Work Function of Materials

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Work Function of Materials

A natural barrier prevents electrons from leaking out from the surface of materials. This barrier is termed the work function (φ) and has a value of a few eV.The sum E_F(Fermi energy) and φ (Work function) for metals is often of ~10 eV.

Table 4959a. Work function of some transition metal nitride compounds obtained with methods of MOS capacitor V_fb (and FN tunnelling).

Transition metal nitride	Dielectrics	φ (eV)	Method
NbSiN	HfO₂	4.8	V_fb
NbSiN	SiO₂	4.7	V_fb
NbN	HfO₂	4.9	V_fb
NbN	SiO₂	4.7	V_fb
MoN	SiO₂	4.7-5.33	V_fb
TaSiN	HfO₂	4.4-4.5	V_fb
TaN	HfO₂	4.34-4.8	V_fb
TaN	SiO₂	4.4-4.7	V_fb
TaN	HfO₂	4.4-4.65	V_fb
HfN	HfO₂	4.75-4.8	V_fb
HfN	SiO₂	4.65-4.7	V_fb
ZrN	SiO₂	4.0-4.9	V_fb + FN
TiAlN	SiO₂	4.36-5.1	V_fb
TiN	Al₂O₃	4.85-5.2	V_fb
TiN	SiO₂	4.15-5.10	V_fb + FN

Table 4959b. Operating parameters and characteristics of electron sources.

Type of source	Tungsten thermionic	LaB₆ thermionic	Schottky emission	Cold field emission
Material	W	LaB₆	ZrO/W	W
d_s (µm)	≈40	≈10	≈0.02	≈0.01
ΔE (eV)	1.5	1.0	0.5	0.3
φ (eV)	4.5	2.7	2.8	4.5
T (K)	2700	1800	1800	300
E (V/m)	Low	Low	≈10⁸	>10⁹
J_e (A/m²)	≈10⁴	≈10⁶	≈10⁷	≈10⁹
β (Am^-2/sr^-1)	≈10⁹	≈10¹⁰	≈10¹¹	≈10¹²
Vacuum (Pa)	<10^-2	<10^-4	<10^-7	≈10^-8
Lifetime (hours)	100	1000	10⁴	10⁴

** d_s -- Effective (or virtual) source diameter; ΔE -- Energy spread of the electron beam; φ -- Work function; T -- Operating temperature; E -- Electric field; J_e -- current density of electron beam; β -- Electron-optical brightness at the cathode.

Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

Work Function of Materials