Chapter 2 Fundamental of GaN-based vertical cavity surface emitting
2.2 Fundamental of semiconductor microcavities
2.2.2 Bose Einstein condensation
Bose Einstein condensation (BEC) [2.22] has been a source of imagination and innovation of physicists ever since its first proposal by Einstein in 1925. The theory mainly focus on describing the characteristics of eigenstates distribution for Bosons, and the most appealing property is that bosons can coexist on the same energy level. In addition, the lower the energy level, the more the particle occupancym, it is far from fermion obeyed “Pauli exclusion principle“. A BEC is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near to absolute zero . Under such conditions, a large fraction of the bosons collapse into the lowest quantum state of the external potential, and all wave functions overlap with each other, then quantum effects become apparent in a macroscopic scale. The first application of BEC to a physical system was by London in 1938 [2.23], right after the discovery of superfluid in liquid helium [2.24]. Though we can observe BEC by the characteristics of superfluid, we can not reach the same phenomena at room temperature It has attracted much attention owing to the polariton splitting phenomena of a planar GaAs microcavity discovered by C. Weisbush et al. and M, Nishioka et al. in 1992. In recent years, much attention has been given to the behavior of these cavity polaritons which is the so-called bosonic particles in the strong coupling regime. One area of interest relates to the BEC of cavity polaritons. These polaritons will condense to their
final state with a gain as a result of certain scattering processes, and then coherent light will be emitted from the polaritons in that state. The BEC of the polaritons is expected to yield new scientific fields, such as the coherent manipulation of bosons in a solid state, and be applied to a new generation of devices, such as polariton lasers [2.25], polariton LED [2.26], and polariton amplification [2.27] without threshold or population inversion .
Figure 2.1 Basic geometry of a vertical cavity surface emitting laser.
Figure 2.2 A typical microcavity structure. The central cavity layer having a thickness equal to an integer number of half-wave-lengths of light at the exciton resonance frequency is sandwiched between two Bragg mirrors. A quantum well (several quantum wells) should be embedded in the antinodes of the cavity mode electric field in order to provide the strongest coupling to light.
Figure 2.3 Schematic draw of the light reflected from the top and bottom of the thin film.
Figure 2.4 Schematic of distributed Bragg reflector incorporating m pairs of two mediums with indices n1 and n2.
750 800 850 900 950 0
20 40 60 80 100
Reflectivity (%)
Wavelength (nm) Cavity Mode
Δλ
Figure 2.5 Reflectance of an λ/2 empty microcavity.
Exciton Photon
E UP E LP
Figure 2.6 Polaritons are produced by interaction between excitons and photons.
k
//E (k
//)
microcavity photon
QW exciton upper polariton
Rabi splitting Ω
bottom of LP branch: ground state
Figure 2.7 When the exciton state is strongly coupled to the cavity-photon mode, quasi-particle called cavity polaritons are produced with an anti-crossing dispersion relation.
Wavevector (cm
-1)
Energy (meV)
(a (b (c
ELP(k//) EUP(k//)
Figure 2.8 Polariton dispersion for different detuning between exciton and photon modes:
(a) δ= positive, (b) δ= zero, (c) δ= negative. Dashed lines show the energies of uncoupled exciton and photon modes.
Ecav(k// Ecav(k//
Ecav(k//
Eexc(k// Eexc(k// Eexc(k//
ELP(k//) ELP(k//) EUP(k//) EUP(k//)
Reference
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[2.19]. C. Weisbuch, M. Nishioka, A. Ishikawa, Y. Arakawa, Observation of coupled exciton–photon mode splitting in a semiconductor quantum microcavity: Phys. Rev. Lett.
69, 3314 (1992).
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Chapter 3
Characteristics of the two dielectric DBR GaN-VCSELs
3.1 Structure design
3.1.1 GaN-based VCSELs with two mirrors
In this study we propose a VCSEL structure consisting two dielectric DBRs and a GaN-based resonant cavity. An epitaxially grown, thick (~4 μm) GaN-based cavity incorporated with InGaN MQWs was separated from the sapphire substrate by using laser lift-off and then embedded the cavity between two dielectric DBRs. By using different dielectric materials with large difference in refractive index (for example, the difference in SiO2 and TiO2 is ~1.58 at 430 nm), a DBR with a high reflectivity and wide stop band could be achieved with less DBR pairs.
SiO2/TiO2 and SiO2/Ta2O5 DBRs were used in our GaN-based VCSELs. The difference of refractive index between SiO2 and TiO2 is larger than that between SiO2 and Ta2O5, therefore SiO2/TiO2 DBR can achieve a high reflectivity with less pair than SiO2/Ta2O5 DBR. Since the absorption coefficient of Ta2O5 for the pumping laser (Nd:YVO4 laser with laser wavelength of 355 nm) is smaller than SiO2, SiO2/Ta2O5 DBR was used in order to reduce the absorption of pumping laser as the pumping laser passes through the DBR. The thickness of p-GaN is chose to be 1.5λ in order to maximize the overlap between anti-node and MQWs. The structure for simulation is based on the fabricated dielectric DBRs VCSLEs. Figure 3.1 shows the simulated standing wave (square of electric field) patterns calculated by transfer matrix inside the cavity of the VCSEL structure [3.1]. The numerical simulated indicates that the ten pairs MQWs cover
efficiently. The thick n-type GaN layer in the structure can prevent the damage on the InGaN/GaN MQWs since the dislocation or defect might migrate into the MQWs during the laser lift-off process [3.2]. From the numerical simulation of the VCSEL structures with different p- and n-GaN thickness, we also found that the overlap between optical field and MQWs strongly depends on the thickness of p-GaN layer, but not on the thickness of the n-type GaN. In addition, since the MQW region with 1/2λ optical thickness can compensate the possible misalignment between the anti-nodes of the standing wave pattern and the active region position, the effect of the thickness variation of n-GaN that can not be controlled preciously during laser lift-off can be minimized.
3.1.2 Laser lift-off technique
In 1999, Song et al. demonstrated a dielectric DBR VCSEL structure consisting of InGaN MQWs and 10-pair HfO2/SiO2 top and bottom DBR using laser left-off (LLO) technology [3.3]. The reflectivity of top and bottom DBRs were 99.5% and 99.9%, respectively. Now, we also use the same technique to fabricate our sample. Then, the bonding energy of GaN is high as 8.92 eV/molecule, results in the higher melting temperatures and good thermal stability of the GaN compounds compared to other compound semiconductors. The activation energy for GaN decomposition is 3.25 eV/atom. As to the observation of Ga droplets during decomposition in vacuum indicating that GaN decomposes into solid gallium and gaseous nitrogen was reported by Groh et al [3.4]. Sun et al. [3.5] found the thermal decomposition of MOCVD grown GaN on r-plane sapphire occur at a temperature of 1000 oC in a hydrogen ambient. Their report indicated decomposition of the GaN→2Ga(l)+N2(g) will occur at a critical temperature of ~1000 oC at atmospheric pressure [3.4, 3.6]. In this study, a KrF excimer
laser with a wavelength of 248 nm (5 eV) was used to decompose the GaN grown on c-plane sapphire. The laser illuminated on the surface between GaN and sapphire and decomposed the GaN into Ga and N2, hence, the grown GaN-based LED or micro-cavity structure were transferred from the sapphire substrate to host substrate.
3.1.3 Sample structure
The GaN/InGaN microcavity devices was fabricated by a standard epitaxial growth, followed by dielectric coating, laser lift off, and another dielectric coating to finally form a surface emitting microcavity. The device was grown on a (0001)-oriented sapphire substrate by metalorganic chemical vapor deposition (MOCVD). The layer structures are:
a 30nm nucleation layer, a 4 μm GaN bulk layer, MQWs consisting of 10 periods of 5 nm GaN barriers and 3 nm In0.1Ga0.9N wells, and a 200 nm GaN cap layer. The photoluminescence (PL) emission peak of the fabricated MQW was at 420 nm. Then, a 6 pairs of SiO2/TiO2 dielectric DBR was deposited on the top surface. In order to measure the spectral reflectivity of the deposited DBR, a glass substrate served as a monitor sample was deposited in the same deposition run. The reflectance spectrum of the SiO2/TiO2 DBR is obtained by measuring the monitor sample and the PL spectrum of the as-grown sample as shown by Figure 3.2. Next, a silica substrate was expoxied onto the BDR surface, which is nearly transparent to the wavelengths of the pumping laser and our VCSEL. In order to enhance the adhesion between the epitaxial layers and the silica substrate, an array of disk-like patterns with a diameter of 60 μm was formed by standard photolithography and the SiO2/TiO2 DBR mesas were formed using a buffer oxide etcher.
A pulsed excimer laser was then focused through sapphire substrate onto sapphire GaN interface to remove sapphire substrate by thermal ablation. After the LLO process, the
sample was dipped in HCl solution to remove residual Ga droplets on the exposed GaN buffer layers. In the next step, the sample was lapped and polished using diamond powders to smooth the GaN surface since the LLO process left a roughened surface.
However, to prevent the possible degradation of the quality of MQWs during lapping, the 4.2 μm GaN bulk layer was preserved, followed by a eight pairs of SiO2/ Ta2O5 DBR dielectric coating on the polished GaN surface. The final finished Fabry-Perot cavity formed by these two DBR mirrors has a vavity length of 4 μm. Figure 3.3 shows the complete sample structure and Figure 3.4 shows the fabrication process of the GaN-based dielectric DBRs VCSEL. Figure 3.5 (a) shows the microscopic image of a fabricated 2x2 VCSEL array and the circular areas are the locations of VCSELs with DBRs, also serving the emission apertures. Figure 3.5 (b)、 (c) shows a photograph of the fabricated VCSEL on a silica host substrate and a Si substrate, respectively. In this chapter, we observed the characteristics of VCSEL bonded on the Si substrate.
3.2 Measurement setup
The fabricated two dielectric GaN-based VCSELs were optically pumped by a Nd:
yttrium aluminum garnet (YAG) laser (PowerChip NanoLaser CDRH model, JDS Uniphase) whose lasing wavelength is 355 nm with a repetition rate of 1 k Hz and a pulse width of 0.5 ns, and the other source is 325 nm HeCd continuous wavelength (CW) laser.
The system have two optical pumping sources, two optical incident paths, two methods for collecting photoluminescence and two ways to collect surface images of the sample as shown in Figure 3.6, then the setup mentioned before represents the so-called angle-resolved μ-PL (AR μ-PL) system. As shown in Figure 3.6, the incidence path of Nd:
YVO4 pulse laser whose laser beam was focused with a spot of x-axis about 50 μm and
y-axis about 130 μm in an elliptical shape by a convex lens with 10 cm focus. It is obliquely incident on the VCSEL sample from the SiO / Ta O2 2 5 DBR in order to reduce the absorption of the pumping laser by the DBR. The light emission from the VCSEL sample was collected by a 15X objective lens and then straightly transmitted to a spectrometer (Jobin-Yvon IHR320 Spectrometer) with a spectral resolution of 0.07 nm or collected by a fiber with a 600 μm core. Also, the incidence path of HeCd CW laser whose laser beam was focused with a spot size of about 1 μm in diameter by an objective lens (x15) and is vertically incident on the VCSEL sample from the SiO / Ta2 2O5 DBR.
The light emission from the sample was gathered by a 15X objective lens and straightly collected by spectrometer, too. The samples are optically pumped by laser beam with an incident angle of 0° or 60° for measuring the divergent angle. The VCSEL sample was put in a cryostat chamber for measuring the temperature dependent characteristics. In addition, a charge-coupled device (CCD) camera was used to locate the aperture and observe the emission patterns of the VCSEL.
3.3 Threshold condition and spectrum evolution
Figure 3.7 indicates that pumping energy is below the threshold, meanwhile, the spontaneous emission spectrum have multiple cavity modes. The cavity length of the VCSEL can be estimated by
,
where λ is the wavelength of cavity mode, L is cavity length and is refractive index of the cavity with taking wavelength dispersion into consideration. The cavity
modes spacing show by the PL emission is about 7 nm corresponding to a cavity length of 4.2 μm, which is nearly equal to the thickness of the epitaxial cavity. The linewidth of each individual cavity mode is 0.4 nm. The cavity quality factor (Q factor), which is a measure of the shapness or selectivity of a resonant cavity, therefore cab be estimated from the ratio of wavelength to linewidth (λ/Δλ) is about 1000. Considering the optical absorption of the GaN layer, the estimated effective cavity reflectivity based on this Q factor is about 98%, which is close to the cavity reflectivity achieved by the two dielectric DBRs. This result indicates that the laser cavity structure was nearly intact after laser lift-off process. Figure 3.8 shows the evolution of the VCSEL emission spectrum under different pumping levels at room temperature. As the pumping energy increased, a lasing mode was obtained from one of the cavity modes that can be observed below threshold condition. Figure 3.9 shows laser emission intensity obtained from the emission spectra as a function of pumping energy at room temperature. As pumping energy increased above the threshold, a dominant laser emission line appeared at 412 nm with a narrow linewidth of about 0.26 nm. The lasing wavelength is located at one of the cavity modes near the peak emission wavelength of the InGaN MQWs. The pumping laser beam was focused with a spot size of about 80 μm, while the measurement setup will be introduced in Chapter 4. The threshold condition was obtained at a pumping energy of Eth=784 nJ corresponding to an energy density of 15.6 mJ/cm2 and the inset represents one of the lasing conditions, whose pumping power is 0.89mW. Output laser intensity from the sample increased linearly with pumping energy beyond the threshold. The estimated carrier density at the threshold is on the order of 1020 cm-3 assuming that the pumping light with an emission wavelength of 355 nm has experienced a 60%
transmission through the SiO2/Ta O2 5 DBR layers and undergone a 98% absorption in the thick GaN layer. Figure 3.10 shows the far-field pattern (FFP) of the laser emission. The laser emission has a full-width at half maximum
(FWHM) of the FFP is about 5◦ in both horizontal and vertical directions. We measured the laser emission polarization contrast between two orthogonal directions by placing a polarizer in front of the entrance of the spectrum analyzer. The laser emission intensity varied as a function of polarizer rotation angle as shown in Figure 3.11. We used the curve with a function of sinθ to fit the angle dependent laser intensity. The difference between the two angles of minimum intensities is 180o indicating the emission laser a linear polarization. The degree of polarization of the VCSEL emission is about 79.4%
according to the definition of
min max
min max
I I
I P I
+
= − , where Imax and Imin is the intensity
maximum and minimum of the laser emission, respectively.
3.4 Temperature characteristic
The temperature dependence of the lasing threshold of the VCSEL is shown in Figure 3.12. The threshold pumping energy increased gradually with increasing temperature.
From the activation dependence of Eth and the dependence of the threshold condition on the temperature can be expressed as E (T) = Eth 0 exp(T/T ), where E0 0 is a constant and T0
is the characteristic temperature. We obtained a characteristic temperature of about 130 K for this dielectric type VCSEL for the temperature range of 70 to 300 K by linearly fitting the experimental result. This T value is higher than the reported T0 0 of 82 K or 120 k [3.7]
for the GaN-based edge-emitting laser diode. High T0 value could be attributed to a better gain-alignment of the MQWs with the cavity mode and a lower threshold carrier density
3.5 The gain characteristics for different temperature
3.5.1 Temperature dependent gain characteristics by a Nd: yttrium aluminum garent (YAG) laser
Figure 3.13 shows the photoluminescence spectra of the GaN-based VCSEL under different pumping power levels at 80 K. Above the threshold condition, only one lasing mode at about 407 nm dominates. The Hakki-Paoli method is one of the most common method to extract net optical gain from amplified spontaneous emission (ASE) spectra.
Therefore, the optical gain can be therefore estimated using the Hakki-Paoli [5.14 pig]
method to analyze these multiple cavity modes from the photoluminescence spectra below the threshold condition. To derive the net optical gain, we first consider a semiconductor laser in a Fabry-Perot cavity. The reflectivities of the two mirrors are R1
and R2, respectively. Now, a field P1 incident on mirror 1 and the amplitude of the reflected wave is R11/2F1. This first reflection travels towards morror 2 with a propagation constant k-j (α /2), where αi i is the internal loss per unit length. When a wave bounces back and forth in a Fabry-Perot cavity, its amplitude after one round trip of distance 2L has to remain at least the same to obtain gain. When the multiple reflections interfere constructively and destructive, the total incident field in a single mode are
⎪⎪
The maximum and minimum intensities with spectral measurements of Fabry-Perot modes in the cavity are I+ and I-, respectively. Therefore, αi can be obtained from Eq. (3.1)
( ) ( ) ( )
(3.2) whereλ is the wavelength at which the cavity modes are being measured. Confinement factor of the laser structure is estimated as Γ = 0.7% by calculating the spatial overlap between the optical field and MQWs layers in the VCSEL cavity, da is the thickness of ten quantum wells, I+ and I- are the maximum and minimum PL intensities for each cavity mode obtained from the measured PL spectra, R1 and R2 are DBRs reflectivities which are 99% and 98%, respectively, αi is the average internal loss of the cavity, which is dominated by the absorption of thick GaN layer and was set to be 42 cm-1 at room temperature [3.8] and L is the cavity length. Under different pumping levels, the I+ and I -would vary and the individual gain for each cavity modes can be obtained from the eq.
(3.2). The gain spectra of the VCSEL under different pumping power levels at 80 K are shown in Figure 3.14. Each data point was calculated from the corresponding cavity mode in Figure 3.13. The gain curves show an increasing trend as the pumping intensity
(3.2). The gain spectra of the VCSEL under different pumping power levels at 80 K are shown in Figure 3.14. Each data point was calculated from the corresponding cavity mode in Figure 3.13. The gain curves show an increasing trend as the pumping intensity