Основы физики и химии полупроводников - 38 стр.

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kT
E
p
e
h
kTm
p
P
S
'
3
2
3
)2(
2
, (3.24)
ɝɞɟ m
p
ɷɮɮɟɤɬɢɜɧɚɹ ɦɚɫɫɚ ɞɵɪɨɤ. ȼɟɥɢɱɢɧɚ ȝ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɛɭɞɟɬ
ɪɚɜɧɚ ɪɚɫɫɬɨɹɧɢɸ ɨɬ ɞɧɚ ɡɨɧɵ ɩɪɨɜɨɞɢɦɨɫɬɢ ɞɨ ɭɪɨɜɧɹ Ɏɟɪɦɢ. ȼ
ɩɨɤɚɡɚɬɟɥɟ ɷɤɫɩɨɧɟɧɬɵ ɜ ɮɨɪɦɭɥɟ (3.24) ɫɬɨɢɬ ɜɟɥɢɱɢɧɚ¨E – ȝ =
= –(¨E + ȝ). ɂɡ ɫɨɨɬɧɨɲɟɧɢɣ (3.24, 3.22) ɫɥɟɞɭɟɬ, ɱɬɨ ɤɨɧɰɟɧɬɪɚɰɢɹ
ɫɜɨɛɨɞɧɵɯ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ ɜ ɞɚɧɧɨɣ ɡɨɧɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɫɬɨɹɧɢɟɦ
ɷɬɨɣ ɡɨɧɵ ɨɬ ɭɪɨɜɧɹ Ɏɟɪɦɢ. ɑɟɦ ɛɨɥɶɲɟ ɷɬɨ ɪɚɫɫɬɨɹɧɢɟ, ɬɟɦ ɧɢɠɟ
ɤɨɧɰɟɧɬɪɚɰɢɹ ɧɨɫɢɬɟɥɟɣ.
Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɨɬɞɟɥɶɧɨ ɤɨɧɰɟɧɬɪɚɰɢɸ ɧɨɫɢɬɟɥɟɣ ɜ
ɫɨɛɫɬɜɟɧɧɵɯ ɢ ɩɪɢɦɟɫɧɵɯ ɩɨɥɭɩɪɨɜɨɞɧɢɤɚɯ.
ȼ ɫɨɛɫɬɜɟɧɧɨɦ ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ ɤɨɧɰɟɧɬɪɚɰɢɹ ɷɥɟɤɬɪɨɧɨɜ ɜ ɡɨɧɟ
ɩɪɨɜɨɞɢɦɨɫɬɢ ɪɚɜɧɚ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɪɨɤ ɜ ɜɚɥɟɧɬɧɨɣ ɡɨɧɟ n
i
= p
i
,
ɩɨɷɬɨɦɭ, ɩɪɢɪɚɜɧɹɜ ɩɪɚɜɵɟ ɱɚɫɬɢ ɪɚɜɟɧɫɬɜ (3.22) ɢ (3.24), ɩɨɥɭɱɢɦ
kT
E
p
kT
n
emem
PP
'
2
3
2
3
)()(
.
Ɉɬɤɭɞɚ
n
p
ɮ
m
m
kT
ȿ
ȿ ln
4
3
2
'
P
. (3.25)
ɂɬɚɤ, ɩɪɢ m
ɪ
= m
n
ɢ ɩɪɢ Ɍ = 0 Ʉ ɭɪɨɜɟɧɶ Ɏɟɪɦɢ ɜ ɫɨɛɫɬɜɟɧɧɨɦ
ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ ɩɪɨɯɨɞɢɬ ɬɨɱɧɨ ɩɨɫɟɪɟɞɢɧɟ ɡɚɩɪɟɳɟɧɧɨɣ ɡɨɧɵ. ɇɨ
ɷɮɮɟɤɬɢɜɧɵɟ ɦɚɫɫɵ ɷɥɟɤɬɪɨɧɨɜ ɢ ɞɵɪɨɤ ɜ ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ ɧɟ ɪɚɜɧɵ, ɤɚɤ
ɩɪɚɜɢɥɨ m
ɪ
> m
n
, ɢ ɩɨɷɬɨɦɭ ɭɪɨɜɟɧɶ Ɏɟɪɦɢ ɜ ɫɨɛɫɬɜɟɧɧɨɦ
ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ ɪɚɫɩɨɥɨɠɟɧ ɛɥɢɠɟ ɤ ɡɨɧɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɢ ɩɪɢ
ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɫɦɟɳɚɟɬɫɹ ɜɜɟɪɯ.
ɉɨɞɫɬɚɜɢɜ ɩɨɥɭɱɟɧɧɨɟ ɞɥɹ E
ɮ
ɜɵɪɚɠɟɧɢɟ (3.25) ɜ ɮɨɪɦɭɥɵ (3.22) ɢ
(3.24), ɩɨɥɭɱɢɦ ɞɥɹ ɤɨɧɰɟɧɬɪɚɰɢɢ ɫɜɨɛɨɞɧɵɯ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ ɜ
ɫɨɛɫɬɜɟɧɧɨɦ ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ ɨɤɨɧɱɚɬɟɥɶɧɨɟ ɜɵɪɚɠɟɧɢɟ
kT
E
pnii
emmhkTpn
2
4
3
3
2
3
)()2(2
'
S
. (3.26)
ɂɡ ɷɬɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ ɜɢɞɧɨ, ɱɬɨ ɪɚɜɧɨɜɟɫɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ
ɧɨɫɢɬɟɥɟɣ ɬɨɤɚ ɜ ɫɨɛɫɬɜɟɧɧɨɦ ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɲɢɪɢɧɨɣ
ɡɚɩɪɟɳɟɧɧɨɣ ɡɨɧɵ ɢ ɬɟɦɩɟɪɚɬɭɪɨɣ ɩɨɥɭɩɪɨɜɨɞɧɢɤɚ.
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɭɦɟɧɶɲɟɧɢɟ ¨ȿ ɫ 1,12 ɷȼ (ɤɪɟɦɧɢɣ) ɞɨ 0,08 ɷȼ
(ɫɟɪɨɟ ɨɥɨɜɨ) ɩɪɢ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɟɦɩɟɪɚɬɭɪɟ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ n
ɧɚ 9 ɩɨɪɹɞɤɨɜ. ɍɜɟɥɢɱɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɝɟɪɦɚɧɢɹ ɫɨ 100 Ʉɞɨ 600 Ʉ
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