Spontaneous emission control has been achieved in GaAs/AlGaAs quantum well lasers by the use of Bragg reflectors to define a micro-cavity perpendicular to the quantum wells. The room temperature emission is inhibited whilst below 130K there is an enhancement. These changes to the spontaneous recombination process directly effect the threshold current producing a 25% reduction at room temperature. Theoretical modeling of the lasers is in agreement with the experimental results and highlights the effect of the micro-cavity in altering the overlap of the electro-magnetic field with the quantum well dipole oscillators.
© 1998 Optical Society of America
Laser diodes are versatile and compact devices because the energy bands within semiconductor crystals allow the direct conversion of electrical energy into light. The presence of a broad band of electronic states does, however, limit the intrinsic efficiency of semiconductor lasers as spontaneous emission into a large number of electro-magnetic modes must be supported in order to produce single mode, coherent emission. Thus even within an ‘ideal’ laser with no non-radiative recombination or carrier leakage effects there is a minimum ‘threshold’ current due to spontaneous recombination. The use of low-dimensional, epitaxially grown, structures such as quantum wells can be used to alter the density of electronic momentum states and hence change the energy distribution of emission . The step-like density of states function of the quantum well produces a high density of states at the band edge which concentrates the charge carriers into the energy range over which population inversion is achieved. In a device context this causes a reduction in the spontaneous recombination current within quantum well lasers relative to bulk devices. The link between the spectral width of the spontaneous emission and the recombination current leads to an increase in laser threshold current with temperature. As the device temperature increases the Fermi-Dirac occupation function broadens and so increases the spontaneous recombination current. Direct observation of the spontaneous emission from quantum well lasers graphically indicates this spectral broadening and its direct link to the increased current with temperature . Further quantisation of the gain medium into quantum wires or dots enhances the band edge concentration of electronic states thus further reducing the spontaneous emission band width and recombination current.
A simpler approach to limiting the spontaneous emission is to ensure that higher energy electronic states remain unoccupied by reducing the quasi-Fermi-level energies within the semiconductor. The most immediate way of doing this is to keep the losses within the laser cavity to a minimum to reduce the threshold gain value and hence the injected charge carrier density. The use of pseudomorphic quantum wells also reduces the quasi-Fermi levels due to the strain induced changes in the electronic band structure. In particular, the reduced density of states in the valence band and the increased energy separation of the light and heavy hole bands lead to a reduction in the spontaneous emission from the higher energy sub-bands of the quantum well [3 ].
The existence of a broad band of electronic states is not sufficient in itself to increase the threshold current. The key factor which determines the amount of spontaneous recombination is the recombination time, τspon and it is this parameter which controls the contribution of the spontaneous recombination path to the total current. Thus above threshold the differential efficiency of an ideal laser tends to unity because the stimulated recombination lifetime, τstim ≪ τspon and the vast majority of injected carriers undergo stimulated recombination. The detrimental effect of the spontaneous recombination current can therefore be reduced by increasing the τspon of the electronic states rather than decreasing their energy distribution. The recombination lifetime is dependent upon the density of electro-magnetic field modes into which the electron dipole oscillator can couple. The spontaneous emission problem can thus be addressed from the alternative perspective of altering the photonic rather than the electronic mode density. In this paper we present details of experiments following this approach in which the optical mode distribution within edge-emitting diode lasers has been altered. This has been achieved by the use of Bragg reflectors to define a micro-cavity perpendicular to the quantum well plane. The micro-cavity is designed such that all allowed photon modes lie at wavelengths outside of the quantum well, free-space, spontaneous emission spectrum. The emission in the perpendicular direction is therefore inhibited leading to an increased τspon and a reduced recombination current. These experiments are similar in concept to recent work on resonant-cavity light-emitting diodes  with the contrast that in the LED’s the micro-cavity increases the optical mode density within the emission spectrum and hence enhances rather than inhibits the spontaneous emission. We show that the inclusion of a vertical micro-cavity can decrease the room temperature threshold current of an edge-emitting laser by up to 25% and also present calculations from a theoretical model which confirm that this reduction is due to inhibition of the spontaneous recombination within the quantum wells.
The experimental structures were grown by metalorganic vapour phase epitaxy (MOVPE) and contain three 80Å GaAs quantum wells, separated by 80Å Al0.23Ga0.77As barriers, within a 3200Å wide, Al0.3Ga0.7As waveguide. The waveguide core is bounded by AlAs/Al0.14Ga0.86As Bragg reflector pairs; 17 periods in the p-type mirror and 27 periods in the n-type. A conventional separate confinement heterostructure was grown as a control sample with the same quantum well and waveguide structure and with Al0.58Ga0.42As cladding layers. The cladding layers were designed to match the effective refractive index of the Bragg stacks and hence provide the same optical confinement factor as the micro-cavity laser sample. The wafers were processed into 50μm wide oxide stripe lasers and driven with 250ns long pulses at a 1khz repetition frequency.
A number of initial experiments were carried out to confirm that the two samples were identical apart from the Bragg reflectors :
- The slopes of the light-current characteristic, above threshold, were similar indicating similar values of the internal quantum efficiency, ηi.
- The near and far-field radiation patterns were the same indicating a common value for the optical confinement factor, Γ.
- The lasing wavelength is the same for both sets of samples over a wide temperature range (100K–300K) indicating the same quantum well structure.
Thus any differences in the performance of the two samples can be attributed to the presence of the micro-cavity. Devices of all lengths containing the Bragg reflectors showed a 25% reduction in room temperature threshold current compared to the control lasers. Analysis of the Jth versus 1/Lc data confirms that the two sets of lasers have similar values of the gain coefficient, gt and so the lower Jth values in the micro-cavity lasers are not due to differences in their intrinsic gain vs carrier density characteristics .
The reduction in Jth cannot be unambiguously attributed to an inhibition of the spontaneous emission, however, as other processes must be considered :
- The analysis described above only considers radiative recombination and the differences in threshold current could be due to non-radiative recombination currents.
- The thermal activation energy of charge carriers out of the quantum wells may be different in the two samples thus giving different leakage currents.
- The reduction in threshold current could be due to photon recycling by the Bragg mirrors which increases the effective spontaneous recombination lifetime.
The reflection spectrum of the Bragg stacks shifts very little with temperature whereas the spontaneous emission spectrum should move at a rate determined by the temperature coefficient of the bandgap. Thus by changing the temperature the spontaneous emission spectrum can be moved outside the reflection spectrum of the mirrors. If the observed threshold current differences are due to (i) above they should still be observed at low temperature; if they are due to (ii) or (iii) the plots of Jth vs T should converge. The change in wavelength of the cavity mode and emission spectrum can be seen in the spontaneous emission spectra, shown in figure 1. At room temperature the cavity mode lies well away from the spontaneous emission peak. As the temperature is decreased the emission peak blue shifts with the QW bandgap, ~ 2ÅK-1, whilst the cavity mode blue shifts at a lower rate of ~ 0.3ÅK-1.
Thus the relative wavelength changes bring the spontaneous emission spectrum closer to the cavity mode. Therefore to differentiate between processes i–iii outlined above, and spontaneous emission control effects, the threshold current of the lasers was measured as a function of temperature; the results are shown in figure 2.
The difference in Jth between the two sets of devices is reduced as the temperature decreases and at 130K the micro-cavity and control lasers have similar Jth values. These trends continue at lower temperatures so that below 130K the control sample has the lower Jth. The threshold current of the two sets of devices could be expected to converge at lower temperature if the differences in value were due to additional current paths but it is difficult to see why they should cross-over. Similarly any photon recycling effects would be weakened at lower temperatures as the reflection wavelength of the Bragg mirrors is shifted away from the QW emission but this should bring the threshold currents back to a similar value. We believe therefore that the spontaneous recombination rate is indeed altered by the presence of the vertical micro-cavity. At room temperature the spontaneous emission in inhibited and Jth reduced. At temperatures < 130K there is an enhancement of the emission due to the relative spectral shifts of the Bragg cavity and quantum well bandgap with temperature which result in an enhancement of the spontaneous emission by the micro-cavity. This leads to an increased Jth in the micro-cavity lasers relative to the control devices.
To validate the hypothesis outlined above and to provide further insight into the physical processes affecting Jth we have developed a theoretical model of the laser structures which includes the following features :
- The electro-magnetic field states are calculated, for both TE and TM polarisations, from the boundary conditions of the two structures using a three-dimensional Transfer Matrix Method .
- The spontaneous emission rate is then obtained by considering the interaction of the electronic dipole oscillators with each of the electro-magnetic modes, according to Fermi’s Golden Rule. This is described in equation 1:
The strength of the photon-electron coupling is determined by the dipole matrix element, Mk for electron to heavy and light hole transitions and the optical overlap factor of the electro-magnetic mode with the quantum wells, Γk. The total recombination rate for a particular k-state is then a product of the coupling strength and the number of electron dipole oscillators within the well, Ndip, which is calculated using standard semiconductor electronic theory . The calculation range for the k-vector is set to cover the emission spectrum of the quantum wells. It is important to note that the dipole oscillator orientation is not fixed but is determined by the wave vector of the electronic states within the quantum well as described by the semiconductor band structure.
- A homogeneous optical scattering loss, αi=10cm-1 is included within the complex part of the refractive index to account for the reduction in the cavity Q due to loss within the Bragg stacks.
- The effects of electronic, carrier-carrier scattering are implemented as a constant lifetime (τ=0.1ps), Lorentzian broadening of the optical transitions.
- When calculating the temperature dependence of Rspon the reflectivity spectrum of the Bragg stacks is shifted relative to the quantum well emission spectrum by the rate shown in the experimental results of figure 1.
- The model also calculates the optical gain within the quantum wells and this is used to set the carrier density at which Rspon is found.
The results from the model for the structures described earlier are shown in figure 3. The data shown is for a typical threshold gain, gth = 1,000cm-1well-1. The modeled results are in excellent agreement with experiment (fig. 2). The model confirms that both inhibition and enhancement of the spontaneous emission can be achieved with a micro-cavity structure and that these changes directly effect the recombination current. Analysis of the model shows that the primary effect of the micro-cavity is to alter the optical overlap factor, Γk. At room temperature the electro-magnetic field strength of the cavity modes within the spontaneous emission spectrum is minimised at the quantum wells thus reducing the dipole interaction. At low temperatures the field at these wavelengths forms standing wave modes, peaked at the quantum wells, which give enhanced coupling with the electronic dipole.
We have fabricated edge-emitting GaAs/AlGaAs quantum well lasers with a vertical micro-cavity in order to control the spontaneous emission from the wells. At room temperature the devices exhibit a 25% reduction in threshold current compared to control lasers whilst at low temperature their threshold current is higher than the standard devices. Analysis of these structures by detailed theoretical modeling indicates that the Bragg reflectors in the micro-cavity sample can either inhibit or enhance the spontaneous emission thus altering the emission rate and changing the device threshold current. The model shows that the process producing these changes is the change in the overlap of the electromagnetic field modes with the electronic dipoles within the quantum wells.
References and links
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