Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Electrical resistance and conductance wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Cross section (physics) wikipedia , lookup
Superconductivity wikipedia , lookup
Condensed matter physics wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Monte Carlo methods for electron transport wikipedia , lookup
Analysis of electron mobility dependence on electron and neutron irradiation in silicon J.V.VAITKUS, A.MEKYS, V.RUMBAUSKAS, J.STORASTA, Institute of Applied Research, Vilnius University, Vilnius, Lithuania Classical effects, that works well in the classical situations, can be used for analyze conditions in the samples that are not traditional: irradiated-Si The free carrier mobility is on of most important parameters in radiation detector analyze because as usually it goes together with the electric field: vdrift=E. Therefore the knowledge of mobility predicts a correct values of electric field in the devices. Our attempts: an investigation of low field electron mobility in the irradiated by neutrons Si, taking in account that at high fluence sample may became inhomogeneous due to overlap of the clusters space charge regions, therefore we measured the Hall and magnetoresistance mobilities. μH = rH μ, μM = rH ζ μ = rM μ. It was found the ratio of magnetoresistance and Hall mobilities μM/μH = 1.15. [A. Mekys, V. Rumbauskas, J. Storasta, L. Makarenko, N. Kazuchits, J.V. Vaitkus. Hall effect and magnetoresistance investigation of fast electron irradiated silicon. Lithuanian (And presented earlier RD50 Workshop.) Journal of Physics, 54, 94–98 (2014)]. Hall effect measurement scheme. 1Sample; 2- electrometer (KEITHLEY 6514); 3- source meter (KEITHLEY 6430); 4magnet source; 5- thermo resistance meter (Agilent 34401A); 6- heater source (TTi QL564P); 7- computer; 8- magnet; 9cryostat. Electron mobility dependence on the fluence in the irradiated and annealed Si samples. 1400 T (K) MR 260 280 1200 O After annealing 24h @ 80 C T (K) 260 280 1200 , cm /Vs 1000 2 2 , cm /Vs 1000 800 600 800 600 12 10 13 10 14 15 10 cm 10 16 10 12 10 -2 13 10 1 / 1 / phon(i.e.,independent on fluence) S phon = 1260 cm2/sV & S=1.5·10-17 sV 14 15 10 10 -2 , cm 16 10 Probably the crystal became similar to the disordered media. in the just-irradiated Si phon = 1300 cm2/sV & S=0.2·10-17 sV in the annealed for 24 h@800. Hall and magnetoresistance dependence on T (the Fig. was presented in the previous workshops) Fluence 2 (n/cm ) M 1000 12 2 H, m (cm /Vs) 10 13 10 14 3*10 15 10 16 10 H 12 100 180 • • • • • 200 220 240 260 T (K) 280 300 10 13 10 14 3*10 15 10 16 10 The magnetoresistance mobility dependence on temperature was similar to predicted for scattering on the clusters, however the mobility value at room temperature was not far away from limited by scattering by phonons. Therefore it was necessary to analyse contributions of all possible scattering processes using the Matthiesen rule and to use the approximation of mobility dependence on temperature as =aT, where index depends on the scattering mechanism, and analyse performed in a narrow range of temperature. As the simulation [Huhtinen] showed the neutron irradiation creates rather compact generation of defects, and a remaining material volume is free from the defects. Therefore the simulation of mobility dependence on temperature has to take into account the scattering of carriers as in a high quality silicon crystal that could be approximated by a power law =aT with =(-2.4), but in the compensated samples =(-1.4) was observed, that could be a result of additional scattering on the ionized impurities. For the scattering on the point defects that can be charged =1.5. If the defects are neutral, their contribution can be independent on temperature with =0. The scattering of clusters is most indefinite: – – it could follow the same dependences with = (-1.0) or (-5/6) the contribution of dipole scattering that could appear due to difference of vacancies and interstitials location inside the cluster. The dipole scattering can be approximated by ~ T0.5. Fitting of mobility dependence on T 2500 1800 1400 1600 1400 2 Mcm /sV 2 H, m (cm /Vs) 1600 1200 2 Fluence, n/cm Experiment Approximation 1e12 1e13 3e14 1e15 1e16 3e16 2000 2 Fluence n/cm Experiment Approximation 12 10 13 10 14 3*10 15 10 16 10 , cm /Vs 1800 2 1200 1000 Si-KEF2 nonirradiated a fit (Table 1, line to 10) -2 Si-KEF2 irradiated F=1e14 cm a fit (Table 1, line to 11) -2 Si-KEF2 irradiated F=1e15 cm a fit (Table 1, line to 12) 1500 1000 800 800 600 180 200 220 240 260 280 300 600 220 240 260 T (K) 280 300 T, K 1000 200 225 250 275 T, K Hall mobility and magnetoresistive mobility dependence on temperature in the neutron irradiated samples. The fluence and the mobility type are shown in the inset. a. – the high resistivity Si samples, b. annealed samples, c – the low resistivity Si samples. 300 Table 1. The parameters used for a fit of experimental data to the relation: = 1/(1/phon+1/ionized+1/clusters+1/dipoles)= =1/(1/aT + 1/bT1.5 + 1/cT-1+ 1/dT0.5) Fluence cm-2 Sample Phonons ( value before irradiation) a Ionized point defects Clusters Dipoles c D b 12 1·10 1·1012 1·1013 3·1014 3·1014 1·1015 1·1015 1·1016 3·1016 nonirradiated 1·1014 1·1015 J-I HR Annealed HR J-I HR J-I HR Annealed HR J-I HR Annealed HR J-I HR Annealed HR KEF2 KEF2 KEF2 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -2 -2 -2 6 4.2·10 4.6·106 4.2·106 4.2·106 4.2·106 4.2·106 4.2·106 4.2·106 4.2·106 1.1·108 1.1·108 1.15·108 1.5 1 1.8 3 1.1 2 1 3 0.8 4 3.3 8 0.8·107 1·107 2·106 6.5·105 6.5·105 5·105 6.5·105 5·105 5·105 0 1.2·108 4·107 1.6·103 4·103 1·103 1·103 4·103 1·103 4·103 1·103 2·104 0 3.4·103 5·103 The cluster model 12 10 15 10 13 10 12 10 13 10 15 3 10 14 10 16 10 11 Ec-EM, meV 134, - deepest, 220, 260, 10 -3 10 9 10 8 10 7 10 shallow, 270, 70 , 280 13 NM-NK or NM , cm 10 -3 10 360 E 400 12 10 n, cm 14 14 3 10 16 3 10 ni E 410 410 410 430 430 440 10 11 10 C F 10 10 9 10 8 6 10 5 10 10 7 10 0.004 0.006 0.008 1/T, 1/K 0.010 12 10 13 10 14 15 10 10 -3 Fluence, cm E 16 10 V The temperature dependence of the electron concentration in the irradiated samples. The fluence value in neutrons/cm2 is given in the insets. The lines correspond to the result of fitting to the experimental data. The cluster model that allows an existence of the dipole x Electron irradiation (6,6 MeV, “low resistivity” Si) KDBMH300 KDBMH250 KEFMH300 KEFMH250 A Linear fit 2400 2200 2000 1800 1400 2 H (cm /Vs) 1600 600 550 500 450 400 350 0 1 2 3 16 4 5 2 Fluence x 10 e/cm A.Mekys, V.Rumbauskas, J.Storasta, L.Makarenko, J.V.Vaitkus. Defect analysis in fast electron irradiated silicon by Hall and magnetoresistivity means. NIMB 338, 95100 (2014) This work is performed in frame of CERN RD50 collaboration. Thanks to Lithuanian Science Council for the grant TAK-10001 and Lithuanian Academy of Sciences for continuing support of this research and grants CERN-VU-2013-2015 . Thank you for your attention! CERN Mobilities: • Magnetoresistant mobility in this work was calculated using the following relation: (1) • Here B is the magnetic field induction, I0 is the electric current in the sample when magnetic field is not present and IB is the same current with the presence of the magnetic field. • The Hall mobility was calculated using: (2) • Here l is the distance between the electric current contacts (1,2) and UX is the voltage applied, w is the distance between the Hall contacts (3,4).