# Exciton Recombination Mechanisms in General

| In chapter 5.1.3 several questions concerning exciton recombination mechanisms were asked:
|  | Why GaP? How about other III-V compound semiconductors?
|  | How about more exotic semiconductors? The II-VI system, organic semiconductors?
|  | Anything similar for elemental semiconductors? Afer all, putting Ge into Si also changes the potential locally.
|  | How about other defects, not necessarily isoelectronic ones? For example, ionized donors and acceptors also attract and possibly "bind" freee electrons or holes, respectively?
| Lets see about some answers. But first some more data to excitons in general

Excitons in Semiconductors

| First lets look at the binding energy of free excitons in various semiconductors
|  | The values for the effective masses, m* e and m*h (in units of the free electron mass) are included (compare with the values given before to see how literature values can differ).
|  | For completeness, we also give the numbers for er and the nominal exciton Bohr radius rX at which the particles would circle each other.
|  | We have kTroom » 25 meV; only exciton energies > 20 meV are usable; those are colored blue.
Material | m *e | m*h | er | Eb [meV] | rX [nm]
--- | --- | --- | --- | --- | ---
BN | 0.752 | 0.38 | 5.1 | 131 | 1.1
GaN | 0.20 | 0.80 | 9.3 | 25.2 | 3.1
GaAs | 0.063 | 0.50 | 13.2 | 4.4 | 12.5
InP | 0.079 | 0.60 | 12.6 | 6.0 | 9.5
GaSb | 0.041 | 0.28 | 15.7 | 2.0 | 23.2
GaP |  |  |  |  |
InAs | 0.024 | 0.41 | 15.2 | 1.3 | 35.5
InSb | 0.014 | 0.42 | 17.3 | 0.6 | 67.5
ZnS | 0.34 | 1.76 | 8.9 | 49.0 | 1.7
ZnO | 0.28 | 0.59 | 7.8 | 42.5 | 2.2
ZnSe | 0.16 | 0.78 | 7.1 | 35.9 | 2.8
CdS | 0.21 | 0.68 | 9.4 | 24.7 | 3.1
ZnTe | 0.12 | 0.6 | 8.7 | 18.0 | 4.6
CdSe | 0.11 | 0.45 | 10.2 | 11.6 | 6.1
CdTe | 0.096 | 0.63 | 10.2 | 10.9 | 6.5
HgTe | 0.031 | 0.32 | 21.0 | 0.87 | 39.3
Si |  |  |  | 7.5 |
|  | There is a definite correlation of the binding energy Eb with the bandgap as shown in the following figure. Since GaP was not contained in the origial data, an indication of its probable position is included.

How About Bound Excitons in Other III-V Semiconductors?

| There are a couple of other semiconductors where isoelectronic "dopant" atoms play some role:
|  | Bi replacing P in InP
|  | N, or N-N pairs, replacing P or As in GaAs1-xPx

Anything Similar for Elemental Semiconductors?

| Yes – at low temperatures!
|  | In Si, the radiative part of the recombination proceeds to about 85 % via (free) excitons at 85 K, and at 20 K it is close to 100 %.
|  | Recombination due to excitons bound to As+ donors have been obseved, too. The binding energy is about 6.5 meV.
|  | However, non-radiative recombination is still the major channel, so even at low tempertures Si is not a good emitter of light.

With frame

5.1.2 Recombination and Luminescence

5.1.3 Doping of Compound Semiconductors

© H. Föll (Semiconductors - Script)