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Electro Optical Characterisation of Short Wavelength Semiconductor ...

Basic Concepts 1.2.2 Light in Crystal The interaction process **of** electromagnetic waves and matter can be studied in two different points **of** view; microscopic and macroscopic. energy Ec Ev Absorption Stimulated Emission Spontaneous Emission Figure 1.6: The three different processes possible when describing the interaction between light and matter: absorption, stimulated emission and spontaneous emission. EV is the energy **of** the valence band; EC energy **of** the conducting band. Microscopic Aspects The basic interaction mechanisms between light and matter are absorption, spontaneous emission and stimulated emission, as depicted in Fig. 1.6. These are transitions **of** charge carriers in the matter between different energy levels evoked by the photons. Different energy levels in a semiconductor material are determined by the band structures, see 1.4. The energy difference between the valence band and the conducting band is the band gap energy and is given by, ∆E = EC − EV = Eg. (1.5) The energy difference is a key value when dealing with the interaction between light and matter since the electron can only make transitions that involve an exchange **of** energy that equals ∆E. With having this picture in mind and assuming an extremely simplified two state model, the following cases are conceivable, 8 • Absorption. The electron can begin from its ground state and make a transition to its excited state by absorbing a photon with frequency ω = ∆E/. The photon disappears as a result **of** interaction meaning the energy in the amount **of** ∆E is transferred from the electromagnetic field to the electron such that the total energy **of** the whole system is conserved. • Stimulated Emission. If an incident photon with energy ∆E = ω hits an electron with its electron in the excited state it can induce with a certain probability a transition **of** the electron from the excited state to the ground state. In this process a second photon is created which is identical in momentum, energy, polarisation and phase to the incident one. This process can be used to amplify a photon field. It is therefore

Physics **of** **Semiconductor** Lasers the basic mechanism for all lasers (Light Amplification by Stimulated Emission **of** Radiation). Absorption and stimulated emission are closely related events. • Spontaneous Emission. This is when the excited atom emits a photon by releasing energy in the amount **of** ∆E by transitioning from its excited state to its ground state. In case **of** a laser the, gain is achieved if more photons **of** energy Eg leave the structure than enter it. This compensates the loss **of** energy due to spontaneous emission and nonradiative recombinations. This condition occurs in case **of** inversion, i.e., more carriers are in the excited than the ground state. This point is called laser threshold. Below the threshold, spontaneous emission dominates. Exactly at threshold, the semiconductor is transparent. Gain equals loss in this case (for detailed calculations see [36]). Above the threshold, stimulated emission dominates. This amplifies the light passing through. Absorption and stimulated emission are closely related events and absorption is the dominating **of** them both due to the fact that the electron population in the valence band exceeds that in the conducting band. Thus it would be **of** interest to calculate the condition **of** optical gain. This is obtained from the occupation probabilities **of** electrons **of** the energy Ec in the conduction band fc(Ec) and holes **of** energy Ev in the valence band fv(Ev). These are determined by the Fermi-Dirac statistics, with the quasi-Fermi levels Efc and Efv in the conduction band and the valence band respectively [37], fc(Ec) = 1 Ec−Efc k e B T + 1 and fv(Ev) = 1 Ev−Efv k e B T + 1 , (1.6) where kB is the Boltzmann constant and T is the temperature measured in Kelvin. If photons **of** energy E = hν = Ec + Ev + Eg impinge on the semiconductor **of** band gap Eg, they can be absorbed, creating electrons **of** energy Ec and holes **of** energy Ev at a rate Ra, Ra = B[1 − fc(Ec)][1 − fv(Ev)]ρ(E). (1.7) B is the transition probability and ρ(E) is the density **of** photons **of** energy E. It is **of** importance to be mentioned that the Fermi-Dirac statistics determines the statistical distribution **of** fermions. It is known that they obey the Pauli exclusion principle , i.e., no more than one particle my occupy the same quantum state at the same time. Thus [1 − fc(Ec)] delivers the probability that the electron state with the energy Efc is not occupied whereas [1 − fv(Ev)] implies the probability **of** a free hole state **of** energy Efv. Furthermore, the stimulated emission can occur at a rate Re, Stimulated emission dominates absorption if and only if Using Eqs. 1.7, 1.18 and 1.9 directly yields Re = Bfc(Ec)fv(Ev)ρ(E). (1.8) Re > Ra. (1.9) fc(Ec) + fv(Ev) > 1 (1.10) 9

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- Page 6 and 7: CONTENTS 4.2.1 Characterisation of
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ZnSe threshold current density valu

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Bibliography [1] N. G. Basov, O. N.

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BIBLIOGRAPHY [56] G. Snider, 1D Poi