulated system after the injection events; Step (7): Repeat the iterative loop from step (3) to step (6) until the set simulation termination condition is met; Step (8) is to characterize and output the simulation results of one or more defects in terms of regional or concentration changes when the simulation ends, thus achieving the simulation termination conditions.

[0023] The following is based on Figures 1 to 3 In a more detailed embodiment, the method of this application is described.

[0024] Detailed Implementation Examples In this detailed embodiment, the ionization damage effect of the oxide layer in a microelectronic device is simulated using the KMC simulation method. The microelectronic device can be a MOS structure device, including a metal, a semiconductor, and an oxide layer. The oxide layer can be a silicon dioxide layer.

[0025] The physical basis and detailed simulation process of this invention are described in detail below.

[0026] Consider a system undergoing a memoryless random walk on a potential energy surface. Assume that the frequency of transitions in the system remains constant over a sufficiently long period of time, and denote this transition frequency as . It can be known that within a unit of time... Within, the probability of a transition is This is directly proportional to the length of a unit of time. Considering a second-order small quantity, we can deduce that within the interval... Within the system, the probability F of no transition event is:

[0027] Similarly, for intervals The probability F that the system does not experience a transition event is:

[0028] By analogy, when At that time, in the interval Within the system, the probability that no transition event occurs is:

[0029] Similarly, when tending to When the system does not undergo a transition, the probability is:

[0030] Based on this, define The probability of a transition occurring in the system per unit time is: Since the transition probability at a certain moment should be the derivative of the transition probability of the system before that moment, it is easy to obtain:

[0031] The above derivation process can be compared with the theoretical derivation related to radioactive element decay. Due to the similar principles, similar results will be obtained. In reality, for any given system, there may be many different transition paths, each corresponding to a different transition frequency. Therefore, the total jump probability is the sum of the jump probabilities of all paths:

[0032] The subscript "ij" indicates that the system transitions from state i to state j. From the above formula, we can also determine the probability of each process occurring and the transition probability of that process. Proportional.

[0033] From the above derivation, it can be seen that at any given moment, the probability distribution of a transition in the system follows an exponential distribution. Therefore, it can be inferred that the time interval between two adjacent events is... It also exhibits an exponential distribution. Let Indicates a Given a uniformly distributed random sequence within a range, the time interval between adjacent events is: .

[0034] In the above derivation, there is actually only one unknown. However, determining its value is a very difficult task. The transition frequency represented is a fairly microscopic quantity. If the tracking of events is refined to the bottom of the atomic trajectory, it's essentially reverting to the old methods of MD simulation. This would drastically increase the event cost of the KMC method, negating its advantages. Therefore, KMC generally uses Transition State Theory (TST) for calculations.

[0035] In short, in transition state theory, the transition rate of a system depends only on the highest energy point on the lowest energy path between two adjacent states, i.e., the saddle point energy. Using relevant theories of statistical physics, and with some simplifications, the transition frequency can be expressed in a relatively simple form. :

[0036] in, The height of the potential barrier during the migration process. Boltzmann's constant, It is the thermodynamic temperature. This is a simplified constant derived for practical considerations, and is often taken as the Debye vibration frequency of the material. For example, for metals, If the oxide layer system in this project is silicon dioxide, then take... .

[0037] The calculations require determining the lowest energy path during the migration process and the saddle point energy along the path, thus necessitating the identification of the transition state configuration. Many algorithms exist for searching transition states, such as the micro-motion elastic band method, the Newton-Raphson method, and the synchronous transition method. In this project, particle migration... The particle reaction is obtained by inversely calculating the mobility. The reaction barriers in the quantitative model are directly used, and these barriers are calculated using the first principles of density functional theory.

[0038] The simulation method is explained below.

[0039] It introduces the free diffusion and migration process of mobile particles, the setting of boundary conditions, and the distribution of defects in the system.

[0040] (1) Free diffusion of mobile particles This model involves four types of mobile particles, whose diffusion coefficients at room temperature (300 K) are known. The concentration distribution of mobile particles in the region can be obtained based on the drift-diffusion equation. The formula is as follows. Where... and These represent the diffusion coefficient and mobility of the particle, respectively. For electric field, and Let f be the generation and composition functions of electron-hole pairs.

[0041]

[0042] Analyze the free diffusion term caused by the diffusion coefficient. In KMC, describing the motion of particles requires a migration barrier. and migration step size Two parameters. Although the diffusion coefficient cannot be directly input into the simulation parameters, given the migration barrier and migration step size, an approximate value of the diffusion coefficient over a certain time interval can be obtained using the mean square displacement (MSD). The particle diffusion coefficient is related to the MSD as follows:

[0043] The value of the MSD (Mean Scaling Depth) can be obtained by tracking the trajectories of particles within the system. Although the MSD value is not constant due to the extensive use of random numbers in the KMC program, its expected value can be rigorously derived theoretically, and the expected value of the MSD corresponds to the theoretical value of the diffusion coefficient. It can be proven that the diffusion coefficient... Barrier and migration step size The following relationship exists between them. The constants inherent in the KMC method are often taken as the Debye vibration frequencies of the material. For example, for metals, In this work, the system is silicon dioxide, and the following is taken: Therefore, by determining either the migration barrier or the migration step size, a definite set of parameters can be given.

[0044]

[0045] According to the transition state theory, the relationship between the diffusion coefficient and the migration barrier can be determined under a simplified model as follows:

[0046]

[0047] in is the lattice constant. This is the Debye vibration frequency. It can be used to estimate the frequency of the SiO2 crystal. Approximately 0.01cm 2 / s, thus allowing the calculation of the migration barrier and migration step size of a mobile particle. For example, its diffusion coefficient is known. D ,Pick Given the estimated value, the migration barrier can be calculated as 0.4605 eV. Therefore, the corresponding migration step size can be calculated as 0.5708 nm.

[0048]

[0049]

[0050] Based on this method, the migration barriers and migration step lengths of four types of mobile particles can be obtained. It can be seen that the migration step lengths of the four types of particles all match the lattice constant of SiO2 crystal (~0.54 nm) and are all in the range of 0.1 nm to 1 nm.

[0051] The table below lists the corresponding parameters of the four mobile particles involved in this detailed embodiment (electron, hole, proton and hydrogen molecule in order).

[0052]

[0053] (2) Migration of mobile particles in an electric field The migration process of charged particles in an electric field can be determined by mobility. This parameter describes mobility. With diffusion coefficient The relationship between them conforms to Einstein's relation, as shown in the formula.

[0054]

[0055] In KMC, the electric field does not directly determine the direction of charged particle motion. Instead, it indirectly and statistically demonstrates the directional movement of particles by influencing the probability of movement. Using the Metropolis criterion, when a particle migration event is selected, the particle will randomly choose one of its six adjacent positions in the 3D grid to attempt movement. Whether the movement is accepted depends on the probability of movement. It is determined by the following formula:

[0056] in It is the total electric potential energy of a particle before it attempts to move, including the electric potential energy interacting with an external electric field and the electric potential energy interacting with other charged particles. This is the total electric potential energy of the particle after it attempts to move. The total electric potential energy of a charged particle, numbered i, at a certain position can be expressed by the following formula. The first term is the electric potential energy of the particle interacting with the external electric field, and the second term is the electric potential energy of the particle interacting with other charged particles. is the relative permittivity of SiO2.

[0057]

[0058] Similar to the diffusion coefficient, mobility cannot be directly input into the KMC program as a parameter, but a statistical approximation of mobility can be calculated by statistically analyzing the directional migration rates of charged particles in an electric field. It can be proven that by selecting the movement event based on the difference in electric potential energy before and after the movement, under a low electric field approximation (less than or equal to...), a statistical approximation of mobility can be obtained. ), migration rate With diffusion coefficient The relationship between them basically satisfies Einstein's relation. As the electric field strength increases, the mobility decreases slowly, which is consistent with experimental results.

[0059] (3) Overview of the behavior of mobile particles within the system The particles may be generated by irradiation and appear directly at the initial position; or they may be generated by a reaction, with the particles appearing randomly in one of the six directions of the fixed defect at a distance of 1.05 times the reaction distance of 20 Å, to prevent the binding-decomposition process from repeating indefinitely.

[0060] For particle transport, particles will only migrate along 3 pairs of orthogonal directions, for a total of 6 possible directions. The specific migration step size and migration direction selection are described in the simulation methods (1) and (2) above.

[0061] For particle elimination, the first step is migration outside the simulated region, specifically outside the metal and semiconductor contact surfaces. In this case, the particle is directly deleted, and the possibility of it returning to the simulated region through thermal motion is no longer considered. The second step is recombination, where only electrons and holes recombine. The set recombination distance is 10 Å, but in reality, due to Coulomb forces, they generally attract each other at distances much greater than 10 Å. The final step is the reaction between particles and defects. Regardless of the charge conditions of the reacting parties, the reaction distance is uniformly set to 20 Å.

[0062] (4) Setting boundary conditions For metal and semiconductor interfaces, an absorption boundary condition is applied to electrons, holes, hydrogen molecules, and protons (hydrogen atoms) that have trapped electrons. A very high potential barrier (tentatively set at 10 eV) is set for the protons to prevent them from passing through.

[0063] For the other four boundaries, approximate periodic boundary conditions are used, described as follows: It is possible to pass through the boundary and emerge from the opposite side boundary, but the description of the Coulomb force is not entirely based on periodic boundaries. The interaction of each pair of charged particles is considered only once, and calculated according to the direction of closest distance. For example, the side length in the y-direction is 100. =1, =99, then only according to Calculate once.

[0064] (5) The distribution and number of defects within the system In this detailed embodiment, the specific types of defects include: Neutral deep-level defects and their hydrogenation defects include: ; Charged deep-level defects and their hydrogenation defects include: ; Neutral shallow-level defects and their hydrogenation defects include: ; Charged shallow-level defects and their hydrogenation defects include:

[0065] Dangling Si-H bonds and interface trap charges N it .

[0066] There are a total of 14 defects.

[0067] In different simulation scenarios, different defect types can be selected according to different devices, and different corresponding locations and concentrations can be set. The following table shows the defect types and their concentration values ​​selected in a simulation scenario.

[0068]

[0069] Testing revealed that distributing deep-level defects near the interface yielded results closer to experimental findings. While the distribution pattern had a relatively small impact on the interface trap charge, it significantly influenced the charge variation of the stabilized oxide layer. Therefore, in this simulation, the defect distribution was set such that all deep-level defects were uniformly distributed within a 1 nm depth range from the semiconductor contact surface, while all shallow-level defects were uniformly distributed throughout the remaining areas of the oxide layer. A potential problem with this distribution pattern is that the number of deep and shallow level defects calculated simply using density differs under different thickness conditions. The defect concentration beyond the 1 nm range varies considerably with different thicknesses; in particularly thin (several nm scales) or very thick layers, the defect concentration in one region may be far greater than the experimentally observed value.

[0070] In this detailed embodiment, the reactions in the event include reactions between movable particles and reactions between movable particles and defects.

[0071] Reactions between mobile particles include: High-energy photons interact with amorphous SiO2, ionizing it to generate electron-hole pairs. Some of these electron-hole pairs recombine after a period of time. (1) The interaction between mobile particles and defects includes: (a) The interaction between holes and defects; Holes interact with six types of neutral defects within the oxide layer to form six types of positively charged defects, mainly through the following six reaction processes.

[0072] A. Neutral deep-level defects They are mainly concentrated near the Si / SiO2 interface, trapping holes to form positively charged oxygen vacancy defects. For a positive reaction barrier, It is a reverse reaction barrier.

[0073] (2) B. Neutral shallow level defects Primarily distributed within the SiO2 oxide layer, holes jump back and forth in shallow energy level defects, which can regulate the kinetics of hole transport within the oxide layer.

[0074] (3) C. Neutral monohydrogenation deep level defects The oxygen vacancy in the deep energy level of the single hydrogenation traps a hole and becomes a positively charged oxygen vacancy defect.

[0075] (4) D. Neutral monohydrogenation shallow level defect The shallow-level oxygen vacancy of the single-hydrogenated oxygen vacancy traps a hole and becomes a positively charged oxygen vacancy defect.

[0076] (5) E. Neutral double hydrogenation deep level defects Deep-level oxygen vacancies undergoing double hydrogenation capture holes, becoming positively charged oxygen vacancy defects.

[0077] (6) F, Neutral dihydrogenation shallow level defect The shallow-level oxygen vacancy, after double hydrogenation, captures a hole and becomes a positively charged oxygen vacancy defect.

[0078] (7) (b) The interaction between electrons and defects; Electrons interact with six positively charged defects within the oxide layer to form six neutral defects, which mainly involve the following six reaction processes.

[0079] A. Charged deep-level defects They are mainly concentrated near the Si / SiO2 interface and can serve as recombination centers at the interface. (8) B. Shallow charged level defects (9) C. Charged single-hydrogenation deep-level defects (10) D. Charged single-hydrogenation shallow level defect (11) E. Charged double-hydrogenated deep-level defects (12) F. Charged double-hydrogenated shallow level defects (13) (c) Defects decompose hydrogen molecules to release protons; The basic physical process consists of two parts. The first step is the direct decomposition of charged dihydrogenation defects, releasing H2, which involves the following two reactions.

[0080] A. The decomposition of charged double-hydrogenated deep-level defects releases hydrogen molecules. (14) B. The decomposition of charged, shallow-level hydrogenation defects releases hydrogen molecules. (15) The second step involves the interaction of charged defects with hydrogen molecules, resulting in the formation of monohydrogenated defects that release protons. This process involves the following two reactions.

[0081] A. Charged deep-level defects break down hydrogen molecules and release protons. (16) B. Charged shallow-level defects break down hydrogen molecules and release protons. (17) (d) The defect decomposes directly, releasing protons; Charged single and double hydrogenation defects decompose directly, releasing protons. This includes the following four reactions.

[0082] A. Charged single-hydrogenated deep-level defects directly decompose, releasing protons. (18) B. Charged single-hydrogenated shallow-level defects directly decompose, releasing protons. (19) C. Charged double-hydrogenated deep-level defects directly decompose, releasing protons. (20) D. Charged double-hydrogenated shallow-level defects directly decompose, releasing protons. (twenty one) (e) Formation of interface trap charges.

[0083] Protons are transported to the interface under the influence of an electric field, react with hydrogen-passivated dangling bonds, and generate interfacial trap charges. .

[0084] (twenty two)

[0085] The following reaction table can be used to summarize:

[0086] (6) Simulated irradiation method In the KMC simulation, irradiation involves injecting a pair of electron-hole pairs at fixed time intervals. Under the current settings, the positions of the electrons and holes are independent and generated completely randomly throughout the region. The program treats each injection as an event, and to ensure a fixed injection time interval, it performs a check after each selected event. If the event occurs before the next injection, it proceeds normally; if it occurs after the next injection, it is prevented from occurring, and the injection is rescheduled to occur at the next scheduled injection time.

[0087] (7) Setting the waiting time The purpose of setting a waiting time is to allow the system to stabilize at a relatively high dose rate before counting. This can be simply understood as the time required to allow the device defects to evolve and stabilize before testing. The waiting time should be chosen to ensure that the transport processes of all holes and protons within the system are essentially complete. Unless the reverse space electric field reaches the magnitude of the external electric field, the basic requirement is that there are no free holes (and unstable shallow-level charged defects) and free protons in the system. On the other hand, the waiting time should not be too long, because the total time itself is one of the causes of the dose rate effect, and an excessively long waiting time will partially weaken this effect. The waiting time is related to factors such as system thickness, external electric field strength, and temperature; currently, the time used in this simulation is mostly in the range of 0.2 s to 2 s.

[0088] (8) Special treatment for proton to capture electrons During program execution, it is observed that due to the Coulomb attraction between protons and electrons, protons attract nearby electrons, which cannot escape, significantly slowing down the program. Therefore, a new mobile particle, the hydrogen atom, is defined. The proton and the attracted electron are considered as a single entity, and the diffusion coefficient of the hydrogen atom is consistent with that of the proton. The hydrogen atom can undergo any reaction that electrons can undergo, including recombination, which manifests as the loss of an electron and the release of a proton. However, conversely, in this simulation, it is currently assumed that the hydrogen atom cannot undergo the series of reactions in which protons can participate. In actual tests, the production of hydrogen atoms is an extremely rare event, and its impact on the system is minimal when the electron-hole pair concentration is low.

[0089] (9) Verification of migration and diffusion reliability 100 independent electrons are added to the system, and the region size is set to infinite. The statistical approximation of the electron diffusion coefficient and the relationship between the electron free diffusion time are obtained by calculating the MSD, as shown below. Figure 1 As can be seen, once the motion time statistics reach the time required for stabilization, the statistical approximation of the diffusion coefficient will stabilize near the theoretical value.

[0090] 1000 independent electrons were added to the system, the region size was set to infinite, and different external electric fields were applied. The average migration rate of electrons under different external electric fields was statistically analyzed, and the corresponding mobility statistics were calculated. The relationship between the mobility statistics and the magnitude of the external electric field is as follows: Figure 2 As shown. It can be observed that when the electric field is not too large, that is, less than or equal to The mobility statistics remain relatively stable and are roughly equal to the theoretical mobility derived from Einstein's relation. As the electric field strength increases, the mobility statistics gradually decrease and approach zero because the migration rate tends to saturate. This demonstrates that it is feasible to use the Metropolis criterion to describe the migration of charged particles in an electric field under low electric fields.

[0091] In this detailed embodiment, the simulation method can be implemented using a computer program.

[0092] Figure 3 A schematic diagram of the program's main structure is shown.

[0093] The programming language used is C++, and considering that scientific computing needs to run on a Linux system, the program structure is described as follows: (1) Generate and read the initial state file based on the physical model. The initial state includes the number and position information of various particles. The program calculates all possible events (including particle migration and reactions) and the corresponding transition frequencies. And record the sum of all transition frequencies. .

[0094] (2) Generate a random number between 0 and 1 If the inequality is satisfied Then the j-th random process occurs, updating the particle, possible events, and the sum of transition frequencies. .

[0095] (3) Generate another random number between 0 and 1 Calculate the time interval between the current event and the previous event. Update time .

[0096] (4) When certain conditions are met, new particles are added to simulate continuous irradiation, and possible events and the sum of transition frequencies are updated synchronously. wait.

[0097] Repeat steps (2)-(4) until the termination condition is met, at which point the program ends.

[0098] In summary, the selection of events determines the direction of system evolution in the above procedure. Within the oxide layer of interest in this procedure, all events revolve around defects and mobile particles, and can be broadly categorized into three types: migration and diffusion of mobile particles, reactions between particles and defects, and electron-hole pair generation caused by irradiation events. The generation of electron-hole pairs depends on external photon injection and is therefore scheduled to occur periodically under different conditions. The migration and diffusion of mobile particles and the reactions between particles and defects occur spontaneously, and whether and when these events occur depends on the random number selection.

[0099] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. In the embodiments provided by this invention, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between devices or units through some interfaces, and may be electrical, mechanical, or other forms.

[0100] The integrated units implemented as software functional units described above can be stored in a computer-readable storage medium. These software functional units, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0101] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for simulating the ionization damage effect of oxide layers in microelectronic devices, characterized in that, include: Step (1): Based on the oxide layer structure of the microelectronic device to be simulated, establish an initial state model of the simulation system. The initial state model includes the spatial range and boundary of the system, the set types of mobile particles and their concentrations within the spatial range, and the preset types of defects and their regions and concentrations within the spatial range. Step (2): Construct an event table, which includes migration events and reaction events. The migration events define the transition modes of various mobile particles, and the reaction events include the reactions between mobile particles and the reactions between mobile particles and defects. Step (3): Based on the constructed event table and the state of the simulation system, calculate the transition frequencies of all possible event combinations of particle transitions and reactions in the simulation system; Step (4): Based on the first random number and the transition frequencies of various event combinations of the simulated system, determine the event combinations to occur before the next simulation time step, and determine the system state after the event combinations. Step (5): Based on the second random number, determine the duration of the simulation time step and update the simulation time of the simulation system; Step (6): Based on the set conditions, simulate radiation with injection events, and update the state of the simulated system after the injection events; Step (7): Repeat the iterative loop from step (3) to step (6) until the set simulation termination condition is met; Step (8) is to characterize and output the simulation results of one or more defects in terms of regional or concentration changes when the simulation ends, thus achieving the simulation termination conditions.

2. The method according to claim 1, characterized in that, In step (1), the movable particles include: electrons, holes, protons and hydrogen molecules.

3. The method according to claim 2, characterized in that, The boundary includes the boundary of the contact surface between metal and semiconductor in a microelectronic device, as well as the boundary of other non-contact surfaces. For the boundary of the contact surface, a barrier is preset to prevent the movement of a certain type of movable particle. For other boundaries, periodic boundary conditions are applied to movable particles of a given type.

4. The method according to claim 1, characterized in that, In step (2), during the migration event, each type of mobile particle corresponds to a diffusion coefficient, a migration barrier, and a migration step size. In a simulated time step, the movable particle migrates randomly in six directions.

5. The method according to claim 4, characterized in that, The defects include deep-level defects and shallow-level defects; the deep-level defects are distributed at a set concentration within a set depth range from the contact surface; the shallow-level defects are uniformly distributed in the remaining area of ​​the oxide layer.

6. The method according to claim 1, characterized in that, In step (6), the injection event occurs at fixed time steps.

7. The method according to claim 6, characterized in that, During the injection event, multiple types of movable particles are generated at multiple random locations within the spatial range of the system.

8. The method according to claim 6, characterized in that, In each iteration, if the calculated simulation time step is longer than the fixed time step, the event combination selected based on the first random number will not occur.

9. A computer system, characterized in that, It includes a processor and a memory, the memory storing a computer program, which is executed by the processor to implement the method of claims 1-8.

10. A computer storage medium, characterized in that, The device contains a computer program that is executed by a processor to implement the method described in claims 1-8.

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