推荐回答(2个)
实验发现,导体的电流密度与外加电场成正比,并有如下关系:
, (4-4-1)
其中μ为迁移率,从杜鲁德模型可得(4-2-1)式,计及电子有效质量,得:
, (4-4-2)
从索未菲模型出发:
(4-4-3)
(这里省去星号,把m看成是有效质量)。对平衡态, , 有 状态的电子就必然有- 状态的电子存在,费米球心在原点;对于非平衡态, 电子在外电场下加速,费米球心作位移: .
, (4-4-4)
, (4-4-5)
(4-4-6)
由于某种原因*,电子通过碰撞而失去加速所获得的动量和能量, 因而, 位移后的费米球处于一稳定态, 设碰撞时间为τ, 则速度增量:
稳定态.
与经典电子气模型相仿可推出电导率及迁移率.
稳定态下费米球心位移: ;只有费米面附近的电子**才对电导有贡献:
(4-4-7)
(4-4-8)
从 有:
; (4-4-9)
〖或更一般性地:
(略去 的二次项)
;以上用到(4-3-14)式及(4-3-11)式, 其结果与近似计算比较差一个因子3。
以上近似结果与经典电子气模型的结果相同。用自由电子气模型来讨论金属的电导是不恰当的, 因为自由电子在电场的作用下将不断地加速。〗
*后面将学到,实际上是电子与杂质等晶格缺陷及声子之间的相互碰撞。
**其数目为: n'= D(EF)△EF/V,其中D(EF)中已考虑自旋因子2。
YS/T478-2005
附 录 A
(资料性附录)
导电率、电导率与电阻系数之间的对应关系
导电率/%IACS 电导率/(MS/-) 电阻系数/(II·-m,/.)
102 59.16 0.016903
101 58.58 0.017070
100 58.00 0.017241
99 57.42 0.017415
98 56.84 0.017593
97 56.26 0.017774
96 55.68 0.017959
95 55.10 0.018148
94 54.52 0.018341
93 53.94 0.018539
92 53.36 0.018740
91 52.78 0.018946
90 52.20 0.019157
85 49.30 0.020284
80 46.40 0.021551
75 43.50 0.022988
70 40.60 0.024630
65 37.70 0.026525
60 34.80 0.028735
55 31.90 0.031347
50 29.00 0.034482
45 26.10 0.038313
40 23.20 0.043103
35 20.30 0.049260
30 17.40 0.057470
25 14.50 0.068964
20 11.60 0.086205
15 8.70 0.114940
10 5.80 0.172410
5 2.90 0.344820
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