Tarea #1 Dispositivos
Semiconductores
JUAN HERÓN RODRÍGUEZ RESÉNDIZ
LUIS EDUARDO ARENAS DESEANO
Agosto-Diciembre 2021 INAOE | Dispositivos Semiconductores | 21/09/2021
Ejercicio 6
Constantes y tablas de masa efectiva
masa efectiva para la densidad de estados a 300 K
Ge
Si
GaAs
mn*
0.55
1.18
0.066
mp*
0.36
0.81
0.52
kb(J)
kb(eV)
masa electron vacio
h(J*s)
h(eV*s)
1.38E-23
8.60E-05
9.11E-31
6.626E-34
4.14E-15
Valores obtenidos de Eg
Elemento
Si
Si
Si
Si
Ge
Ge
Ge
Ge
GeAs
GeAs
GeAs
GeAs
Si
Temperatura(K) Eg(0) (eV) (banda prohibida a 0 K)
300
400
500
600
300
400
500
600
300
400
500
600
77
1.1660
1.1660
1.1660
1.1660
0.7437
0.7437
0.7437
0.7437
1.5190
1.5190
1.5190
1.5190
1.1660
alfa
(meV/K)
beta (K)
4.73E-04
636
4.73E-04
636
4.73E-04
636
4.73E-04
636
4.77E-04
235
4.77E-04
235
4.77E-04
235
4.77E-04
235
5.41E-04
204
5.41E-04
204
5.41E-04
204
5.41E-04
204
4.73E-04
636
Eg (eV)
1.1205E+00
1.0929E+00
1.0619E+00
1.0282E+00
6.6346E-01
6.2351E-01
5.8146E-01
5.3805E-01
1.4224E+00
1.3757E+00
1.3269E+00
1.2768E+00
1.1621E+00
Valores obtenidos de Nv
Elemen Temperatura me*(masa efectiva portadores)
to
(K)
(mp*)
kb(J)
1.38ESi
300
0.81
23
1.38ESi
400
0.81
23
1.38ESi
500
0.81
23
1.38ESi
600
0.81
23
1.38EGe
300
0.36
23
1.38EGe
400
0.36
23
1.38EGe
500
0.36
23
1.38EGe
600
0.36
23
1.38EGaAs
300
0.52
23
1.38EGaAs
400
0.52
23
1.38EGaAs
500
0.52
23
1.38EGaAs
600
0.52
23
8.60ESi
77
0.81
05
h(J*s)
6.626E34
6.626E34
6.626E34
6.626E34
6.626E34
6.626E34
6.626E34
6.626E34
6.626E34
6.626E34
6.626E34
6.626E34
4.14E15
Nv(m^3)
1.83E+
25
2.81E+
25
3.93E+
25
5.17E+
25
5.42E+
24
8.34E+
24
1.17E+
25
1.53E+
25
9.40E+
24
1.45E+
25
2.02E+
25
2.66E+
25
1.52E04
Nv(cm^3)
1.8283E+
19
2.8149E+
19
3.9339E+
19
5.1713E+
19
5.4172E+
18
8.3404E+
18
1.1656E+
19
1.5322E+
19
9.4043E+
18
1.4479E+
19
2.0235E+
19
2.6600E+
19
1.5212E10
Valores obtenidos de Nc
Elemen Temperatura me*(masa efectiva electron)
to
(K)
(me*)
Si
300
1.18
Si
400
1.18
Si
500
1.18
Si
600
1.18
Ge
300
0.55
Ge
400
0.55
Ge
500
0.55
Ge
600
0.55
GaAs
300
0.066
GaAs
400
0.066
GaAs
500
0.066
GaAs
600
0.066
77
1.18
Si
kb(J)
h(J*s)
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
1.38E- 6.626E23
34
8.60E4.14E05
15
Nc(m^3)
3.21E+2
5
4.95E+2
5
6.92E+2
5
9.09E+2
5
1.02E+2
5
1.57E+2
5
2.20E+2
5
2.89E+2
5
4.25E+2
3
6.55E+2
3
9.15E+2
3
1.20E+2
4
2.67E04
Nc(cm^3)
3.2147E+
19
4.9494E+
19
6.9170E+
19
9.0927E+
19
1.0230E+
19
1.5750E+
19
2.2011E+
19
2.8934E+
19
4.2525E+
17
6.5471E+
17
9.1498E+
17
1.2028E+
18
2.6747E10
Valores obtenidos de ni
Elemento
Si
Si
Si
Si
Ge
Ge
Ge
Ge
GeAs
GeAs
GeAs
GeAs
Si
Temperatura
300
400
500
600
300
400
500
600
300
400
500
600
77
Eg(eV)
kb(eV)
ni(cm^-3)
1.1205E+00
8.60E-05
8.9884E+09
1.0929E+00
8.60E-05
4.7081E+12
1.0619E+00
8.60E-05
2.2637E+14
1.0282E+00
8.60E-05
3.2289E+15
6.6346E-01
8.60E-05
1.9400E+13
6.2351E-01
8.60E-05
1.3285E+15
5.8146E-01
8.60E-05
1.8547E+16
5.3805E-01
8.60E-05
1.1458E+17
1.4224E+00
8.60E-05
2.1347E+06
1.3757E+00
8.60E-05
6.3748E+09
1.3269E+00
8.60E-05
8.5720E+11
1.2768E+00
8.60E-05
2.3964E+13
1.1621E+00
8.60E-05
1.5793E-48
Ejercicio 8
Resultados obtenidos de Ei
Temperatura(k) Ei - (Eg/2) Ei = (Ei - Eg/2) + Eg/2 Eg/2
Ei - Eg/2
77 -0.001869
0.57916
0.58103 -0.001869
300 -0.007280
0.55298
0.56026 -0.007280
400 -0.009707
0.53677
0.54647 -0.009707
Ejercicio 9
Constantes y formulas utilizadas.
Silicio (Si)
Constantes
ni(cm^-3)
k (eV)
Temperatura(k)
Ei = Eg/2(eV) (300k)
Eg(eV) (300k)
1.00E+10
8.60E-05
300
0.56
1.12
Formulas
n*p = ni^2
ND = n
n = ni exp(Ef-Ei/k*T)
Caso (1) con ND = n
ND=n (cm^-3) p
Tipo n o p
1.00E+12
1.00E+08 tipo n
1.00E+16
1.00E+04 tipo n
1.00E+18
1.00E+02 tipo n
5.00E+19
2.00E+00 tipo n
Ef -Ei = k*T*ln(n/ni) Ef (eV) = (Ef-Ei) + Ei Ec (eV) = Eg - Ef
0.118813
0.678813
0.441187
0.356440
0.916440
0.203560
0.475254
1.035254
0.084746
0.576184
1.136184
-0.016184
Caso (2) con NA = p
NA = p (cm^-3) n
Tipo n o p
1.00E+12
1.00E+08 tipo p
1.00E+16
1.00E+04 tipo p
1.00E+18
1.00E+02 tipo p
5.00E+19
2.00E+00 tipo p
Ef - Ei = k*T*ln(p/ni) Ef (eV) = Ei - (Ef -Ei) Ev (eV) = Eg - Ef
0.118813
0.441187
0.441187
0.356440
0.203560
0.203560
0.475254
0.084746
0.084746
0.576184
-0.016184
-0.016184
Ejercicio 9
Caso (1) ND = no
no = ND
Nc
Ec-Ef = k*T*ln(Nc/n0) Ef (eV) = (Ec-Ef) - Ec
1.00E+12
2.80E+19
0.442411
0.677589
1.00E+16
2.80E+19
0.204784
0.915216
1.00E+18
2.80E+19
0.085971
1.034029
5.00E+19
2.80E+19
-0.014959
1.134959
Caso (2) NA = po
po = NA
Nv
Ef-Ev = k*T*ln(Nv/p0) Ef (eV) = (Ef-Ev) + Ev
1.00E+12
1.04E+19
0.416859
0.416859
1.00E+16
1.04E+19
0.179232
0.179232
1.00E+18
1.04E+19
0.060419
0.060419
5.00E+19
1.04E+19
-0.040512
-0.040512