Основы физики и химии полупроводников - 28 стр.

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ɦɨɠɟɦ ɫɱɢɬɚɬɶ ɷɬɨɬ ɷɥɟɤɬɪɨɧ ɫɜɨɛɨɞɧɵɦ ɢ ɨɩɢɫɵɜɚɬɶ ɟɝɨ ɞɜɢɠɟɧɢɟ ɜɨ
ɜɧɟɲɧɟɦ ɩɨɥɟ ɬɚɤ, ɤɚɤ ɨɩɢɫɵɜɚɟɬɫɹ ɞɜɢɠɟɧɢɟ ɨɛɵɱɧɨɝɨ ɫɜɨɛɨɞɧɨɝɨ
ɷɥɟɤɬɪɨɧɚ.
Ɉɞɧɚɤɨ ɷɮɮɟɤɬɢɜɧɚɹ ɦɚɫɫɚ, ɡɚɤɥɸɱɚɹ ɜ ɫɟɛɟ ɜɫɸ ɨɫɨɛɟɧɧɨɫɬɶ, ɩɪɢ-
ɫɭɳɭɸ ɞɜɢɠɟɧɢɸ ɷɥɟɤɬɪɨɧɚ ɜ ɩɟɪɢɨɞɢɱɟɫɤɨɦ ɩɨɥɟ ɤɪɢɫɬɚɥɥɚ, ɹɜɥɹɟɬɫɹ
ɜɟɫɶɦɚ ɫɜɨɟɨɛɪɚɡɧɨɣ ɜɟɥɢɱɢɧɨɣ. ɉɪɟɠɞɟ ɜɫɟɝɨ ɨɧɚ ɦɨɠɟɬ ɛɵɬɶ ɤɚɤ ɩɨ-
ɥɨɠɢɬɟɥɶɧɨɣ, ɬɚɤ ɢ ɨɬɪɢɰɚɬɟɥɶɧɨɣ; ɩɨ ɚɛɫɨɥɸɬɧɨɦɭ ɡɧɚɱɟɧɢɸ ɨɧɚ ɦɨɠɟɬ
ɛɵɬɶ ɤɚɤ ɜɨ ɦɧɨɝɨ ɪɚɡ ɛɨɥɶɲɟ, ɬɚɤ ɢ ɜɨ ɦɧɨɝɨ ɪɚɡ ɦɟɧɶɲɟ ɦɚɫɫɵ ɬ
0
ɩɨɤɨɹ
ɷɥɟɤɬɪɨɧɚ.
Ⱦɥɹ ɷɥɟɤɬɪɨɧɨɜ, ɪɚɫɩɨɥɚɝɚɸɳɢɯɫɹ ɭ ɞɧɚ ɡɨɧɵ, ɷɧɟɪɝɢɹ
E
ɞɧɨ
= ȿ
ɦɢɧ
+ Ⱥ
ɞ
(ka)
2
, (2.12)
ɜɬɨɪɚɹ ɩɪɨɢɡɜɨɞɧɚɹ ɨɬ ɧɟɟ ɩɨ k ɪɚɜɧɚ d
2
E/dk
2
= 2Ⱥ
ɞ
ɚ
2
.
ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜ (2.11), ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɟɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ
ɷɮɮɟɤɬɢɜɧɨɣ ɦɚɫɫɵ ɷɥɟɤɬɪɨɧɚ, ɤɨɬɨɪɭɸ ɦɵ ɨɛɨɡɧɚɱɢɦ ɱɟɪɟɡ m
n
.
2
2
2 aA
m
Ⱦ
n
=
. (2.13)
Ɍɚɤ ɤɚɤ Ⱥ
ɞ
> 0, ɬɨ m
n
> 0. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɧɵ, ɪɚɫɩɨɥɚɝɚɸ-
ɳɢɟɫɹ ɭ ɞɧɚ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɡɨɧɵ, ɨɛɥɚɞɚɸɬ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɷɮɮɟɤɬɢɜɧɨɣ
ɦɚɫɫɨɣ. ɉɨɷɬɨɦɭ ɜɨ ɜɧɟɲɧɟɦ ɩɨɥɟ, ɫɨɡɞɚɧɧɨɦ ɜ ɤɪɢɫɬɚɥɥɟ, ɨɧɢ ɜɟɞɭɬ ɫɟɛɹ
ɧɨɪɦɚɥɶɧɨ, ɭɫɤɨɪɹɹɫɶ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɞɟɣɫɬɜɭɸɳɟɣ ɫɢɥɵ. Ɉɬɥɢɱɢɟ ɬɚɤɢɯ
ɷɥɟɤɬɪɨɧɨɜ ɨɬ ɫɜɨɛɨɞɧɵɯ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɢɯ ɷɮɮɟɤɬɢɜɧɚɹ ɦɚɫɫɚ ɦɨɠɟɬ
ɡɧɚɱɢɬɟɥɶɧɨ ɨɬɥɢɱɚɬɶɫɹ ɨɬ ɦɚɫɫɵ ɩɨɤɨɹ. ɂɡ (2.13) ɜɢɞɧɨ, ɱɬɨ ɱɟɦ ɛɨɥɶɲɟ Ⱥ
ɞ
,
ɬ. ɟ. ɱɟɦ ɲɢɪɟ ɪɚɡɪɟɲɟɧɧɚɹ ɡɨɧɚ, ɬɟɦ ɦɟɧɶɲɟ ɷɮɮɟɤɬɢɜɧɚɹ ɦɚɫɫɚ
ɷɥɟɤɬɪɨɧɨɜ, ɪɚɫɩɨɥɚɝɚɸɳɢɯɫɹ ɭ ɞɧɚ ɷɬɨɣ ɡɨɧɵ. Ⱦɥɹ ɷɥɟɤɬɪɨɧɨɜ,
ɧɚɯɨɞɹɳɢɯɫɹ ɭ ɜɟɪɲɢɧɵ ɡɨɧɵ, ɷɧɟɪɝɢɹ ȿ
ɜɟɪɲ
= E
ɦɚɤɫ
– Ⱥ
ɜ
(ka)
2
, ɜɬɨɪɚɹ
ɩɪɨɢɡɜɨɞɧɚɹ ɨɬ ȿ ɩɨ k ɪɚɜɧɚ d
2
E/dk
2
= –2Ⱥ
ɜ
ɚ
2
ɢ ɷɮɮɟɤɬɢɜɧɚɹ ɦɚɫɫɚ,
ɤɨɬɨɪɭɸ ɦɵ ɨɛɨɡɧɚɱɢɦ ɱɟɪɟɡ ɬ
ɩ
, ɪɚɜɧɚ
2
2
'
2 aA
m
ɜ
n
=
. (2.14)
Ɉɧɚ ɹɜɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɨɬɪɢɰɚɬɟɥɶɧɨɣ. Ɍɚɤɢɟ ɷɥɟɤɬɪɨɧɵ ɜɟɞɭɬ ɫɟɛɹ
ɜɨ ɜɧɟɲɧɟɦ ɩɨɥɟ, ɫɨɡɞɚɧɧɨɦ ɜ ɤɪɢɫɬɚɥɥɟ, ɚɧɨɦɚɥɶɧɨ: ɨɧɢ ɭɫɤɨɪɹɸɬɫɹ ɜ
ɧɚɩɪɚɜɥɟɧɢɢ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɦ ɞɟɣɫɬɜɢɸ ɜɧɟɲɧɟɣ ɫɢɥɵ. Ⱥɛɫɨɥɸɬɧɚɹ
ɜɟɥɢɱɢɧɚ ɬ'
n
ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɲɢɪɢɧɨɣ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɡɨɧɵ:
ɱɟɦ ɲɢɪɟ ɡɨɧɚ, ɬɟɦ ɦɟɧɶɲɟ ɬ
n
.
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