Chapter 4 Characteristics of semiconductor microcavity
4.2 Strong cavity polariton dispersion in multimode GaN microcavity…
The PL spectra at different pump power levels are shown in Figure 4.2(a) along w om in Figure 4.2 (b) around the GaN wavelength region. The GaN and InGaN QW transitions, 365 nm and 420 nm, were both excited. Multimode peaks can be identified from 370 nm all the way to 470 nm. Multiple Lorentzian profiles are used to fit the spectral peaks from 360 nm to 390 nm to identify their exact locations. Two typical fitting results are shown in Figure 4.2 (c) and (d) for high and low pump power levels.
The sums of the fitted Lorentzian profiles are also displayed and both show fairly good fits. For those peaks can be clearly identified, the fitted peak position do not have noticeable changes within the range of different pump power levels. The mode spacing
x dispersion cause the mode spacing to decreases by almost a factor of five from 470 nm to 370 nm. It could be attributed to one of the two reasons: (1) the material index dispersion, (2) the polariton dispersion.
Because the top and bottom DBR are not a pair of perfect reflective mirrors, we must consider the induced phase shift in the cavity, as shown in Figure 4.3. We can find the variance of the phase for different wavelength as the blue curve depicted in Figure 4.3, while the red curve is the reflectivity of DBR.
Firstly, we discuss that if the material inde
decrease gradually from 470 nm to 370 nm. A theoretical index dispersion equation derived from semiconductor near band edge absorption and Kramers-Krong relation [4.1,4.2]
. n(hω)= C(x)+A(hω/Eg)−2(2−(1+hω/Eg)1/2 −(1−hω/Eg)1/2 (4.1) where hω is the photon energy. Eg is the direct band gap of AlxGa1-xN, C is photon energy independent for a fixed Al content, A(x) have a relationship with photon energy and oscillator strength of the optical transition. Our sample is GaN-based, so the Al content is zero [4.3]. The blue curve is the refractive index of a similar GaN sample without DBR cavity measured by an ellipsometer, then we use the red curve out of eq.
(4.1) to fit the blue curve, which show a fairly good agreement to our fit, as shown in Figure 4.4. The measured index dispersion along with the effective index dispersion
) ( m
nPL λ derived from the resonant peaks of PL spectrum are shown with blue square n Figure 4.5. The effective index nPL(λm) is obtained by the resonant condition
ms λ
where L is the cavity length, m is the mode number, and are the observed PL peaks.
Since we know the cavity length is L = 4.2 μm, φ is the phase degree, and mode number start from m = 43 from the above curve fitting, we can obtain nPL(λm). C, A, and energy band gap Eg are fitting parameters. Figure 4.5 shows the fitting of index dispersion disagree with the nPL(λm) value.
Secondly, we discuss the effect of polariton dispersion. In the strong interaction regime, exciton and photon form two coupled cavity polariton states. The two polariton states, upper and lower branch, have an unique anti-crossing dispersion characteristic.
The observed resonant frequencies versus cavity axial mode wave numbers are shown with red square legends in Figure 4.6. The observed peaks are fitted by the lower branch cavity polariton dispersion equation,
ω
pol,n =(Ω+ω
n)/2− (Ω−ω
n)2 +4g2 /2 , where Ω is the exciton frequency, ωn is the photon frequency of nth cavity mode, which is concerning about the DBR phase shift, and it could be expressed asnL m c
n ( ))2
1
( π
λ
ω = + −φ , ωpol,n is the corresponding polariton frequency, and g is the
exciton photon interaction constant. The blue line is the fitted curve and it shows an excellent fit with the fitting parameters, h = 3.50 eV, Ω = 0.29 eV, and n = 2.4.
The exciton energy = 3.5 eV from fitting is reasonably close to the 3.45 eV value cited in literatures. The exciton and photon energies versus wave number k obtained from the curve fitting are shown with two straight lines where the black triangle legends are the cavity photon modes coupled to excitons to form cavity polaritons. The interaction constant of = 290 meV is the highest value reported so far to the best of our
hg hΩ
hg
values obtained from Rabi splitting measurement in III-nitride based devices, where Rabi splittings of 50meV and 56meV were reported for 3λ/2 and 3λ cavity respectively [4.4,4.5]. The PL resonant peaks on the other hand are well described by the polariton dispersion equation as shown in Figure 4.6. This confirms that the observed PL peak dispersion can not be solely attributed to material dispersion and the full consideration of the interaction between exciton and cavity photons is required to explain the observed PL spectrum. There are some subtleties in PL spectra worth of attention.
First, the upper polariton modes were not observed. We remark that it is probably because the energy levels of upper polariton are many times of thermal energy higher and are thermalized by a Boltzmann distribution factor with respect to those of the lower polaritons [4.6].
RS =2hg Ω
CCD
Figure 4.1 Schematic diagram of measurement setup.
He-Cd laser Triax 320
Flip mirror
Dichroic mirror
Fiber
Objective lens
360 380 400 420 440 460 480
360 370 380 390 400
0
355 360 365 370 375 380 385 390 0
200 400 600 800 1000 1200
Intensity (arb. unit)
Wavelength(nm)
Pump=12.3mW
(c)
355 360 365 370 375 380 385 390 0
100 200 300 400 500
Intensity (arb. unit)
Wavelength(nm)
Pump=5.7mW
(d)
Figure 4.2 The PL spectra of optically pumped GaN/InGaN surface emitting microcavity.
(a) PL spectra at various pump power levels. The GaN and InGaN/GaN QW transitions are both excited. The resonant spacing decreases by almost a factor of five from 470 nm to 370 nm.
(b) A zoom in spectrum around GaN transition wavelength region. (c) (d) Typical multiple
Figure 4.3 Phase shift and reflectance of DBR
Figure 4.4 The index of refraction measured by ellipsometer (blue curve) is fitted by a theoretical index dispersion equation (red curve).
300 350 400 450 500 550
Phase dispersion of DBR
0 50 100 150 200 250 300 350
400 Reflectance of DBR
Wavelength (nm)
Phase (degree)
0 20 40 60 80 100
Reflectivity (%)
2.6 2.8 3.0 3.2 3.4
2.4 2.6 2.8
Index of refraction
Ellipsometer
Index dispersion fitting to Ellip. Data
Energy (eV)
2.4 2.6 2.8 3.0 3.2 3.4
Figure 4.5 The effective index from PL resonant peaks (blue square legend) are fitted by a theoretical index dispersion equation (red curve).
2.4 2.6 2.8
Index of refraction
Energy (eV)
Effective index from PL peals Index dispersion fitting to PL peaks
Ω
Figure 4.6 The red square legends are the observed multimode energy positions plotted versus equally spaced wave numbers. The blue line is the fitted curve based on cavity polariton dispersion equation. The two straight lines are the exciton and photon energies obtained from fitting parameters. The black triangle legends are the corresponding cavity photon modes.
ω
pol,n−ωn
13 14 15 16 17 18 19 20 21
2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
Wave number (x106 m-1)
Energy (eV)
2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
Energy (eV)
Reference
[4.1] P.Y. Yu and M. Cardona: Fundamentals of Semiconductors (Springer, Berlin,1996) [4.2] D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R.D. and O.
Ambacher, and M. Stutzmann: Appi. Phys. Lett. 82,5090 (1997)
[4.3] D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Ho¨ pler, R. Dimitrov, O.
Ambacher,a) and M. Stutzmann: J. Appl. Phys. 82,5090 (1997)
[4.4] G. Christmann, R. Butte, E. Feltin, A. Mouti, P.A. Stadelmann, A. Castiglis, J.-F.
Carlin, and N. Grandjean: Phys. Rev. B 77,085310 (2008).
[4.5] G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean: Appl. Phys. Lett.
93 051102 (2008).
[4.6] R.P. Stanley, R. Houdre, C. Weisbuch, U. Oesterle, and M. Ilegems: Phys. Rev. B 53,10995 (1996)
Chapter 5
Conclusions and Future Work 5.1 Conclusion
5.1.1 Two dielectric DBRs VCSELs
We proposed a GaN-bsed VCSEL structure consists of InGaN/GaN MQWs and two dielectric DBRs with high reflectivity. The GaN-based cavity including MQWs was gown on a sapphire substrate. Then the grown cavity was embedded by two dielectric DBRs and transferred onto a silica substrate or a Si substrate.
The laser emission characteristics of a GaN-based vertical-cavity surface-emitting laser with two dielectric distributed Bragg reflectors were investigated under optically pumped operation at room temperature. The Q factor of the VCSEL is about 1000, indicating a good interfacial layer quality of the structure. The laser emits emission wavelength at 412 nm with a linewidth of 0.26 nm. The measurement results, including the linewidth reduction, degree of polarization of 79.4%, and the divergent angle of 5°
are obtained. The laser has a threshold pumping energy of 784 nJ at room temperature and the characteristic temperature of 130K. Hakki-Paoli method was applied to analyze the temperature dependent optical gain and linewidth enhancement factor of the VCSELs.
Due to the multiple cavity modes in the structure, the optical gain can be obtained by measuring the photoluminescence spectra below the threshold condition. At 80 K, the optical gain of 2.2×103 cm-1 was estimated at the threshold condition with a carrier density of 6.8×1019 cm-3 by pulse laser. Under the different temperature, it is found that the gain increases more rapidly as a function of the injected carrier density at lower
temperature. The α-factor at 80 K was estimated as 0.6 and increased to as high as 4.3 at 300K. The characterization of temperature dependent gain and α-factor provides further understanding in operation of the GaN-based VCSEL. Micro-PL intensity mapping indicated that the nonuniform PL emission intensity across the VCSEL aperture. The gain values of the highest PL intensity are larger than the ones of lower PL intensity. We obtained the sharp slope of gain spectrum from 400 nm to 420 nm while the slope of the gain spectrum ranging from 420 nm to 445 nm is smooth.
5.1.2 Cavity polariton dispersion in multimode GaN microcavity
The frequency spacing between adjacent PL peaks decreases by almost a factor of five from 470 nm to 370 nm. We use the material index dispersion and polariton dispersion to fit the experimental data, it shows that the latter fitting curve is much better than the former one. It is shown a very strong polariton dispersion in a multimode GaN surface emitting microcavity at room temperarure. There are multiple photon modes simultaneously in interaction with exciton. The dispersion in PL peaks can be described very well by the lower branch cavity polariton dispersion equation. The fitting gives an exciton-photon interaction constant is 290meV.
5.2 Future works
The DBR reflectivity has a roll off from 90% reflectivity at 383 nm to the first reflectivity minimum at 368 nm, as shown in Figure 4.3. The 4 μm bulk GaN layer has a PL peak at 365 nm with a linewidth of 7 nm. The Lorentzian roll off of GaN PL spectrum still has 7% of its peak value at 380 nm. The roll off of DBR reflectivity and that of the Lorentzian tail of GaN PL spectrum are in opposite directions but still have a overlap between 370 nm and 380 nm. Normally, this is not an optimized cavity reflectivity
condition for investigating exciton-photon interaction. Therefore, we will fabricate the DBR with stop band center tuned to 370 nm and hope to measure the dispersion of upper and lower polariton branches.