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Hemispherical electron energy analyzer

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135: 1448: 190: 69: 17: 2311:) mode can be used. This mode exploits the relation between the kinetic energy of a photoelectron and its position inside the detector. If the detector energy range is wide enough, and if the photoemission signal collected from all the channels is sufficiently strong, the photoemission spectrum can be obtained in one single shot from the image of the detector. 2303:) mode, the voltages of the two hemispheres – and hence the pass energy – are held fixed; at the same time, the voltages applied to the electrostatic lenses are swept in such a way that each channel counts electrons with the selected kinetic energy for the selected amount of time. In order to reduce the acquisition time per spectrum, the so-called 1443:
As can be seen in the pictures of calculated electron trajectories, the finite slit width maps directly into energy detection channels (thus confusing the real energy spread with the beam width). The angular spread, while also worsening the energy resolution, shows some focusing as the equal negative
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also improve the resolution, but then the electron transmission probability is reduced, and the signal-to-noise ratio deteriorates accordingly. The electrostatic lenses in front of the analyzer have two main purposes: they collect and focus the incoming photoelectrons into the entrance slit of the
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It consists of two concentric conductive hemispheres that serve as electrodes that bend the trajectories of the electrons entering a narrow slit at one end so that their final radii depend on their kinetic energy. The analyzer, therefore, provides a mapping from kinetic energies to positions on a
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Distance from the central trajectory at the exit of a hemispherical electron energy analyzer depending on the electron's kinetic energy, initial position within the 1 mm slit, and the angle at which it enters the radial field after passing through the slit. Dispersion is nearly linear in energy,
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on the other side of the hemispheres will register only the electrons of a single kinetic energy. The detection can, however, be parallelized because of nearly linear dependence of the final radii on the kinetic energy. In the past, several discrete electron detectors
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held at proper voltages. In such a system, the electrons are linearly dispersed, depending on their kinetic energy, along the direction connecting the entrance and the exit slit, while the electrons with the same energy are first-order focused.
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Calculated trajectories for three different kinetic energies and four starting positions within the slit. Slit width maps directly into energy detection channels, worsening the resolution.
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Calculated trajectories for five different kinetic energies and five initial angles. Initial angular spread, dependent on the chosen slit and aperture width, worsens the energy resolution.
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linear in initial position, and quadratic in angle. The latter two map into energy channels of the detector, spoiling the resolution. Data was calculated for R
779: 37: 251:, are applied to the inner and outer hemispheres, respectively, the electric potential in the region between the two electrodes follows from the 1904: 452: 1990: 68: 32:
is a type of electron energy spectrometer generally used for applications where high energy resolution is needed—different varieties of
261: 2479: 49: 16: 662: 41: 1762:{\displaystyle r_{\pi }\approx R_{\textrm {P}}(1+2\varepsilon -\sigma -2\alpha ^{2}+2\varepsilon ^{2}-6\alpha ^{2}\varepsilon )} 2442:
Hadjarab, F.; J.L. Erskine (1985). "Image properties of the hemispherical analyzer applied to multichannel energy detection".
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An ideal hemispherical analyzer consists of two concentric hemispherical electrodes (inner and outer hemispheres) of radii
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at the detector side. But there, this additional width is interpreted as energy dispersion, which is, to the first order,
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The electric field, pointing radially from the center of the hemispheres out, has the familiar planetary motion
1101: 2395:"Imaging properties of hemispherical electrostatic energy analyzers for high resolution momentum microscopy" 1463: 1863: 33: 739: 252: 2112:, of the incoming photoelectrons, which is itself dependent on the width of the aperture and slit, is 2348: 2266: 2236: 2207: 1006: 633: 2072:. It follows that the instrumental energy resolution, given as a function of the width of the slit, 2497: 2372: 1460:
When these deviations from the central trajectory are expressed in terms of the small parameters
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Tusche, Christian; Chen, Ying-Jiun; Schneider, Claus M.; Kirschner, Jürgen (2019-11-01).
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itself is small (of the order of 1°), the final radius of the electron's trajectory,
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analyzer, and they decelerate the electrons to the range of kinetic energies around
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to account for the finite aperture and slit widths (typically 0.1 to 5 mm):
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Practical surface analysis : by auger and x-ray photoelectron spectroscopy
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The voltages are set in such a way that the electrons with kinetic energy
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wide, they would be imaged on the other end of the analyzer as a spot
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with respect to the normal to the entrance, and for the initial radii
2474:. Briggs, D. (David), 1948-, Seah, M. P. Chichester: Wiley. 1983. 2339:
Roy, D.; Tremblay, D. (1990). "Design of electron spectrometers".
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In general, these trajectories are described in polar coordinates
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The potential difference between the two hemispheres needs to be
401:{\displaystyle V(r)=-\left\cdot {\frac {R_{1}R_{2}}{r}}+const.} 725:{\displaystyle R_{\textrm {P}}={\tfrac {1}{2}}(R_{1}+R_{2})} 1901:
is acquired, and a single energy channel is smeared over
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wide. If their maximal angular spread at the entrance is
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Main parts of a hemispherical electron energy analyzer.
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Journal of Electron Spectroscopy and Related Phenomena
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and positive deviations map to the same final spot.
2284: 2254: 2225: 2192: 2104: 2084: 2064: 1979: 1893: 1852: 1832: 1812: 1800:were entering the analyzer through a slit that is 1792: 1761: 1641: 1612: 1592: 1535: 1478: 1432: 1269: 1138: 1090: 1066: 1024: 991: 859: 765: 724: 651: 619: 589: 438: 400: 243: 216: 178: 122: 95: 2204:The analyzer resolution improves with increasing 1593:{\displaystyle r_{0}=(1+\sigma )R_{\textrm {P}}} 736:along the path is imposed by the electric field 1433:{\displaystyle c^{2}=R_{\textrm {P}}\left^{-1}} 1270:{\displaystyle r(\varphi )=r_{0}\,\left^{-1}} 8: 179:{\displaystyle \rho =r_{0}-R_{\textrm {P}}} 2410: 2275: 2274: 2268: 2245: 2244: 2238: 2216: 2215: 2209: 2179: 2162: 2161: 2148: 2136: 2135: 2120: 2097: 2077: 2056: 2047: 2040: 2034: 2018: 2013: 2006: 1994: 1992: 1971: 1966: 1960: 1932: 1927: 1920: 1908: 1906: 1885: 1880: 1874: 1865: 1845: 1825: 1805: 1784: 1778: 1747: 1731: 1715: 1677: 1676: 1663: 1657: 1625: 1605: 1583: 1582: 1554: 1548: 1526: 1525: 1497: 1491: 1465: 1421: 1404: 1403: 1390: 1363: 1353: 1339: 1338: 1327: 1326: 1319: 1306: 1305: 1292: 1286: 1258: 1247: 1201: 1187: 1181: 1175: 1154: 1139:{\displaystyle r_{0}\equiv r(\varphi =0)} 1109: 1103: 1083: 1053: 1015: 1014: 1008: 982: 981: 964: 954: 948: 937: 927: 921: 906: 897: 884: 878: 824: 823: 817: 805: 804: 798: 781: 749: 741: 713: 700: 681: 671: 670: 664: 642: 641: 635: 611: 605: 579: 568: 558: 551: 535: 522: 510: 497: 490: 475: 461: 456: 454: 430: 421: 416: 365: 355: 348: 332: 319: 307: 294: 287: 263: 235: 229: 208: 202: 169: 168: 155: 143: 114: 108: 87: 81: 48:(AES) or in imaging applications such as 38:angle-resolved photoemission spectroscopy 2331: 2292:, in order to increase the resolution. 659:follow a circular trajectory of radius 20:Hemispherical electron energy analyzer. 2495: 1003:A single pointlike detector at radius 26:hemispherical electron energy analyzer 7: 2388: 2386: 1479:{\displaystyle \varepsilon ,\sigma } 1078:for electrons impinging at an angle 2092:, and the maximal incidence angle, 1894:{\displaystyle 2R_{P}\,\alpha ^{2}} 2122: 2041: 1999: 1913: 14: 1773:If electrons of one fixed energy 766:{\displaystyle -e\mathbf {E} (r)} 50:photoemission electron microscopy 30:hemispherical deflection analyzer 750: 462: 42:X-ray photoelectron spectroscopy 2285:{\displaystyle E_{\textrm {P}}} 2255:{\displaystyle E_{\textrm {P}}} 2226:{\displaystyle R_{\textrm {P}}} 1045:and camera detection prevail. 1025:{\displaystyle R_{\textrm {P}}} 652:{\displaystyle E_{\textrm {P}}} 2412:10.1016/j.ultramic.2019.112815 2341:Reports on Progress in Physics 2014: 1995: 1928: 1909: 1756: 1684: 1636: 1630: 1575: 1563: 1518: 1506: 1207: 1188: 1165: 1159: 1133: 1121: 792: 786: 760: 754: 719: 693: 476: 472: 466: 457: 274: 268: 54:low-energy electron microscopy 1: 2456:10.1016/0368-2048(85)80021-9 2361:10.1088/0034-4885/53/12/003 46:Auger electron spectroscopy 2539: 2295:When acquiring spectra in 1860:, an additional width of 1600:, and having in mind that 1067:{\displaystyle r,\varphi } 2105:{\displaystyle \alpha } 1853:{\displaystyle \alpha } 1642:{\displaystyle r(\pi )} 1613:{\displaystyle \alpha } 1091:{\displaystyle \alpha } 627:equal to the so-called 439:{\displaystyle 1/r^{2}} 2502:: CS1 maint: others ( 2286: 2256: 2227: 2194: 2106: 2086: 2066: 1981: 1895: 1854: 1834: 1814: 1794: 1763: 1649:, can be expressed as 1643: 1614: 1594: 1537: 1480: 1457: 1434: 1271: 1140: 1092: 1068: 1043:phosphorescent screens 1026: 993: 861: 773:. 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55: 51: 47: 43: 39: 35: 31: 27: 18: 2470: 2464: 2447: 2443: 2437: 2402: 2398: 2344: 2340: 2334: 2308: 2304: 2300: 2296: 2294: 2203: 1772: 1459: 1442: 1076:great circle 1047: 1035:channeltrons 1002: 869: 628: 599: 410: 196: 75: 58: 29: 25: 23: 1486:defined as 629:pass energy 52:(PEEM) and 2450:(3): 227. 2405:: 112815. 2327:References 60:detector. 44:(XPS) and 40:(ARPES), 2498:cite book 2421:0304-3991 2377:250872079 2369:0034-4885 2177:α 2123:Δ 2100:α 2042:Δ 2020:ε 2008:π 2000:Δ 1969:α 1940:α 1934:σ 1922:π 1914:Δ 1883:α 1848:α 1754:ε 1745:α 1738:− 1729:ε 1713:α 1706:− 1703:σ 1700:− 1697:ε 1670:≈ 1665:π 1634:π 1608:α 1573:σ 1516:ε 1474:σ 1468:ε 1423:− 1397:− 1376:− 1373:α 1370:⁡ 1260:− 1238:φ 1235:⁡ 1229:α 1226:⁡ 1220:− 1217:φ 1214:⁡ 1195:− 1163:φ 1125:φ 1116:≡ 1086:α 1062:φ 946:− 891:− 744:− 549:⋅ 529:− 504:− 484:− 346:⋅ 326:− 301:− 281:− 162:− 146:ρ 2517:Category 2429:31325896 2315:See also 2305:snapshot 2301:scanning 64:Function 56:(LEEM). 36:such as 2490:9556397 2349:Bibcode 2488:  2478:  2427:  2419:  2375:  2367:  732:. The 2373:S2CID 2309:fixed 2297:swept 1279:where 1041:with 446:form 2504:link 2486:OCLC 2476:ISBN 2425:PMID 2417:ISSN 2365:ISSN 2307:(or 2299:(or 224:and 103:and 2452:doi 2407:doi 2403:206 2357:doi 1361:cos 1232:sin 1223:tan 1211:cos 28:or 2519:: 2500:}} 2496:{{ 2484:. 2448:36 2446:. 2423:. 2415:. 2401:. 2397:. 2385:^ 2371:. 2363:. 2355:. 2345:53 2343:. 1543:, 255:: 24:A 2506:) 2492:. 2458:. 2454:: 2431:. 2409:: 2379:. 2359:: 2351:: 2277:P 2272:E 2247:P 2242:E 2218:P 2213:R 2200:. 2187:) 2181:2 2173:+ 2164:P 2159:R 2155:2 2151:w 2145:( 2138:P 2133:E 2129:= 2126:E 2080:w 2058:P 2054:E 2049:/ 2045:E 2036:P 2032:R 2028:2 2025:= 2015:| 2004:r 1996:| 1973:2 1962:P 1958:R 1954:2 1951:+ 1948:w 1945:= 1937:, 1929:| 1918:r 1910:| 1887:2 1876:P 1872:R 1868:2 1828:w 1808:w 1786:k 1782:E 1769:. 1757:) 1749:2 1741:6 1733:2 1725:2 1722:+ 1717:2 1709:2 1694:2 1691:+ 1688:1 1685:( 1679:P 1674:R 1661:r 1637:) 1631:( 1628:r 1585:P 1580:R 1576:) 1570:+ 1567:1 1564:( 1561:= 1556:0 1552:r 1528:P 1523:E 1519:) 1513:+ 1510:1 1507:( 1504:= 1499:k 1495:E 1471:, 1454:p 1426:1 1418:] 1413:) 1406:P 1401:R 1392:0 1388:r 1383:( 1379:2 1365:2 1355:0 1351:r 1341:P 1336:E 1329:k 1324:E 1316:[ 1308:P 1303:R 1299:= 1294:2 1290:c 1263:1 1255:] 1249:2 1245:c 1241:+ 1208:) 1203:2 1199:c 1192:1 1189:( 1185:[ 1177:0 1173:r 1169:= 1166:) 1160:( 1157:r 1134:) 1131:0 1128:= 1122:( 1119:r 1111:0 1107:r 1059:, 1056:r 1033:( 1017:P 1012:R 999:. 984:P 979:E 974:) 966:2 962:R 956:1 952:R 939:1 935:R 929:2 925:R 918:( 912:e 909:1 904:= 899:2 895:V 886:1 882:V 855:. 852:t 849:s 846:n 843:o 840:c 837:+ 832:r 826:P 821:R 813:e 807:P 802:E 796:= 793:) 790:r 787:( 784:V 761:) 758:r 755:( 751:E 747:e 720:) 715:2 711:R 707:+ 702:1 698:R 694:( 688:2 685:1 679:= 673:P 668:R 644:P 639:E 613:k 609:E 581:2 577:r 570:2 566:R 560:1 556:R 545:] 537:1 533:R 524:2 520:R 512:1 508:V 499:2 495:V 488:[ 481:= 477:| 473:) 470:r 467:( 463:E 458:| 432:2 428:r 423:/ 419:1 396:. 393:t 390:s 387:n 384:o 381:c 378:+ 373:r 367:2 363:R 357:1 353:R 342:] 334:1 330:R 321:2 317:R 309:1 305:V 296:2 292:V 285:[ 278:= 275:) 272:r 269:( 266:V 237:2 233:V 210:1 206:V 171:P 166:R 157:0 153:r 149:= 116:2 112:R 89:1 85:R

Index


electron spectroscopy
angle-resolved photoemission spectroscopy
X-ray photoelectron spectroscopy
Auger electron spectroscopy
photoemission electron microscopy
low-energy electron microscopy



Laplace equation
centripetal force
channeltrons
microchannel plates
phosphorescent screens
great circle

Mass spectrometry
Bibcode
1990RPPh...53.1621R
doi
10.1088/0034-4885/53/12/003
ISSN
0034-4885
S2CID
250872079


"Imaging properties of hemispherical electrostatic energy analyzers for high resolution momentum microscopy"
doi

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