rus
Issue #5/2023
А.А.Glushko, М.R.Gusev, V.V.Makarchuk
RESEARCH OF THE DEPENDENCE OF THE COLLECTED CHARGE IN A MOS TRANSISTOR ON LINEAR ENERGY TRANSFER OF HEAVY IONS
RESEARCH OF THE DEPENDENCE OF THE COLLECTED CHARGE IN A MOS TRANSISTOR ON LINEAR ENERGY TRANSFER OF HEAVY IONS
DOI: https://doi.org/10.22184/1993-8578.2023.16.5.298.305
A technological simulation of a MOS transistor exposed to a heavy ion has been carried out. A hypothesis about linear dependence of the collected charge in the device on the magnitude of linear energy transfer of a particle hitting it is proposed and tested. The most sensitive to radiation exposure areas of the considered transistor are determined.
A technological simulation of a MOS transistor exposed to a heavy ion has been carried out. A hypothesis about linear dependence of the collected charge in the device on the magnitude of linear energy transfer of a particle hitting it is proposed and tested. The most sensitive to radiation exposure areas of the considered transistor are determined.
Теги: cmos technology heavy ions technological cad vlsi кмоп-технология сбис технологическая сапр тяжелые заряженные частицы
INTRODUCTION
Despite a large number of publications on the topic of radiation resistance of semiconductor devices, a universal methodical and mathematical apparatus for designing integrated circuits with enhanced resistance to radiation exposure has not been formed so far [1-5]. In the process of development of such products, taking into account the effect of heavy ions may be performed at different levels [6]:
when modelling at device level in technology CAD process;
when simulating the operation of an electrical circuit in a circuit engineering CAD system;
at register transfer level by designing digital units using modern simulators;
at system level by injecting faults directly into memory, which can be used in program development and debugging.
Finding analytical dependencies of probability of occurrence of a single failure on the value of collected charge during heavy ion transit and value of linear energy transfer (LET) would allow creating compact models that could be used in designing VLSI on the level of schematic circuit. Such a hypothetical compact model could receive as input parameters not only the device size, but also the failure probability, so that the designer at the stage of circuit design could more accurately assess performance of the selected circuit variant and its suitability for functioning under heavy ion impact.
It is known that many particles created by solar, space or other activities enter the space and terrestrial environment. These can be charged particles (electrons, protons or heavy ions) or electromagnetic radiation. Particularly noticeable effect of various kinds of charged particles affects semiconductor devices, which are part of equipment operating in outer space. Such devices are affected by both the Earth’s radiation belts and galactic particle streams during their operation. When a charged particle flies through the volume of a crystal, it loses its energy through the electron-hole pairs generation. The result of such interaction is a current pulse, approximately described by the following expression [7]:
I(t) = I0 (exp(–t/τF) – exp(–t/τR), (1)
where I0 is the maximum value of current pulse; τR is the characteristic current rise time related to the time of carrier drift through the space charge region of the p-n junction; τF is the characteristic current fall time, t is the time.
The maximum value of collected charge Qcoll resulting from heavy ion can be approximated by the following expression:
Qcoll = I0(τF – τR). (2)
In order to calculate the accumulated charge value more accurately the integral of the current pulse should be used.
In turn, the value of Qcoll determines the SER failure rate [8], which can be expressed as follows:
, (3)
where С is a process-dependent constant; Φ is particle flux; А is the area of the circuit sensitive to impact; Qcrit is the minimum charge required to cause a failure (usually determined by circuit modelling).
Determining the collected charge value is an important step for modelling the circuit operation, taking into account the failure frequency.
In order to create the compact model mentioned above, it is primarily of great interest to find an analytical relationship between the collected charge and parameters such as heavy ion energy and trajectory of its flight. The study of this dependence is discussed below.
DESCRIPTION OF THE COMPUTATIONAL EXPERIMENT
This study is devoted to determining the magnitude of charge accumulated in the volume of semiconductor device during heavy ion transit through it on LET. At the first stage of research it was considered that heavy ion transit through the device strictly vertically, that is, the angle of its meeting with the surface of the semiconductor structure is 90°, and the considered device was a transistor structure made on a silicon-on-insulator (SOI) substrate according to a technological process with a minimum feature size of 0.35 microns. In the considered structure (in the layer of cut-off silicon) presented in Fig.1 five significant regions of the device were distinguished: drain (5), source (1), body (3), LDD areas of source and drain (2, 4).
The aim of the computational experiment was to determine the shape of the current pulse in the device through instrumental simulation and use it to calculate the total collected charge. Conducting the experiment for different values of the LET of the particle passing through the transistor and causing the current pulse and calculating the collected charge corresponding to these values was aimed at confirming the hypothesis about the proportional character of the relationship between the value of the collected charge and the LET value.
For performing the above described calculations in the technology computer-aided design system we used the heavy ion model where the following parameters were used: time of heavy ion penetration into the transistor volume (Time parameter), distance l, covered by heavy ion in the volume of semiconductor material (Length parameter), characteristic distance wt(l), which is in general a function of distance l (Wt_hi parameter), and also LET value (LET_f parameter). Figure 2 shows schematically the trajectory of a heavy ion falling at an angle of 90° to the surface of the device.
Based on the above input data the generation rate of electron-hole pairs G was calculated in the model according to the expression:
GLET(l, w, t) = GLET(l)R(w, l)T(t), (4)
where GLET(l) is a function describing the heavy ion energy loss, T(t) is a function of the temporal distribution of the generation rate, R(w, l) is the spatial distribution of the generation rate.
The spatial distribution of the generation rate R(w, l) can be calculated as an exponential or Gaussian function [9]. In this computational experiment the Gaussian function was used.
The input parameter values were based on calculations obtained in the openly distributed SRIM program, which uses as input parameters the type and energy of heavy ion (in the range of 10 eV-2 GeV), as well as the material of one or more layers of the target. As simulation outputs, a three-dimensional distribution of heavy ion trajectories in the solid volume, as well as their parameters such as penetration depth and scattering along and across the ion beam, have been obtained.
The LET_f = [0.005 0.01 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.2 0.4] pC/μm were chosen as examples. The remaining numerical parameters of the heavy ion model are summarised in Table 1. In this model it was assumed that the characteristic distance wt(l) is constant and weakly dependent on the l parameter.
The calculation was carried out for a two-dimensional technology model of an n-channel MOSFET, whose electrophysical characteristics were calculated according to the hydrodynamic model equations, which allowed a more accurate description of the device behaviour compared to the standard drift-diffusion model.
The device had 5 electrical contacts: drain, source, gate, substrate and body. At the initial moment of the simulation zero voltage was present at all contacts of the device. Then the voltage at the transistor drain was increased to +3.3 V. The transistor remained off at this time. A simulation of the heavy ion transit event was then performed for the transistor in the closed state. As a result the time dependences of the drain current were obtained, an example of which is shown in Fig.3.
A Tcl script was used to obtain the collected charge value during the heavy ion transit by calculating the following integral:
, (5)
where Idrain(t) is the time response of the drain current; t1 is the start time of the drain current rise and t2 is the end time of the drain current fall according to Fig.3.
In the framework of the described computational experiment, all the values of the accumulated charge during heavy ion transit from 0.005 to 0.4 pC/μm were calculated along all 5 vertical sections shown in Fig.1.
RESULTS OF MODELLING
As a result of the simulation process, a set of dependencies of the collected charge on the LET of the heavy ion was obtained. In order to identify the analytical relationship, the events causing the highest value of collected charge were selected, as they are the ones most likely to cause failures. For these cases the graphs shown in Fig.4 were generated.
All of the presented graphs clearly show the linear dependence of the collected charge on the LET, which is confirmed by the approximation lines shown in the graphs, their equations as well as the approximation confidence factor calculated with the LibreOffice spreadsheet.
Considering the fact that the free coefficients values for the obtained linear dependences of approximating curves are several orders of magnitude smaller than the angular coefficients of their linear dependences, it can be stated that discussed dependence has a direct proportionality. Then, with a sufficient degree of certainty, it can be represented in the following form:
Qcoll = k∙LET, (6)
where k is the proportionality factor.
The proportional coefficients obtained in the computational experiment were different for the different cross sections of the device. Their values are summarised in Table 2.
It should be additionally noted that the analysis of the simulation results showed that LET penetration into the LDD area of the source, as well as in the area of drain and source contacts (sections 1, 2 and 5) practically does not cause current surge.
CONCLUSIONS
In order to assess the impact of heavy ion with different LET values penetration into the device, a technological simulation of a MOSFET manufactured according to the SOI process with a minimum feature size of 0.35 μm in 5 selected areas was conducted. Analysis of obtained results allowed to confirm the following hypotheses:
In a transistor structure, the most sensitive areas can be clearly identified, where the heavy ion passing through causes a high charge build-up in the device, which therefore means a high probability of failure. These areas include the LDD drain region and the transistor body. At the same time, heavy ion penetration into the drain and source areas has practically no effect on the functioning of the device under investigation.
The dependence of the collected charge on the LET value of the heavy ion is approximated to have a direct proportionality. Indeed, the higher energy particle causes the generation of more electron-hole pairs which contribute to the value of the collected charge. No effects that slow down the growth of the collected charge value when a certain LET value is exceeded were found in this computational experiment.
Further work could include setting up a computational experiment with heavy ion hitting the MOSFET at an angle, which would mean flying through several regions at once, and further generalising the analytical description of transistor behaviour under radiation exposure to create models suitable for use in circuit calculations.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Despite a large number of publications on the topic of radiation resistance of semiconductor devices, a universal methodical and mathematical apparatus for designing integrated circuits with enhanced resistance to radiation exposure has not been formed so far [1-5]. In the process of development of such products, taking into account the effect of heavy ions may be performed at different levels [6]:
when modelling at device level in technology CAD process;
when simulating the operation of an electrical circuit in a circuit engineering CAD system;
at register transfer level by designing digital units using modern simulators;
at system level by injecting faults directly into memory, which can be used in program development and debugging.
Finding analytical dependencies of probability of occurrence of a single failure on the value of collected charge during heavy ion transit and value of linear energy transfer (LET) would allow creating compact models that could be used in designing VLSI on the level of schematic circuit. Such a hypothetical compact model could receive as input parameters not only the device size, but also the failure probability, so that the designer at the stage of circuit design could more accurately assess performance of the selected circuit variant and its suitability for functioning under heavy ion impact.
It is known that many particles created by solar, space or other activities enter the space and terrestrial environment. These can be charged particles (electrons, protons or heavy ions) or electromagnetic radiation. Particularly noticeable effect of various kinds of charged particles affects semiconductor devices, which are part of equipment operating in outer space. Such devices are affected by both the Earth’s radiation belts and galactic particle streams during their operation. When a charged particle flies through the volume of a crystal, it loses its energy through the electron-hole pairs generation. The result of such interaction is a current pulse, approximately described by the following expression [7]:
I(t) = I0 (exp(–t/τF) – exp(–t/τR), (1)
where I0 is the maximum value of current pulse; τR is the characteristic current rise time related to the time of carrier drift through the space charge region of the p-n junction; τF is the characteristic current fall time, t is the time.
The maximum value of collected charge Qcoll resulting from heavy ion can be approximated by the following expression:
Qcoll = I0(τF – τR). (2)
In order to calculate the accumulated charge value more accurately the integral of the current pulse should be used.
In turn, the value of Qcoll determines the SER failure rate [8], which can be expressed as follows:
, (3)
where С is a process-dependent constant; Φ is particle flux; А is the area of the circuit sensitive to impact; Qcrit is the minimum charge required to cause a failure (usually determined by circuit modelling).
Determining the collected charge value is an important step for modelling the circuit operation, taking into account the failure frequency.
In order to create the compact model mentioned above, it is primarily of great interest to find an analytical relationship between the collected charge and parameters such as heavy ion energy and trajectory of its flight. The study of this dependence is discussed below.
DESCRIPTION OF THE COMPUTATIONAL EXPERIMENT
This study is devoted to determining the magnitude of charge accumulated in the volume of semiconductor device during heavy ion transit through it on LET. At the first stage of research it was considered that heavy ion transit through the device strictly vertically, that is, the angle of its meeting with the surface of the semiconductor structure is 90°, and the considered device was a transistor structure made on a silicon-on-insulator (SOI) substrate according to a technological process with a minimum feature size of 0.35 microns. In the considered structure (in the layer of cut-off silicon) presented in Fig.1 five significant regions of the device were distinguished: drain (5), source (1), body (3), LDD areas of source and drain (2, 4).
The aim of the computational experiment was to determine the shape of the current pulse in the device through instrumental simulation and use it to calculate the total collected charge. Conducting the experiment for different values of the LET of the particle passing through the transistor and causing the current pulse and calculating the collected charge corresponding to these values was aimed at confirming the hypothesis about the proportional character of the relationship between the value of the collected charge and the LET value.
For performing the above described calculations in the technology computer-aided design system we used the heavy ion model where the following parameters were used: time of heavy ion penetration into the transistor volume (Time parameter), distance l, covered by heavy ion in the volume of semiconductor material (Length parameter), characteristic distance wt(l), which is in general a function of distance l (Wt_hi parameter), and also LET value (LET_f parameter). Figure 2 shows schematically the trajectory of a heavy ion falling at an angle of 90° to the surface of the device.
Based on the above input data the generation rate of electron-hole pairs G was calculated in the model according to the expression:
GLET(l, w, t) = GLET(l)R(w, l)T(t), (4)
where GLET(l) is a function describing the heavy ion energy loss, T(t) is a function of the temporal distribution of the generation rate, R(w, l) is the spatial distribution of the generation rate.
The spatial distribution of the generation rate R(w, l) can be calculated as an exponential or Gaussian function [9]. In this computational experiment the Gaussian function was used.
The input parameter values were based on calculations obtained in the openly distributed SRIM program, which uses as input parameters the type and energy of heavy ion (in the range of 10 eV-2 GeV), as well as the material of one or more layers of the target. As simulation outputs, a three-dimensional distribution of heavy ion trajectories in the solid volume, as well as their parameters such as penetration depth and scattering along and across the ion beam, have been obtained.
The LET_f = [0.005 0.01 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.2 0.4] pC/μm were chosen as examples. The remaining numerical parameters of the heavy ion model are summarised in Table 1. In this model it was assumed that the characteristic distance wt(l) is constant and weakly dependent on the l parameter.
The calculation was carried out for a two-dimensional technology model of an n-channel MOSFET, whose electrophysical characteristics were calculated according to the hydrodynamic model equations, which allowed a more accurate description of the device behaviour compared to the standard drift-diffusion model.
The device had 5 electrical contacts: drain, source, gate, substrate and body. At the initial moment of the simulation zero voltage was present at all contacts of the device. Then the voltage at the transistor drain was increased to +3.3 V. The transistor remained off at this time. A simulation of the heavy ion transit event was then performed for the transistor in the closed state. As a result the time dependences of the drain current were obtained, an example of which is shown in Fig.3.
A Tcl script was used to obtain the collected charge value during the heavy ion transit by calculating the following integral:
, (5)
where Idrain(t) is the time response of the drain current; t1 is the start time of the drain current rise and t2 is the end time of the drain current fall according to Fig.3.
In the framework of the described computational experiment, all the values of the accumulated charge during heavy ion transit from 0.005 to 0.4 pC/μm were calculated along all 5 vertical sections shown in Fig.1.
RESULTS OF MODELLING
As a result of the simulation process, a set of dependencies of the collected charge on the LET of the heavy ion was obtained. In order to identify the analytical relationship, the events causing the highest value of collected charge were selected, as they are the ones most likely to cause failures. For these cases the graphs shown in Fig.4 were generated.
All of the presented graphs clearly show the linear dependence of the collected charge on the LET, which is confirmed by the approximation lines shown in the graphs, their equations as well as the approximation confidence factor calculated with the LibreOffice spreadsheet.
Considering the fact that the free coefficients values for the obtained linear dependences of approximating curves are several orders of magnitude smaller than the angular coefficients of their linear dependences, it can be stated that discussed dependence has a direct proportionality. Then, with a sufficient degree of certainty, it can be represented in the following form:
Qcoll = k∙LET, (6)
where k is the proportionality factor.
The proportional coefficients obtained in the computational experiment were different for the different cross sections of the device. Their values are summarised in Table 2.
It should be additionally noted that the analysis of the simulation results showed that LET penetration into the LDD area of the source, as well as in the area of drain and source contacts (sections 1, 2 and 5) practically does not cause current surge.
CONCLUSIONS
In order to assess the impact of heavy ion with different LET values penetration into the device, a technological simulation of a MOSFET manufactured according to the SOI process with a minimum feature size of 0.35 μm in 5 selected areas was conducted. Analysis of obtained results allowed to confirm the following hypotheses:
In a transistor structure, the most sensitive areas can be clearly identified, where the heavy ion passing through causes a high charge build-up in the device, which therefore means a high probability of failure. These areas include the LDD drain region and the transistor body. At the same time, heavy ion penetration into the drain and source areas has practically no effect on the functioning of the device under investigation.
The dependence of the collected charge on the LET value of the heavy ion is approximated to have a direct proportionality. Indeed, the higher energy particle causes the generation of more electron-hole pairs which contribute to the value of the collected charge. No effects that slow down the growth of the collected charge value when a certain LET value is exceeded were found in this computational experiment.
Further work could include setting up a computational experiment with heavy ion hitting the MOSFET at an angle, which would mean flying through several regions at once, and further generalising the analytical description of transistor behaviour under radiation exposure to create models suitable for use in circuit calculations.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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