2000 has been accepted as satisfactory in partial fulfillment of the requirement for the degree MASTER OF SCIENCE IN ELECTRICAL AND ELECTRONICS ENGINEERING on 19/0 I/2002. Proposed dependence of excess carrier lifetime on temperature. Calculated PL dependence on temperature under constant photo-excitation using previously proposed lifetime dependence on temperature.
Acknowledgement
Introduction
- Objective of the work
We will study the spontaneous and stimulated emission of erbium at different temperatures and excitation conditions. Room temperature conditions will be included in the concept of reverse energy transfer from erbium atoms.
1.2 Organization of the thesis
In chapter three, the introductory concepts of laser will be discussed to aid in the understanding of stimulated excitation and de-excitation mechanism. Mathematical model of excitation and de-excitation of Er in Si will be developed in chapter four.
Luminescence from Silicon
Direct and indirect bandgap
The recombination energy is released in the form of photons with energy corresponding to the bandgap energy. The electron must undergo a change in propagation constant, as well as in momentum and energy, for the transition, and the recombination energy is generally given as heat dissipated in the crystal lattice.
Luminescence from Silicon
- Impurity enhanced luminescence from Silicon
In indirect bandgap materials, recombination cannot occur directly, but through a recombination level within the bandgap or by involving a third particle such as a charge carrier or phonon. The recombination level through which the transition can occur can be introduced by impurity doping or by a lattice defect. through isovalent centers [7) and luminescence through rare earth impurities (RE) [8,9, I 0).
Excitation mechanism of Erbium in Silicon
They pointed out that after generating excess carriers by electrical or optical excitation, electrons from the conduction band recombine with holes in the valence band via Er-related levels within the Si band gap. The excitation rate is determined by the emission and collection rates of electrons and holes according to Er-related levels.
De-excitation mechanisms of Erbium in Silicon
21] have mathematically expressed this process by defining a lifetime related to the energy back transfer process as follows. Energy feedback can successfully explain the high-temperature quenching phenomenon of Er luminescence in Si.
Shockley-Read-Hall (SRH) generation -recombination kinetics
Hole trapping: The rate of recombination of holes on a trap level is proportional to the number of holes available and nllmber of electron-occupied trap centers. Hole release: The generation rate of holes due to this process is proportional to the number of empty trap sites.
Recent work on Erbium luminescence in Silicon
Priolo etc. [IS] suggested that thermalization of electrons bound in the conduction band is the cause of temperature quenching. They and Palm et al. [19] proposed that the non-radiative energy transfer process is the cause of temperature quenching.
Effect of short excitation pulse on Erbium luminescence in Silicon
[30] have shown that efficient and rapidly modulating LEDs can be fabricated upon exciting the Er ions in the depletion region of an oppositely biased p+-n+ junction. During operation, the Auger quenching within the depletion region is inhibited due to the absence of free carriers, but it suddenly comes into operation when, upon turning off the diode, the depletion region shrinks [16]. So far, very little work has been done on the possible realization of LASER from Er-doped Si.
[13] and it has been theoretically shown that a LASER can be obtained if an extremely efficient pumping mechanism can be used. They demonstrated that Er3+ ions are still excited at an appreciable rate even 50 Jis after the excitation pulse is turned off. From this phenomenon, they concluded that Er3+ ions in Si are excited by the recombination of carriers trapped in the forbidden gap state of Si. and supported the possibility of the involvement of bound excitons in the excitation process.
Laser Theory
- Emission and absorption
- Einstein relations
- Absorption of radiation
- Optical feedback
- Threshold conditions
- Lineshape function
- Stimulated emission from Erbium in Silicon
The populations of different energy levels of a system in thermal equilibrium are given by Boltzmann statistics. 324) where Nj is the population density of the energy level Ej, No is the total population density and gj is the degeneracy of the jth level. So to obtain amplification, we need to create a non-equilibrium distribution of atoms across different energy levels of the atomic system. Where the emitted photon moves along the axis of the system. amplified as it passes through the medium and is fed back by the mirrors.
With regard to population inversion, there will be a threshold value Nth = [NZ - (gz /g])N d th corresponding to ktil' In steady state mode [N z -(gz/g]) Nd remains equal to Nth regardless of the amount by which the threshold pump speed is exceeded. It can be shown that g(vs) =_1_, where Vs is the frequency at which the value of.
Mathematical Model for Erbium Luminescence
- Steady state excitation and de-excitation mechanism
- Time dependent rise of Erbium luminescence
- Time dependent electron occupied Erbium states
- Time dependent Erbium luminescence
- Decay profile of Erbium luminescence
- Stimulated emission from Erbium in Silicon
- Condition for LASER action - threshold
- A proposed laser device using Erbium doped Silicon
- Structure
- Formulation
Thus at steady state the number of excited Er atoms per unit volume is given by. In this case, both the number of electron-occupied Er sites and that of excited Er atoms are functions of time. Then the corresponding time-dependent Er luminescence can be determined by solving the rate equation of excited Er atoms.
As in section 4.2, both the number of electron-occupied Er sites and the number of excited Er atoms are time-varying. Correspondingly, stimulated emission rate is proportional to the number of excited Er atoms and power density.
Results and Discussion
Parameters for Erbium incorporated Silicon
The electron capture coefficient, Cn=anYth. The hole capture coefficient, cp=apYth where,. an =cross-sectional area of electron capture ap =cross-sectional area of hole capture m•=effective mass of electron or hole. For optical excitation, a 514.5 nm laser with a spot diameter of 3 mm and a penetration depth of 1 µm was used. During our calculation we neglected the value of the intrinsic carrier density as it is very small (cm3 at 3000 K) compared to typical optically generated.
This is due to the fact that only a fraction of optically generated carriers recombine through Erbium-related levels. However, the value is consistent with the fact that the Auger effect with free carriers is weaker in p-type Si than in n-type Si as suggested by [16].
Erbium luminescence as a function of excitation
But the stronger effect is the non-radiative energy back transfer that occurs at higher temperature [16, I 9]. Also at higher doping level, the contribution of level donor (or acceptor) level to thermally generated excess carrier density increases. An increase in excess carrier density leads to higher non-radiative decay rate via impurity Auger process with free carriers.
It has been shown experimentally in [16] that for similar background doping levels, the PL intensity obtained from p-type Si is greater than that from n-type Si. We have included this effect in our model by obtaining a smaller value of the Auger coefficient for the p-type material than that for the n-type material.
Erbium luminescence as a function of temperature
Such pattern of lifetime variation is expected due to small dissociation energy of free and bound excitons. The sample used in the experiment had an Er concentration of 8x 1018 per cm3. But with such a high concentration, not all the Er sites are electrically or optically active [20]. It is clear that using the proposed lifetime dependence on temperature excellent fit with the experimental data can be obtained.
The relatively slow decrease in PL intensity up to 90 °K can be attributed to Auger processes of impurities, while above this back transfer begins to dominate the non-radiative decay process.
Photoluminescence decay profile
As the impurity temperature increases, the Auger effect with free carriers and the reverse energy transfer increase, which increases the rate of nonradiative decay of excited Er atoms. Within the plot, the intensities have been normalized to their initial values to better illustrate the nature of the intensity decay. Als6 thermally generated carrier density increases, which in turn increases the impurity Auger process with free carriers.
As suggested by [16], the impurity Auger effects with free and bound carriers are weaker in p-type Si than in n-type Si. A higher decay rate of n-type Si is therefore expected, all other conditions being equal.
Effect of short excitation pulse on Erbium luminescence
Initially when a large number of Er atoms are available for excitation, the pumping rate is very high compared to decay rate. When the pumping rate is equal to the decay rate, the intensity is maximum, which is indicated by a light dashed line in the figure. After that, the pumping rate becomes smaller than the decay rate and PL intensity starts to decrease.
From our previous discussion it can be predicted that if we manage to increase the decay rate of excited Er, the problem regarding this extended rise can be overcome. Another way to increase the decay rate is to increase the excess carner density by increasing the excitation power.
Stimulated emission and absorption
To find out the value of (N2 - NIl required at the threshold, i.e. Ntll', the values of the following parameters are taken from Xie et al. Although the values used in [13] are said to be overly optimistic, we have discovered This shows that the required value of Nth is 4.3532x10J7 per cm3, indicated by a dotted line in Figure 5.15. Ignoring Pv below the threshold, we have calculated the value of the excess carrier density at the threshold, ntlJrUsing equation (4.5.I) and then calculated the corresponding current density using equation (4.6.2.3).
From ntllfSwe we increased the value of injected excess carrier density and the equations presented in sections 4.5 and 4.6.2 calculated the corresponding values of power density, Pv and current density, J. Although it was not possible for us to obtain the exact numerical value of output power for a particular injection.
Conclusion
Recommendation for future work
61 More research is needed on reducing luminescence quenching at higher temperatures to fabricate Si:Er optoelectronic devices that operate at room temperature. Although we suggested a way to reduce the effect in section 5.5, more research can be conducted in this area. In our study, we only performed a theoretical analysis of the possible achievement of laser from Er-doped Si.
In our analysis, we assumed that the beam remains completely confined within the Er-shelled region which is not practical. Study of Sil_,GexlSi:Er systems for good optical as well as electrical confinement can be carried out.
Bibliography
Priolo, “Effects of oxygen and defects on the deep-level properties of Er in crystalline Si,” Appl. Carey, "Erbium-Impurity Interaction and Its Effect on the 1.54 ~lm Luminescence of Er3+ in Crystalline Silicon," Appl. 22] Shun Lien Chuang, Physics of Optoelectronic Devices, 2nd ed., John Willy & Sons, New York, 1995.
Serna, “Temperature dependence and quenching processes of the intra-4f luminescence of Er in crystalline Si,” Phys. Spinella, “Mechanism and Performance of 13:54 Forward and Reverse Bias Electroluminescence from Er-doped Si Diodes,” J .
Appendix B
Expression for excited Erbium atoms considering stimulated emission and absorption
