Основы физики и химии полупроводников - 31 стр.

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ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɷɥɟɦɟɧɬ ɨɛɴɟɦɚ ɩɪɨɫɬɪɚɧɫɬɜɚ ɤɨɨɪɞɢɧɚɬ, ¨Ƚ
Ɋ
=
= dp
x
dp
y
dp
z
– ɷɥɟɦɟɧɬ ɨɛɴɟɦɚ ɩɪɨɫɬɪɚɧɫɬɜɚ ɢɦɩɭɥɶɫɨɜ. Ɍɚɤ ɤɚɤ ɭ
ɤɥɚɫɫɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ ɤɨɨɪɞɢɧɚɬɵ ɢ ɫɨɫɬɚɜɥɹɸɳɢɟ ɢɦɩɭɥɶɫɚ ɦɨɝɭɬ
ɦɟɧɹɬɶɫɹ ɧɟɩɪɟɪɵɜɧɨ, ɬɨ ɷɥɟɦɟɧɬɵ ¨Ƚ
v
, ¨Ƚ
ɪ
, ɚ ɜɦɟɫɬɟ ɫ ɧɢɦɢ ɢ ɷɥɟɦɟɧɬ ¨Ƚ
ɦɨɝɭɬ ɛɵɬɶ ɫɤɨɥɶ ɭɝɨɞɧɨ ɦɚɥɵɦɢ.
Ⱦɥɹ ɫɢɫɬɟɦɵ ɧɟɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɱɚɫɬɢɰ, ɧɟ ɩɨɞɜɟɪɠɟɧɧɨɣ
ɜɥɢɹɧɢɸ ɜɧɟɲɧɟɝɨ ɩɨɥɹ, ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰ ɪɚɜɧɚ ɧɭɥɸ. Ɍɚɤɢɟ
ɱɚɫɬɢɰɵ ɧɚɡɵɜɚɸɬɫɹ ɫɜɨɛɨɞɧɵɦɢ. Ⱦɥɹ ɧɢɯ ɭɞɨɛɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɧɟ
ɲɟɫɬɢɦɟɪɧɵɦ ɮɚɡɨɜɵɦ ɩɪɨɫɬɪɚɧɫɬɜɨɦ, ɚ ɬɪɟɯɦɟɪɧɵɦ ɩɪɨɫɬɪɚɧɫɬɜɨɦ
ɢɦɩɭɥɶɫɨɜ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɷɥɟɦɟɧɬ ¨Ƚ
V
ɪɚɜɟɧ ɩɪɨɫɬɨ ɨɛɴɟɦɭ V, ɜ ɤɨɬɨɪɨɦ
ɞɜɢɠɭɬɫɹ ɱɚɫɬɢɰɵ, ɩɨɫɤɨɥɶɤɭ ɧɢɤɚɤɢɯ ɞɪɭɝɢɯ ɨɝɪɚɧɢɱɟɧɢɣ ɧɚ ɢɯ ɞɜɢɠɟɧɢɟ
ɧɟ ɧɚɥɚɝɚɟɬɫɹ.
ɇɟɫɤɨɥɶɤɨ ɢɧɚɱɟ ɨɛɫɬɨɢɬ ɞɟɥɨ ɫ ɞɟɥɟɧɢɟɦ ɮɚɡɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɧɚ
ɷɥɟɦɟɧɬɵ ɨɛɴɟɦɚ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɱɚɫɬɢɰɟɣ ɹɜɥɹɟɬɫɹ ɷɥɟɤɬɪɨɧ ɢɥɢ
ɥɸɛɨɣ ɞɪɭɝɨɣ ɦɢɤɪɨɨɛɴɟɤɬ, ɨɛɥɚɞɚɸɳɢɣ ɜɨɥɧɨɜɵɦɢ ɫɜɨɣɫɬɜɚɦɢ. ɋɨɝɥɚɫɧɨ
ɩɪɢɧɰɢɩɭ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɟɣ ɧɟɥɶɡɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɬɨɱɧɨ ɢɡɦɟɪɢɬɶ
ɤɨɨɪɞɢɧɚɬɭ ɱɚɫɬɢɰɵ ɢ ɟɟ ɢɦɩɭɥɶɫ. ɉɪɨɢɡɜɟɞɟɧɢɟ ɩɨɝɪɟɲɧɨɫɬɢ ɢɡɦɟɪɟɧɢɹ
ɤɨɨɪɞɢɧɚɬɵ ɢ ɢɦɩɭɥɶɫɚ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɦɟɧɶɲɟ, ɱɟɦ h:
hxp
x
t''
;
hyp
y
t''
;
hzp
z
t''
.
ɉɨɷɬɨɦɭ ɞɥɹ ɦɢɤɪɨɱɚɫɬɢɰ ɧɟɜɨɡɦɨɠɧɨ ɪɚɡɥɢɱɚɬɶ ɞɜɚ ɫɨɫɬɨɹɧɢɹ (ɯ, ɭ, z,
p
x
, ɪ
ɭ
, p
z
) ɢ (ɯ + dx, ɭ + dy, z + dz, ɪ
ɯ
+dp
x
, p
y
+ dp
y
, p
z
+ dp
z
), ɟɫɥɢ ɩɪɨɢɡ-
ɜɟɞɟɧɢɟ dx·dy·dz·dp
x
·dp
y
·dp
z
ɨɤɚɠɟɬɫɹ ɦɟɧɶɲɟ h
3
. Ɍɚɤ ɤɚɤ ɷɬɨ ɩɪɨɢɡɜɟɞɟɧɢɟ
ɜɵɪɚɠɚɟɬ ɷɥɟɦɟɧɬ ɨɛɴɟɦɚ ɲɟɫɬɢɦɟɪɧɨɝɨ ɮɚɡɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɬɨ ɨɬɫɸɞɚ
ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɡɥɢɱɧɵɦ ɷɥɟɦɟɧɬɚɦ ɨɛɴɟɦɚ ɲɟɫɬɢɦɟɪɧɨɝɨ ɮɚɡɨɜɨɝɨ
ɩɪɨɫɬɪɚɧɫɬɜɚ ɛɭɞɭɬ ɨɬɜɟɱɚɬɶ ɪɚɡɥɢɱɧɵɟ ɤɜɚɧɬɨɜɵɟ ɫɨɫɬɨɹɧɢɹ
ɦɢɤɪɨɱɚɫɬɢɰɵ ɥɢɲɶ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɪɚɡɦɟɪ ɷɬɢɯ ɷɥɟɦɟɧɬɨɜ ɨɛɴɟɦɚ ɧɟ
ɦɟɧɶɲɟ h
3
. ɉɨɷɬɨɦɭ ɜ ɤɜɚɧɬɨɜɨɣ ɫɬɚɬɢɫɬɢɤɟ ɡɚ ɷɥɟɦɟɧɬɚɪɧɭɸ ɹɱɟɣɤɭ
ɲɟɫɬɢɦɟɪɧɨɝɨ ɮɚɡɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɩɪɢɧɢɦɚɟɬɫɹ ɨɛɴɟɦ, ɪɚɜɧɵɣ
¨Ƚ = ¨Ƚ
V
¨Ƚ
Ɋ
= h
3
. (3.3)
Ⱦɥɹ ɫɜɨɛɨɞɧɵɯ ɦɢɤɪɨɱɚɫɬɢɰ, ɞɥɹ ɤɨɬɨɪɵɯ ¨Ƚ
V
= V, ɷɥɟɦɟɧɬ ɬɪɟɯ-
ɦɟɪɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɢɦɩɭɥɶɫɨɜ ɪɚɜɟɧ
¨Ƚ
Ɋ
= h
3
/V (3.4)
Ʉɚɠɞɨɦɭ ɬɚɤɨɦɭ ɷɥɟɦɟɧɬɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɜɚɧɬɨɜɨɟ ɫɨɫɬɨɹɧɢɟ, ɨɬ-
ɥɢɱɢɦɨɟ ɨɬ ɞɪɭɝɢɯ ɫɨɫɬɨɹɧɢɣ. ɉɪɨɰɟɫɫ ɞɟɥɟɧɢɹ ɮɚɡɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɧɚ
ɹɱɟɣɤɢ ɤɨɧɟɱɧɨɣ ɜɟɥɢɱɢɧɵ (h
3
ɢɥɢ h
3
/V) ɧɚɡɵɜɚɸɬ ɤɜɚɧɬɨɜɚɧɢɟɦ ɮɚɡɨɜɨɝɨ
ɩɪɨɫɬɪɚɧɫɬɜɚ.
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