В этой заметке мы разберем метод определения ширины запрещенной зоны полупроводника методом
Tauc plot
Для этого нам понадобится коллоид наночастиц Cu2O. Запишем его спектр оптического поглощения.
Пересчитаем его в координатах $h\nu$ и $(\alpha h\nu)^{1/r}$ с помощью Gnuplot
plot [200:800] 'Cu2O-UV' u 1:2 w l f(x) = a*x + b fit [2.6:5.4] f(x) 'Cu2O-UV' u (1239.84/$1):(($2*1239.84/$1)**2.0) via a, b plot [1.4:5.5][0:] 'Cu2O-UV'' u (1239.84/$1):(($2*1239.84/$1)**2.0) w l, f(x)Мы вычислили ширину запрещенной зоны для прямого (оптического) разрешенного перехода ($1/r=2$), т.е. direct allowed transitions Которая в нашем случае составила для наночастиц Cu2O величину примерно 2.7 эВ. Исходный спектр наночастиц приведён ниже.
УФ-спектр поглощения наночастиц Cu2O в воде
#Wavelength (nm), Abs 800.0065308 0.01255773753 799.0047607 0.01218323782 798.0027466 0.01219668239 797.0001831 0.01253567543 795.9973755 0.01253399719 794.9940796 0.01296904404 793.9903564 0.01214655396 792.9862061 0.01250969805 792.0164185 0.0135039594 791.0114746 0.01286672056 790.0062256 0.01290997211 789.0004883 0.01305279788 787.9944458 0.0125807859 786.987915 0.0130309239 786.0158081 0.01278518885 785.0085449 0.01281648781 784.0008545 0.01323791314 782.9927979 0.01318590343 781.984375 0.01365568861 781.0102539 0.01331232395 780.0010986 0.01353285369 778.991394 0.01332254708 778.0162354 0.01390814502 777.0058594 0.01335658133 775.9950562 0.01409311779 774.9838257 0.0137343118 774.0071411 0.01386717241 772.9951172 0.01411656942 771.9828491 0.01425818726 771.0049438 0.01449209731 769.9918823 0.01421974879 769.0133667 0.01449563075 767.9994507 0.01421009284 766.9851685 0.01431409828 766.0054321 0.01427431777 764.9904175 0.01469930355 764.0100098 0.01491946634 762.9942017 0.01480291598 762.0131226 0.0144878421 760.996521 0.01485190634 760.0147095 0.01523965318 758.9973755 0.01526694745 758.0147705 0.01522278972 756.9967041 0.01474587061 756.0134277 0.0149769634 754.9945679 0.01559713017 754.010498 0.0152889872 752.9909668 0.01539904345 752.0061646 0.01548933052 750.9858398 0.01522563118 750.0003662 0.01579884999 749.0144653 0.01544944197 747.993042 0.01573120616 747.0064697 0.01572175883 745.984314 0.01584682427 744.9970093 0.01605798118 744.0093994 0.01611122303 742.986084 0.01628071629 741.9977417 0.01606273651 741.0090332 0.01629778184 739.9846191 0.01623089425 738.9951782 0.01637296006 738.0054932 0.01652152836 737.0153809 0.01672308519 735.989563 0.01651633717 734.9987183 0.01687960327 734.0075073 0.01710722968 733.0160522 0.01714875177 731.9887085 0.0169135686 730.996521 0.01691623218 730.0039673 0.01719504409 729.0110474 0.01724174619 727.9822998 0.01751605235 726.9887085 0.01720902324 725.994751 0.0174853541 725.0004883 0.01768118702 724.0057983 0.01791956648 723.0108643 0.01785682328 722.0155029 0.01784937829 720.984314 0.01792501472 719.9883423 0.01779915951 718.9919434 0.01790211163 717.9953003 0.01830177382 716.99823 0.01826988719 716.0009155 0.01829729229 715.0031738 0.01874212548 714.005127 0.01859150082 713.0067749 0.01836093515 712.0081177 0.01848198287 711.0090332 0.01882881299 710.0096436 0.01875728928 709.0098877 0.01897573471 708.0098267 0.01897446252 707.0094604 0.01919783279 706.008728 0.01928141713 705.0077515 0.01934753172 704.0062866 0.0195805449 703.0045776 0.01946081594 702.0025635 0.01961572282 701.000061 0.01967197657 699.9974365 0.02019479685 698.9943848 0.02007281035 697.9910278 0.0199986957 696.9873047 0.02028426901 695.9832764 0.02009731904 695.0147705 0.02053797618 694.0101318 0.02018847875 693.005127 0.02062222548 691.9997559 0.0205725804 690.9940796 0.02087914571 689.9881592 0.02096962743 689.0177612 0.02111510187 688.0111694 0.02122754231 687.0041504 0.02149066888 685.9968872 0.02144301869 684.9893188 0.02157159336 684.017395 0.02141171694 683.0091553 0.02139314264 682.0006714 0.02195215598 680.9916992 0.02219744213 679.982605 0.02200016193 679.0090942 0.02228021435 677.9992676 0.02210335247 676.9890747 0.02252617665 676.0147705 0.02261212096 675.0039673 0.02257498167 673.9928589 0.02293606661 673.0177002 0.02245635912 672.0059204 0.02308834344 670.9938965 0.02286119014 670.0176392 0.02327197045 669.0050659 0.02328958549 667.9920654 0.02335617878 667.0149536 0.02344786189 666.0014038 0.02376376279 664.9874878 0.0238016881 664.0095215 0.02386964485 662.9949951 0.02396050468 662.0164795 0.02422679774 661.0012817 0.02447854728 659.9858398 0.02476848103 659.0063477 0.02478029206 657.9902954 0.02475190163 657.0101929 0.02486309409 655.9935913 0.02503217198 655.0129395 0.02538087033 653.9956665 0.02541234903 653.0144653 0.02567500249 651.996582 0.0256686043 651.0147705 0.02554625086 649.9962769 0.02593149617 649.013855 0.0260120444 647.994812 0.02634021454 647.0117798 0.0264705494 645.9921875 0.02660194412 645.0084839 0.02649333142 643.9883423 0.02697256394 643.0042114 0.02722307108 641.9832764 0.0270539932 640.9985962 0.02723329701 640.0135498 0.02735973895 638.9918213 0.02774118818 638.0062866 0.02797165327 636.9839478 0.02804664336 635.9977417 0.02823406458 635.0114136 0.02833410539 633.9881592 0.02852886543 633.0011597 0.02862814441 632.013916 0.02882809937 630.9898682 0.02895542234 630.0020142 0.02926336601 629.013916 0.02936372906 627.9889526 0.02950569615 627.0002441 0.02971877903 626.0113525 0.02983202785 624.9855347 0.03016354144 623.9960327 0.03013365902 623.0062256 0.03032914363 622.0162354 0.03061634302 620.9892578 0.03083049878 619.9986572 0.0308754947 619.0077515 0.03108630143 618.0166626 0.03135196492 616.9885254 0.03150791675 615.9968262 0.03184898943 615.0048828 0.03189952299 614.0126953 0.03209290653 612.9834595 0.03255640343 611.9906616 0.03241039068 610.9976196 0.0326844044 610.0043335 0.03288466856 609.0106812 0.0332332775 608.0168457 0.03345035017 606.9859619 0.03378813714 605.9915161 0.03373643383 604.9969482 0.0341822803 604.0020142 0.03433927894 603.0068359 0.03444056958 602.0113525 0.03497575969 601.015686 0.03504571319 599.9827881 0.03524816781 598.9865112 0.03563725948 597.9900513 0.03583759815 596.9932251 0.0359008275 595.9961548 0.03613237664 594.9989014 0.03643836081 594.0014038 0.03700096905 593.00354 0.03720205277 592.0054321 0.03721034154 591.0071411 0.03741646186 590.0084839 0.03777129948 589.0096436 0.03812450171 588.0105591 0.038303148 587.0111694 0.03862968087 586.0115356 0.03893264383 585.0116577 0.03915283829 584.0115356 0.03956064582 583.0111694 0.03984799981 582.010498 0.03996400535 581.0095825 0.04025168717 580.0084229 0.0405857414 579.006958 0.04098618776 578.0053101 0.04119595885 577.0033569 0.04158967361 576.0012207 0.04182969034 574.9987793 0.04217999429 573.9960938 0.04247548431 572.9931641 0.04265424609 571.9899292 0.04301890731 570.9865112 0.04338707402 569.9828491 0.04367044941 569.0160522 0.04403888434 568.0119019 0.04455630109 567.0074463 0.04462853074 566.0027466 0.04513696954 564.9978638 0.04567059129 563.9926758 0.04583427683 562.9872437 0.04619689286 561.9816284 0.04647484794 561.0129395 0.0469233878 560.0068359 0.04736566544 559.0003662 0.04789697379 557.9937744 0.04808093235 556.9868774 0.04858992994 556.0170288 0.04902373627 555.0095825 0.0492442362 554.0020142 0.04967173189 552.9942017 0.05007870495 551.986145 0.05037406459 551.0151367 0.05099974573 550.0065308 0.05135813728 548.9977417 0.05164206773 547.9887085 0.05228476226 547.0167236 0.05259138718 546.0073242 0.05308455229 544.9974365 0.05347757787 543.9874878 0.05408833548 543.0147095 0.0545225963 542.0042114 0.05512821674 540.9934692 0.05529350415 539.9825439 0.05591556802 539.0088501 0.05649780855 537.9974365 0.05688458309 536.9857178 0.05744938925 536.0112915 0.05786782876 534.9992676 0.05855218321 533.9869385 0.05906975642 533.0118408 0.05951721966 531.9990234 0.06014343724 530.9859619 0.06079196557 530.0102539 0.06130618975 528.9965270 0.0624561049 527.0066528 0.06295644492 525.9924316 0.06359872967 525.015564 0.06417462975 524.0010376 0.06487485766 522.986145 0.06550232321 522.008667 0.06605187804 520.9933472 0.0668611154 520.0154419 0.06744816154 518.9996338 0.06822665781 517.9837036 0.06887964159 517.0050659 0.06944867224 515.9887085 0.07041721791 515.0097046 0.0709015578 513.9927368 0.07171079516 513.0134277 0.07245271653 511.9960632 0.07326298207 511.0162048 0.07398687303 509.9984131 0.07491657138 509.018158 0.07569009811 508.0000305 0.07657518983 506.9815674 0.07765888423 506.0006714 0.07825426757 504.981781 0.0792080611 504.0004883 0.08016499132 502.9811707 0.08133704215 501.9994507 0.08223600686 501.0174866 0.08315198869 499.9975281 0.084142223 499.0151978 0.08521377295 497.9947815 0.08622671664 497.0120239 0.08736762404 495.991272 0.08837035298 495.0080872 0.08980119973 493.9868774 0.09094394743 493.0032043 0.09230054915 491.9815674 0.09336166084 490.9975891 0.09461408108 490.0133667 0.09621798247 488.9911499 0.09751337767 488.0064697 0.09872315079 486.9838257 0.1001481488 485.9988403 0.1017531902 485.0135498 0.1032905579 483.9902649 0.1047433689 483.0046387 0.1062881351 482.0187683 0.108003296 480.9949036 0.1098260134 480.008667 0.1117500216 478.984314 0.1135132164 477.9977112 0.1153559536 477.0108948 0.1173111126 475.9859619 0.1194883958 474.9987183 0.1213757768 474.0112915 0.1235824302 472.9858093 0.1256736517 471.9979553 0.127500087 471.0099792 0.1299407184 469.9837952 0.1322698444 468.9954834 0.1343719959 468.006897 0.136580646 467.018158 0.1388962567 465.9912109 0.1415064037 465.0020447 0.1440091878 464.0127563 0.1463292092 462.9851379 0.1490950286 461.9954224 0.1514825821 461.0054932 0.1537575722 460.0154419 0.1561527997 458.9870911 0.1589318961 457.9966125 0.1613219082 457.0059814 0.1637553275 456.0151367 0.1664267927 454.9860229 0.1690883189 453.994812 0.1714437157 453.0033875 0.1735293865 452.0117798 0.1763572991 450.981842 0.1790753901 449.9898987 0.1813954711 448.9977417 0.1837027669 448.0054626 0.1859440804 447.0129395 0.1882166415 445.9820862 0.1905896664 444.9892273 0.1927859038 443.9961243 0.1947074085 443.0028687 0.1970398128 442.009491 0.1992138922 441.0158691 0.2012152523 439.9838867 0.2031671405 438.9899292 0.2050726712 437.9957886 0.2070022821 437.0014648 0.2088708282 436.0069885 0.2107375115 435.0123291 0.2125622183 434.0174561 0.2143542022 432.9841309 0.2159832418 431.9889221 0.2178158909 430.9935608 0.2195139378 429.9979858 0.220932737 429.0022583 0.2225941569 428.0063477 0.2242125869 427.0102844 0.2257309854 426.0139771 0.2276166826 425.0175781 0.2288288921 423.982666 0.2304789126 422.9858398 0.2320256829 421.9888916 0.2335039675 420.9917908 0.2351029813 419.9945068 0.2363699824 418.9969788 0.2378083616 417.9993286 0.2392594665 417.0015564 0.2407241017 416.0036011 0.2423740774 415.0054321 0.2437465191 414.0071106 0.2451779395 413.0086365 0.246764943 412.0099792 0.2483499199 411.0111389 0.2500455678 410.0121765 0.2512839437 409.013031 0.2528226078 408.0136719 0.2545606494 407.0142212 0.2561466098 406.0145569 0.2576802075 405.0147705 0.2591069043 404.0147705 0.2607487738 403.0146179 0.2624567449 402.0143433 0.2641362548 401.0138245 0.2659447491 400.0132141 0.2674967051 399.0124207 0.2694134712 398.0114441 0.2710880041 397.0103149 0.2728696764 396.0090637 0.2747395039 395.0075989 0.2765857279 394.006012 0.2783995569 393.0042419 0.2802259624 392.0023193 0.2822113633 391.0002441 0.284006536 389.9979858 0.2859140635 388.995575 0.2875141501 387.9930115 0.289519608 386.9902954 0.2915418446 385.9874268 0.293518573 384.9844055 0.2952962816 383.9812012 0.2969563305 383.0164795 0.2988653183 382.0129395 0.3008533716 381.0093384 0.3028095365 380.0054932 0.3045793474 379.0015564 0.306284368 377.9974365 0.3083942533 376.9931641 0.3102215528 375.988739 0.3120807409 374.9841614 0.3139910102 374.0180969 0.3155599535 373.0132446 0.3174476624 372.0082092 0.3195008636 371.0030518 0.3214408755 369.9977112 0.3231185675 368.9922485 0.3245065808 367.9866028 0.3264555335 366.980835 0.3282990754 366.0136108 0.3302026391 365.0075378 0.3315865397 364.0013123 0.3329133391 362.9949646 0.3345375359 361.9884338 0.3360665441 360.981781 0.3373195529 360.0137024 0.3387392163 359.0067749 0.3398883939 357.9996948 0.3413062096 356.9924316 0.3423948288 355.9850769 0.343518883 355.0162659 0.3446127176 354.008606 0.3455503881 353.0007935 0.3462450802 351.9928589 0.3474620581 350.9847412 0.3481847942 350.0152588 0.3487376571 349.0069275 0.3493920267 347.9983826 0.3500837684 346.9897461 0.3506371379 345.9809265 0.3509123623 345.0108337 0.3514224589 344.0017395 0.3517419696 342.9925232 0.3519333899 341.9831543 0.3521957397 341.0124817 0.3520888388 340.0028687 0.3525113463 338.993103 0.3524944186 337.9832153 0.3527641892 337.0120239 0.3526249826 336.0018311 0.3524917662 334.9915466 0.3524803817 333.9810791 0.3526809216 333.0093689 0.3527384698 331.9986877 0.3528383374 330.9878235 0.3529728055 330.0157471 0.3528104722 329.0046082 0.3530774117 327.9933777 0.3532334864 326.9819946 0.3536608815 326.0093689 0.3537948132 324.9977722 0.3541184962 323.9859924 0.3545587361 323.013031 0.35516271 322.0010071 0.3558099568 320.9888611 0.3561401963 320.0154724 0.3569248021 319.0030823 0.3578017354 317.9905396 0.3586034179 317.0168152 0.3594931662 316.0040283 0.3607389927 314.9911194 0.3619912267 314.0169983 0.3630000055 313.0038147 0.3642749786 311.9905396 0.3657827973 311.0161133 0.3671698272 310.002533 0.3687185347 308.9888916 0.3702765703 308.0140686 0.3719595969 307.0001221 0.3737115562 305.986084 0.3754031062 305.0108948 0.3773103058 303.9966431 0.3790136874 302.9821777 0.3810620904 302.0066833 0.3829732239 300.9920654 0.3850145936 300.0163269 0.3869015574 299.0014038 0.3886863291 297.9863892 0.3905514181 297.0103149 0.392455101 295.9950562 0.3941937387 295.0187378 0.3958979547 294.0032654 0.39745 292.9876404 0.3990533054 292.0109863 0.400521636 290.9951172 0.4017695785 290.018219 0.4031996727 289.0021667 0.4043375552 287.9859924 0.4051796496 287.0087891 0.4060237408 285.9923706 0.4067691565 285.0149231 0.4074435532 283.9982605 0.4077593386 282.9815369 0.4082051218 282.0037842 0.4085300565 280.9867859 0.4087808132 280.0087891 0.4089276791 278.9915771 0.4090313315 278.0133972 0.4090982676 276.9959717 0.408959657 276.0175171 0.4092032313 274.9998779 0.4090636373 273.9821167 0.4088105559 273.003418 0.408798933 271.9854126 0.4085874557 271.0064697 0.4084347486 269.9883118 0.4084289074 269.0091553 0.4083512127 267.9907532 0.4082684815 267.0113831 0.4083483219 265.9927673 0.4084282219 265.0132141 0.4082923532 263.9943848 0.4081104696 263.0146179 0.4081658721 261.995575 0.4083960652 261.015625 0.407962054 259.9963684 0.4083657265 259.0162048 0.4085684419 257.9967346 0.4084689021 257.0163879 0.4084433019 255.9967346 0.4083847404 255.0161743 0.408451438 253.9962921 0.4080747664 253.015564 0.4079721868 251.9955139 0.4079269469 251.0145416 0.4079419374 249.9942627 0.4074141085 249.0131531 0.4074421227 247.992691 0.4073877633 247.0113525 0.4077083468 245.9906769 0.4075018167 245.0091858 0.4075708985 243.988327 0.4076016247 243.0066071 0.4079410434 241.9855499 0.4086118937 241.0036774 0.4093708396 239.9824219 0.4102807343 239.000351 0.4111827612 238.0182037 0.4121513069 236.9966736 0.4134986699 236.014328 0.4148510695 234.9925842 0.4160552025 234.0101013 0.4172031879 232.9881897 0.4180876911 232.0054779 0.4191904366 230.9833679 0.4201743007 230.0005035 0.4204597771 229.0175323 0.4209492803 227.9951935 0.4212741852 227.0120697 0.4207710922 225.9895172 0.4205128253 225.0061798 0.4195667207 223.9834747 0.4186830223 222.9999695 0.4173018038 222.0164185 0.4158354998 220.9934235 0.4143491983 220.0096893 0.4120408297 218.9865112 0.4099385142 218.0026398 0.4071815014 217.018631 0.4044723809 215.995224 0.4015476406 215.0110474 0.3987031579 213.9874725 0.3956611753 213.0031433 0.3923184872 212.0187531 0.3889003098 210.9948883 0.385818392 210.0103607 0.3819032907 208.9863281 0.3789326847 208.0015869 0.3753180206 207.0168152 0.3720583916 205.9925385 0.3696687222 205.0075989 0.3671162128 203.9831543 0.3650553524 202.9980621 0.363494426 202.0128632 0.3625882268 200.9881897 0.362157464 200.0028687 0.3625331521
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