Page 176 - Electrical Properties of Materials

158 Semiconductors

Further, there are two reaction pathways for GaN deposition,

GaCl(g) + NH 3 (g) = GaN(s) + HCl(g) + H 2 (g)
3GaCl(g) + 2NH 3 (g) = 2GaN( s) + GaCl(g) + 3H 2 (g).

The snag in this process is that the decomposition of ammonia is only about
◦
3–4% even at a substrate temperature of 950 C, and the excess H 2 and HCl
are no help in the reaction and encourage GaN deposition in other parts of
the apparatus. There is also the familiar problem of no readily available, GaN
substrate, so sapphire ( Al 2 O 3 ) is usual, but ZnO, SiC, and Si have been used
frequently. As well as threading dislocations from the lattice mismatch, there
are also stacking dislocations caused by uneven growth. The main results re-
ported so far have been with layers 10–100 μm thick grown in a few hours,
which have produced successful LEDs and lasers. Some layers have been
grown up to 300 μm. A major interest is getting free-standing GaN films by
removing the substrate. One way of doing this is by focusing a laser through
the layer on to the sapphire substrate, and by heating it at several points in-
ducing it to crack off. Other substrates such as Si can be etched away with
HCl. SiC can be removed by ion etching in SF 6 . A very direct method for any
substrate is mechanical abrasion with diamond impregnated cloths or a slurry.
There is a lot of work going on to improve GaN quality and one possible
route to success is by chemical or heat treating free-standing slices for further
epitaxy by one of these methods.

Exercises

8.1. Indicate the main steps (and justify the approximations) Calculate (i) the energy gap between the valence and con-
used in deriving the position of the Fermi level in intrinsic duction bands, and (ii) the effective mass of electrons at the
semiconductors. How near is it to the middle of the gap in bottom of the conduction band.
GaAs at room temperature? The energy gap is 1.4 eV and Assume that the Fermi level is halfway between the valence
the effective masses of electrons and holes are 0.067m 0 and and conduction bands.
0.65m 0 respectively.
8.4. The variation of the resistivity of intrinsic germanium
8.2. Show that the most probable electron energy in the with temperature is given by the following table:
1
conduction band of a semiconductor is kT above the bottom T(K) 385 455 556 714
2
of the band (assume that the Fermi level is several kT below ρ( m) 0.028 0.0061 0.0013 0.000274
the conduction band). Find the average electron energy.
It may be assumed, as a rough approximation, that the
hole and electron mobilities both vary as T –3/2 , and that the
8.3. In a one-dimensional model of an intrinsic semicon-
forbidden energy gap, E g , is independent of temperature.
ductor the energy measured from the bottom of the valence
band is (i) Determine the value of E g .
2 2
2
k 1 (k – k 1 ) 2
E = + . (ii) At about what wavelength would you expect the onset of
3m 0 m 0 optical absorption?
This is an approximate formula accurate only in the vicinity
of the minimum of the conduction band, which occurs when 8.5. What is the qualitative difference between the absorp-
k = k 1 = π/a,where a the lattice spacing is 0.314 nm. The tion spectrum of a direct gap and that of an indirect gap
Fermi energy is at 2.17 eV. semiconductor?