Example ODI questions.
\r\n\t
",isbn:"978-1-80355-607-9",printIsbn:"978-1-80355-606-2",pdfIsbn:"978-1-80355-608-6",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,isSalesforceBook:!1,hash:"6cf0b844f6881c758c61cca10dc8b134",bookSignature:"Associate Prof. Gülşen Akın Evingür and Dr. Önder Pekcan",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/11830.jpg",keywords:"Elasticity, Toughness, Modulus, Compression, Extension, Optical Properties, Swelling, Drying, Diffusion, Release, Transmission Loss, Sound Absorption Coefficient",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"April 5th 2022",dateEndSecondStepPublish:"May 3rd 2022",dateEndThirdStepPublish:"July 2nd 2022",dateEndFourthStepPublish:"September 20th 2022",dateEndFifthStepPublish:"November 19th 2022",remainingDaysToSecondStep:"15 days",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"Dr. Evingür is a researcher in polymer composites and a lecturer at a maritime university. 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The titled of her thesis was 'Electrical Properties of Polystyrene”. She received her PhD from Physics Engineering at İstanbul Technical University in 2011. The title of the thesis was 'Phase Transitions in Composite Gels”. She worked as an Assistant Professor between 2011 and 2018, and she is currently working as an Assosciate Professor at Pîrî Reis University, Istanbul, Turkey. She has been engaged in various academic studies in the fields of composites and their mechanical, optical, electrical, and acoustic properties. She has authored more than 60 SCI articles, 92 proceedings in national and international journals, respectively. 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He became Associate Professor at Hacettepe University in 1979. \nHe visited ICTP Trieste, Italy as Visiting Scientist between June and August 1980. Between 1980 and 1981 he was a Visiting Scientist at the Technical University of Gdansk, Poland. \nHe worked as Visiting Professor at the Department of Chemistry, University of Toronto, Canada between 1981 and 1988. \nHe was appointed as full Professor at the Department of Physics, Istanbul Technical University, Turkey and worked there between 1988 and 2005. \nHe became an Elected Member of the Turkish Academy of Sciences (TÜBA) in January 1995. \nHe became the Dean of School of Arts and Sciences at the Istanbul Technical University in 1997. \nHe received the Science Award from the Scientific and Technological Research Council of Turkey (TÜBİTAK) in 1998. 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Churchill, Maja Dutour Sikirić, Božana Čolović and Helga Füredi Milhofer",coverURL:"https://cdn.intechopen.com/books/images_new/8812.jpg",editedByType:"Edited by",editors:[{id:"219335",title:"Dr.",name:"David",surname:"Churchill",slug:"david-churchill",fullName:"David Churchill"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"6851",title:"New Uses of Micro and Nanomaterials",subtitle:null,isOpenForSubmission:!1,hash:"49e0ab8961c52c159da40dd3ec039be0",slug:"new-uses-of-micro-and-nanomaterials",bookSignature:"Marcelo Rubén Pagnola, Jairo Useche Vivero and Andres Guillermo Marrugo",coverURL:"https://cdn.intechopen.com/books/images_new/6851.jpg",editedByType:"Edited by",editors:[{id:"112233",title:"Dr.Ing.",name:"Marcelo Rubén",surname:"Pagnola",slug:"marcelo-ruben-pagnola",fullName:"Marcelo Rubén Pagnola"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"72061",title:"A Mixed Methods Study of the Experiences and Effectiveness of a Soft Brace for Adults with Degenerative Scoliosis",doi:"10.5772/intechopen.92387",slug:"a-mixed-methods-study-of-the-experiences-and-effectiveness-of-a-soft-brace-for-adults-with-degenerat",body:'Surgery is the only form of treatment currently offered by the United Kingdom National Health Service (NHS) as standard care for adults who develop scoliosis. However, this treatment method has associated risks, such as trauma to the body, substantial blood loss and a high complication rate [1]. Operative treatment for adult lumbar scoliosis has a complication rate ranging between 56 and 75% with an 18–58% re-operative rate [2]. Compared to adolescents, adults and older adults who develop scoliosis have a greater risk of suffering from surgical complications due to age, as degenerative scoliosis predominantly develops in older adults.
An alternative method of treatment to surgery is bracing. There are several types of braces used to treat adults with scoliosis; the most frequently used brace is the thoracolumbar-sacral orthoses (TLSO). This type of brace is a two-piece plastic brace that is required to be worn full time [3]. One type of TLSO brace is the Boston brace. This brace is made from prefabricated polypropylene material and is used to treat deformities that range from spinal regions T5 to L4 [4, 5]. Most braces are made up from at least one rigid component that affects the overall comfort and hence the efficacy of the brace. Additionally, most braces require a wearing time in excess of 12 hours, which has the potential to have an impact on wearers’ lives.
This mixed methods study evaluated both the subjective patients’ views of the effectiveness of the soft brace as well as the objective results of brace effectiveness [6]. The brace encourages corrective movements in the spine through manipulation using soft flexible bands, which are altered on a regular basis depending on the progress of the individual. The brace is made up from three individual sections: pelvic shorts, a body jacket and elastic corrective bands. The pelvic shorts act as an anchor and attachment point for the elastic corrective bands with the jacket acting as the second attaching point. The bands are designed to encourage spinal correction by reactivating (pulling the muscles back into the correct position and training the muscles to stay in that position) the spinal muscles. Furthermore, the brace aims to improve the patients’ coronal and sagittal plane balance through the use of the corrective elastic bands as past research has indicated that an improvement in the coronal and sagittal plane can lead to an improvement in pain and/or functionality [7, 8].
To our knowledge, this is the first study to explore the experiences of wearing a spinal brace in a group of older adults with degenerative scoliosis using a qualitative design as previously this type of brace has only been used on adolescents [9, 10, 11, 12]. The practicalities of the brace design for adults were unknown. Therefore, the use of a qualitative data collection method allowed for this new information to be gathered. For these reasons, it was decided that semi-structured interviews would provide a deeper understanding of the issues faced by patients with scoliosis than quantitative data by providing a much richer in-depth account and would allow the participants to give detailed descriptions of their experiences of living with scoliosis and wearing the brace [13].
Only two previous studies have examined the views of patients regarding the impact of scoliosis on their lives. Schwab et al. [14] in 2003 reported a self-assessment of 49 patients, 22 of whom had adolescent onset scoliosis and 27 patients who had degenerative scoliosis. Participants had a mean age of 63. The main aim of their study was to investigate the impact scoliosis had on health. They found that when comparing the SF-36 questionnaire data between patients with adult scoliosis against adults who experienced lower back pain, those with scoliosis had significantly higher perceptions of their health than those who had lower back pain. One of the main limitations of this study was that 22 of the patients had adult idiopathic scoliosis and their analysis did not differentiate between the two groups.
The second paper investigated individuals’ self-assessment of their health-related quality of life when living with scoliosis [15]. The scores on the SF-36 and the Walter Reed Visual Assessment Scale questionnaires (WRVAS) were collected on 71 individuals who had an age range of 17–66, with a mean age of 33. They concluded that on both the SF-36 and WRVAS, older adults reported more pain than younger ones. However, one of the main issues with the study was that no Cobb angle measurements were taken; this is a limitation as previous research [16] has shown that there are correlations between an individual’s Cobb angle and self-assessment. The second limitation is related to the ratio of gender in the sample: of the 71 participants, only 13 were male.
All other papers we found focused upon adult idiopathic scoliosis or solely operative management methods to treat scoliosis and therefore were not relevant to this study. Although the two papers described above did not present qualitative accounts, they are based on the self-assessment of living with scoliosis. The primary aim of this study was to explore patients’ experiences of living with scoliosis using a qualitative approach. The secondary aims of the study were to evaluate patient perceptions of wearing a soft spinal brace and to explore the functionality and practicalities of wearing this type of brace.
For participants to be eligible for this part of the overall study, they were required to wear the brace for 6 months. This time period was selected as clinicians felt it would be where the most noticeable changes in the patients’ health and pain scores would be observed. Furthermore, 6 months gave enough time for any initial teething problems with wearing the brace to be identified and resolved, as well as allowing the patients to reflect on their experiences of wearing the brace over a reasonable period of time. In total, eight participants, 1 male and 7 female, aged 55 and over were eligible for the semi-structured interviews.
Ethical approval was granted by the NHS and the university research ethics committee of the first author. All participants were provided with a participant information sheet which provided a detailed explanation of the purpose of the study. A consent form asked participants to confirm that they had read the information sheet and fully understood what was being asked and whether they were happy to take part, if they met the inclusion criteria and did not match any of the exclusion criteria. Potential participants were also informed that the interview would be audio-recorded and that they had the right to withdraw their data up to 2 weeks after participating, after which time the data would be anonymised.
In this study, participants were asked about their experiences of living with scoliosis before they received the brace and once they had received the brace. From the overall larger themes that were generated from the participants’ answers, sub-themes were then extracted [17]. Braun and Clarke [17] recommend that thematic analysis should be seen as the foundation method for all qualitative analysis. They describe thematic analysis as a method for identifying, analysing and reporting patterns and themes within data. No specific interview schedule was used when carrying out the interviews; however, a list of overall questions was used to ensure consistency throughout all the interviews.
Semi-structured interviews are a common technique used in qualitative research as the method allows flexibility for both the researcher and the participant in regard to the fluidity and structure of the questions [18]. For this study, the semi-structured interview transcripts were analysed using thematic analysis [17]. Thematic analysis was adopted as it allows flexibility with regard to how the participants’ answers are organised, analysed and grouped [17]. Furthermore, the aim of thematic analysis is to obtain and extract themes from the written transcripts generated from the interviews.
An interview schedule was prepared at the beginning of the study. However, as the interviews were semi-structured, the schedule was only a guide, and based on the responses from the participants, further questions were also asked. The main areas covered by the interview schedule are related to the participants’ lives before they received the brace and whether the brace had changed the individuals’ quality of life. The questions were focused on gaining an insight into any changes to the participants’ scoliosis that they thought were due to wearing the brace. The third set of questions focused on gaining an insight and understanding into the patients’ feelings towards the brace. These questions asked the participants if they would change any aspect of the brace’s design, and what if any problems they encountered (if any) whilst wearing the brace.
Participants who dropped out of the study were also interviewed, but with a slightly different interview schedule. Instead of the final set of questions focusing on satisfaction, the questions focused on the reasons why the participants dropped out and what could be improved in the future to stop this from occurring. Participants 1–6 continued with the trial, whilst participants 7 and 8 dropped out of the trial shortly after the interviews took place.
From the interview transcripts, four major themes emerged as follows: the persistence of pain, the impact of the brace on pain and daily living, problems with the device and trial satisfaction.
The overall emerging theme reported by participants was the persistence of pain as a result of their scoliosis. This replicates earlier work that has found that for patients who have a form of degenerative scoliosis, lower back pain is the most common presenting symptom [19, 20]. Further work has found that older adults with degeneration believe they are in more pain than both younger adults and adults with standard lower back pain [7, 15]. This research study has highlighted the severity of pain that older people with degenerative scoliosis experience. When the researcher asked the participants questions about their pain and how much pain they were in, they reported a number of difficulties in carrying out everyday activities as a result of the severity of their pain as seen below:
Further analysis indicated that the pain the participants were living with had substantial limiting effects on both their activity levels and the activities that they could participate in; these activities were virtually limited to home-based stationary activities such as watching TV. Furthermore, household tasks were also limited to very basic chores such as folding, washing or drying dishes:
Participants also identified problems with sleeping before they received the brace, stating that the constant pain they experienced due to their scoliosis significantly disrupted their sleeping patterns.
Other individuals also echoed that before receiving the brace, their activity levels were minimal as a result of their scoliosis.
In essence, pain was a central theme of the patients’ experiences of living with scoliosis: all participants explained that they were in constant pain as a result of their scoliosis. From the responses the participants made in relation to living with scoliosis, it was apparent that pain had a substantial effect on all aspects of their lives and on a daily basis. Upon further analysis, a sub-theme emerged which focused on how the pain limited participation in activities, with some reporting only being able to carry out essential household tasks (P6), to the basic challenges of sleeping (P5). Furthermore, the participants’ answers to the questions also gave the researcher a base for comparison before they started the trial and once they received the brace.
The next theme that emerged from the researcher’s questions indicated that the patients experienced a small reduction in pain whilst wearing the brace, which in turn led to a positive impact on their activity levels. When the participants were asked if the brace had allowed them to be able to participate in any additional activities or participate longer in activities they could already do, the participants gave answers such as:
Further quotes revealed the brace reduced the level of pain that participants reported whilst walking or carrying out everyday tasks.
However, it emerged a reduction in pain was not the belief or views of all the participants, as other participants did not believe they received any benefits from the brace, to the extent that one participant even believed wearing the brace was leading to an increase in their pain.
In summary, the participants generally indicated that the brace was having a positive impact in terms of improving their quality of life and their overall activity levels. With regard to participants 7 and 8, both dropped out of the trial shortly after this interview.
Patients reported several design problems with the brace that limited the amount of time the participants were able or willing to wear the brace. This was particularly problematic as previous research has shown that bracing is only effective when worn for the recommended time (Rowe et al. and Maruyama et al.) [21, 22]. Participants indicated that they were not adhering to the 8 hours a day, 7 days a week, minimum recommended wearing time that was required to achieve maximum efficiency. They gave a number of reasons for this. When asked how long they were wearing the brace, the participants answered:
Further probing revealed the main reason the participants were not keeping to the recommended wearing time was the brace’s practicality and functionality with regard to using the toilet, due to the design of the shorts.
Furthermore, additional problem participants identified, as a reason for not fulfilling the recommended wearing time, was the cosmetic appearance of the brace under their clothes.
In summary, participants reported several design issues with the brace, which limited the amount of time they could wear the brace for. As a result of these problems, the optimum recommended wearing time was not achieved, which would have reduced any benefit of the brace. The main reason reported for this noncompliance wearing the brace was toileting as a result of the design of the brace shorts, a problem that was exacerbated by the fact that several participants could not remove or fit the brace independently.
From the final set of questions, the theme that emerged was that participants were happy with the format of the brace trial. This was in regard to the frequency and duration of the clinical visits and the questionnaires the participants had received.
The answers from the remaining participants who reached the 6-month treatment point also indicated they were happy to continue with the trial. Participants gave generally brief responses to these questions; they did not expand or give any extra information to the questions asked. Participants indicated they were happy with the format of the trial and felt the questionnaires were appropriate; they also indicated they were happy to continue with the trial.
The interviews with the participants who had dropped out of the trial were carried out over the telephone and recorded with their permission; consent forms were sent out in the post prior to the interview. The interview schedule followed the same progression as the treatment group, with the initial questions focused on the participants’ life before they received the brace. The participants indicated the primary complaint of living with scoliosis was their persistent pain.
The next set of question focused on why the participants dropped out of the trial. Participants provided answers identifying the primary reasons being the fitting of the brace.
Furthermore, one participant indicated the reason they dropped out of the trial was due to the bracing causing them even more pain.
In summary, it was apparent the design of the brace and its practicalities were the main factors for these participants dropping out. Furthermore, the brace also led one participant to believe their pain increased; however, as stated earlier in this study, this participant was only included due to the small study numbers and at the specific request of the consultants.
The primary aim of this study was to use a qualitative approach to explore the patients’ experiences of living with scoliosis. Furthermore, the secondary aims of the study were to obtain rich and in-depth qualitative information with regard to how the brace affected the scoliosis, together with the functionality and practicalities of the brace design. The results and themes generated from the semi-structured interviews indicated that the primary experience of living with scoliosis is one of persistent pain and limited activity, with all participants who were interviewed identifying these two factors as the main issues. Furthermore, the results from the interviews also identified and highlighted design problems and limitations with the brace shorts that were previously unknown. As the brace has previously only been used on adolescents [9, 23, 24], the problems experienced by adults with regard to the design of the shorts were previously unknown. It is unclear why older women had a problem with the design when this issue has not to our knowledge been reported elsewhere.
An additional result from this study was the identification that the literature on adults’ experience of living with scoliosis is very sparse. The data obtained from this study contributes significantly to the gap in knowledge with regard to the experiences of living with scoliosis and its effectiveness. From the responses participants gave, the brace did offer a reduction in the participants’ reported pain and allowed them to take part in a wider range of activities. However, for a more definitive conclusion and indication as to how successful the brace has the potential to be, this study would need to be carried out on a larger sample size. Furthermore, the participants would need to be willing and able to wear the brace for the recommended time and would need to fully match the study criteria.
Furthermore, as the interviews provided a greater reflection of the experiences of living with scoliosis, it is suggested that each participant should receive a minimum of three interviews in any future trial. The first interview would be scheduled at the beginning of the trial, one in the middle and one at the end of the study. The implementation of three interviews would also allow for a more in-depth comparison to be obtained, as the interviews would be more frequent and the participants would be able to give more detailed descriptions of their experiences of living with the brace.
The information obtained from the qualitative interviews allowed for a greater understanding of patients’ experiences of living with scoliosis that the questionnaires failed to capture, such as problems with the brace and the extent to which the brace was helping with their pain and activity levels. Furthermore, Participant 4’s answer to the set of questions regarding trial satisfaction also showed how some patients found it difficult to that they experienced was due to IBS or scoliosis. This qualitative study also revealed that patients’ experiences of pain had a limited effect on the amount of activity they could do due to their degenerative scoliosis.
The study was initially going to be carried out as a randomised control trial (RCT) for 24 months. The RCT study design is considered to be the highest level of scientific testing as it minimises patient control bias [25]. However, halfway through the recruitment process, it became apparent that the numbers required to achieve an RCT would not be met due to a number of factors that were out of the control of the research team. These factors included a drop in patient referrals due to a reform in the referral process from primary care into secondary care, a lack of engagement by treatment centres in terms of not fully understanding which healthcare professionals could refer patients into the trial and a small number of eligible participants who matched the study inclusion criteria. Therefore, after the discussions with the consultants, brace clinicians and research team, it was decided that the best solution to these problems would be to continue the trial as a prospective study with a control group for 6 months. There are several reasons for the reduction in the trial time scale. Firstly, it took over 13 months to gain NHS ethics; secondly, the participant referrals dramatically decreased after the first 12 months due to NHS reforms, and therefore any new entries into the trial would not have finished their treatment program before the scholarship of the primary author concluded. Therefore, recruitment was halted after 18 months. As a result of this, the data presented in this work are from 6 months of data collection.
The participants for the study were recruited and identified by consultants, physiotherapists and spinal nurses when they attended their regular orthopaedic clinics. When attending these appointments, the patients were screened by their consultants to ensure they were suitable and matched the study criteria. Participants for the study were initially going to be recruited from three different treatment centres; however, only one referred any participants into the trial. Once a participant was referred into the trial, they were randomised into either the treatment or control group; this was done through a computer randomisation program. Participants in the treatment group received the soft brace in addition to the standardised assessment tools described below.
To ensure that appropriate patients were recruited for the trial, after a number of discussions amongst the research team, brace manufacturers, surgeons and physiotherapists, a set of inclusion and exclusion criteria was drawn up. This was to ensure that the participants would be able to fully partake in the trial without having any additional problems or issues placed upon them as a result of participating.
Patients were included from the study if they had any of the following
Patients were required to be 50 years old or over, of either gender, to ensure the scoliosis was that of a degenerative origin and not a missed case of adolescent idiopathic scoliosis.
Patients whose scoliosis had a Cobb angle of ≥20° with associated vertebral rotation, previously confirmed on a full spine standing posterior anterior X-ray. The reason for this was because it was thought if the brace could reduce the pain in patients with a large Cobb angle, it should be able to ease the pain in patients with Cobb angles of over 20°.
The curve needed to have an apical vertebra (situated at the apex) level at T12 or below (this included double and triple curves) to ensure the scoliosis was degenerative.
Participants were required to have an ODI score of ≥32 to allow minimal changes in ODI scores to be detected.
Patients were excluded from the study if they had any of the following:
Leg pain that was linked to lumbar spine pain, as a number of additional health problems could have led to the development of leg pain
If the participants were unable to fit the brace on their own or did not have someone to help with this process
If the participants were not ambulant, as the brace was designed to treat patients who were not confined to bed
If the participant had already received instrumental thoracic or lumbar surgery as the brace was designed to delay the need for surgery
The following study questionnaires were used to measure and monitor the effectiveness of the brace. Three questionnaires were used. The first questionnaire that was used to assess pain was the Oswestry Disability Index Questionnaire v2.1a (ODI) [26]. The second questionnaire that was used to assess the patients’ quality of life was the EQ5D-5L [27]. The final questionnaire was used to assess the patients’ mental and physical health, the Short Form-36 Version 2 (SF-36v2) [12]. The participants in the control group received the questionnaires together with the standard NHS treatment; this comprised a yearly follow-up appointment with their regular consultant to assess whether the curve had progressed to the point where a surgical approach was required.
The ODI v2.1a questionnaire is one of the most commonly used questionnaires to assess lower back pain. The ODI is one of the most valid and reliable outcome measures with regard to the patient’s perception of the ‘pain they feel today’ [28]. The ODI comprises of 10 sections; each section has six statements (see example below; Table 1). Responses are made on a five-point scale. As shown in the example below, the first statement is marked 0, and the last statement is marked 5. All additional statements are scored according to rank, with the highest score being taken if more than one box is marked in each section. Once the questionnaire is complete, the score is then calculated using the following formula: ODI % = Total score/5 × number of questions answered × 100. Therefore, if the ODI score is 40 based on the participant answering 4 for all 10 sections, the percentage of disability is determined: 40/5 × 100 = 80% disability. Since the initial publication, the ODI has been widely validated [29] and deemed to be a reliable measure for detecting small reductions in pain and disability before and after treatment [30].
Section 2: personal care | Score |
---|---|
I can look after myself normally without causing extra pain | 0 |
I can look after myself normally but it causes extra pain | 1 |
It is painful to look after myself and I am slow and careful | 2 |
I need some help but manage most of my personal care | 3 |
I need help every day in most aspects of self-care | 4 |
I do not get dressed, wash with difficulty and stay in bed | 5 |
Example ODI questions.
The ODI correlates positively with the SF-36 and EQ5D questionnaires. In essence, a reduction in pain attained from the ODI correlates with an improvement in mental and physical health on the SF-36 questionnaire and an improvement in quality of life from the EQ5D for patients who had lower back pain [31, 32]. Wittink et al. [32] compared the outcomes of 424 patients with chronic pain who had been referred to a multidisciplinary pain centre where each patient was required to complete the SF-36, Multidimensional Pain Inventory (MPI) and the ODI before or on the date of their first appointment. They found that the MPI, SF-36 and ODI had good psychological measurements. The study also concluded that the ODI had the least amount of respondent burden and was easier to score, although the questionnaire does not provide as much detail as the MPI or the SF-36.
The EQ5D-5L is a widely used generic measurement of health-related quality of life that requires patients to self-report problems with regard to five elements: mobility, self-care, usual activities, pain/discomfort and anxiety/depression [33]. The questionnaire is split into two parts with the first part containing five questions that explore different elements of health, with each of the five questions containing three levels of severity, no problem, some problem or extreme problem, allowing patients to be classified into 1 of 243 states [34, 35]. An example question (see Table 2) from the EQ5D questionnaire is seen below:
Please mark accordingly |
I have no problems in walking about |
I have slight problems in walking about |
I have moderate problems in walking about |
I have severe problems in walking about |
I am unable to walk about |
Example EQ5D questions.
From these 243 health states, a time trade-off (TTO) is calculated; this TTO is used to represent a person’s quality of life. A value of 1 represents full health and a value of 0 represents being dead [36]. For this research study, the TTO scores were calculated using the software provided by EuroQual who designed the questionnaire. The second part of the EQ5D-5L requires the patient to indicate how ‘good’ or ‘bad’ their perception of their own general health is by marking a visual analogue scale (VAS). A VAS is a measurement tool that aims to measure an attribute of health that is believed to be on a continuous range across a continuous value. The scale ranges across a horizontal line that starts at 0 representing no pain and moves gradually to 100 representing extreme pain. The line is 100 mm in length and words are placed at the start of the continuum (0) representing no pain, and at the end of the line a100mm line representing extreme severe pain (see Figure 1 below).
Example of a visual analogue scale.
The validity and reliability of the EQ5D questionnaire have previously been confirmed by Brazier et al. [37] who compared the results of the EQ5D to the SF 6D (a development from the SF-36). Brazier’s research study [37] found that on a data set of 2436 patients with a wide range of medical conditions ranging from lower back pain, chronic obtrusive pulmonary disease and irritable bowel syndrome, the questionnaire showed signs of being sensitive to change and having a strong coefficient of internal consistency.
The last questionnaire used in this study was the SF-36v2. This questionnaire is a multidimensional, non-diagnostic-specific measure of pain that consists of eight health scales: physical functioning (10 items), role limitations—physical (4 items), bodily pain (2 items), general health (5 items), vitality (4 items), social functioning (2 items), role limitations due to emotional problems (3 items) and mental health (5 items) [38]. The scale is directly transformed into a 0–100 scale based on the assumption that each question carries equal weight. The lower the score, the greater the disability; in essence, a score of 0 is equivalent to a maximum disability, and a score of 100 is equivalent to no disability. The SF-36v2 has been reported to be both a reliable and valid measurement of health and has been shown to be sensitive to changes in health conditions [39].
Medical staff including consultants, physiotherapists and spinal nurses were the primary recruiters for participants for the study. Participants were recruited when they attended their regular orthopaedic clinics. Once consent was attained, the participants were then randomised into either the treatment or control group by a computer randomisation program. As part of the standard NHS procedure, on arrival the participants received a routine clinical examination. This included the measurement of the Cobb angle and pelvic/shoulder tilt, in addition to a posterior/anterior X-ray using the soft brace X-ray protocol. The soft brace X-ray protocol was used for all clinical visits as it provided a standardised foot position, which in turn kept the patient’s posture natural and standardised from visit to visit. The protocol also allowed for direct comparison of frontal and lateral X-rays and increased the inter-session reliability. If the participant fulfilled the study criteria, they were offered the opportunity to participate in the trial; if they declined, they then continued along the standard NHS treatment pathway.
If the patient chose to participate in the study, they were given the participant information sheet (PIS) together with the series of questionnaires described above to complete (ODIv2.1a, EQ5D-5 L and SF-36v2). Further information about the trial and details of future clinical appointments were also included in the PIS. The information sheet gave details about future clinical appointments, how the trial would run and what was expected of the individual with regard to their participation (such as being able and willing to attend the clinical appointments, adhere to the 8 hours wearing time and complete the questionnaires on time). The lead researcher then explained to the patients that they would be randomly allocated by a computer program into either the treatment group where they would receive the brace and questionnaires or the control group where they would follow the standard NHS treatment and also receive the study questionnaires. If participants were placed in the treatment group, they were given an appointment where the brace was fitted by a trained soft brace clinician.
The baseline questionnaire data were then administrated and collected by the lead researcher. A follow-up appointment was also made 1 month into treatment where an additional in-brace X-ray was taken as specified by the study protocol. This additional X-ray was not part of the standard NHS treatment; however, it was deemed necessary to assess whether the brace was having any immediate effect on the shape and position of the spine. This extra dose of radiation that the patients received as a result of the additional X-ray was deemed to be acceptable by the research ethics committee. Patients were also informed that they would be required to attend future appointments at 1, 3 and 6 months. This was in addition to their standard clinical appointments to see their regular consultant at 12 months to assess the long-term effects of the brace. Upon attending these routine clinic visits, the brace was adjusted by the soft brace clinicians if it was deemed to be too loose or ill-fitting as a result of any changes in their shape and/or posture.
The brace is recommended by the manufacturer to be worn for 8–12 hours per day for the first 3 months and then adjusted to the individual’s requirements after this. These adjustments included changing the wearing time and/or adapting the position of the bands if they had become loose or ill-fitting. Apart from the first appointment, which lasted approximately 90 minutes, each follow-up clinical visit lasted no longer than 40 minutes. The first appointment was slightly longer as this was where the participants were fitted and measured for their brace, whilst also providing them with the opportunity to ask the chief investigator (CI) or clinicians any further questions regarding their participation in the trial.
The participants in the control group received the ODIv2.1a, EQ5D-5L and the SF-36v2 questionnaire at home at months 1, 3 and 6 months, in addition to their standard treatment pathway. A follow-up yearly X-ray together with an appointment with their consultants was also made to see if surgery would be required due to curve progression. Both groups of participants were asked to complete and return all documents to the first author’s University in a prepaid envelope. If individuals decided they did not want to participate in the trial or if they decided to have surgical treatment, they were followed up at 12 months by their consultant with an X-ray to assess if any curve progression was apparent.
If patients chose to enter the trial, they were told that they could withdraw at any stage without giving a reason and it would not affect their future treatment. Participants were then provided with a participant information sheet and offered the opportunity to discuss the study with their consultant or a member of the research team. If patients agreed to participate in the trial, the consultants obtained signed consent. These completed forms were then passed on to the researcher who contacted the individual to verify they were still interested in participating in the trial (with at least a 24-hour gap after completing the slip). Once the patients confirmed they were still interested in participating, it was at this stage of the trial that they were informed which group they had been randomised into. At this point if the participants decided not to participate in the trial, it was explained they would follow the standard NHS treatment pathway. Each participant was also informed that if they did participate, all data they provided would be kept confidential and anonymised.
A sample size of 102 for this study was originally calculated based on literature from previous back pain studies. An attrition rate of 10% was also added to the sample size [40], meaning a total sample size of 112 participants was required. Due to recruitment issues, this number of participants was not achieved. In total only 15 participants were recruited to the study. However, as randomisation took place before the research team had the opportunity to meet and screen the potential participants, two participants who were included by the consultants did not meet the inclusion criteria and were therefore not eligible, ultimately resulting in only 13 participants being involved. Given the low sample size, it is important to establish that the appropriate analyses (and therefore appropriate conclusions) were applied to the data. Research [41] has shown that even with a sample size of two people in a series of fake t-tests, the Type 2 error that occurred did not surpass the acceptable value of 5%; this has also been confirmed in studies by [42, 43]. Therefore, the small numbers in this study should not have any effect on the validity of the results generated from the questionnaires, although of course the small study numbers must be recognised in the interpretation of the results, as it is possible that the participants may not form a typical cross section of patients with degenerative scoliosis.
All study data were anonymised and analysed using a two-way repeated measure analysis of variance in SPSS [44]. The two-way analysis of variance (ANOVA) was used as it allows the differences between group means and their treatment methods to be compared over several time points [45]. The treatment group was compared against the mean data from the control group for each of the three time points to determine whether any significant differences were present. In-group comparisons were also calculated for both groups to see if any significant in-group changes occurred.
Any missing data or data belonging to participants who withdrew from the study were analysed based on an intention-to-treat (ITT) basis. It was important to use ITT as the main problem researchers find when using an RCT study design is that participants do not always follow the instructions or they drop out of the trial [46]. The benefits of using ITT are that the analysis still reflects clinical situations and it gives unbiased estimations on the effectiveness of the proscribed treatment [47]. Furthermore, the use of ITT maintains the original sample size; if dropouts were excluded from the overall data set, a reduction of statistical power may occur.
The primary outcome measure for this study was a change in the participants’ ODI scores over the 6-month duration. Secondary outcome measures were any changes in the EQ5D-5L and SF-36v2 scores.
The baseline data in Table 3 show that the treatment group had a higher mean ODI than the control group upon initial consultation, although this difference was not statistically significantly different. Furthermore, a greater standard deviation was also present which indicated that a larger variation from the mean score was present within the treatment group. After 3 months, the mean ODI calculated from the treatment group’s data showed a reduction of 9% in the ‘pain they feel today’ from baseline, in comparison to a 6.25% increase from the control group, although the standard deviation remained similar for both groups.
Analysis of ODI scores over 6 months.
At the 6-month stage of the trial, the treatment groups’ mean ODI decreased by a further 1.6%; this indicated a decrease in pain. This is in contrast to the control group, who as a group had a mean ODI change from data collected between months 3 and 6 of the study of 19%. The scores represent an overall decrease of 10.6% from the treatment group over the 6-month trial compared to an overall increase of 25.25% over the course of the 6-month trial from the control group.
1M0 represents the baseline mean ODI scores, M3 represents month 3 mean scores and M6 represents month 6 mean ODI scores. The +/− column represents score changes between months. Treatment represents the treatment group and control represents the control group. Furthermore, there was no significant difference between the treatment and control group over the course of the 6-month study (see Table 3). Also, there was no significant difference or in-group interaction amongst the groups between the treatment time points.
The data presented in Table 4 show that at baseline, the control group’s reported health state appeared worse than the treatment group. As the score gets closer to 0, the closer the individual feels to a state of death. The control group had an initial TTO 22.2% higher than that of the treatment group even before receiving the brace, which means that they felt less well than those in the treatment group. The mean TTO data from month 3 showed that both groups’ health state changed, with a 21.4% increase coming from the control group, and the treatment group’s mean TTO score improved by 10.62%.
EQ5D health states over 6 months.
Data from the 6-month collection point presented a further increase for the treatment group with an improvement in score of 7.69% and with an overall increase in score of 18.31% over the duration of the study with regard to their TTO health state. Furthermore, although no change in score was found for the control group in the final 3 months, over the full duration of the study, a total improvement of 22.2% was calculated. From the EQ5D questionnaire, it was also found that over the course of the 6-month study period, no statistically significant differences were found between the groups’ TTO scores or in-group interaction.
The results from the initial month’s questionnaires show that both groups of patients had similar mean scores in terms of their mental health (see Table 5). After 3 months in the brace, the treatment groups reported mental health score decreased by 8.26%. However, this change in reported mental health was smaller than that of the decrease calculated from the control group questionnaires whose mean score decreased by 11.84%. The results from the month 6 time point indicated that both groups’ mental health increased between the months of 3 and 6. The treatment groups’ mean scores increased by 4.87%, whilst the control group’s score increased by 6.94%.
SF-36 mental health scores.
The initial month’s mean SF-36 physical health scores show that the treatment group had an inferior physical health score of 25% compared to the control group, as the closer the score to 0, the lower the individuals’ physical health. Data collected from 3 months into the study show that wearing brace for 3 months leads to the treatment group having an increase in their scores of 16.95%. This was in comparison to the control group, whose scores showed signs of their physical health decreasing by 3.31%. The scores calculated from data collected between the months of 3 and 6 show the treatment group’s mean physical health decreased by 3.67%. The results also demonstrated that no significant differences or group interactions were found between the treatment group’s physical health score and the control group’s physical health score at 6 months (Table 6).
SF36 physical health scores.
The primary aim of this study was to obtain both patients’ quantitative experiences of living with scoliosis together with developing an understanding of the pain they experienced and their quality of life. The secondary aims of this study were to investigate the effects the soft brace had on adults with degenerative scoliosis. Another aim of the study was to compare the questionnaire results from the treatment group against the questionnaire results from adults who did not receive the soft brace.
The study inclusion and exclusion criteria were designed to recruit individuals who were at the end of the non-operative treatment pathway. For these participants the next stage of treatment would be surgery. However, as discussed previously, due to the complications and difficulties of the procedure, the need for a surgery should if possible be delayed or avoided especially in those patients who have additional underlying health conditions such as irritable bowel syndrome (IBS) and arthritis. These dangers are further highlighted as the complication rates of surgery in older adults range from 20% to as high as 80% [48].
The anthropometric data of nine patients (8 female, 1 male) in the treatment group and six (all female) in the control group were as follows: the female patients in the treatment group had an average weight of 75.3 kg with an average height of 155.4 cm; the one male participant had a height of 165.2 cm and weight of 84.7 kg. This is in comparison to the six female participants recruited into the control group, who had an average weight of 77.6 kg and average height of 153.8 cm. In comparison to the average healthy individual who has an ODI score of 10.19 [49], the mean ODI score of the individuals in this trial was 47. Moreover, the mean ODI score of 47 was also substantially higher than the minimum ODI score of 32 outlined in the initial study inclusion criteria. In comparison the control group showed an 8.18% increase in ODI in comparison to the data collected between the initial month and month 3.
The results further demonstrated that there were no significant differences or interactions between the treatment group’s physical health score and the control group’s. The average healthy individual has an ODI score of 10.19 [49], whilst the mean benchmark ODI score of the individuals in this trial was 47. Moreover, the mean ODI score of 47 was also substantially higher than the minimum ODI score of 32 outlined in the initial study inclusion criteria. In addition to a higher mean ODI score than the average healthy individual, participants also had a lower mean score in terms of SF-36 MH and SF-36 PH than the average healthy individual. A healthy individual’s SF-36 MHS score is on average 50.17 and PHS 50.1 [50].
The mean baseline mental and physical health scores of the patients in this trial were 45.5 and 26.4, respectively. Additionally, a mean health TTO score of the average healthy individual is 0.94 [51] compared to the mean TTO score of 0.32 obtained from those in this trial. Furthermore, the inclusion criteria required participants’ Cobb angle to be a minimum of 20. The average Cobb angle measurement of patients in this trial was 43° (+/−12), again highlighting the severity of the degenerative scoliosis our participants had. The questionnaire data showed that over the course of 6 months, patients treated with a soft brace had a reduction in their ODI score regarding the ‘pain they felt today’. However, no significant differences or interactions were observed over the 6 months of the trial. In addition to the change in the ODI scores, changes in the TTO and mental and physical health scores were also calculated from the treatment group’s data. However, again no significant differences were found between questionnaire scores.
Like the treatment group, participants in the control group also showed no significant changes over the course of the 6-month study period. Furthermore, as seen in the tables above, the participants in the control group had a lower baseline ODI, EQ5D and SF-36 scores than the average healthy individual. It was difficult to compare the results of this study to previous work as little research has compared braced patients with patients who received no or standard NHS treatment. Furthermore, although several studies have been published [9, 52], these investigated the effectiveness of bracing on adolescents which has a different aetiology to adult scoliosis.
In this study, the treatment group’s data showed no significant difference in changes over the duration of the trial for all questionnaires. This contrasts with research [53, 54] which found a significant difference between the effectiveness of a surgical approach and a non-operative method of treatment. Research from Grubb et al. (1994) [53] examined the effectiveness of a surgery on 28 adults with idiopathic scoliosis and 25 adults with degenerative scoliosis. In comparison to the 10.6% change in scores over the 6-month treatment period for the present study [53], Grubb et al. found that patients who had degenerative scoliosis and were treated operatively reported a decrease in their pain scores of 70% whilst patients with adult adolescent scoliosis reported an 80% reduction. Furthermore, both sets of patients reported improvements in their health-related quality of life in addition to improvements in standing and walking over the 2–7 year follow-up period.
Li et al. [54] compared self-reported outcome scores from patients treated operatively to those treated non-operatively. They found that patients who received operative treatment reported significantly better self-outcome scores in the EQ5D VAS and SRS-22, but not in the ODI or the SF-12. Although the results from our quantitative work showed no significant difference over time for braced patients, discussions between patients and clinicians gave insight into the benefits of the brace. Patients spoke about how the brace reduced their pain, allowing their participation in new activities or longer participation in activities that they could already carry out. Some participants discussed how for the previous few weeks their pain levels were low, but when the time came to complete the questionnaires, they were having a ‘bad week’, due to their scoliosis pain or pain from other underlying health conditions. With a small sample size, the effect of ‘bad weeks’ would have a substantial effect on the results obtained, with potentially a Type 2 error where actual differences between groups may not have been detected. Furthermore, from the questionnaire results, it would appear that the questionnaires may not have been sensitive enough to assess small changes for patients who received the brace.
In conclusion this small pilot study has demonstrated that a soft brace has a potential as a treatment for degenerative scoliosis. In interviews, patients who were given the brace reported an improved quality of life, although such improvements were not detected in the questionnaire data. A larger, sufficiently powered, quantitative study is required to provide a clearer understanding of the effect of a soft brace on pain and quality of life for older people with degenerative scoliosis.
At the horizon of 2035 and beyond, the very large electronic equipment for command and diagnostic operations of future fusion power machines, such as ITER, the international thermonuclear experimental reactor [1], will embrace a wide variety of semiconductors materials. Indeed, new materials, such as SiC, Ge, GaN, or GaAs, are envisaged to progressively replace the traditional silicon of microelectronics for high temperature, high performance, or high-speed electronics/optoelectronics applications [2, 3, 4, 5]. These equipment will be directly or partially (behind radiation shielding) exposed to a complex radiation field due to primary fusion neutrons created in the core of the plasma and then transported outside the machine [6]. These neutrons are produced in the deuterium–tritium (D–T) reaction that has been identified as the most efficient for fusion devices [7]:
However, one must also consider deuterium–deuterium (D–D) reaction because this less efficient fusion reaction will be used to study, during the development and commissioning of future machines, their operation before introducing tritium fuel. D–D fusion following the two main reactions with equal probability of occurrence:
For future fusion power machines, the radiative reliability issue for the envisaged new material-based electronics arises now, even if—(i) most of these components have not yet been manufactured and tested, and (ii) the design and the integration of machine electronics equipment will not take place for many years. In such a long-term development, numerical simulation offers a very promising solution to anticipate, in the first step at the material level, this reliability issue for semiconductors whose radiative response is little or poorly known.
In the direct continuation of our previous works [8, 9, 10] that investigated the atmospheric radiation response of a wide variety of semiconductors, the present chapter focuses on the radiation response of Group IV (Si, Ge, SiC, diamond) and III-V (GaAs, GaN, GaP, GaSb, InAs, InP, InSb, AlAs) semiconductors subjected to D–D (2.45 MeV) and D–T (14 MeV) neutrons.
In this work, the response of each material has been systematically investigated through a direct calculation using nuclear cross-section libraries, MCNP6, and Geant4 numerical simulations. In the following, for the 12 semiconductor materials considered, we will investigate in detail the reaction rates per type of reaction (elastic, inelastic, and nonelastic) and propose an exhaustive classification of all the neutron-induced secondary products as a function of their nature and distribution in the energy. Implications for quantifying the susceptibility of these related semiconductor-based electronics to neutron fusions will be finally presented and discussed.
Table 1 summarizes the natural isotopic abundance of the different chemical elements entering the composition of the studied semiconductor materials. Nitrogen, phosphorus, and arsenic have only a single natural isotope which simplifies the calculations to come for these elements. On the contrary, the other elements have two (C, N, Ga, In, Sb), three (Si), and up to five (Ge) different natural isotopes. Nevertheless, for C and N, the relative weight of the minority isotope is less than or around the percent, so we can consider that the natural carbon and nitrogen consist only of the simple isotopes 12C and 14N, respectively, with a very good approximation. The other isotopes listed in Table 1 must be considered with their respective weight in atomic composition for correctly simulating the neutron response of the natural materials to which they relate.
Symbol | Z | Nuclide (100×Z+A format) | Natural abundance (%) |
---|---|---|---|
C | 6 | 6012 | 98.93 |
6013 | 1.07 | ||
N | 7 | 7014 | 99.6 |
7015 | 0.4 | ||
Al | 13 | 13027 | 100 |
14028 | 92.22 | ||
Si | 14 | 14029 | 4.68 |
14030 | 3.09 | ||
P | 15 | 15031 | 100 |
Ga | 31 | 31069 | 60.1 |
31071 | 39.9 | ||
32070 | 20.52 | ||
32072 | 27.45 | ||
Ge | 32 | 32073 | 7.76 |
32074 | 36.52 | ||
32076 | 7.75 | ||
As | 33 | 33075 | 100 |
In | 49 | 49115 | 95.7 |
49113 | 4.3 | ||
Sb | 51 | 51121 | 57.4 |
51123 | 42.6 |
Natural abundance of nuclides related to the materials studied in this work. Z refers to the atomic number, A to the atomic mass.
Table 2 reports the value of the energy bandgap, the number of atoms per square centimeter, the density, and the value of the energy for electron-hole pair creation in bulk material for the 12 semiconductors studied in this work. Due to their atomic composition and crystallographic structure, all these materials are denser than Si (2.33 g/cm3) and three materials exhibit a much larger number of atoms per square centimeter than Si—SiC, diamond, and GaN. This can have a direct consequence on the number of neutron interactions per unit volume of the material, as discussed in the following. In addition, seven materials (SiC, diamond, GaAs, AlAs, InP, GaN, and GaP) exhibit a bandgap larger than Si and logically, a larger electron-hole pair creation energy (3.6 eV for Si) [10], four materials (Ge, InAs, GaSb, and InSb) are low-bandgap semiconductors (< 1eV) with lower electron-hole pair creation energy than Si. The electrical consequences of this important parameter are discussed in Section 5.
Material | Bandgap at 300 K (eV) | Number of atoms per cm3 ( ×1022) | Density (g/cm3) | E-h pair creation energy Eeh (eV) |
---|---|---|---|---|
Si | 1.124 | 5.0 | 2.329 | 3.6 |
Ge | 0.661 | 4.42 | 5.3267 | 2.9 |
SiC (4H) | 3.23 | 9.64 | 3.21 | 7.8 |
Diamond | 5.47 | 17.6 | 3.515 | 12 |
GaAs | 1.42 | 4.42 | 5.32 | 4.8 |
AlAs | 2.16 | 4.42 | 3.76 | 6.8 |
InP | 1.34 | 3.96 | 4.81 | 4.5 |
InAs | 0.36 | 3.59 | 5.67 | 1.8 |
GaSb | 0.73 | 3.53 | 5.61 | 2.7 |
InSb | 0.17 | 2.94 | 5.78 | 1.1 |
GaN | 3.39 | 8.85 | 6.15 | 8.9 |
GaP | 2.26 | 4.94 | 4.138 | 6.8 |
The susceptibility of the different semiconductors to neutron irradiation can be firstly evaluated via the calculation of the number of neutron-material interactions under 2.45 or 14 MeV neutrons. This can be performed via a direct analytical calculation using neutron cross-section library data; we considered here the TENDL-2021 nuclear data library [11]. The number of interactions in the target at a fixed neutron energy E is simply given by:
where σi is the value at energy E of the cross section for isotope i (in barn), fi is the fraction of isotope i in the target isotopic composition, e is the target thickness, NV is the number of atoms per unit volume, and M is the number of incident monoenergetic neutrons; in this work, fixed to the arbitrary value of 5 × 108 for standardization purpose (introduced in other previous studies [8, 9, 10], M initially corresponds to the number of atmospheric neutrons impacting a surface of 1 cm2 at sea level exposed to natural radiation during 25 × 106 h).
Figure 1 illustrates the extraction from TENDL-2021 library data of the neutron cross-section values at 2.45 and 14 MeV for two different isotopes. Total, elastic, and inelastic data, respectively, correspond to reaction type numbers MT = 1, 2, and 4 in the standardized ENDF format [12]. When it is not available, the cross-section value for the sum of all nonelastic channels (MT = 3) is obtained by subtracting elastic + inelastic cross sections to the total cross section.
Example of neutron cross sections (total, elastic and inelastic) extracted from TENDL-2021 nuclear data library [
As the result of this analytical evaluation using Eq. (4), Table 3 gives the total number of interaction events in a target (1cm2 × 20 μm) composed of a single chemical element with an isotope distribution corresponding to the natural abundance (Table 1) and subjected to 2.45 or 14 MeV neutrons. Values reported in Table 3 correspond to a normalized value NV = 1.0 × 1022 at/cm3 for all targets.
Target (1.0×1022 at/cm3) | Z | N(E) from Eq.(4) and TENDL-2021 | |||||
---|---|---|---|---|---|---|---|
2.45 MeV | 14 MeV | ||||||
Elastic | Inelastic | Nonelastic | Elastic | Inelastic | Nonelastic | ||
C | 6 | 16,146 | 0 | 0 | 8360 | 4240 | 674 |
N | 7 | 13,201 | 22 | 1675 | 9697 | 3658 | 2328 |
Al | 13 | 25,564 | 4171 | 61 | 7798 | 4598 | 5050 |
Si | 14 | 18,857 | 6321 | 0 | 7555 | 4922 | 6706 |
P | 15 | 28,196 | 5378 | 472 | 7522 | 2910 | 8552 |
Ga | 31 | 16,150 | 15,009 | 61 | 16,839 | 5908 | 9892 |
Ge | 32 | 17,572 | 16,013 | 329 | 17,203 | 7306 | 8626 |
As | 33 | 16,008 | 17,718 | 649 | 17,934 | 5874 | 10,119 |
In | 49 | 31,349 | 22,255 | 1735 | 25,669 | 4173 | 16,178 |
Sb | 51 | 35,376 | 15,712 | 612 | 26,909 | 3832 | 15,941 |
Total number of interaction events in a target (1cm2 × 20 μm) composed of a single chemical element with an isotope distribution corresponding to the natural abundance (Table 1) and subjected to 2.45 or 14 MeV neutrons. Values are calculated from Eq. (4) with a normalized value NV = 1.0 × 1022 at/cm3 for all targets.
From the data of Table 3, it is now easy to evaluate the neutron response for any material composed of these elements. Figure 2 shows the results of this evaluation for the different semiconductor materials, considering their stoichiometry and their exact number of atoms per square centimeter, given in Table 2. All numerical values for Figure 2 are detailed in the Appendix (Table 6). From the results of Figure 2, we can formulate the following observations:
Elastic and inelastic interactions dominate for all materials at 2.45 MeV whereas nonelastic interactions represent very roughly one-third of the total number of events at 14 MeV.
All studied materials exhibit a larger total number of interaction events than silicon, both at 2.45 and 14 MeV.
Two semiconductors, C (diamond) and GaN show the largest neutron susceptibility at these two energies, followed by SiC.
Diamond at 2.45 MeV exhibits a pure and extremely high elastic response; this behavior is due to the combination of an important elastic cross section (1.62 barn at 2.45 MeV) and the highest NV value (1.76 × 1023 at/cm3) between all materials.
Only a single material, GaN, demonstrates a frank higher response at 14 MeV than at 2.45 MeV in terms of total events (elastic + inelastic + nonelastic), due to an elevated number of nonelastic events, the highest at 14 MeV for all materials.
AlAs exhibits the smallest neutron response after silicon.
Number of elastic, inelastic, and nonelastic interaction events in a target (1cm2 × 20 μm) composed of natural semiconductors and subjected to 5 × 108 neutrons of 2.45 or 14 MeV. Values are deduced from
All these results are now investigated in detail in the next section via more complete numerical simulations.
The neutron susceptibility of the studied materials has been in-depth analyzed using the Monte Carlo radiation transport codes Geant4 (version 10.07 patch 02, G4NDL4.6 neutron library [13, 14, 15]) and MCNP6 (version 6.2 [16, 17]). In a similar way to previous analytical estimations, natural semiconductor targets (1 cm2 × 20 μm) have been subjected to incoming 2.45 or 14 MeV neutrons perpendicularly to their largest surface. The same number of 5 × 108 incident neutrons has been considered for each simulation run.
For Geant4, a simulation run produces a single output file containing all the information related to the neutron interaction events in the target material—nature of the interaction, spatial coordinates of the reaction vertex, and exhaustive list of secondary particles produced during the interaction (energy and emission direction vector for each of these emitted particles). A post-treatment eliminates all gamma photons, neutral and light particles (e−, e+, η), not able to induce significant single-event effects in electronics.
For MCNP6 simulation, PTRAC card options were activated to obtain, for each event, the nature and the coordinates of the vertex of the interaction and the final energy of the neutron after the interaction. It is thus possible to count and to discriminate interactions as a function of the target atom and as a function of their nature (elastic, inelastic, and nonelastic).
Figures 3 and 4 show the number of interaction events for the different semiconductor targets subjected to 2.45 and 14 MeV neutrons, respectively. All the numerical values for these two figures are reported in Table 6 of the Appendix. These results show a good agreement, on one hand, between analytical and numerical estimations, and, on the other hand, between Geant4 and MCNP6 results. If we consider the total number of interaction events (Table 6), analytical and numerical results agree within 6% on average at 2.45 MeV and within 2.4% on average at 14 MeV. Between Geant4 and MCNP6 results, agreements are better, within 3% on average at
Number of elastic, inelastic, and nonelastic events estimated by Geant4 and MCNP6 as a function of the nature of the target material for 2.45 MeV incoming neutrons.
Number of elastic, inelastic, and nonelastic events estimated by Geant4 and MCNP6 as a function of the nature of the target material for 14 MeV incoming neutrons.
2.45 MeV and within 1.6% on average at 14 MeV. The best agreement is obtained for diamond, GaN, and GaAs at 14 MeV, the largest difference is for GaP at 2.45 MeV, with 11.5% of the variation between Geant4 and MCNP6, the number of elastic events being larger than 14% for Geant4 with respect to MCNP6. Globally, one can see that the different sets of results agree very satisfactorily.
In the following and because Geant4 can track all particles and, consequently, give more exhaustive information about secondaries than MCNP6, we will explore in detail the distributions and characteristics of secondaries produced in the interaction events at both 2.45 and 14 MeV from Geant4 results.
Figures 5–7 shows the energy histograms of the secondaries produced by 2.45 MeV neutrons in the targets composed of the different natural semiconductor materials under investigation. In the particular case of C (diamond), shown in Figure 5, all secondaries are exclusively elastic carbon recoil nuclei. They form a continuum from zero to a maximum energy Emax theoretically equal to [18]:
Energy histograms of secondaries produced in the diamond target by 2.45 MeV neutrons and obtained from Geant4 and MCNP6 simulations. All secondaries are elastic recoil nuclei.
Energy histograms of secondaries produced by 2.45 MeV neutrons in targets of Si, Ge, GaAs, SiC, AlAs, InAs, InSb, and GaSb semiconductor materials.
Energy histograms of secondaries produced by 2.45 MeV neutrons in targets of GaP, InP, and GaN semiconductor materials.
where A is the mass number of the target nucleus and E is the energy of the incident neutrons. Here, for carbon, A = 12 and with E = 2.45 MeV, we obtain a theoretical value of Emax = 0.696 MeV, in excellent agreement with the cutoff value of 0.7 MeV extracted from Figure 5. This figure also shows a direct comparison between MCNP6 and Geant4 simulation results because, in the case of elastic events, it is possible from MCNP6 output data to compute the energy distribution of recoil nuclei; an estimation unfortunately not possible for inelastic and nonelastic events.
Figures 6 and 7 show Geant4 results for the other target materials. For Si, Ge, SiC, AlAs, GaAs, InAs, InSb, and GaSb (Figure 6), 2.45 MeV neutrons produce quasi exclusively, via elastic, inelastic, and nonelastic interactions, secondaries with the same atomic number than one of the elements of the target. The heavier the recoil nucleus or secondary product, the more the distribution is shifted toward the lower energies. This shift is more marked as the difference in atomic number is greater, for example for InP (Z = 15 and 49). Only three materials, i.e., GaN, GaP, and InP, show (Figure 7) a significant production of secondaries at 2.45 MeV that differ from target elements:
For GaP and InP, the presence of phosphorus makes possible the nonelastic reaction 31P(n,p)31Si that produces a proton with mean energy around 890 keV. Following this reaction scheme, 980 protons are emitted in GaP and 755 in InP. 31P(n,p)31Si represents 88% (resp. 28%) of the nonelastic interactions in GaP (resp. in InP).
For GaN, the presence of nitrogen makes possible the two nonelastic reactions 14N(n,α)11B and 14N(n,p)14C that respectively produce an alpha particle (around 1.6 MeV) and a proton (around 2.7 MeV). 4555 alphas and 614 protons are emitted following these two reaction schemas. 14N(n,α)11B and 14N(n,p)14C, respectively, represent 84 and 11% of the nonelastic interactions in GaN.
In addition to the previous analysis, Figure 8 (left) gives, for each material, the sum of the initial kinetic energy for all produced secondaries (we recall here that neutrons, gamma rays, and light particles, such as electrons or positrons are not considered, only charged particles with Z ≥ 1 are considered). Such a quantity represents the energy susceptible to be deposited by all these secondaries in the considered target if they are totally stopped (after transferring the totality of their kinetic energy, essentially by ionization process). This energy amount is the highest for C (about 105 MeV), followed by SiC, GaN, Si, and GaP (all above 104 MeV); it is minimum for InSb (around 3 × 103 MeV). Figure 8 (right) gives the average energy conveyed per particle for the four categories of secondaries. The consequence of this result on the electrical point-of-view and in the framework of single-event effect occurrence is be discussed in Section 5.
Left: Sum of the kinetic energy of all secondaries produced by 2.45 MeV in the different targets (charged particle with Z ≥ 1). Right: Average particle energy per particle type (same legend as for the left figure).
Figures 9 and 10 show the energy histograms of the secondaries produced by 14 MeV neutrons in the different targets. Contrary to the previous case at 2.45 MeV, a significant number of nonelastic reaction channels is opened at this higher neutron energy. The ratio of the number of nonelastic reactions with respect to the total number of events varies from about 5% in the case of C up to 38% for InP; it is around 33% for Si. These nonelastic reactions produce several types of ions, protons, and alpha particles—their respective numbers are given in Table 4 which also indicates the number of secondary ions produced characterized by the same atomic number as target nuclei. This last category includes, of course, all recoil nuclei produced in elastic and inelastic reactions but also ions produced in certain nonelastic reactions, for example, in the (n,n’γ) or (n,2n’γ) reactions that are increasingly frequent when increasing the atomic number of the target element. These nonelastic reactions give a final nucleus with a lighter mass with respect to the initial impacted nucleus (for example, 74Ge(n,2n)73Ge or 115In(n,2n)113In, etc.).
Energy histograms of secondaries produced by 2.45 MeV neutrons in targets of GaN, GaP, GaAs, GaSb, InSb, InP, InAs, and AlAs III-V semiconductor materials.
Energy histograms of secondaries produced by 2.45 MeV neutrons in targets of Si, SiC-4H, Ge, and C (diamond) Group-IV semiconductor materials.
Target | Number of ions with the same Z as target nuclei | Number of protons, deuterons, and tritons | Number of alpha particles | Number of other ions |
---|---|---|---|---|
Si | 58,293 (Si) | 16,815 | 10,245 | 22,968 |
Ge | 107,913 (Ge) | 1910 | 1042 | 2152 |
C | 222,165 (C) | 2 | 11,460 | 11,445 |
SiC | 56,611 (Si) + 60,415 (C) | 16,376 | 13,101 | 25,577 |
AlAs | 26,836 (Al) + 52,924 (As) | 10,003 | 3186 | 5530 |
GaAs | 51,729 (Ga) + 52,697 (As) | 3238 | 806 | 1713 |
GaN | 102,776 (Ga) + 59,190 (N) | 9377 | 7295 | 12,278 |
GaP | 57,127 (Ga) + 26,396 (P) | 19,439 | 4126 | 7938 |
GaSb | 40,309 (Ga) + 53,776 (Sb) | 1874 | 438 | 1105 |
InAs | 53,690 (In) + 42,455 (As) | 1409 | 237 | 1094 |
InP | 58,842 (In) + 20,892 (P) | 13,994 | 2814 | 5725 |
InSb | 43,067 (In) + 44,737 (Sb) | 458 | 54 | 484 |
Number of secondaries produced by 14 MeV neutrons in the different targets.
For the good understanding of Figures 9 and 10, Table 5 indicates the main nonelastic reactions leading to the production of protons and alpha particles. The energy ranges of the ejected particles are also reported. Protons, deuterons, and tritons (Z=1) are produced in large numbers in six materials, by order of importance—GaP, Si, SiC, InP, AlAs, and GaN. The main reactions for these targets are the following (we indicated in parenthesis the energy threshold of the reactions): 31P(n,n’p)30Si (7.5 MeV), 31P(n,p)31Si (0.7 MeV), 31P(n,d)30Si (5.2 MeV), 28Si(n,p)28Al (4 MeV), 27Al(n,p)27Mg (1.9 MeV), 14N(n,d)13C (5.7 MeV). Protons and deuterons are also observed in smaller numbers in the other materials, i.e., GaAs, Ge, GaSb, InAs, and InSb. Only two tritons are observed for C, they are produced in the rare reaction 13C(n,t)11B. Concerning alpha particles (Z=2), they are produced in large or significant numbers in seven materials—SiC, C, Si, GaN, GaP, InP, and AlAs. The main reactions for these targets are the following—28Si(n,α)25Mg (2.7 MeV), 12C(n,α)9Be (6.2 MeV), 14N(n,α)11B (0.17 MeV), 31P(n,α)28Al (2 MeV), 27Al(n,α)24Na (3.2 MeV). Traces of alpha particles are also observed in Ge, GaAs, GaSb, and InSb.
Element | Main reactions for α, p or d production (14 MeV neutrons) | Energy range of the ejected particle |
---|---|---|
C | 12C(n,α)9Be | 0.2–7 MeV |
N | 14N(n,α)11B 14N(n,d)13C 14N(n,p)14C | 0.01–14 MeV 0.1–9 MeV 5–12 MeV |
Al | 27Al(n,α)24Na 27Al(n,p)27Mg | 1.8–14 MeV 0.4–13 MeV |
Si | 28Si(n,d)27Al 28Si(n,p)28Al 28Si(n,α)25Mg | 10–50 keV (peak at 34 keV) 2–10 MeV 0.5–13 MeV |
P | 31P(n,α)28Al 31P(n,n’p)30Si | 0.2–12 MeV 0.4–11 MeV |
Ga | 69Ga(n,α)66Cu 69Ga(n,p)69Zn | 4–14 MeV 0.01–14 MeV |
Ge | 70Ge(n,α)67Zn 70Ge(n,p)70Ga | 4–14 MeV 1.5–13 MeV |
As | 75As(n,α)72Ga 75As(n,p)75Ge | 4–14 MeV 1–13 MeV |
In | 115In(n,p)115Cd | 10–14 MeV |
Sb | 123Sb(n,p)123Sn | 12–14 MeV |
Figure 11 (left) shows the sum of the kinetic energy of all secondaries produced by 14 MeV in the different targets. Figure 11 (right) gives the average energy conveyed per particle for the four categories of secondaries. Protons and alphas are of prime importance in the radiation response of these materials insofar as they convey a very important part of the total kinetic energy; this part is predominant in the case of five materials—Si, SiC, AlAs, GaN, and GaP. As compared to Figure 8 (left) obtained for 2.45 MeV neutrons, the amplification factor of the total kinetic energy at 14 MeV for all secondaries is minimal for C (×2.5) and InSb ((×3.5) and maximal for InP, GaP, AlAs (around ×10), and Si (×14.3).
Left: Sum of the kinetic energy of all secondaries produced by 14 MeV in the different targets (charged particle with Z ≥ 1). Right: Average particle energy per particle type (same legend as for the left figure).
In this last section, we examine the previous results in light of the mechanisms of creation of single-event effects (SEEs) in electronics subjected to fusion neutrons. We recall here that these SEEs are initiated by neutron-matter interactions in four main steps—(1) interactions produce secondary fragments or recoil nuclei from target nuclei. (2) The produced ion(s) interact(s) with material to generate free charge carriers via the production of electron and hole pairs. (3) Electrons and holes are transported by drift-diffusion mechanisms through the circuit materials (oxides and semiconductors) up to a sensitive node (reversely biased junctions); free carriers also recombine during their transport. (4) The collected charge on a sensitive node can significantly alter its voltage that leads to a change in device or circuit operation. This voltage glitch may propagate through the circuit. The present work allows us to provide quantitative information on steps 1 and 2 in so far as from step 3, it would be necessary to consider the circuit architecture, the applied polarizations, and the transport and recombination properties of the materials. In the following, we examine the different materials in light of the number of interactions and of the number of e-h pairs created on average per interaction.
Concerning the first metric, the number of SEEs susceptible to be created in an electronic circuit (of the same geometry as the target for simplicity) is at most equal to the number of interaction events that can deposit enough energy, i.e., create a sufficient electrical charge able to disturb the circuit operation (in the case of an SRAM memory, this minimum amount of charge susceptible to upset a memory cell is called a critical charge). This number of SEEs is not easy to evaluate but it can be upper bounded by the number of events that can deposit energy and therefore generate an electrical charge greater than or equal to the critical charge of the circuit. To roughly estimate this metric from the histogram of the energies/charges deposited per event, a simple transformation is necessary, as illustrated in Figure 12. Figure 12 (left) shows the energy histograms (frequency and cumulative frequency histograms) for all the events produced by 2.45 MeV and 14 MeV neutrons in GaP. The relationship between energy (bottom scale) and charge (top scale) considers the energy value of the creation of electron-hole pairs, as given in Table 2.
Left: Histogram and cumulative histogram of the energy deposited per event for all interaction events in GaP target. Right: Reversed cumulative histogram from the left figure expressed in charge deposited per event (MeV).
At fixed energy or charge, the cumulative frequency histogram directly indicates the number of events for which the total energy deposited is below this value. In practice, it is more convenient to have the complementary value, i.e., the number of events above this value is plotted in Figure 12 (right), and directly expressed in electrical charge instead of energy. Applying this transformation to all targets gives the ensemble of cumulative histograms, as shown in Figures 13 and 14.
Reversed cumulative histogram of the energy deposited per event for all interaction events in GaP, GaN, InSb, GaSb, InP, AlAs, GaAs, and InAs targets subjected to 2.45 MeV and 14 MeV neutrons. For a fixed value of the deposited charge, the curves give the number of interactions able to deposit at most this energy in the corresponding target.
Reversed cumulative histogram of the energy deposited per event for all interaction events in Si, Ge, SiC, and C (diamond) targets subjected to 2.45 MeV and 14 meV neutrons. For a fixed value of the deposited charge, the curves give the number of interactions able to deposit at most this energy in the corresponding target.
These figures can be directly used to estimate the number of events able to deposit an electrical charge superior to a given value. From this data and knowing a minimum of geometric and electrical characteristics of the circuit to be evaluated from a radiative point of view (number and geometry of the sensitive volumes, critical charge, etc.), it would be possible, in future studies, to estimate the number of events susceptible to produce SEEs at both 2.45 and 14 MeV.
Figures 13 and 14 provide also other interesting information about the difference in the neutron susceptibility of a given material at these two energies—the greater this difference, the more the material, and therefore, the circuit based on this semiconductor will be likely to present a significant difference in its radiative SEE response. This difference can be appreciated following two criteria—the respective amounts of events at the lowest charge deposited per event (here at 10−2 fC) and the “distance” between the shoulders of the curves at the highest charge values. For example, a circuit based on diamond or GaN semiconductor may logically presents less difference between its SEE responses at 2.45 MeV and 14 MeV than a circuit based on germanium, InSb, or InAs. Of course, this difference in neutron sensitivity is also dependent on the critical charge value of the considered circuit. In the case of GaAs, for example, a circuit with a 10 fC of critical charge should be quasi-immune to
2.45 MeV neutrons but sensitive to 14 MeV. To go further in this analysis and be quantitative, it would be of course necessary to consider the cumulative histograms of the charge collected at each event. The passage from the deposited charge to the collected charge requires numerical simulations on a given architecture and modeling of transport, recombination, and collection mechanisms, a work currently in progress.
Concerning the second metric, Figure 15 gives the number of e-h pairs created in average per interaction for the different targets at the two neutron energies. At 2.45 MeV, this value is minimum for AlAs (78,000) and maximum for diamond (29,000) and Si (27,000). The average level and the relative low dispersion of these values indicate that recoil nuclei, very widely produced in these elastic and inelastic reactions, deposit small amounts of charges over very short distances of a few nanometers to a few hundred nanometers (data not shown). At 14 MeV, the results of Figure 15 (right) show higher values (approximately ×3 to × 12 for the different materials, and × 20 for Si) due to the contributions of nonelastic reactions that produce the most energetic secondaries, notably protons and alpha particles. Surprisingly and contrary to the case of irradiation with atmospheric neutrons [10], Silicon sensibly differs from the other materials at 14 MeV since it has the greatest multiplying factor between
The average number of e-h pairs created per interaction event in the different targets subjected to 2.45 MeV (left) and 14 MeV (right) neutrons.
2.45 and 14 MeV. This is due to a relatively low number of events (86 kilo events) at this energy with respect to the other semiconductors (Table 6) combined with an important level of production of protons and alpha particles (Table 3) and also with an energy value of e-h pair creation inferior to the average value (around 5 eV) for all materials (Table 2). The other materials which exhibit high values are SiC, GaP, and InP. Statistically, in these four materials, a neutron-target interaction at 14 MeV will deposit more charge than in the other materials, which potentially makes these events more threatening for the creation of SEEs. The balance between all these factors is, therefore, not obvious when one remains at the only “material” level for these studies. This point requires numerical simulations at the circuit level to go further in the investigation of the level of SEE in electronics based on these different materials.
This work explored the radiation response of Group IV (Si, Ge, SiC, diamond) and III-V (GaAs, GaN, GaP, GaSb, InAs, InP, InSb, AlAs) semiconductors subjected to D–D (2.45 MeV) and D–T (14 MeV) neutrons. This first study was limited to the level of the neutron response of bulk materials, an essential step to be able, subsequently, to study the response of electronic components and circuits based on these materials. The response of each semiconductor has been systematically investigated through a direct calculation using nuclear cross-section libraries, MCNP6, and Geant4 numerical simulations. The counting of reaction rates per type of reaction (elastic, inelastic, nonelastic), as well as the classification of all neutron-induced secondary products as a function of their nature and energy, gives a first very complete picture of the behavior of these materials in a fusion environment under D–D or D–T neutrons. Although all studied materials exhibit a larger total number of interaction events than silicon, both at 2.45 and 14 MeV, there is nothing to conclude at this stage that they will present a larger response in terms of SEEs at circuit level since this higher neutron susceptibility only relates to the overall number of events and not to the production of the most energetic particles, such as protons or alpha particles. Moreover, such a higher neutron response may be compensated by other mechanisms at the electronics level, for example, a higher energy value of e-h pair creation (which has the effect of reducing the charge deposited) or higher carrier mobility (which can increase the performance of transistors and strengthen the resilience of circuits to single events). Future studies at the circuit level, following a methodology similar to a first study carried out on GaN subjected to atmospheric neutrons [19], will be largely based on the interaction event databases compiled during this first work and will provide more quantitative information to precisely assess the D–D and D–T neutron radiation response of future circuits based on these alternative materials to the classical silicon of microelectronics.
The authors declare no conflict of interest.
Target (natural material) | Library or simulation code | Number of interaction events (1cm2 × 20 μm, 5×108 neutrons) | |||||
---|---|---|---|---|---|---|---|
2.45 MeV | 14 MeV | ||||||
Elastic | Inelastic | Nonelastic | Elastic | Inelastic | Nonelastic | ||
Si | TENDL-2021 | 94,285 | 31,604 | 0 | 37,776 | 24,611 | 33,529 |
Geant4.10.07 | 92,927 | 27,897 | 4 | 34,665 | 23,623 | 28,341 | |
MCNP6.2 | 94,098 | 30,426 | 22 | 33,452 | 26,309 | 28,547 | |
Ge | TENDL-2021 | 77,667 | 70,778 | 1456 | 76,038 | 32,294 | 38,127 |
Geant4.10.07 | 77,565 | 70,315 | 305 | 77,241 | 30,662 | 40,281 | |
MCNP6.2 | 80,378 | 70,084 | 323 | 79,224 | 24,639 | 43,772 | |
C | TENDL-2021 | 284,170 | 0 | 0 | 147,136 | 74,624 | 11,862 |
Geant4.10.07 | 283,451 | 0 | 0 | 146,732 | 75,433 | 11,462 | |
MCNP6.2 | 282,482 | 0 | 0 | 142,767 | 74,664 | 14,726 | |
SiC-4H | TENDL-2021 | 168,715 | 30,466 | 0 | 76,711 | 44,162 | 35,570 |
Geant4.10.07 | 167,221 | 26,879 | 7 | 73,700 | 43,317 | 30,745 | |
MCNP6.2 | 168,151 | 29,333 | 20 | 71,230 | 45,704 | 31,559 | |
AlAs | TENDL-2021 | 71,069 | 72,328 | 1570 | 56,868 | 23,143 | 33,523 |
Geant4.10.07 | 70,519 | 50,256 | 208 | 57,846 | 21,907 | 34,300 | |
MCNP6.2 | 71,557 | 53,096 | 194 | 55,500 | 23,968 | 35,153 | |
GaAs | TENDL-2021 | 69,858 | 72,905 | 334 | 76,848 | 26,038 | 44,225 |
Geant4.10.07 | 69,858 | 72,905 | 334 | 78,127 | 26,069 | 43,719 | |
MCNP6.2 | 74,428 | 71,515 | 354 | 73,757 | 30,081 | 43,452 | |
GaN | TENDL-2021 | 129,877 | 66,514 | 7683 | 117,421 | 42,330 | 54,074 |
Geant4.10.07 | 130,978 | 65,011 | 5420 | 119,180 | 42,761 | 52,815 | |
MCNP6.2 | 138,249 | 55,632 | 5573 | 114,349 | 47,939 | 50,588 | |
GaP | TENDL-2021 | 109,534 | 50,357 | 1317 | 60,171 | 21,781 | 45,557 |
Geant4.10.07 | 111,630 | 49,735 | 1111 | 60,853 | 22,646 | 44,911 | |
MCNP6.2 | 98,073 | 46,664 | 1309 | 64,006 | 32,412 | 30,478 | |
GaSb | TENDL-2021 | 90,943 | 54,223 | 1189 | 77,215 | 17,192 | 45,596 |
Geant4.10.07 | 90,310 | 57,992 | 1072 | 72,605 | 21,477 | 46,037 | |
MCNP6.2 | 101,262 | 46,366 | 1026 | 71,519 | 26,181 | 42,512 | |
InAs | TENDL-2021 | 85,006 | 71,752 | 4280 | 78,268 | 18,035 | 47,203 |
Geant4.10.07 | 82,040 | 64,307 | 2007 | 78,346 | 17,799 | 46,801 | |
MCNP6.2 | 88,362 | 63,776 | 1824 | 83,978 | 15,828 | 45,441 | |
InP | TENDL-2021 | 117,899 | 54,714 | 4370 | 65,719 | 14,025 | 48,965 |
Geant4.10.07 | 118,171 | 45,215 | 2689 | 65,177 | 14,538 | 48,000 | |
MCNP6.2 | 109,501 | 43,783 | 2720 | 77,879 | 16,575 | 35,607 | |
InSb | TENDL-2021 | 98,085 | 55,811 | 3451 | 77,290 | 11,768 | 47,215 |
Geant4.10.07 | 96,303 | 52,707 | 2264 | 72,622 | 15,152 | 47,707 | |
MCNP6.2 | 107,126 | 43,471 | 2080 | 79,225 | 14,813 | 43,781 |
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The CC BY 3.0 and CC BY 4.0 license permits Works to be freely shared in any medium or format, as well as the reuse and adaptation of the original contents of Works (e.g. figures and tables created by the Authors), as long as the source Work is cited and its Authors are acknowledged in the following manner:
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