spacer spacer Go to Kaye and Laby Home spacer
spacer
spacer spacer spacer
spacer
spacer
spacer
spacer spacer

You are here:

spacer

Chapter: 4 Atomic and nuclear physics
    Section: 4.3 Work function

spacer
spacer

spacer

« Previous Section

Next Section »

Unless otherwise stated this page contains Version 1.0 content (Read more about versions)

4.3 Work function

Energy required to extract an electron from a solid

The work function is the energy required to remove an electron from the highest filled level in the Fermi distribution of a solid so that it is stationary at a point in a field-free zone just outside the solid, at absolute zero. An estimate of the work function can be obtained thermionically from Richardson's equation

I = AT 2 exp(−/kT)

where I is the thermionic current, T the absolute temperature, k is Boltzmann's constant and A is a constant having the theoretical value 120 amp cm−2 deg−2. Since A contains the reflection coefficient, which varies with temperature, observed A values usually differ from the theoretical value. too varies very slightly with temperature, but for most metals the difference between at absolute zero and at room temperature is less than experimental errors.
      may also be estimated photoelectrically for metals. Einstein’s expression for the photoelectric effect is hv = e + E, where E is the kinetic energy of the ejected photoelectron. The photoelectric current J released when light of energy hv falls on the surface of a metal, for which the threshold frequency is given by hv0 = e (for then E = 0), is given by the Fowler equation

J = B(kT2).f{(hvhv0)/kT}

where f is a universal function of (hvhv0)/kT and B is constant provided that hv is near to hv0.
      The third common method of measuring is by the contact potential difference (c.p.d.) VAB that exists between the surfaces of two solids A and B of work functions A and B, when connected electrically, since

BA = eVAB

for the two solids at the same temperature. The method involves a prior knowledge of the work function of one of the solids if that of the other is to be measured absolutely.
      A fourth method involves the field emission of electrons when an external electric field F is applied. The field emission current density, J, is given by

   

J = 1.54 x 10−6

F2

 t2(y)exp[−6.83 × 107 3/2f(y)/F]

where f(y) and t(y) are slowly varying elliptic functions of F and .
     Typical errors of the tabulated quantities for the metals are 0.02 eV. Note that adsorbates or contaminants will usually reduce the measured and that different crystal faces of the same material have differing values of .


Work functions

Metal

Work function φ/eV

 Metal

Work function φ/eV

  

Photoelectric

 C.P.D.

 

Thermionic

Photoelectric

C.P.D.

             

Li     .    .    .    .    .

2.32

Nb   .    .    .    .    .

4.30

4.37

Na   .    .    .    .    .

2.36

2.46

Mo   .    .    .    .    .

4.33

4.49

4.21

K     .    .    .    .    .

2.30

2.01

Ta    .    .    .    .    .

4.33

4.30

4.22

Rb    .    .    .    .    .

2.05

W    .    .    .    .    .

4.55

4.55

4.55

Cs    .    .    .    .    .

1.95

1.82

Re    .    .    .    .    .

4.72

             

Be    .    .    .    .    .

3.91

Ti     .    .    .    .    .

4.10

4.33

4.20

Mg   .    .    .    .    .

3.61

Cr    .    .    .    .    .

4.60

4.44

Ca    .    .    .    .    .

2.87

Mn   .    .    .    .    .

4.08

Ba    .    .    .    .    .

2.52

2.35

Fe    .    .    .    .    .

4.60

4.16

  

  

  

Co   .    .    .    .    .

4.97

Zn    .    .    .    .    .

3.63

4.11

Ni    .    .    .    .    .

5.24

5.15

5.25

Cd   .    .    .    .    .

4.22

 

 

  

 

  

  

 

Zr    .    .    .    .    .

 4.00

Al    .    .    .    .    .

4.28

4.19

Hf    .    .    .    .    .

 3.65

Ga   .    .    .    .    .

4.35

 

 

  

   

In    .    .    .    .    .

4.08

Ru    .    .    .    .    .

4.71

4.73

  

 

  

Rh    .    .    .    .    .

4.72

Sn   .    .    .    .    .

4.28

4.43

Pd    .    .    .    .    .

5.40

Pb   .    .    .    .    .

4.25

3.83

Ir      .    .    .    .    .

4.57

 

 

  

Pt     .    .    .    .    .

5.36

5.63

Cu   .    .    .    .    .

4.65

4.51

 

 

 

 

Ag   .    .    .    .    .

4.26

4.29

Th    .    .    .    .    .

3.71

Au   .    .    .    .    .

5.10

5.28

U     .    .    .    .    .

3.47

3.47

3.63

             

As   .    .    .    .    .

4.79

C (dag) .    .    .    .

4.65–5.0

Sb   .    .    .    .    .

4.56

Si     .    .    .    .    .

4.95

4.75

Bi    .    .    .    .    .

4.34

Ge   .    .    .    .    .

5.15

4.83

  

  

 

 

 

  

 

Note: Values selected from the articles by J. C. Rivière, Solid State Surface Science (ed. Mino Green), Vol. 1, 1969 (Marcel Dekker, New York), and by J. Hölzl and F. K. Schulte, Springer Tracts in Modern Physics, 85, 1 (1979).


M.P. Seah

spacer


spacer
spacer
spacer spacer spacer

Home | About | Table of Contents | Advanced Search | Copyright | Feedback | Privacy | ^ Top of Page ^

spacer

This site is hosted and maintained by the National Physical Laboratory © 2017.

spacer