520
21 Diodes
Table 21.2 Values of the work function W m of various metals
Z
Element
W m (eV)
Z
Element
W m (eV)
Z
Element
W m (eV)
3
Li
2.4
37
Rb
2.1
64
Gd
3.1
4
Be
3.4
38
Sr
2.59
65
Tb
3.0
5
B
4.5
39
Y
3.1
66
Dy
–
6
C
4.8
40
Zr
3.8
67
Ho
–
12
Mg
3.66
41
Nb
4.3
68
Er
–
13
Al
4.2
42
Mo
4.2
69
Tm
–
14
Si
4.2
44
Ru
4.71
70
Yb
–
19
K
2.2
45
Rh
4.6
71
Lu
3.3
20
Ca
2.87
46
Pd
5.0
72
Hf
3.9
21
Sc
3.5
47
Ag
4.7
73
Ta
4.1
22
Ti
4.1
48
Cd
4.0
74
W
4.55
23
V
4.3
49
In
4.12
75
Re
5.0
24
Cr
4.4
50
Sn
4.3
76
Os
4.8
25
Mn
3.89
51
Sb
4.1
77
Ir
4.6
26
Fe
4.4
52
Te
4.8
78
Pt
5.3
27
Co
5.0
55
Cs
2.14
79
Au
4.8
28
Ni
4.9
56
Ba
2.5
80
Hg
4.49
29
Cu
4.5
57
La
3.5
81
Tl
3.8
30
Zn
4.3
58
Ce
2.9
82
Pb
4.0
31
Ga
4.2
59
Pr
-
83
Bi
4.4
32
Ge
4.8
60
Nd
3.2
90
Th
3.5
33
As
5.1
62
Sm
2.7
92
U
3.6
34
Se
5.9
63
Eu
2.5
(a)
(b)
Fig. 21.3 Schematic band diagram of a metal-semiconductor junction that is dominated by bulk properties of the
semiconductor. a no contact, b metal and semiconductor in contact. w denotes the width of the depletion layer. Outside
the depletion layer the semiconductor is neutral. F B,n denotes the Schottky barrier height, V bi denotes the built-in voltage
(here V bi > 0)
forms at the interface. The subscript ‘n’ stands for the contact on an n-type semiconductor. Surface/interface effects such as non-matching bonds, surface states, etc. are neglected at this point. In the
semiconductor there exists a positively charged region that is called the depletion layer or space-charge
region [1689]. Its extension (w in Fig. 21.3b) and properties will be discussed in Sect. 21.2.2. The space
charge region in the metal is very thin due to the small screening length.
For a contact on a p-type semiconductor the barrier F Bp (to the valence band) is (see Fig. 21.4d)
21 Diodes
Table 21.2 Values of the work function W m of various metals
Z
Element
W m (eV)
Z
Element
W m (eV)
Z
Element
W m (eV)
3
Li
2.4
37
Rb
2.1
64
Gd
3.1
4
Be
3.4
38
Sr
2.59
65
Tb
3.0
5
B
4.5
39
Y
3.1
66
Dy
–
6
C
4.8
40
Zr
3.8
67
Ho
–
12
Mg
3.66
41
Nb
4.3
68
Er
–
13
Al
4.2
42
Mo
4.2
69
Tm
–
14
Si
4.2
44
Ru
4.71
70
Yb
–
19
K
2.2
45
Rh
4.6
71
Lu
3.3
20
Ca
2.87
46
Pd
5.0
72
Hf
3.9
21
Sc
3.5
47
Ag
4.7
73
Ta
4.1
22
Ti
4.1
48
Cd
4.0
74
W
4.55
23
V
4.3
49
In
4.12
75
Re
5.0
24
Cr
4.4
50
Sn
4.3
76
Os
4.8
25
Mn
3.89
51
Sb
4.1
77
Ir
4.6
26
Fe
4.4
52
Te
4.8
78
Pt
5.3
27
Co
5.0
55
Cs
2.14
79
Au
4.8
28
Ni
4.9
56
Ba
2.5
80
Hg
4.49
29
Cu
4.5
57
La
3.5
81
Tl
3.8
30
Zn
4.3
58
Ce
2.9
82
Pb
4.0
31
Ga
4.2
59
Pr
-
83
Bi
4.4
32
Ge
4.8
60
Nd
3.2
90
Th
3.5
33
As
5.1
62
Sm
2.7
92
U
3.6
34
Se
5.9
63
Eu
2.5
(a)
(b)
Fig. 21.3 Schematic band diagram of a metal-semiconductor junction that is dominated by bulk properties of the
semiconductor. a no contact, b metal and semiconductor in contact. w denotes the width of the depletion layer. Outside
the depletion layer the semiconductor is neutral. F B,n denotes the Schottky barrier height, V bi denotes the built-in voltage
(here V bi > 0)
forms at the interface. The subscript ‘n’ stands for the contact on an n-type semiconductor. Surface/interface effects such as non-matching bonds, surface states, etc. are neglected at this point. In the
semiconductor there exists a positively charged region that is called the depletion layer or space-charge
region [1689]. Its extension (w in Fig. 21.3b) and properties will be discussed in Sect. 21.2.2. The space
charge region in the metal is very thin due to the small screening length.
For a contact on a p-type semiconductor the barrier F Bp (to the valence band) is (see Fig. 21.4d)