Free-Electron Screening Mechanism of the Shallow Impurity Breakdown in n-GaAs: Evidences from the Photoelectric Zeeman and Cyclotron Resonance Spectroscopies

<div>Dependence of the breakdown electric field <svg height="9.14241pt" id="M183" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 17.6694 9.14241" width="17.6694pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"><path d="M372 352C427 368 507 407 507 502C507 548 486 592 451 616C420 638 376 650 301 650H44V622C124 616 128 610 128 527V123C128 40 122 34 36 28V0H257C336 0 402 12 453 40C512 72 548 124 548 191C548 291 471 335 372 350V352ZM213 362V558C213 591 216 602 226 608C235 614 258 618 282 618C377 618 415 558 415 490C415 406 369 362 260 362H213ZM213 328H258C380 328 450 283 450 181C450 76 377 35 296 34C231 34 213 53 213 125V328Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.319,3.132)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g></svg> on the magnetic field <i>H</i> for different <svg height="8.98583pt" id="M184" style="vertical-align:-0.2324905pt" version="1.1" viewbox="-0.0498162 -8.75334 40.5377 8.98583" width="40.5377pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 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348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z"></path></g></svg> samples when the electric <svg height="9.14241pt" id="M185" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 17.6694 9.14241" width="17.6694pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"><path d="M372 352C427 368 507 407 507 502C507 548 486 592 451 616C420 638 376 650 301 650H44V622C124 616 128 610 128 527V123C128 40 122 34 36 28V0H257C336 0 402 12 453 40C512 72 548 124 548 191C548 291 471 335 372 350V352ZM213 362V558C213 591 216 602 226 608C235 614 258 618 282 618C377 618 415 558 415 490C415 406 369 362 260 362H213ZM213 328H258C380 328 450 283 450 181C450 76 377 35 296 34C231 34 213 53 213 125V328Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.319,3.132)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g></svg> and magnetic <svg height="8.79011pt" id="M186" style="vertical-align:-0.04980946pt" version="1.1" viewbox="-0.0498162 -8.7403 10.3168 8.79011" width="10.3168pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M746 650H445V615C520 608 528 602 528 517V370H255V517C255 602 263 608 335 615V650H35V615C112 608 121 602 121 517V133C121 48 112 42 39 35V0H337V35C263 42 255 48 255 133V319H528V133C528 48 520 42 441 35V0H746V35C670 42 662 48 662 132V517C662 602 668 608 746 615V650Z"></path></g></svg> fields are (1) perpendicular <svg height="11.9218pt" id="M187" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -8.7403 43.906 11.9218" width="43.906pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g 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transform="matrix(.013,0,0,-0.013,33.538,0)"><path d="M746 650H445V615C520 608 528 602 528 517V370H255V517C255 602 263 608 335 615V650H35V615C112 608 121 602 121 517V133C121 48 112 42 39 35V0H337V35C263 42 255 48 255 133V319H528V133C528 48 520 42 441 35V0H746V35C670 42 662 48 662 132V517C662 602 668 608 746 615V650Z"></path></g></svg> and (2) parallel <svg height="12.4698pt" id="M188" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 33.2496 12.4698" width="33.2496pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 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-163V703H102V-163H162ZM309 -163V703H249V-163H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.894,0)"><path d="M746 650H445V615C520 608 528 602 528 517V370H255V517C255 602 263 608 335 615V650H35V615C112 608 121 602 121 517V133C121 48 112 42 39 35V0H337V35C263 42 255 48 255 133V319H528V133C528 48 520 42 441 35V0H746V35C670 42 662 48 662 132V517C662 602 668 608 746 615V650Z"></path></g></svg> each other. A weak dependence of <svg height="9.14241pt" id="M189" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 17.6694 9.14241" width="17.6694pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"><path d="M372 352C427 368 507 407 507 502C507 548 486 592 451 616C420 638 376 650 301 650H44V622C124 616 128 610 128 527V123C128 40 122 34 36 28V0H257C336 0 402 12 453 40C512 72 548 124 548 191C548 291 471 335 372 350V352ZM213 362V558C213 591 216 602 226 608C235 614 258 618 282 618C377 618 415 558 415 490C415 406 369 362 260 362H213ZM213 328H258C380 328 450 283 450 181C450 76 377 35 296 34C231 34 213 53 213 125V328Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.319,3.132)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g></svg> on <i>H</i> may be caused by an error in the setting of a rotation angle of the sample.</div>

Journal of Spectroscopy

fig2

Figure 2

Figure 2: Free-Electron Screening Mechanism of the Shallow Impurity Breakdown in n-GaAs: Evidences from the Photoelectric Zeeman and Cyclotron Resonance Spectroscopies 

Figure 2 | Free-Electron Screening Mechanism of the Shallow Impurity Breakdown in n-GaAs: Evidences from the Photoelectric Zeeman and Cyclotron Resonance Spectroscopies 