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Diamond and graphite properties

The electronic configuration of carbon is 1s22s22p2, i.e. with four valence electrons spread in the s and p orbitals. In order to create covalent bonds in diamond, the s orbital mixes with the three p orbitals to form sp3 hybridization. The four valence electrons are thus equally distributed among the sp3orbitals, while each orbital points to one of the four corners of a tetrahedron. The tetrahedral structure, together with the highly directed charge density, give strength and stability to the bonds. Consequently, all the bonds in diamond are of the same length (1.54 $\AA$), with the same bond angle (109.47o).

Natural diamond can be divided into four types, according to the percentage and kind of impurities they contain, mainly nitrogen and boron. Type IIa diamond is the purest natural diamond and contains very few nitrogen atoms, of the order of 1018 cm-3, while the atomic density of diamond is 1.77 $\times 10^{23}$ cm-3. It has a high electronic mobility of 1800 cm2/V sec at room temperature, compared to 1500 cm2/V sec in silicon. The donor level associated with nitrogen lies relatively deep, at $\sim$ 1.7 eV, while the band gap in diamond is 5.47 eV. Diamond is an insulator at room temperature, with a resistivity larger than 10 $^{12} \ \Omega$ cm.

Type IIb natural diamond contains boron, with a density of 1017cm-3. It has a p-type conductivity, with an activation energy of 0.37 eV. The hole mobility measured at room temperature is $\sim$ 1500 cm2/V sec, compared to 450 cm2/V sec in silicon.

In Type Ib natural diamond the concentration of nitrogen is $\sim 5
\times 10 ^{18}$ cm-3, with a resistivity similar to that of type IIa diamond at room temperature, but much lower at high temperature. A very low electronic mobility was measured at room temperature, of the order of 100 cm2/V sec.

Finally, type Ia natural diamond has the highest concentration of nitrogen, namely $\sim 10^{20}$ cm-3. However the nitrogen atoms can appear not only as substitutional impurities but also as aggregates in the form of platelets or adjacent pairs. In that case, in addition to the 1.7 eV energy level, another level at $\sim$ 4 eV below the conduction band exits.

In the graphite crystal, the s orbital mixes with two p orbitals only, and each of the new three sp2 orbitals points to one of the three vertices of a triangle which lies in the x-y plane (for instance). Three electrons occupy these orbitals and one electron stays in the pz orbital which is directed perpendicular to the x-y plane. Hence, the carbon atoms are bonded by three $\sigma$bonds (the charge density lies between two atoms) and one $\pi$ bond (the charge density is concentrated above and under the x-y plane, perpendicular to the atomic bond). Since there is no preference as to which atom the pz-electron should bond to, the bond formed ($\pi$bond) with all three neighbors is weaker than the $\sigma$ bonds, this electron is more free to move and contributes to conduction. Furthermore, the $\pi$ bond stabilizes the structure and ``locks'' it in the plane. The whole crystal is made of sheets held together by weak Van der Waals forces, separated by a distance of 3.40 Å. This gives softness to the structure [1,2].

The stable bonding configuration of carbon at NTP is graphite, as shown in figure 2.1, with an energy difference between the graphite and the diamond of $\approx$ 0.02 eV per atom. Due to the high energetic barrier between the two phases of carbon, the transition from diamond to the stablest phase of graphite at normal conditions is very slow. This transition can also occurs more rapidly, when diamond is exposed to ion bombardment or high temperature for example. Due to the high anisotropy in the graphite structure compared to that of diamond, the electronic, mechanical and optical properties of these two phases of carbon are very different. In table 2.1 few properties of diamond and graphite crystals are presented. In the column related to graphite, the in-plane properties appears on the left and the transverse one on the right.

Figure: P, T phase diagram of carbon reproduced from ref. [3]
\begin{figure}\centerline{\epsfxsize=12.0cm \epsfbox{}}

Table 2.1: Properties of diamond and graphite.


Graphite Diamond
Lattice constant (RT) [$\AA$] 2.462 6.708 3.567
Bond length (RT) [$\AA$] 1.421 1.545
Atomic density [cm-3] 1.14 $\times 10^{23}$ 1.77 $\times 10^{23}$
Thermal conductivity [W/cm-K] 30 0.06 25
Debye temperature [K] 2500 950 1860
Electron mobility [cm2/V-sec] 20 $\times 10^3$ 100 1800
Hole mobility [cm2/V-sec] 15 $\times 10^3$ 90 1500
Melting point K 4200 4500
Band gape [eV] -0.04 5.47


next up previous contents
Next: Ion implantation Up: No Title Previous: Introduction
David Saada