Three different kinds of crystal structures

face centered cubic(fcc)

body centered cubic(bcc)

and hexagonal close packed(hcp) structures with eight valence electrons in each primitive unit cell were studied.In th

E

F

ramework of free electron approximation

their Fermi level

E

F

were determined by Fermi sphere according to the theory of free electron gas

and the average-bond-energies

E

m

were calculated by free electronic band model.The calculated results of

E

F

and

E

m

indicate that the average bond energies

E

m

of three different crystal structures (therefore their electron densities are different) correspond to their Fermi levels

E

F

respectively.In the semiconductor energy band

the average bond energy

E

m

is defined as th

E

m

id point of the energy gap between

E

b

(bonding orbital energy) which is the avergage valence band level of th

E

F

our highest valence band levels

and

E

a

(anti bonding orbital energy) which is the average conduction band level of th

E

F

ive lowest conduction band levels in the whole Brillouin zone eigenvalues.It is the reference energy level in our theoretical calculation of heterojunction band offset.Therefore

the relationship between

E

F

and

E

m

found here is helpful to understand the physical concept of average-bond-energy

E

m

and the reason why it aligns at the two sides of the heterojunction interface.It also suggests a new method to calculate th

E

F

ermi level

E

F

of free electron systems through free electronic band model.