Analysis of cosmic ray neutron-induced single-event phenomena

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1 Analysis o cosmic ray neutron-induced single-event phenomena Yasuyuki TUKAMOTO Yukinobu WATANABE and Hideki NAKASHIMA Department o Advanced Energy Engineering Science Kyushu University Kasuga Fukuoka Japan Corresponding watanabe@aees.kyushu-u.ac.jp We have developed a database o cross sections or the n+ 8 Si reaction in the energy range between MeV and 3 GeV in order to analyze single-event upset ( phenomena induced by cosmic-ray neutrons in semiconductor memory devices. The data are applied to calculations o cross sections using the Burst Generation Rate (BGR model including two parameters critical charge and eective depth. The calculated results are compared with measured cross-sections or energies up to 160 MeV and the reaction products that provide important eects on are mainly investigated. 1. Introduction In recent years much concerns has been paid to cosmic-ray induced sot errors in semiconductor memory devices used on ground level[1]. Cosmic-rays on ground level consist o mainly neutrons with wide energy range rom MeV to GeV. A microscopic picture o the cosmic ray induced sot errors is the ollowing. Energetic neutrons interact with materials used in the devices and light charged particles and heavy ions can be generated via a nuclear reaction with a silicon nucleus. They can give rise to local charge burst in a micron volume which results in upsets o the memory cell inormation quantum that are called single-event upsets (s. Thereore quantitative estimation o the sot errors requires reliable nuclear reaction data or silicon in the high-energy range and modeling o charge transport in microelectronics devices. So ar we have developed a database o cross sections or 8 Si at neutron energies between 0 MeV and 3 GeV which is necessary or sot error simulation[]. The database was successully applied to calculations o neutron-induced cross sections using the Burst Generation Rate (BGR model [3] and a neutron-induced sot-error simulation code system or semiconductor memory devices[4]. In the uture the size o memory devices will be reduced and it is expected that the inluence o low energy neutrons on s cannot be ignored because a critical charge causing the becomes smaller[5]. In the present work thereore we have extended the database so as to include the cross sections below 0 MeV. Double-dierential cross sections or all recoils in the n+ 8 Si reaction are necessary or estimation o neutron-induced sot-errors. They were obtained using a kinematics calculation with the JENDL-3.3 library[6]. Finally the cross section data were used to analyze some experimental data up to 160 MeV[78] by the BGR model calculation. In this report we will discuss some results o the analysis paying particular attention to s or neutron energies below 0 MeV.. Development o database or n+ 8 Si reaction.1 Outline The JENDL-3.3 library[6] was used to obtain the double-dierential cross sections (DDXs or light charged particles (p and α and all recoils( 45 Mg 78 Al and 78 Si in the n+ 8 Si reaction at energies between and 0 MeV. A method o processing the JENDL-3.3

2 library will be described in the next subsection. The data or energies between 0 to 150 MeV were taken rom the LA150 library[9] in which the DDXs o all recoils are included. We have calculated the cross sections or energies above 150 MeV using the QMD[10] plus statistical ay model (GEM[11] calculation.. Calculation o double-dierential cross sections or recoils with JENDL-3.3 For neutron elastic and inelastic scattering the emission energy and angle o the recoiled nucleus 8 Si can be easily obtained using the two-body kinematics [1] and the DDXs o 8 Si in the oratory system are also converted rom the data o dierential neuron elastic and inelastic scattering cross sections in the JENDL-3.3 library. The same kinematics calculation was also applied to two heavy recoils 8 Al and 5 Mg produced by (np and (nα reactions. Cross Section (barns elastic inelastic (nnp (np (nα (nnα (nn (np Neutron Energy (ev Fig.1 JENDL-3.3 cross sections or various reactions at neutron energies up to 0 MeV As shown in Fig.1 two particle emission such as (nnp and (nnα becomes dominant as the incident neutron energy increases and the inluence on s is expected to become crucial. However it is not simple to obtain the DDXs o the recoils produced by the twoparticle emission because exclusive energy spectra or the second particle emission are not included in the JENDL-3.3. Note that the DDX spectra o the irst neutron emission are included as MF=6 MT=16 and 8 in the JENDL-3.3. Hence we assume that two-particle emission occurs via two-body sequential ay rom the excited residual nucleus ater the irst particle emission: a + X + b1 b + where a and X are incident particle (neutron and target nucleus ( 8 Si and is the residual nucleus 8 Si ater the irst neutron (b 1 emission and b and are the second emission particle and the recoil respectively. The DDXs o the recoil nucleus in the oratory system are given by the ollowing expression [13]: σ Ω E = = σ Ω E σ Ω E ' ' ' 1 σ (cos θ φ E ( t ' ' dωde σ (cos E E Ω θ φ (cos ' ' ' 1 σ E θ φ dω ( t de ' ' σ (cos E E Ω θ φ (1

3 where ( σ / Ω is calculated rom the data o DDXs o the emitted particle b 1 E using the two-body kinematics and ( / Ω' E' σ is the DDX o the inal recoil in (t the rest rame o the compound nucleus and σ is the integrated cross section over Ω ' and σ / Ω' E' is calculated by assuming the evaporation model or emission E'. ( o b and its isotropic angular distribution. In the evaporation model calculation empirical ormulae given in re.[14] were used or the inverse cross sections o proton α and neutron and the level density ormula based on the Fermi-gas model was employed with the level density parameter a=a/8 where A is the mass number. The DDXs or light-charged particles (proton and α are included in the JENDL-3.3 library. Finally a database o all DDXs or protons α and all recoils( 45 Mg 78 Al and 78 Si emitted in the n+ 8 Si reaction were prepared or energies between and 0 MeV. 3. Modiied Burst Generation Rate (BGR model The rate is deined by rate σ ( E φ( E de ( = n n n where σ is the cross section or the neutron energy E n and φ is the neutron lux. Using the BGR method[3] σ is given by σ = C V BGR( En Qc d (3 where C is the charge collection eiciency and V is the sensitive volume per bit. It should be noted that the product o C and V is treated as a normalization parameter to be determined by itting measured data o σ. The BGR is deined as the probability that a nuclear reaction produces charged particles and ions which deposit the kinetic energy more than E c in a sensitive volume and is given as a unction o incident neutron energy E n and critical charge Q c which can be converted into E c using the relation E c (MeV =.5 Q c (pc. Since the energy deposit o the charged particles and ions in a small volume depends on the linear energy transer (LET we introduce an eective depth d as a parameter or BGR calculations. Thus BGR Qc d = BGR( En Qc d Ai Z i i ( i Emax ( d d σ = NSi dωde i E d i ded (4 ( min ( Ω where N Si is the number density o silicon atoms and the index i stands or the kind o reaction product with mass number A i and atomic number Z i. (d σ/dedω (i is the double-dierential production cross section o the reaction product i. By taking into account the LET the upper and lower limits o the integration E ( i max ( d and E ( i min ( d are estimated as the maximum and minimum energies o the reaction product i that deposits the energy above E c within d. The SRIM code[15] is used or calculations o the LET. It should be noted that isotropic angular distribution is assumed or emission o the reaction products or simplicity. 4. Results and discussion Figures and 3 shows a comparison o the calculation with measured data [78] or SRAMs with 56Kb or 1Mb. The measured data are normalized to the data o Cypress. The ( i

4 normalization constant C V in Eq.(3 was determined so that the BGR unction calculated with Q c =53 C and d=1.0 µm gives a best it to the data o Cypress. The obtained result shows satisactory agreement with the measured data over the whole neutron energy range. The region below 0 MeV in Fig. is expanded in Fig.3. The calculated cross-sections are omposed into individual contribution rom each recoil nucleus. The recoil 5 Mg produced by the (nα reaction shows the largest contribution at energies below 17 MeV. Also the recoil 4 Mg produced by the (nnα reaction aects considerably the s with increase in neutron energy. In Fig.4 the energy spectra o all recoils are plotted at an incident energy o 0 MeV in order to see why these Mg isotopes have signiicant contributions to s. The critical charge Q c =53 C corresponds to the energy deposit E dep =1. MeV. The minimum energy o the recoil that can provide this energy deposit within d=1.0 µm is about 1.8 MeV ( E ( i min ( d in Eq.(4. The energy spectra o Mg isotopes are distributed over the range above 1.8 MeV and have relatively large cross sections as can be seen in Fig.4. This is a possible reason why the Mg isotopes contribute signiicantly to s. Also we have investigated the kind o reaction products that inluence largely the s or energies between 0 MeV and 150 MeV. The result is presented as a raction o each recoil element to total s in Fig.5. It is shown that production o heavy ions such as Al and Mg plays a major role in the s at energies above 40 MeV because such ions have large LET. It is also ound that the contribution rom Si is reduced with rease in neutron energy. This trend can be explained by the act that the elastic and inelastic cross sections become small and their angular distributions become steeper as the neutron energy increases. Finally the incident energy range having the most eect on the rate has been examined by assuming a neutron lux distribution on the ground level given by IBM group[1]. The BGR unctions are plotted or three dierent critical charges Q c = and 30 C in Fig.6. The eective depth d is assumed to be 0.35 µm in the calculation. The product o the BGR and the neutron lux corresponding to the integrand in the right-hand side o Eq.( are shown in Fig.7 to examine the neutron sensitivity. It is ound that the sensitivity increases remarkably at neutron energies below 0 MeV as Q c reases. This indicates that the nuclear data below 0 MeV will become important or estimation o sot-error rates as the size o memory devices is reduced because the reduction o the size leads to that o Q c. 5. Conclusion The database o cross sections or the n+ 8 Si reaction was developed in the energy range between MeV and 3 GeV or evaluations o the sot-errors in semiconductor memory devices induced by cosmic-ray neutrons. The data were applied to calculations o cross sections using the modiied BGR model that takes into account the eective depth in the sensitive volume as a parameter. The calculated results reproduced well the energy dependence o the measured cross-sections or energies up to 160 MeV. It was ound that the reaction products that inluence the s mainly are the heavy ions such as Mg and Al having large LET particularly the Mg isotopes have signiicant contribution at energies below 0 MeV. The dependence o the neutron sensitivity on the critical charge Q c was investigated over neutron energies up to 150 MeV and it was ound that the sensitivity increases remarkably at neutron energies below 0 MeV with rease in Q c. Acknowledgements The authors are grateul to Mr. Y. Kawakami and Dr. M. Hane or valuable discussions on SER simulation calculation.

5 Reerences [1] J.F. Ziegler et al. IBM J. Res. Develop. 40 No.1 (1996. [] T. Ikeuchi et al. J. o Nucl. Sci. and Technol. Suppl (00. [3] J.F. Ziegler and W. Lanord Science (1979. [4] Y. Kawakami et al. NEC Research & Development 43( 146 (00. [5] H. Ibe et al. Applied Physics 70 No (001 [in Japanese]. [6] K. Shibata et al. J. o Nucl. Sci. and Technol (00. [7] K. Johansson et al. IEEE Trans. Nucl. Sci (1998. [8] K. Johansson et al. ibid (1999. [9] M.B. Chadwick et al. Nucl. Sci. Eng (1998. [10] K. Niita et al. JQMD code JAERI-Data/Code (1999. [11] S. Furihata Nucl. Inst. Method in Phys. Res. B (000; S. Furihata and T. Nakamura J. Nucl. Sci. and Technol. Suppl. 758 (00. [1] G.G. Ohlsen Nucl. Instr. Methods (1965. [13] M.D. Baker et al. Nucl. Sci. Eng (1987. [14] A. Chatterjee et al. Pramana (1981. [15] J.F. Ziegler SRIM code (1999. Cross Section (cm /bit SRAM present work (CV=45 [µm 3 /bit] Matra-H.(X Kb Cypress(X Kb Micron(X.1 56Kb Toshiba(X 6.5 1Mb NEC(X 7. 1Mb Neutron Energy (MeV Fig. Comparison o the calculated cross sections with the measured ones taken rom Res.[78]. The measured data are normalized to the data o Cypress. Fig.3 Cross Section (cm /bit Cypress(56Kb present work 8 Si 4 Mg 5 Mg 8 Al 7 Al Neutron Energy (MeV Same as in Fig. but the energy range below 0 MeV.

6 Fig.4 dσ/de(mb/mev E = 0 MeV 4 Mg n 5 Mg 7 Al 8 Al 7 Si 8 Si E(MeV Energy spectra o all recoils or an incident energy o 0 MeV. Fraction (% C Qc=53Cd=1.0µm N O F Ne Na Mg Al Si E(MeV Fig.5 Fraction o each recoil element to total s as a unction o incident neutron energy. BGR(cm /µm 3 Fig C 13.3C 4.4C d=0.35µm Neutron Energy (MeV BGR unctions or Qc= and 30 C and eective depth d=0.35 µm. Flux (arb. /bit-mev-sec Fig C 13.3C 4.4C d=0.35µm Neutron Energy (MeV Sensitivity o the critical charge Qc to s or the cosmic-ray neutron lux given by IBM model[1].

Neutron-Induced Soft Error Analysis in MOSFETs from a 65nm to a 25 nm Design Rule using Multi-Scale Monte Carlo Simulation Method

Neutron-Induced Soft Error Analysis in MOSFETs from a 65nm to a 25 nm Design Rule using Multi-Scale Monte Carlo Simulation Method Shin-ichiro Abe, Yukinobu Watanabe, Nozomi Shibano 2, Nobuyuki Sano 2,