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Simulation, Measurement and Analysis of the Response of Electron- and Position Sensitive Detector

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(9) ƒ–”—Ž›‹†‡„–‡†–‘ǤǤǤ  ǤǤǤ› •—’‡”˜‹•‘”• ƒ† ‹‡ ˆ‘” –Š‡ ‘’’‘”–—‹–› –‘ ‡„ƒ” ‘ ƒ †‘ –‘”ƒ–‡•–—†‹‡•ƒ†ˆ‘”–Š‡•—’’‘”–’”‘˜‹†‡†–Š”‘—‰Š‘—––Š‹•Œ‘—”‡›Ǥ  ǤǤǤ ”‹•–‡” Ž†‡ ˆ‘” ƒ‹‰ –Š‡ Ž‡ƒ”‘‘ ƒ ™‘”‹‰ Ž‡ƒ”‘‘Ǥ ‘‡‘‡Š‡”‡”‡ƒŽŽ›†‘‡•ƒ’’”‡ ‹ƒ–‡›‘—”‰‘‘†™‘”Ǥ  ǤǤǤ‡˜‡”›‘‡ȋˆ”‹‡†•ƒ† ‘ŽŽ‡ƒ‰—‡•Ȍ–‘‘—‡”‘—•–‘ƒ‡Ǧ‡•’‡ ‹ƒŽŽ› ƒ––Š‡Ž‡ –”‘‹ •‡•‹‰‡’ƒ”–‡–Ǧ”‡‘–‡Ž› ‘‡ –‡†‹Š‡Ž’‹‰–‘ƒ‡ Ǯ–Š‹•‰Žƒ••ǯŠƒŽˆˆ—ŽŽǤ  ǤǤǤ–Š‡™‘†‡”ˆ—Ž™‘‡‹›Ž‹ˆ‡ǤǤǤ  ǤǤǤƒ†ǤǤǤ  ǤǤǤǮŠ‡ƒ—’•–ƒ‹”•ǯǤ            . —†•˜ƒŽŽǡ –‘„‡”ͳͲǡʹͲͳʹ  •‡„ƒ‡ǡ‡”˜‹ƒ”‡‹‡. ‹˜. .

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(17) –‡”ˆƒ ‡”ƒ’•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͲ ͵Ǥ͵ ”‡˜‹‘—•–—†‹‡•‘ ƒ•–”ƒ’•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳ ͵ǤͶ ‡ Š‹ ƒŽ‡˜‹‡™•‘ ‹š‡†š‹†‡Šƒ”‰‡ˆǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳʹ ͵Ǥͷ ‹š‡†š‹†‡Šƒ”‰‡‹Ž‡ –”‘‡–‡ –‘”•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͷ Ͷ 

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(22) ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳ͹ ͶǤͳ ‡ ‘„‹ƒ–‹‘‹‡‹ ‘†— –‘”ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳ͹ ͶǤʹ —”ˆƒ ‡‡ ‘„‹ƒ–‹‘‡Ž‘ ‹–›ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͺ ͶǤʹǤͳ —”ˆƒ ‡‡ ‘„‹ƒ–‹‘‡Ž‘ ‹–›‹‡Žƒ–‹‘–‘”ƒ’Ǧ••‹•–‡† ‡ ‘„‹ƒ–‹‘‹ˆ‡–‹‡ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͻ ͶǤ͵ —”ˆƒ ‡ƒ••‹˜ƒ–‹‘ƒ†—”ˆƒ ‡‡ ‘„‹ƒ–‹‘‡Ž‘ ‹–›ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͲ ͶǤͶ ˆˆ‡ –‘ˆ—”ˆƒ ‡‡ ‘„‹ƒ–‹‘‡Ž‘ ‹–›‹Ž‡ –”‘‡–‡ –‘”•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͳ ͷ 

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(26)   ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹ͵ ͷǤͳ –ƒ‰‡

(27) ǣ‹—Žƒ–‹‰–Š‡‡˜‹ ‡™‹–Š ‡ƒ–Ͷƒ†

(28) ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹ͵ ͷǤʹ –ƒ‰‡

(29)

(30) ǣ‹—Žƒ–‹‰™‹–Š‡†‹ ‹Ȁ•—’”‡ͶǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͷ ͷǤ͵ „‹‡–‘†‹–‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͻ ͷǤͶ ”‘™‹‰Š‹ ‹ŽǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵Ͳ ͷǤͷ ‡–ƒŽŽ‹œƒ–‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵Ͳ ͸ 

(31)  ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͳ ͸Ǥͳ –ƒ”–‹‰™ƒˆ‡”ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ʹ ͸Ǥʹ ƒ’Ž‡”‡’ƒ”ƒ–‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ʹ ͸Ǥ͵ ƒ––‡”‹‰ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵͵. ˜. .

(32) ͸ǤͶ

(33) ’Žƒ–ƒ–‹‘‘ˆ

(34) ’—”‹–‹‡•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵Ͷ ͸Ǥͷ ‡ƒŽ‹‰Ȁ‹ˆˆ—•‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵Ͷ ͸Ǥ͸ ”‹† ‘”ƒ–‹‘‘–Š‡ή’‡˜‹ ‡ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵͹ ͹ ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶͳ ͹Ǥͳ ‡ƒ•—”‹‰–Š‡‡•’‘•‹˜‹–›ˆ‘”‹ˆˆ‡”‡–Ž‡ –”‘‡”‰‹‡•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶͳ ͹Ǥʹ ‡–‡ ‘„‹ƒ–‹‘ƒ–‡ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶͺ ͹Ǥ͵ ‡ƒ•—”‹‰–Š‡‹‡ƒ”‹–›ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶͻ ͺ  

(35) ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷ͵ ͺǤͳ ‘ Ž—•‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͶ ›‘’•‹•‘ˆ —–—”‡‘”ȋ•ȌǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷ͸ ͻ  

(36) 

(37) ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷ͹  ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͻ 

(38) ǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥ͸ͻ 

(39)

(40) ǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǤ͹ͻ 

(41)

(42)

(43) ǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥͺͻ 

(44) ǥǥǥǥǥǥǥǥǥǥǥǤǤǤǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥǥͻͻ . ˜‹. .

(45) 

(46)  

(47)  ‹‰ͳ•›‘’•‹•‘ˆ–Š‡”‡•‡ƒ” Š‘„Œ‡ –‹˜‡•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳ ‹‰ʹǤ•›‘’•‹•‘ˆ–Š‡‡–Š‘†‘Ž‘‰›‡’Ž‘›‡†‹–Š‡–Š‡•‹•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ ‹‰͵Ǥ Š‡ƒ–‹ ‹ŽŽ—•–”ƒ–‹‘‘ˆƒ ”‘••Ǧ•‡ –‹‘ƒŽ

(48) ‡š’‡”‹‡–‹ȏʹʹȐ͸ ‹‰ͶǤ‡ ‘†ƒ”›‡Ž‡ –”‘‹ƒ‰‡‘ˆƒƒ‡••ƒƒ–ƒŽƒ–ƒ„—––‡”ˆŽ›™‹‰ȏ͵ʹȐǤǤǤǤͺ ‹‰ͷǤƒ”‹ƒ–‹‘‘ˆ–‹‡ ‘•–ƒ–ƒ•ƒˆ— –‹‘‘ˆ•—”ˆƒ ‡’‘–‡–‹ƒŽˆ‘”–Š‡ ’”‘ ‡••‡•ǢȋƔȌˆ‘”™‡–‰”‘™‘š‹†‡ƒ†”ƒ†‹ƒ–‹‘‹†— ‡†ȋŸȌ‹–‡”ˆƒ ‡–”ƒ’• ˆ‘”†”›Ǧ‰”‘™‘š‹†‡ȏ͵ͺȐȏ͵ͻȐǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳ ‹‰͸Ǥ‡”‹‘Ž‘‰›ˆ‘” Šƒ”‰‡•ƒ••‘ ‹ƒ–‡†™‹–Š–Š‡”ƒŽŽ›‘š‹†‹œ‡†•‹Ž‹ ‘ȏͶͲȐ ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳ ‹‰͹Ǥ—””‡–Ǧ˜‘Ž–ƒ‰‡•‹—Žƒ–‹‘ˆ”‘–Š‡ƒƒŽ›•‹•‘ˆȀ‹ Ž—†‹‰ˆƒ•–‹–‡”ˆƒ ‡ •–ƒ–‡•‘ˆǦ Šƒ‡Ž ȏͶͳȐǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳ͵ ‹‰ͺǤ‡ƒŽ–”‹ƒ‰Ž‡•Š‘™‹‰–Š‡”‡˜‡”•‹„‹Ž‹–›‘ˆŠ‡ƒ––”‡ƒ–‡–‡ˆˆ‡ –‘ˆ‹š‡† ‘š‹†‡ Šƒ”‰‡ȏͶ͹ȐǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͶ ‹‰ͻǤ•‹—Žƒ–‹‘”‡•—Ž–‘–Š‡‹ˆŽ—‡ ‡‘ˆˆ‹š‡†‘š‹†‡ Šƒ”‰‡ǡˆ‘–Š‡ ”‡•’‘•‹˜‹–›‘ˆƒ‡Ž‡ –”‘†‡–‡ –‘”ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͷ ‹‰ͳͲǤƒ•‹ †‹ƒ‰”ƒ•Š‘™‹‰–Š‡’”‘ ‡••‘ˆȋƒȌƒ†Ǧ–‘Ǧ„ƒ†”‡ ‘„‹ƒ–‹‘ ™Š‡”‡„›‡‡”‰›‹•‡š Šƒ‰‡†–‘ƒ”ƒ†‹ƒ–‹˜‡‘”—‰‡”’”‘ ‡••ȋ„Ȍ‘Ǧ ”ƒ†‹ƒ–‹˜‡”‡ ‘„‹ƒ–‹‘ȏ͵͹ȐǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳ͹ ‹‰ͳͳǤ•‹—Žƒ–‹‘”‡•—Ž–‘–Š‡‹ˆŽ—‡ ‡‘ˆ‹–‡”ˆƒ ‡”‡ ‘„‹ƒ–‹‘˜‡Ž‘ ‹–› ‘ˆ‹‘”‹–› ƒ””‹‡”•‘–Š‡”‡•’‘•‹˜‹–›‘ˆƒȌƒ”•‡‹ †‘’‡†ή’†‡–‡ –‘”ǤǤǤǤǤǤǤʹͳ ‹‰ͳʹǤšǦœ’Žƒ‡•‹—Žƒ–‹‘–”ƒŒ‡ –‘”‹‡•‘ˆ‡Ž‡ –”‘ƒ–ͺƒ ‡Ž‡”ƒ–‹‰ ˜‘Ž–ƒ‰‡‹ƒ•‹Ž‹ ‘†‡–‡ –‘”—•‹‰

(49) ˜ʹǤͶʹȋ—„‡”‘ˆ‡Ž‡ –”‘ –”ƒŒ‡ –‘”‹‡••‹—Žƒ–‡†αͳͲͲǡͲͲͲȌǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͶ ‹‰ͳ͵Ǥ•‹—Žƒ–‡†‡ƒ•—”‡‘ˆ–Š‡†‡’–Š’”‘ˆ‹Ž‡‘ˆ–Š‡ƒ„•‘”„‡†‡‡”‰›’‡” ‡Ž‡ –”‘ˆ‘”ͳͲ‡ǡͳͷ‡ƒ†ʹͲ‡–Š”‘—‰Šƒ•‹Ž‹ ‘™ƒˆ‡”—•‹‰ ‡ƒ–ͶǤǤʹͷ ‹‰ͳͶǤ–™‘Ǧ†‹‡•‹‘ƒŽ ”‘••Ǧ•‡ –‹‘˜‹‡™‘ˆȋƒȌšǦœ’Žƒ‡ȋ„ȌšǦ›’Žƒ‡ ȋ–‘’Ǧ†‘™˜‹‡™Ȍ‘ˆƒ„•‘”„‡†‡‡”‰›‹ƒ•‹Ž‹ ‘™ƒˆ‡”•—„•–”ƒ–‡•‹—Žƒ–‡†. ˜‹‹. .

(50) ™‹–Šͺƒ ‡Ž‡”ƒ–‹‰˜‘Ž–ƒ‰‡ȋ—„‡”‘ˆ‡Ž‡ –”‘–”ƒŒ‡ –‘”‹‡••‹—Žƒ–‡†α ͳͲͲǡͲͲͲȌ—•‹‰

(51) ʹǤͶʹǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹ͹ ‹‰ͳͷǤŠ‡†‘’‹‰’”‘ˆ‹Ž‡•‘ˆ–™‘•‹—Žƒ–‡†ή’†‡–‡ –‘”•ǤŠ‡”•‡‹ ƒ† ’Š‘•’Š‘”—•‹‘•™‡”‡‹’Žƒ–‡†–Š”‘—‰ŠƒͷͷͲ%–Š‹ ‹ʹƒ–ƒ ‡Ž‡”ƒ–‹‘ ‡‡”‰‹‡•‘ˆͷ͸ǤͶ‡ƒ†͵Ͳ‡”‡•’‡ –‹˜‡Ž›ǤŠ‡•‹—Žƒ–‹‘‘ˆ–Š‡†‹ˆˆ—•‹‘ ’”‘ ‡••ˆ‘”„‘–Š†‡–‡ –‘”•™ƒ• ƒ””‹‡†‘—–ƒ–ͻͲͲ‘ˆ‘”͵Ͳ‹•‹‹–”‘‰‡ ƒ„‹‡–ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͺ ‹‰ͳ͸Ǥ Ž‘™ Šƒ”–ˆ‘”‰‡‡”‹ †‡–‡ –‘”’”‘ ‡•••‡“—‡ ‡ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͳ ‹‰ͳ͹ǤŠ‡ƒš‹ƒŽ”‡•‹•–‹˜‹–›‘ˆ–Š‡•–ƒ”–‹‰™ƒˆ‡”—•‡†Ǥ

(52) –‹•ƒˆ— –‹‘‘ˆ–Š‡ ’‘•‹–‹‘ƒŽ‘‰–Š‡ ”›•–ƒŽ™Š‡”‡–Š‡›™‡”‡‰”‘™ǤŠ‹•™ƒ•‡ƒ•—”‡†„›–Š‡ʹ ƒ†ͶǦ’‘‹–‡–Š‘†ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ʹ ‹‰ͳͺǤŠ‡†‘’‹‰’”‘ˆ‹Ž‡‘ˆ–Š‡•‹—Žƒ–‡†’ސ†‡–‡ –‘”•ƒ†–Šƒ–‘ˆ–Š‡ ˆƒ„”‹ ƒ–‡††‡–‡ –‘”‡ƒ•—”‡†™‹–Š‡ ‘†ƒ”›‹‘ƒ•••’‡ –”‘‡–”›

(53) Ǥ Š‡†‡˜‹ƒ–‹‘‹–Š‡

(54) ‡ƒ•—”‡‡–ˆ”‘–Š‡•‹—Žƒ–‡††ƒ–ƒȋƒ”‡ƒ‹•‹†‡ –Š‡‡ŽŽ‹’•‡Ȍ‹•ƒ•ƒ”‡•—Ž–‘ˆ–Š‡•‡•‹–‹˜‹–›Ž‹‹–ƒ–‹‘‘ˆ–Š‡†‡–‡ –‹‘Ž‡˜‡Žˆ‘” –Š‡’ƒ”–‹ —Žƒ”†‘’ƒ–ƒ–”‹šȋ‘”‘†‘’ƒ–‹‹Ž‹ ‘ȌǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵Ͷ ‹‰ͳͻǤ‹ƒ‰‡‘ˆ–Š‡ˆƒ„”‹ ƒ–‡†’ސ†‡–‡ –‘”ȏȋƒȌ–‘’•‹†‡Ȁ ‘–ƒ –•ȋ„Ȍ „ƒ •‹†‡Ȁ ‘–ƒ –•ȐǤŠ‡†‡–‡ –‘”‹•ƒ„‘—–ͳʹšͳʹ„›†‹‡•‹‘ǤǤǤǤǤǤǤǤǤ͵ͷ ‹‰ʹͲǤ•—ƒ”›‘ˆ–Š‡’”‘ ‡••‹‰•–‡’• ƒ””‹‡†‘—–†—”‹‰–Š‡ˆƒ„”‹ ƒ–‹‘‘ˆ –Š‡Ϊ’†‡–‡ –‘”ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵͸ ‹‰ʹͳǤ’Žƒ‡’”‘Œ‡ –‹‘‘ˆ‡‡”‰›„›’‘•‹–‹‘‹ƒ‰‡‘ˆ‡Ž‡ –”‘• ƒ„•‘”„‡†‹ƒ’Š‘–‘”‡•‹•––‘’’‡†ǤŠ‡•‹—Žƒ–‹‘™ƒ• ‘†— –‡†ƒ–ͳͷ‡ ƒ ‡Ž‡”ƒ–‹‘‡‡”‰›ǡͳǡͲͲͲǡͲͲͲ‡Ž‡ –”‘•’ƒ”–‹ Ž‡•ƒ†‡Ž‡ –”‘„‡ƒ”ƒ†‹—•‘ˆ ͳͲǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵͹ ‹‰ʹ͵Ǥ‘’–‹ ƒŽ‹ ”‘• ‘’‡‹ƒ‰‡‘ˆ‰”‹†•’ƒ––‡”‡†‘–Š‡•—”ˆƒ ‡‘ˆ–Š‡ —•‹‰’Š‘–‘”‡•‹•–ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͺ ‹‰ʹʹǤ• Š‡ƒ–‹ ‘ˆ–Š‡ˆƒ„”‹ ƒ–‡††‡–‡ –‘”ˆ‡ƒ–—”‡†™‹–Š’Š‘–‘”‡•‹•–‰”‹†• ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͺ ‹‰ʹͶǤ‘–‘—”’Ž‘–•Š‘™‹‰–Š‡’Š‘–‘‰‡‡”ƒ–‹‘‘ˆ‡Ž‡ –”‘ǦŠ‘Ž‡’ƒ‹”•‘ˆƒ Ϊ’†‡–‡ –‘”‹””ƒ†‹ƒ–‡†„›‡Ž‡ –”‘•ǤŠ‡•‡’Š‘–‘‰‡‡”ƒ–‡† ƒ””‹‡”•ƒ”‡ ”‡ƒ–‡†™Š‡ƒ‡Ž‡ –”‘ˆ”‘–Š‡˜ƒŽ‡ ‡„ƒ†„‡ ‘‡‡š ‹–‡†‹–‘–Š‡ ‘†— –‹‘„›–Š‡ƒ„•‘”’–‹‘‘ˆƒ‡Ž‡ –”‘™‹–Š‡‡”‰›‘ˆƒ–Ž‡ƒ•–͵Ǥ͹ͳ‡˜ǤǤǤͶͳ. ˜‹‹‹. .

(55) ‹‰ʹͷȋƒȌǤ Š‡ƒ–‹ •Š‘™‹‰–Š‡‡š’‡”‹‡–ƒŽ•‡–—’™‹–Šƒ• ƒ‹‰‡Ž‡ –”‘ ‹ ”‘• ‘’‡ȋ„Ȍ•‡–—’–‘‡ƒ•—”‡‡Ž‡ –”‘„‡ƒ —””‡–ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶʹ ‹‰ʹ͸ǤȋƒȌ‡Ž‡ –”‘‹ ”‘• ‘’‡‹ƒ‰‡‘ˆ–Š‡’ސ†‡–‡ –‘”—†‡”–‡•–ȋ ƒŽ‡ „ƒ”αͷȌȋ„Ȍƒ’‘”–‹‘‘ˆ–Š‡ή’†‡–‡ –‘”Ȁ•Š‘™‹‰–Š‡’ƒ––‡”‡†‰”‹†•Ǥ Š‡†‡–‡ –‘”•ƒ”‡‹””ƒ†‹ƒ–‡†™‹–Š‡Ž‡ –”‘•‡‡”‰›‘ˆͳͷ‡ǡ„‡ƒ —””‡–α ͳǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶ͵ ‹‰ʹ͹Ǥ‰”ƒ’Š‘ˆ–Š‡‡ƒ•—”‡†’ސƒ†ή’†‡–‡ –‘””‡•’‘•‡–‘‡Ž‡ –”‘•ǤͶͶ ‹‰ʹͺǤ ‘’ƒ”‹•‘‘ˆ–Š‡”‡•’‘•‹˜‹–›‘ˆ–Š‡ˆƒ„”‹ ƒ–‡†’ސƒ†ή’ †‡–‡ –‘”•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶͷ ‹‰ʹͻǤŠ‡‡‡”‰›‘ˆ„ƒ • ƒ––‡”‡†‡Ž‡ –”‘•‡• ƒ’‹‰–Š‡•—”ˆƒ ‡‘ˆ–Š‡ •ƒ’Ž‡‘„–ƒ‹‡†ˆ”‘‹””ƒ†‹ƒ–‹‰ƒ•‹—Žƒ–‡††‡–‡ –‘”™‹–Šƒ ‡Ž‡”ƒ–‹‰ ˜‘Ž–ƒ‰‡‘ˆͳͷ‡Ǥ—„‡”‘ˆ‡Ž‡ –”‘–”ƒŒ‡ –‘”‹‡••‹—Žƒ–‡†αʹͲͲǡͲͲͲǤŠ‡›Ǧ ƒš‹•ȋ ‹–•Ȍ‹•‘ˆ–Š‡• ƒŽ‡‘ˆͳͲǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶ͸ ‹‰͵ͲǤ‹—Žƒ–‡††‘’‹‰’”‘ˆ‹Ž‡‘ˆ–Š‡’ސƒ†ή’†‡–‡ –‘”•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶ͸ ‹‰͵ͳǤ‹—Žƒ–‡†”‡•—Ž–‘ˆƒή’†‡–‡ –‘”ƒ–†‹ˆˆ‡”‡–•—”ˆƒ ‡”‡ ‘„‹ƒ–‹‘ ˜‡Ž‘ ‹–›™Š‡”‡›ƒš‹•‹•–Š‡”‡•’‘•‹˜‹–›ȋȀȌƒ†–Š‡šƒš‹•‹•‡‡”‰›‹ȋ‡Ȍ ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶ͹ ‹‰͵ʹǤ‡–”‡ ‘„‹ƒ–‹‘‹—„‡”’‡” —„‹  ‡–‹‡–‡”’‡”•‡ ‘†’Ž‘––‡† ƒ‰ƒ‹•–†‹•–ƒ ‡ƒŽ‘‰–Š‡•’‡ ‹ˆ‹‡†Ž‹‡–Š”‘—‰Š–Š‡†‡˜‹ ‡ˆ”‘–Š‡’‘‹–‘ˆ ‹’ƒ –‘ˆ„‘–Šƒ”•‡‹ ƒ†’Š‘•’Š‘”—•†‘’‡†Ϊ’†‡–‡ –‘”•Ǥ‡•—Ž–•™‹–Š ƒ†ˆ™‡”‡‘„–ƒ‹‡†™Š‡”‡αͳͲͷ Ȁ•ƒ†ˆαͷšͳͲͳͳȀ ʹǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶͻ ‹‰͵͵Ǥ‘–‘—”•’Ž‘–•‘ˆ ‘•–ƒ–‡–”‡ ‘„‹ƒ–‹‘”ƒ–‡‹͓Ȁ ͵Ǧ•‡ ή’ †‡–‡ –‘”ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͲ ‹‰͵ͶǤŠ‡”‡•’‘•‡ȋšͳƒ†šʹȌˆ”‘–Š‡–™‘„‘––‘ ‘–ƒ –•‘ˆ–Š‡ƒ• ͳͷ‡‘ˆ‡Ž‡ –”‘„‡ƒ•™‡‡’•ƒŽ‘‰–Š‡ƒš‹•’‡”’‡†‹ —Žƒ”–‘–Š‡ ‘–ƒ –•Ǥ Š‡‡Ž‡ –”‘„‡ƒ™‹–ŠͳǤ͹‘ˆ„‡ƒ —””‡– ƒ—•‡ƒ—’™ƒ”†•’‹‡‹ ˜‘Ž–ƒ‰‡ƒ•‹––”ƒ˜‡Ž•ƒ ”‘••ƒ‰”‹†ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͳ . ‹š. .

(56) 

(57)   This thesis is mainly based on the following four papers, herein referred to by their Roman numerals:   ƒ’‡”

(58) ȏ’ƒ‰‡͸ͻȐ ‹‰Š‡•‘Ž—–‹‘ǡ‘™‡”‰›Ž‡ –”‘‡–‡ –‘”. ǤǤ•‡„ƒ‡ǡǤ”ƒ’‘ŠŽǡ ǤŠ—‰•–”ڏƒ† ǤǦǤ‹Ž••‘ ʹͲͳͳ

(59) ͸ͲͳͲͲͳ†‘‹ǣͳͲǤͳͲͺͺȀͳ͹ͶͺǦ ͲʹʹͳȀ͸ȀͲͳȀͲͳͲͲͳ  ƒ’‡”

(60)

(61) ȏ’ƒ‰‡͹ͻȐ —”ˆƒ ‡–ƒ–‡ˆˆ‡ –•‘ή’‘’‡†Ž‡ –”‘‡–‡ –‘”. ǤǤ •‡„ƒ‡ǡ Ǥ ƒƒ”Ž‹‰ǡ Ǥ Š—‰•–”ڏ ƒ† ǦǤ ‹Ž••‘ ʹͲͳͳ

(62) ͸ͳʹͲͳͻ†‘‹ǣͳͲǤͳͲͺͺȀͳ͹ͶͺǦ ͲʹʹͳȀ͸ȀͳʹȀͳʹͲͳͻ  ƒ’‡”

(63)

(64)

(65) ȏ’ƒ‰‡ͺͻȐ  ‹ˆˆ‡”‡– ’’”‘ƒ Š ‘ˆ ‡–‡”‹‹‰ –Š‡ ‡•’‘•‹˜‹–›. ‘ˆή’‡–‡ –‘”••‹‰ ƒ‹‰Ž‡ –”‘‹ ”‘• ‘’› ‡‹‡ ‡”˜‹ƒ” •‡„ƒ‡ǡ ڔƒ Š—‰•–”ڏǡ ƒ•Ǧ”‹ ‹Ž••‘ ʹͲͳʹ Ǥ‡‹ ‘†Ǥ͵͵Ͳ͹ͶͲͲʹ†‘‹ǣͳͲǤͳͲͺͺȀͳ͸͹ͶǦ Ͷͻʹ͸Ȁ͵͵Ȁ͹ȀͲ͹ͶͲͲʹ  ƒ’‡”

(66) ȏ’ƒ‰‡ͻͻȐ  ή’ —‘ǦŽƒ–‡”ƒŽ ‘•‹–‹‘ ‡•‹–‹˜‹–› ‡–‡ –‘” ™‹–Š. ‹‰Š‡•‹–‹˜‹–›–‘‘™‡”‰‡–‹ Ž‡ –”‘• Ǥ Ǥ •‡„ƒ‡ǡ Ǥ —†‰”‡ǡ Ǥ Š—‰•–”ڏ ƒ† Ǧ ‹Ž••‘

(67) ƒ—• ”‹’–           . š. .

(68) Related paper(s) not included in the thesis  ͳ. ’‡ –”ƒŽ ‡”ˆ‘”ƒ ‡ ‘ˆ Š‘–‘ ‘—–‹‰ ‹š‡Ž ‡–‡ –‘” •‹‰––‡—ƒ–‹‘’‡ –”ƒˆ‘”‡•–ƒ’Ž‡• ‡‹‡‡”˜‹ƒ”•‡„ƒ‡ǡڔŒ‡‘”Ž‹ǡƒ† ڔƒŠ—‰•–”ڏ 

(69) ‘ˆǤ”‘ ǤͳʹͲͶǡͳ͹͹ȋʹͲͳͲȌǢ†‘‹ǣͳͲǤͳͲ͸͵ȀͳǤ͵ʹͻͷ͸͵͹ . ʹ. ‹—Žƒ–‹‘ ƒ† ‡ƒ•—”‡‡– ‘ˆ Š‘”–

(70) ˆ”ƒ”‡† —Ž•‡• ‘ ‹Ž‹ ‘‘•‹–‹‘‡•‹–‹˜‡‡˜‹ ‡ Ǥ”ƒ’‘ŠŽǡǤǤ•‡„ƒ‡ǡ ǤǤ‹Ž••‘ƒ† ǤŠ—‰•–”ڏ ʹͲͳͳ

(71) ͸ͲͳͲ͵͸†‘‹ǣͳͲǤͳͲͺͺȀͳ͹ͶͺǦͲʹʹͳȀ͸ȀͲͳȀͲͳͲ͵͸ . š‹. .

(72) š‹‹. .

(73) ͳǤ

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(75)  Radiation detectors, in general, have been employed in a wide spectrum of areas. This thesis concentrates on those detectors that have been employed under the irradiation of electrons as electron detectors and lateral position sensitive detectors (LPSDs). Electron detectors are primarily designed for the capture and detection of electrons and they are mostly designed on silicon wafers as their primary materials and are generally similar to the usual p-n junction photodiodes [1]. A great deal of research has been conducted on the response of electron detectors and on different methods of characterising the responses and behaviours of the detectors [2–8]. Thus, the means by which these electron devices generally respond to a range of electron energy is not a new phenomenon. However, what has been lacking from this area of research field is the reason or effect of surface states and other surface parameters, such as surface recombination, on the responsivity of these detectors. Surface parameters have been widely known to have different effects on the performances of radiation devices in general [9–13] but studies on such effects on electron detectors in particular are few and far between. As a result, a better understanding of how they affect electron detectors will significantly assist in providing solutions with regards ways to improving their responsivity and sensitivity to a wide range of electron energy. A brief insight into the objectives of this thesis can be seen in Fig 1. In researching these detectors as electron detectors, the research focus was streamlined in relation to discovering answers to some research questions bordering on the effect of surface states and surface recombination on the performance of the detector. Specifically, one research question was to investigate the difference in the responsivity of an n+p and a p+n doped detector in terms of the change in the surface state and surface recombination of the detector. The effects of different n+p doping agents were also investigated as well as the influence of varying levels of impurity doping concentration on the responsivity of the detector. The quest in relation to answering these research questions was conducted using the scanning electron microscopy imaging (SEM) technique. The wide use of position sensitive detectors (PSDs) means that there is always a requirement for those with high linearity over the detector's active area. As a result, there was the motivation, as part of this research, to fabricate a PSD with high linearity. There was also a requirement to explore by using the scanning electron microscopy imaging method to characterize the linearity of the PSD at low electron energy.. ͳ.

(76) ‡•‡ƒ” Š—”’‘•‡ - Compare the effect of fixed oxide charge and surface recombination velocity on the responsivity of a p+n and an n+p detector  - Investigate the varying performance in terms of the responsivity of an electron detector when the doping profile is altered in relation the surface states of the detector.  - Investigate the significance of the effect of the minority carriers transport velocity and fixed oxide charge on the responsivity of detectors with different donor impurities  - Characterize the linearity over two-dimensions of a fabricated duo-lateral position sensitive detector PSD using scanning electron microscopy Fig 1. A synopsis of the research objectives. The device was incorporated with special grid-like features and the evaluation was conducted using the basic principles of position sensitive detection. The electrons interact with matter producing signals and through the use of transimpedance circuits and data acquisition apparatus it was possible to draw a pattern of the output signal based on the position/location of the beam on the detector. Simulations were carried out before the processing and fabrication of the devices in the cleanroom. Two sets of simulations were performed - Monte Carlo simulation using Geant4/CASINO and Finite Element simulation using Taurus TSuprem4/Medici. The former was used to track and visualize the passage of the bombarding electron particles through the detector taking into account possible interactions and decay processes.. ʹ. .

(77) ‡•‡ƒ” Š‡–Š‘†‘Ž‘‰› - ›‘–‡ƒ”Ž‘‹—Žƒ–‹‘ Geant4 simulation toolkit CASINO v2.42 Purpose: Investigation of low electron beam interaction in the device(s) Tracking irradiated electrons as they travel through the device(s). Visualization of the electrons trajectories and calculate energy losses - › ‹‹–‡Ž‡‡–‹—Žƒ–‹‘ Taurus TSuprem4/Medici Purpose: Simulating the distribution of impurities Modelling various processing steps Calculation of induced current and observation of the response of the simulated devices  - › ƒ„”‹ ƒ–‹‘ Cleanroom fabrication steps (implantation, diffusion, etching etc). - ›‡ƒ•—”‡‡– Use of scanning electron microscope, data acquisition apparatus, transimpedance circuit etc. Fig 2. A synopsis of the methodology employed in the thesis. The latter was employed to simulate the distribution of impurities, model various detector processing steps and calculate the response of the simulated detectors. An overview of the methodology utilized in this thesis is shown in Fig 2.. ͵. .

(78) ͳǤʹ. Šƒ’–‡”•‡˜‹‡™. The diagram below provides a brief overview of the contents of later chapters (i.e. chapters 2-10) in this thesis This research offers a significant improvement in PSD technology as there is an increased requirement for optical technology in order to determine increasing application in areas as diverse as telecommunication, biomedicine and data storage etc. The result from this research can be applied in relation to electron microscopy in medicine in addition to applications where position sensitivity is important.. Ͷ. .

(79) ʹǤ. . ʹǤͳ. ˜‡”˜‹‡™‘ˆ‡Žƒ–‡†–—†‹‡•‘Ž‡ –”‘‡–‡ –‘”•. Generally, alpha particles, X-rays and electrons, with low energy have a short penetration depth in silicon and in order to detect them, it is imperative that there is a shallow dead region on the surface of the silicon device from where it will be irradiated [14]. A dead region – equivalent silicon layer of micrometer thickness which is not active - of about 100nm thickness with an arsenic implant has been studied and has proved to be a good trade-off between the need for electrical performance (with very low leakage current) and low energy loss in the dead region. In order to measure the shallow penetrating electrons, a study was conducted by Nikzad et al on a fabricated electron detector using a delta doped, fully depleted, high purity silicon p-i-n diode arrays for the direct detection of electrons between 100ev to 20keV. A heavily doped 1nm layer was grown below the surface of the detector, using molecular beam epitaxy, thereby making the device very sensitive to electrons with energy capable of penetrating more than a nanometre into the device [3]. To achieve a similar result, a silicon photodiode for use as low-energy electron detectors was studied. It was fabricated on a pure-boron layer to form the p+-anode region and with a thin front entrance window dead layer of about 1.8 nm. The detector showed a high relative electron signal gain of about 60% at an electron energy as low as 0.5keV [15]. To create a silicon detector for high efficiency low energy electron detection, a study has used a defect-free p+n junction photodiode with p+ region created by a chemical vapour deposition (CVD) surface doping from diborane B2H6 [16]. The diborane p-layer created was used to reduce the dead layer energy loss and the result obtained indicated that the device showed an electron signal gain of 74% at 1keV. There are a number of methods employed in the measurement of the induced current as a result of electron interaction in semiconductors that have been experimentally verified. Popular methods include the use of a measured energy and a beam current [17], the analysis of the pulse magnitudes of single high-energy ions interaction in surface barrier devices [18],[19] and the use of an avalanche photodiode (APD) to measure electrons between 2keV and 40keV [2],[20]. The classic technique, most commonly utilized, is the use of electron beam-induced current (EBIC), which can best be described as the standard method of characterising semiconductor detectors [21]. See Fig 3. ͷ. .

(80) This method which is essentially used to localize buried diffusions and semiconductor defects basically operates from displayed images formed from the electron beam induced current recorded by a picoammeter. . Fig 3. Schematic illustration of a cross-sectional EBIC experiment in SEM [22]. The above techniques are usually very useful and effective for high resolution detection of electrons below 40keV. For measuring those electrons with energy over 40keV, the usage of, for instance, regular APD becomes less suitable as a result of the limitation of the detectable range of the detectors and also because the responses at medium-energy electrons are not linear [23]. For good linearity and high resolution detection of medium-energy electrons, modifications were made to the APDs by making the depletion-layers thicker and the surface dead layer much thinner in order to provide full coverage for electrons of energy up to 100keV [23].. ʹǤʹ ’’Ž‹ ƒ–‹‘•‘ˆŽ‡ –”‘‡–‡ –‘”• There are numerous applications for which electron detectors are used. Such applications sometimes depend on the sensitivity of the particular energy range that the detector is required to possess. The most common are those designed for electrons with energies up to 20keV. An interesting area in which electron detectors have been utilized is within the area of X-ray photoelectron emission microscopy (XPEEM). A research using this application was conducted by characterizing an electron detector in relation to its modulation transfer function and detective quantum efficiency as it collects the photoelectrons emitted when X-rays from a synchrotron light source are irradiated. ͸. .

(81) on a sample [24]. The application of the results obtained in the study is useful in various fields including the study of adsorption on metal films, surface diffusion of metals, growth of films on metals and semiconductors. Another form for which it can be applied is as an Electron Capture Detector (ECD). It is a device applied in the detection of atoms and molecules in a gas for detecting trace amounts of chemical compounds (especially compounds containing halogen elements in gas mixtures) in a sample [25][26]. The ECD operates such that the electrons discharged from the electron emitter collide with the molecules of the makeup gas, emitting free electrons which are attracted towards the anode to generate a current proportional to the degree of electron capture and concentration of chemical compounds. A similar application is in the detection of trace amounts of the radioactive Xenon gas. It was reported in a study that the simultaneous analysis of high resolution X-rays and conversion electrons in a lithium drifted silicon detector using p-i-n electron detectors, provided an enhancement in the Xenon detection limit in contrast to scintillator-based devices [14]. One area in which the application of electrons detectors is rapidly growing is its use as imaging detectors. Research has shown that it can be applied as an imaging detector for a low-voltage transmission electron microscope [27], in Medipix2 imaging systems [28], Simbol-X low energy detector [29], in miniaturized electron optical systems (micro-columns) with low electron energy [4] [6], as a monolithic active pixel sensor for low energy electrons, and for neutron and fluorescence imaging [30]. Though its application in transmission electron microscopy is still experimental, monolithic active pixel sensors for low energy electron imaging has a significant future in bioscience for cell process studies. Additionally, and still in the experimental stage, research has revealed that there is the possibility of using electron detectors in electron-gamma coincidence systems for nuclear parameter measurements [8]. Furthermore, one major use of the detector is as a Secondary Electron Detector for compositional studies of samples such as embedded biological materials [31]. See Fig 4. Secondary electron detectors are important in electron beam lithography, optimum beam calibration and in the detection of alignment marks for calibration [6].. ͹. .

(82) Fig 4. A Secondary electron image of a Vanessa atalanta butterfly wing [32]. A Backscattered Electron Detector (BSE) is another type of commonly used electron detector. It is usually integrated into either an SEM or an electron probe micro-analyzer (EPMA) instrument. It is designed for the simultaneous collection of backscattered electrons in different directions. The quantity of backscattered electrons collected by a BSE usually corresponds to the mean atomic number of the sample under investigation. This detector can, in addition, be used for electron backscattering diffraction investigations of focused ion beam surfaces [33], to determine the crystallographic structure of a sample or for topographical or morphological examinations [34], [35]. A multi-pixel silicon electron p-i-n detector has also been used in more complex applications such as in the Karlsruhe Tritium Neutrino Experiment (KATRIN) neutrino mass experiment. This experiment, based on the energy measurement of electrons emanating from tritium beta decay, is conducted by means of a large electrostatic retarding spectrometer followed by an electron detector [36]..  . ͺ. .

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(86) . ͵Ǥͳ. ‡‹ ‘†— –‘”—”ˆƒ ‡–ƒ–‡•. The theory behind surface states governs the understanding of the aggregate of responses to both internal and external influences of electrons at solid surfaces. This is imperative in gaining an insight into the means by which solid-state devices function and perform. At the surface of materials, electronic states exist, which are referred to as surface states. These states are produced as a result of the steep transition from solid material that terminates with a surface and are located only at the atom layers closest to the surface. The termination of a material with a surface leads to a change of the electronic band structure and, in the case of a semiconductor, surface states are as a result of incomplete covalent bonds at the surface of the semiconductor for which the nearly free electron approximation can be employed to deduce the basic characteristics of surface states for narrow gap semiconductors1. Surface states generally result in electron energy levels within the energy bandgap and are also known as Tamm-Shockley states. The density of such bonds at a silicon surface is about 1015 cm-2, a rather large number considering that the density of donors in a 0.1 mm depletion region in a material with a doping density of 1017 cm-3 is only 1012 cm-2. Depending on whether or not they are neutral when occupied, they can be referred to as either in a donor state or an acceptor state. Surface states can be said to be intrinsic in a situation where surface states arise from clean and well ordered surfaces. This case also involves states arising from reconstructed surfaces, where the two-dimensional translational symmetry gives rise to the band structure in the k space of the surface. For the ‘extrinsic’ surface state, the case is the opposite, namely, that the states do not originate from a clean and well ordered surface and they cannot be easily described in terms of their chemical, physical or structural properties. Examples of such cases are surfaces with defects (caused by among other things, impurities such as oxygen), where the translational symmetry of the surface is broken, or are with adsorbates, interfaces between two materials such as a semiconductor-oxide or semiconductor-metal interfaces as well as interfaces between solid and liquid phases.  1. Nearly-free electron model (otherwise known as NFE model) is a quantum theory model of the physical characteristics of electrons that can migrate almost freely through the crystal lattice of a solid. The model which is closely related to the more conceptual Empty Lattice Approximation LEA enables the understanding and calculation of the electronic band structure of materials.. ͻ. .

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(88) –‡”ˆƒ ‡”ƒ’•. Surface states can present themselves in some form of charges referred to as Interface-trapped charge or fast states (Qit), which reside just at the boundary between (as in the case in this thesis) the silicon and the silicon oxide. This charge lies within the forbidden gap as a result of the shake-up to the periodic lattice structure at the surface of a crystal [37]. Interface-trapped charge (which can be as high as 1015atoms/cm2 but can be counteracted by low-temperature hydrogen annealing of about 450oC) and other charges such as the fixed oxide charge Qf, Oxide-trapped charge Qot, mobile charges and other fast interface states make up the composition of the surface charge density – see Fig 5. The mobile ionic charges are as a result of the sodium or/and other alkali ions that may be present at the SiO2. These charges have been known to be very problematic, especially when the devices are used at elevated temperatures or high electric field operation [35]. As a result, it is highly advisable not to touch the devices with bare hands and especially during processing. The interface states are generally of almost negligible importance in the case of thicker gate oxides but as the oxide thickness is reduced these interface trapped charges become gradually more significant. As a result, the present requirement for very thin oxide in present day devices has made it important to pay special attention to the study of interface traps and other surface states. One of the basic properties of interface traps is that they are located within a few atomic bond distances (approximately 0.5nm) from a silicon lattice to enable electrons and holes in the conduction and valence band quantum mechanical migration into and out of the traps. Studies have shown that the migration between bands exponentially increases as the energy depth of the interface traps decreases. For a typical steam grown oxide on a <100> silicon, the time constant (inverse of the migration rate) as a function of the surface potential is shown in Fig ϲ. From the figure, it is seen that at room temperature, the interface traps migrate at a time constant of 0.01s in comparison with a few microseconds near the band edges. The same can also apply to a typical dry-grown oxide on a <100> silicon. These interface states traps can either be charged or neutral and this is only dependent on whether they hold a carrier. Fast interface states are only exclusively permitted in the semiconductor forbidden bandgap, and they can be termed as either a donor or acceptor of electrons or holes.. ͳͲ. .

(89) Fig 5. Terminology for charges associated with thermally oxidized silicon [40]. . . Fig 6. Variation of time constant as a function of surface potential for the processes; (Ɣ) for wet grown oxide and radiation induced (Ÿ) interface traps for dry-grown oxide [38][39].. ͵Ǥ͵. ”‡˜‹‘—•–—†‹‡•‘ ƒ•–”ƒ’•. A number of studies have been conducted on the various interface surface states and their influence on the performances of devices. One such study on N-Channel MOSFET as regards interface fast traps (positive surface states, na) showed that, as the increase in gate bias results in band-bending at the surface, this in turn causes the potential difference occurring to become smaller. For that reason, a smaller amount of positive charge is included at the interface which causes a deviation in. ͳͳ. .

(90) the “positive states” curve from the “zero charge” curve especially when the gate bias is low compared to higher gate biases – see Fig 7- [41]. The case becomes the reverse when it involves negative surface states, nd. Increasing the gate bias, results in the increase in potential difference during the band bending occurring at the surface thereby causing a larger amount of negative charge to be included at the interface. This causes the “negative” states curve to be shifted farther to the right of the “zero charge” curve at higher gate biases than at lower gate biases. A similar study was conducted in which the flat band voltage shift, due to the generation of interface states as a result of electron trapping in the SiO2 film, was experimentally observed [42]. It was inferred that where electrons can be trapped, the interface states are produced as a result of the collisions of electrons at the SiSiO2 interface. It is widely suggested that the performances of MOS devices become degraded by interface trap generation. The degradation is suspected to be as a result of “hot carrier” injection - where the electrons or holes gain sufficient kinetic energy to overcome an interface state - occurring in the device [43]. Studies have also shown a correlation between interface traps and the gate oxide leakage current in the direct tunneling regime [44]. The study showed that the gate leakage current and the number of interface traps increases in a discrete manner. The density of the interface traps has also been known to multiply during the repeated program-erase cycling of non-volatile floating-gate as well as in transistors such as the Silicon-Oxide-Nitride-Oxide-Silicon memory transistors [45]. As a result, the need to fully understand this interface-trap effect and to tackle this problem is a necessary step towards modeling device reliability and stability.. ͵ǤͶ. ‡ Š‹ ƒŽ‡˜‹‡™•‘ ‹š‡†š‹†‡Šƒ”‰‡ˆ. As already stated, surface charge density is constituted by, among other charges, fixed oxide charge Qf which is usually positive and dependent on oxidation and annealing conditions for the silicon orientation but not on the gate bias.. ͳʹ. .

(91) Fig 7. Current-voltage simulation from the analysis of/including fast interface states of nchannel MOSFET [41]. This charge, otherwise regarded as a charge sheet, is located approximately 3nm from the Si-SiO2 interface and is associated with defects in SiO2. They are also fixed and very difficult to charge or discharge. The typical Qf for a well prepared Si-SiO2 interface Qf is approximately 1010cm-2 for a <100> silicon surface and about 5x1010cm-2 for a <111> silicon surface [46]. The fixed oxide charge Qf has a strong dependence on the oxidation temperature and, as such, the higher the temperature, the lower the fixed oxide charge. Because there is a limitation regarding how high the temperature oxidization can be performed, it is possible to reduce Qf by annealing an oxidized wafer (performed at any sensible temperature) in a nitrogen or argon ambient.. ͳ͵. .

(92) Fig 8. Deal triangle showing the reversibility of heat treatment effect on fixed oxide charge [47]. This method invented by Deal et al shows the reversible relations between Qf and the oxidation and the anneal [47]. The resulting value of Qf being associated with the final temperature and any Qf value resulting from previous oxidation can be reduced to a constant value as shown in the Deal triangle [48]. Various processes can be used to grow silicon oxide for passivation. One of these is Plasma-Enhanced Chemical Vapor Deposition (PECVD). Studies have shown that the use of this method to grow silicon oxide presents the problem of fixed oxide charge [49]. Results have confirmed the fact that the properties of silicon-silicon oxide devices based on steam grown oxides are more heavily affected by radiation than devices based on dry oxides. More importantly, the results show a dependence of fixed oxide charge Qf on the radiation dose that is estimated by a first-order reaction equation [50]. The research inferred that there is a distinct linear correlation between the degradation of low field mobility of, for example, MetalOxide Semiconductors - MOS transistors and the logarithm of the positive oxide charge incorporation during irradiation for wet-oxide samples only.. ͳͶ. .

(93) ͵Ǥͷ ‹š‡†š‹†‡Šƒ”‰‡‹Ž‡ –”‘‡–‡ –‘”• To study the effect of a fixed oxide charge on an electron detector, an oxidationinduced fixed oxide charge was introduced at the interface between the silicon bulk and a 10nm Silicon-Oxide through the oxidation process. A view regarding the effect the charge has on the measure of the input–output gain of an n+p electron detector is shown in the figure below. The study was conducted using fixed oxide charge values ranging from 5x1010C/cm2 to 3x1013C/cm2.. 0.25 0.24. Responsivity. 0.23 0.22 0.21 Simulation: Qf = 5E10. 0.2. Simulation: Qf = 5E11. 0.19. Simulation: Qf = 3E12. 0.18 0.17 0. 10. Energy (keV). 1. 10. . Fig 9. A simulation result on the influence of fixed oxide charge, Qf on the responsivity of an electron detector. While retaining other interface properties at their constant values and sweeping the accelerating electron energy from 0.5keV to 20keV, the finding shows that the responsivity of the electron detector tends to increase as the fixed oxide charge increases, with the increase being more predominant at the lower electron energy. More details are available in paper I.. ͳͷ. .

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(100)  Processes exist in semiconductors whereby mobile charge carriers in the form of electrons and electron holes are either created or destroyed. These processes are respectively known as generation and recombination and are as a result of interactions between electrons and other carriers, either with the lattice of the material, or with irradiated optical photons. Energy may be transferred or gained depending on the movement of electrons from one energy band to another. The gained or transferred energy takes other forms that is able to differentiate between the various types of generation and recombination processes that have taken place. The formation of electron–holes pairs is the fundamental unit of generation and recombination. An electron–hole pair depicts an electron transitioning between the valence band and the conduction band of the semiconductor material energy band.. (a) (b) Fig 10. Basic diagram showing the process of (a) Band-to-band recombination whereby energy is exchanged to a radiative or Auger process (b) non-radiative recombination [37]. . ͶǤͳ. ‡ ‘„‹ƒ–‹‘‹‡‹ ‘†— –‘”. Recombination in a semiconductor exists to recondition the system back to equilibrium when the thermal-equilibrium condition of the semiconductor is disturbed [37]. This process can occur in various forms – radiative or Auger process. The former, otherwise known as photon emission recombination, occurs when the energy of an electron transiting from the conduction band to the valence band is stored by the discharge of a photon. The photon emitted has a wavelength proportional to the energy released and this forms the basis of LED's operation. The direct opposite of this is the direct optical absorption process – in which. ͳ͹. .

(101) absorption is the active process that occurs in solar cells, photodiodes and other photodetectors. See Fig 10 On the other hand, the Auger process occurs when a transiting electron passes its energy to free another electron or hole. This process is a three-particle interaction and only becomes important when the carrier density is very high and the condition is not in a state of equilibrium. This type of recombination is similar to the Auger effect, which is a physical phenomenon in which the transition of an electron in an atom filling in an inner-shell vacancy causes the emission of another electron known as an Auger electron. In commonly used semiconductors such as the silicon Si and germanium Ge, the dominant transitions are usually an indirect recombination via single-level traps in the bulk material, and the energy present in the bandgap. The recombination process though the single level traps can be described by electron capture and hole captures processes and the net rate of transition is defined by Shockley-Read-Hall SRH statistic. U = U n = U p = U SRH + U Auger .  ȋͳȌ where USRH and UAuger are the Shockley-Read-Hall recombination and the Auger recombination respectively. [41].. ͶǤʹ. —”ˆƒ ‡‡ ‘„‹ƒ–‹‘‡Ž‘ ‹–›. The described recombination can occur at the surface or interfaces of a semiconductor. The resultant effect can be of significant importance with regards to the behavior of the semiconductor. The reason for this is because the semiconductor surfaces and interfaces come with a huge number of centers for recombination to take place as a result of the sudden termination of the semiconductor lattice structure, which results in so many electrically active states [51]. These recombination centers lie at an energy level defined as the equilibrium electron and hole concentrations in a sample whose Fermi level coincides with the position of the recombination centers [52]. This signifies that any defect or impurity around the confines of the surface of the semiconductor will assist in the propagation of recombinations. In a solar cell, for example, high recombination rates at the surface or interfaces result in adverse effects on the short-circuit current as well as the open-circuit voltage. This is because the highest generation region of mobile carriers are located at these interfaces and surfaces. Thus, because the surface of the solar cell depicts a massive disruption of the crystal lattice, the surface of the solar cell becomes an attractive region for high recombination. The defects at a semiconductor surface. ͳͺ. .

(102) are caused by the interruption to the periodicity of the crystal lattice, which causes dangling bonds at the semiconductor surface [53]. To compensate for a region where there is a low concentration of carriers, the carriers in a region of higher concentration flow towards that region with the surface recombination rate only being restricted by the rate at which minority carriers move towards the surface. The rate at which these carriers can move to recombine at the surface is regarded as the ‘surface recombination velocity vs’ in units of cm/sec. In a situation where the movement of carriers towards the surface or interface of the semiconductor is zero, this signifies that the surface or interface has no recombination activity present or the surface recombination velocity is zero and vice versa. High surface recombination velocity vs of up to 107 cm/sec can be recorded for most semiconductors. The net recombination rate due to trap-assisted recombination is similar to that of Shockley-Read-Hall recombination – SRH except that the recombination is due to a two-dimensional density of traps that only exist at the surface or interface.. ͶǤʹǤͳ. —”ˆƒ ‡‡ ‘„‹ƒ–‹‘‡Ž‘ ‹–›‹‡Žƒ–‹‘–‘”ƒ’Ǧ ••‹•–‡†‡ ‘„‹ƒ–‹‘‹ˆ‡–‹‡. At every defined point on the discrete mesh of the Si-SiO2 interface, a simple model can be used for which an effective SRH recombination lifetime for each carrier IJneff to relate to the recombination velocities of electrons vs is given by [41]. 1 eff. τ n (i ). =. vs di 1 + Ai τ p (i ). (2). where IJp(i) is the SRH lifetimes that are trap-assisted recombination lifetimes (concentration dependent), Ai the semiconductor area associated with the node; and di, the length of the interface associated with the node2 In the case of a metal acting as a Schottky contact with a semiconductor, finite surface recombination velocities can be determined with the assumption that the electron and hole quasi-Fermi potential (Øn and Øp) are not equal to but, are rather,.  2. Every region of the device structure is divided into a mesh of non-overlapping triangular elements. Solution values during simulations are computed at the mesh nodes. The total number of nodes in an interface region is calculated by adding the number of mesh points in the region, plus the number of mesh points along exposed boundaries. . ͳͻ. .

(103) defined by the current boundary conditions at the surface [54]. The current boundary conditions are defined as. J sn = q vsn ns – neq . . . (3). J sp = q vsp ps – peq .   (4) where Jsn and Jsp are the electron and hole current densities at the contact; ns and ps are the actual surface electron and hole concentrations; neq and peq are the equilibrium electron and hole concentrations, assuming infinite surface recombination velocities.. ͶǤ͵. —”ˆƒ ‡ƒ••‹˜ƒ–‹‘ƒ†—”ˆƒ ‡‡ ‘„‹ƒ–‹‘ ‡Ž‘ ‹–›. The significance of the surface recombination velocity in semiconductor devices in general has made it an area of research interest and efforts are been made by researchers to fully understand this phenomenon. A number of research projects have shown that, in solar cells, the surface recombination velocity has a diverse effect on the open circuit voltage Vo and the short-circuit current Isc and to minimize its effect a thin SiO2 layer is thermally grown on the front surface of both n-doped and p-doped emitters of the device [55]. The SiO2 layer on the front end of the device acts as a ‘passivation’ to reduce the surface recombination of electron and hole carriers. In other words, the solution to the reduction of the quantity which is the root cause of recombination (dangling bonds) and invariably, the recombination, lies in placing a layer of material on top of the semiconductor surface which has the capability of terminating some of these dangling bonds. As an alternative to thermal oxidation (i.e. thermally growing a thin layer of silicon oxide on the surface of a wafer), low-temperature passivation techniques have become increasingly popularly. One such technique is the plasma-enhanced chemical vapor deposition (PECVD) - a process used to deposit thin films (of oxide) from a vapour state to a solid state on the area to be passivated. For SiO2 to be deposited using PECVD, a blend of silicon and oxygen precursor gasses are used at pressures ranging from a few millitorr to a few torr (where 1 Torr is estimated as equal to 1mm of mercury).. ʹͲ. .

(104) ͶǤͶ. ˆˆ‡ –‘ˆ—”ˆƒ ‡‡ ‘„‹ƒ–‹‘‡Ž‘ ‹–›‹Ž‡ –”‘ ‡–‡ –‘”•. The effect of surface recombination velocity on the responsivity of an n+p electron detector was studied. The study was performed by retaining other interface properties at the Si-SiO2 interface constant and sweeping electrons with acceleration energies ranging from 0.4keV to 8keV – see Fig 11. The fixed oxide charge was also maintained at a constant value of 5x1011 cm-2. This value of Qf was chosen because typical values for Qf are of the order of 1010 to 1011 charges per cm2 , depending on the process conditions [46]. Though some research has determined that for some interfaces, the magnitude of the fixed charge can be higher and, in particular, under interface bond strain and bias voltage applied to the detector oxide [56],[57].. 0.25 0.24. Responsivity. 0.23 0.22 0.21. SRV = 1E6 SRV = 1E5 SRV = 1E4 SRV = 1E3 SRV = 1E2 SRV = 1E1. 0.2 0.19 0.18 0.17 0. 10. Energy (keV). 1. 10. . Fig 11. A simulation result on the influence of interface recombination velocity of minority carriers on the responsivity of a) arsenic doped n+p detector.  The result, as seen in the figure above, shows that the surface recombination velocity has a strong effect on the responsivity of a detector especially at low electron energy. It is seen that at 0.5keV, the responsivity of the detector increases by about 40% when the surface recombination velocity of the minority carrier at 106cm/s is reduced by a factor of 10. See paper I for details.. ʹͳ. .

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(109) 

(110)    . In the following sections, the simulation procedures used in this research will be discussed. This is important in order to understand how the electron detector/s will perform in reality under the irradiation of electrons with estimated real life parameters. The simulations were good avenues to model the two-dimensional distributions of potential and carrier concentrations in the anticipated real/fabricated electron detector. The simulation also became useful in forecasting the typical electrical features of the device under different arbitrary bias circumstances. Consideration was given to opting for proper simulation tools that could assist in simulating and replicating the results to be obtained in reality from the processing steps (doping, implantation and diffusion etc) used in the manufacture of silicon integrated circuits and other discrete devices. It was also imperative for the device simulation tools to have the necessary physical equations as well as the capability to include energy balance equations required to describe the semiconductor device and the internal behavior of the system device.. ͷǤͳ. –ƒ‰‡

(111) ǣ‹—Žƒ–‹‰–Š‡‡˜‹ ‡™‹–Š ‡ƒ–Ͷƒ† 

(112) . It was vital to begin by, firstly, accurately simulating the passage of electron particles through a simple silicon wafer and then - Track the particles and the resultant electromagnetic fields through the silicon material. - Visualize the particle trajectories in the detector (see Fig ϭϮ), - As well as observing the response of the constituent sensitive detector components To perform the above routines, the simulation tools known as Geant43 and CASINO4 (derived from "monte CArlo SImulation of electroN trajectory in . 3. Geant4 is a free software package made up of tools for “both full and fast Monte Carlo simulation of detectors in different Energy Physics using Object oriented programming in C++. It is composed of facilities for handling geometry, tracking, detector response, run management, visualization and user interface 4  It is a Monte Carlo simulation tool that can be used to calculate low electron beam trajectory and interaction in semiconductors. It is intended to reproduce scanning electron microscope imaging condition and results.. ʹ͵. .

References

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