µÚÒ»ÕÂϰÌâ
1£®Éè¾§¸ñ³£ÊýΪaµÄһά¾§¸ñ£¬µ¼´ø¼«Ð¡Öµ¸½½üÄÜÁ¿Ec(k)ºÍ¼Û´ø¼«´óÖµ¸½½ü
ÄÜÁ¿EV(k)·Ö±ðΪ£º Ec=
hk223m0?h(k?k1)m022,EV(k)?hk2216m0?3hkm022
m0Ϊµç×Ó¹ßÐÔÖÊÁ¿£¬k1??a,a?0.314nm¡£ÊÔÇó£º
£¨1£©½û´ø¿í¶È;
£¨2£©µ¼´øµ×µç×ÓÓÐЧÖÊÁ¿; £¨3£©¼Û´ø¶¥µç×ÓÓÐЧÖÊÁ¿;
£¨4£©¼Û´ø¶¥µç×ÓԾǨµ½µ¼´øµ×ʱ׼¶¯Á¿µÄ±ä»¯ ½â£º£¨1£©
µ¼´ø£ºÓÉ2?k3m02?342?(k?k1)m0k122?0µÃ£ºk?ÓÖÒòΪ£ºdEcdk2?342?23m0?2?2m0?8?23m0?0ËùÒÔ£ºÔÚk?¼Û´ø£ºdEVdk??6?km022k´¦£¬EcÈ¡¼«Ð¡Öµ?0µÃk?06?2ÓÖÒòΪdEVdk2??34m0?0,ËùÒÔk?0´¦£¬EVÈ¡¼«´óÖµ?k122Òò´Ë£ºEg?EC(k1)?EV(0)?12m0?0.64eV
(2)m*nC??22dECdk2k?34k1?38m0
1
(3)m*nV??22dEVdk2k?01??m06(4)×¼¶¯Á¿µÄ¶¨Ò壺ËùÒÔ£º?p?(?k)k?34p??k?(?k)k?0??34k1?0?7.95?10?25
N/sk1
2. ¾§¸ñ³£ÊýΪ0.25nmµÄһά¾§¸ñ£¬µ±Íâ¼Ó102V/m£¬107 V/mµÄµç³¡Ê±£¬ÊÔ·Ö±ð¼Æ
Ëãµç×Ó×ÔÄÜ´øµ×Ô˶¯µ½ÄÜ´ø¶¥ËùÐèµÄʱ¼ä¡£ ½â£º¸ù¾Ý£ºf?qE?h?(0??t1??1.6?10?k?t µÃ?t???k?qE
?a)?10)?1072?19?8.27?10?8s?(0??t2??1.6?10?a
?8.27?10?13?19s ²¹³äÌâ1
·Ö±ð¼ÆËãSi£¨100£©£¬£¨110£©£¬£¨111£©ÃæÃ¿Æ½·½ÀåÃ×ÄÚµÄÔ×Ó¸öÊý£¬¼´Ô×ÓÃæÃܶȣ¨Ìá
ʾ£ºÏÈ»³ö¸÷¾§ÃæÄÚÔ×ÓµÄλÖúͷֲ¼Í¼£©
SiÔÚ£¨100£©£¬£¨110£©ºÍ£¨111£©ÃæÉϵÄÔ×Ó·Ö²¼Èçͼ1Ëùʾ£º
£¨a£©(100)¾§Ãæ £¨b£©(110)¾§Ãæ
2
£¨c£©(111)¾§Ãæ
11?4? 224£¨100£©£º??22aa(5.43?10112?4??2? 42£¨110£©£º?2a?a114??2??22 111£©£º4£¨?3a?2a
2
?8
)2?6.78?1014atom/cm242a43a22?9.59?1014atom/cm2
?7.83?1014atom/cm2 ²¹³äÌâ2
һά¾§ÌåµÄµç×ÓÄÜ´ø¿ÉдΪE£¨k)?ʽÖÐaΪ ¾§¸ñ³£Êý£¬ÊÔÇó
£¨1£©²¼ÀïÔ¨Çø±ß½ç£» £¨2£©ÄÜ´ø¿í¶È£»
£¨3£©µç×ÓÔÚ²¨Ê¸k״̬ʱµÄËÙ¶È£»
* £¨4£©ÄÜ´øµ×²¿µç×ÓµÄÓÐЧÖÊÁ¿mn£»
?22ma(78?coska?18cos2ka)£¬
£¨5£©ÄÜ´ø¶¥²¿¿ÕѨµÄÓÐЧÖÊÁ¿mp
½â£º£¨1£©ÓÉ
dE(k)dk?0 µÃ k?n?a*
£¨n=0£¬?1£¬?2¡£© ½øÒ»²½·ÖÎök?(2n?1)?a £¬E£¨k£©Óм«´óÖµ£¬
3
E£¨k)MAX?2?ma22
k?2n?aʱ£¬E£¨k£©Óм«Ð¡Öµ
?aËùÒÔ²¼ÀïÔ¨Çø±ß½çΪk?(2n?1)
2?ma?22(2)ÄÜ´ø¿í¶ÈΪE£¨k)MAX?E(k)MIN?
14(3£©µç×ÓÔÚ²¨Ê¸k״̬µÄËÙ¶Èv?£¨4£©µç×ÓµÄÓÐЧÖÊÁ¿ m?*n1dE?dk?ma(sinka?sin2ka)
?22dEdk2?(coska?2n?am12cos2ka)
ÄÜ´øµ×²¿ k?* ËùÒÔmn?2m
(5)ÄÜ´ø¶¥²¿ k?ÇÒmp??mn£¬
**(2n?1)?a£¬
ËùÒÔÄÜ´ø¶¥²¿¿ÕѨµÄÓÐЧÖÊÁ¿mp?*2m3
4