# Why metals more dense than semiconductors?

1. May 20, 2006

this question was in my material science exam .
by the way i'm not very good at this subject

2. May 20, 2006

### Staff: Mentor

Not all metals have greater density than semiconductors, Si (2.330 g/cc) and Ge (5.323 g/cc). The group 1 and most 2 elements have lower density than Ge, several have lower density than Si.

See - http://www.webelements.com/webelements/properties/text/image-balls/density.html

Besides increasing atomic mass, the crystal structure determines the density, i.e. the lattice parameters or interatomic spacing.

Si: Space group: Fd-3m (Space group number: 227)
http://www.webelements.com/webelements/elements/text/Si/xtal.html
Structure: diamond
Cell parameters:
a: 543.09 pm
b: 543.09 pm
c: 543.09 pm

Ge: Space group: Fm-3m (Space group number: 225)
http://www.webelements.com/webelements/elements/text/Ge/xtal.html
Structure: ccp (cubic close-packed)
Cell parameters:
a: 565.75 pm
b: 565.75 pm
c: 565.75 pm

Fe: Space group: Im-3m (Space group number: 229)
Structure: bcc (body-centred cubic)
Cell parameters:
a: 286.65 pm
b: 286.65 pm
c: 286.65 pm

Ni:Space group: Fm3m (Space group number: 225)
Structure: ccp (cubic close-packed)
Cell parameters:
a: 352.4 pm
b: 352.4 pm
c: 352.4 pm

Look at crystal structures -
http://www.webelements.com/webelements/elements/text/periodic-table/xtal.html
Click on particular element in table to see crystallographic information.

3. May 23, 2006

### Finestructure

A general quick and dirty formula

Consider the equation for the density:

$$\rho=\frac{An}{N_AZ}$$

Where
$$\rho$$ = the density

n = the density of electrons in the conduction band

A = atomic mass, consider this to be a constant

$$N_A$$= Avogadro´s number

Z = valence, consider this to be a constant.

The key is n, the density of electrons in the conduction band. For metals, this is much larger than for semiconductors. In fact that´s the main difference between semiconductors and metals.

I´ll admit this is not a very satisfactory way of doing it, but I really think this is what they´re looking for. This equation allows you to compare metals and semiconductors on the same level since the atomic mass, valence and in a way, the cell structure are constants.

Now if you wanted to go further you run into problems because elemental semiconductors tend to form covalent bonds which are very directional bonds. Thus you would be forced to consider the cell structure. But in the process, you would loose the generality since metals don´t generally have the same cell structure as semiconductors. As the previous post demonstrates you begin to compare apples to oranges.

Last edited: May 23, 2006
4. May 23, 2006

### Gokul43201

Staff Emeritus
Where did you find this equation ?

It certainly looks like you are applying it beyond its range of applicability.

By your analysis, if the density is proportional to n, then metals should be many, many orders of mangitude more dense than insulators - that you would see the same range of magnitudes in density as you see in electrical conductivity. This is certainly not true !

In fact, the statement that metals are more dense than semiconductors itself is fallacious in the absence of further clarification.

Last edited: May 23, 2006