Chapter 2 Fundamentals of Photonic Crystal Surface Emitting Lasers
III. M3 numerical results
3.3 Process flowchart
Figure 3.3 SEM image of plane view and cross section
3.3 Process flowchart
The PCSELs was fabricated by following process steps. In the beginning, the hard mask SiN 200nm was deposited by PECVD. Then PMMA layer (150nm) was spun by spinner and exposed using E-beam writer to form soft mask. The pattern on soft mask was transferred to SiN film to form the hard mask by using ICP-RIE (Oxford Plasmalab system 100), and then the PMMA layer was removed by dipping ACE . The pattern on hard mask was transferred to GaN by using ICP-RIE (SAMCO RIE-101PH) to form the PC layer. Finally, the sample dips in BOE to remove the hard mask.
SiN film PMMA
E-beam writing & developing Mask transfer by ICP-RIE
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Remove PMMA by acetone ICP dry etching
Complete device after removing SiN film
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To completely describe the process flowchart, each process conditions are entirely listed in the table.
Step Process Conditions
1 Soft mask
(1) I.C.
) (2) Deposit 200nm SiN by PECVD.
) (3) Spin 150nm PMMA by spinner (4) Define PCSELs pattern by EBL.
(5) Development.
(6) Hard bake
2 Hard mask
(1) Dry etching by ICP-RIE (Oxford Plasmalab system 100) to form the hard mask.
(2) Remove PMMA by ACE.
(3) Hard bake.
3 PCSELs
(1) Dry etching by ICP-RIE ((SAMCO RIE-101PH) to transfer the hard mask to GaN.
(2) Remove hard mask by BOE.
(3) Hard bake.
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Chapter 4
Optical Characteristics of GaN-based 2D Photonic Crystal Surface Emitting Lasers
4.1 The design for PCSELs
In this section, we focus on the design of our GaN-based 2D PCSELs. Initially, we calculate the band diagram with TE like mode to determine the normalized frequency which we choose for specific band-edge groups. Normalized frequency is the ratio of the wavelengths of optical modes to the PC lattice constants. The lasing wavelength could be expected while the lattice constant is determined. The lasing wavelength is located within the emission of the active layer. According to the theory described in chapter 2, 2D periodic structure embedded in the laser could induce Bragg diffraction, which results in Multi-directional coupling. This coupling can effectively increase the Bragg mode density of several band edges, Γ、K and M. The couple wave could emit normally from the sample surface due to the first Bragg diffraction. Therefore, we can design a GaN-based 2D PCSEL operating at the designed lasing wavelength with the optimized lattice constant at Brillouin zone boundary, Γ、K and M point, which can be defined in the photonic band diagram.
In this study, we fabricate several devices with the consistent r/a value (r/a=0.28) and calculate the band diagram of PC using 2D plan wave expansion method (PWEM). In fact, the 2D PWEM couldn’t precisely evaluate the photonic band diagram of our 3D structure. That means we should do some modification to parameters describing our structure and then bring them into the 2D PWEM to approximate real condition.
Therefore, according to reference [1], we further bring two parameters, confinement factor (Γg) and effective refractive index (neff) into our calculation. Γg is the ratio of
41
the light confined within the 2D PC structure to the light inside the whole device, and neff is the effective refractive index of the entire device with PC structure. Γg and neff
could be used to estimate the effective dielectric constant of nano-hole (εa) and the background (εb) for 2D PWEM calculation to further approximate the 3-D structure.
These two parameters can be obtained by solving the distribution of the optical field in the in-plane direction. The Γg and neff for describing our structure are estimated to be 0.563 and 2.495, respectively. It is first estimated by transfer matrix method and shown in Fig 4.1.
Figure 4.1 The lowest guided mode optical field distribution
Then, we could determine εa and εb using two conditions:
b
eff f a f
n 2= ε +(1− )ε ) ( mat air
g a
b ε ε ε
ε
ε = − =Γ −
Δ
where the f is a filling factor, εmat is the dielectric constant of semiconductor, and εair is the dielectric constant of air. For a triangular lattice PC, f is written as:
(4.1)
(4.2)
Γ
g= 0.563
n
eff= 2.495
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2 2
3 2
a f = πr
Therefore, the value of εa and εb in unit cell for our PC device could be obtained to be 4.11 and 7.07, respectively. To bring εa and εb into the calculation, a band diagram of the 2D triangular lattice PC structure for TE like mode with r/a=0.28 on our sample structure could be estimated as shown in Fig 4.2. It is reasonable to consider only the TE-like mode, we assume that since the carriers in the InGaN layers are confined in the well, they do possess a significant in-plane dipole, which can couple to TE mode.
The figure shows that the each mode dispersion curve cross and splits at specific band-edges, the mode density is higher at those boundaries, light at these points can propagate along different direction and have chance to couple and form a laser cavity.
According to the theory described in chapter 2, the lasing action of the photonic crystal grating structure could only occur as the Bragg condition is satisfied.
Figure 4.2 The TE band dispersion diagram of our design
In order to have a high probability to meet those modes satisfying Bragg condition, the lattice constant of photonic crystal were determined to range between 190nm to
(4.3)
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300nm (the normalized frequency ranges between 0.45 and 0.7) considering a PL peak wavelength of ~425 nm as shown in Fig 3.2.
4.2 Optical pumping system and low temperature system
The optical pumping was performed using a frequency tripled Nd:YVO4 355nm pulsed laser with a pulse width of ~0.5ns at a repetition rate of 1KHz. The pumping laser beam had a spot size of 50um and was normally incident onto the sample surface covering the whole PC pattern area. The light emission from the sample was collected by a 15X objective lens through a fiber with a 600um core, and couple into a spectrometer with a charge-coupled device (Jobin-Yvon Triax 320 Spectrometer). The spectral resolution is about 0.1nm for spectral output measurement. Fig 4.3 shows the setup of our optical pumping system. The GaN-based PCSELs were placed in a cryogenics controlled chamber for obtaining the characteristic temperature. The temperature of the chamber can be controlled from room temperature 300K down to 100K using the liquid nitrogen as shown in Fig 4.4.
Figure 4.3 The setup of optical pumping system
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Figure 4.4 The setup of u-PL low temperature system
4.3 Characteristics of GaN-based 2D PCSELs
ThresholdThe threshold characteristics of the GaN- based 2D PCSEL were measured using the optical pumping with a pumping spot size of around 50 μm. The lasing action was clearly observed in several different devices with different lasing wavelength from 395 nm to 425 nm. Take the PC lattice constant 254 nm for example. Fig 4.5 shows the output emission intensity as a function of the pumping energy density. The clear threshold characteristic is observed at the threshold pumping energy density of 2.8mJ/cm2. Then the laser output intensity increases abruptly and linearly with the pumping energy above the threshold energy. Fig 4.6 shows the excitation energy dependent emission spectra. These spectra clearly show the transition behavior from spontaneous emission to stimulated emission. Above the threshold, we can observe only one dominant peak wavelength of 419.7nm with a linewidth of 0.19nm.
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Moreover, it is interesting to show the emission image below and above the threshold.
As the pumping power was below the threshold, the spontaneous emission is uniform above the PC region with a spot size of about 50um. With increasing the pumping power, the stimulated emission occurs over a large area. The lasing area of the GaN- based PCSELs, obtained by a CCD camera which covers almost whole area of PC pattern with only one dominant lasing wavelength. However, Fig 4.5 shows the lasing area is not cover full of the PC region. It could be attributed to the disorder of PC, non-uniformity of pumping laser beam, or inhomogeneiety of InGaN-based gain material. Nevertheless, the nitride based 2D PCSEL could actually have an obviously larger lasing area than that of nitride based VCSEL, which is just several micro-meters.
Figure 4.5 The laser intensity versus pumping energy density
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
0 1 2 3 4 5 6 7 8
Intensity(arb. unit)
Pumping energy density ( mJ/cm
2)
E
th~2.85 mJ/cm
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Figure 4.6 Excitation energy density versus emission spectrum
The diagram of normalized frequencies as a function of r/a ratio is shown in Fig. 4.7.
On the other hand, the PWEM in 2D case is being used to consider the effects of partial modal overlap of electromagnetic fields with the PC structures and obtain the band diagram of the hexagonal PC patterns in this structure. The solid (black), dot (red), and dash (green) lines are the calculated band-edge frequencies at the Г, K and M Brillouin zone boundaries as a function of r/a ratio, which were in accordance with the measured results.
In order to exam the relationship between lasing wavelength and lattice constant, we plot the normalized frequency ω = a/λ as a function of a in Fig 4.8a , where a is the lattice constant and λ is the lasing wavelength in free space. After normalization, it can be seen clearly that lasing occurs at several normalized frequencies. We also plot the corresponding photonic band structure of 2D triangular photonic crystal using the same normalized frequency in Fig 4.8b Comparing the Fig 4.8a with Fig 4.8b it is
410 415 420 425
0 3 6 9 12 15
0.79Eth 1.0Eth 1.16Eth 1.32Eth
Wavelength(nm)
FWHM~0.19nm
~419.7nm
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clearly seen that the normalized frequency ω precisely coincides with the three band-edge frequencies (Γ1, K2, M3), indicating that the lasing action could only occur at the specific normalized frequencies that satisfy the Bragg condition.
Furthermore, we can confirm the laser operation is provided by multidirectional distributed feedback in the 2D case. The characteristics of Γ1, K2, M3 points lasing can be further identified by the polarization angle of the output beam emission, which will discussed in next section. Note that the output intensity is higher when some of the lasing frequencies are in the stopband of DBR, which could be due to that the bottom DBR here could be treated as a high reflectivity reflector, facilitating top emission efficiency.
Figure 4.7 Normalized frequency (ω = a/λ) as a function of r/a
0.18 0.21 0.24 0.27 0.30 0.40
0.45 0.50 0.55 0.60 0.65 0.70
N o rm al ized frequ e ncy ( a/ λ )
r/a ratio
Lasing modes Simulation M Simulation Γ Simulation K
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Figure 4.8 (a) Normalized frequency (ω = a/λ) versus lattice constant (b) Photonic band structure of 2D hexagonal photonic crystal
Polarization
The polarization of the laser was measured by inserting and rotating a polarizer in front of a fiber which collects light into a spectrometer. Fig 4.9 shows the laser emission intensity as a function of the angle of the polarizer. Here, defined the degree of polarization (DOP) as DOP = (Imax-Imin)/( Imax+Imin), where Imax is the maximum intensity and Imin is the minimum intensity. From the figure, the laser degree of polarization was estimated to be about 53%. In fact, the calculation of electric-field vectors in triangular lattice PCs was reported [2], and results suggested that this kind of the laser has weightless polarization property of the laser emission. This could explain the low DOP of our lasers.
It is expected that the lasing oscillation directions are different at different band-
150 200 250 300
49
edges based on 2D DFB theory described in Chapter 2. Therefore, in order to confirm the identification of lasing modes, we measured the polarization states of each band-edge, including Г , K and M. To forecast each polarization states, we draw the laser oscillation direction of each band-edge for triangular lattice in Brillouin zone as shown in Fig 4.10. For TE like mode, it is expected that the polarization direction is orthogonal to the laser oscillation. Once the fabrication process occur structural imperfection or asymmetry, which can be the path for laser beam to diffract normal to PC surface. Therefore, the laser polarization states can be measured by spectrometer.
It is noted that all the PC structure are aligned in the same direction which can be seen on the CCD. The measured results of polarization states for different band-edge are plotted in Fig 4.11. It is explicitly show that the polarization states direction are closely matched to Fig 4.10 we draw, which is a clear evidence to prove the existence of the lasing modes correspond to specific band-edges.
Figure 4.9 The degree of polarization state
02 4 6
0 30 60
90 120
150
180
210
240
270
300
330 0
2 4 6
data points fitting curve
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Figure 4.10 The lasing oscillation for
Г K M
band-edge in K spaceFigure 4.11 The polarization state spectrum for Г K M band-edge
5 6 7 8 9
0 30 60
90 120
150
180
210
240
270
300
330 5
6 7 8 9
Γ
K M
Intensit y(arb. unit )
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Divergence angle
We also varied the detecting angle of a fiber which collects light into a spectrometer to measure the laser emission. The fiber is mounted on a stage which could be rotated from -90° to 90°. We measured the emission intensity every 10 degree. Here the 90°
is the direction parallel to the sample surface. Fig 4.12 shows the laser emission intensity as a function of the detecting angle of the fiber. The result suggests the laser is vertically emitted. This characteristic is a strong enough evidence to reveal the PCSEL is a kind of considerably excellent single-mode surface emitting laser.
Figure 4.12 The laser intensity of our PCSELs as a function of detecting angle of fiber
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Spontaneous emission coefficient
We plot the threshold of our PCSELs device with lattice constant a=234nm with threshold density is about 2.7 mJ/cm2 as shown in Fig 4.13 and further re-plot it in logarithmic scale as shown in Fig. 4.14 and then calculated the difference between the heights of the emission intensities before and after the threshold which should correspond roughly to the value of β. The β value of our PCSEL was estimated about 5×10-3. Interestingly, this value is smaller than the GaN-based vertical cavity surface emitting lasers [3]. However, the β factor is still larger than the typical edge emitting lasers (normally about 10-5) indicating the enhancement of the spontaneous emission into a lasing mode by the high quality factor in GaN-based PCSELs
Figure 4.13 Laser emission as a function of pumping energy at room temperature
Pumping energy density(mJ/cm
2)
390 395 400 405 410 415
0.0
Pumping energy density(mJ/cm
2)
390 395 400 405 410 415
0.0
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2 3 4 5 6
10
110
210
310
4Intensity(arb. unit)
Pumping Energy Density(mJ/cm2) β=0.005
Figure 4.14 Laser emission intensity versus pumping energy in a log
scale.
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Characteristic temperature
Fig 4.15 shows the semi natural-logarithm plots of the dependence of the threshold pumping energy (ln
( )
Eth ) on the operation temperature (To). The threshold energy gradually increased as the operation rose from 100 to 300K. The relationship between the threshold energy and the operation temperature could be characterized by the equation: Eth =Eo×eT/To, where To is the characteristic temperature and Eo is a constant. Therefore, we obtain a characteristic temperature of about 148K by linear fitting of the experiment data. This value is smaller than VCSEL but similar to EEL.According to theory, To is affected by the material and structure. The material for PCSEL is similar to VCSEL which are GaN based material. The structure for VCSEL its cavity length is much shorter than PCSEL results in smaller T0 property.
Figure 4.15 The threshold energy as a function of temperature in log scale
100 150 200 250 300
5.6 6.0 6.4 6.8
7.2
Experiment dataLinear fit of Experiment data
ln ( E th )
Temperature (K)
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4.4 Calculation of coupling coefficient
In section 2.3, the 2D couple-wave model for triangular lattice PC structure has been discussed. Therefore, we further calculate the coupling coefficient at Г1, K2 M3 band- edge according to the design of our PCSELs.
Г1 numerical results
The design for lasing action at Г1 device which parameters are described as follows:
r/a=0.25, a=180nm, nb=2.65, na=1.87, neff=2.495
put these parameters in R-soft software and plot the dispersion diagram for TE-like mode as shown in Fig 4.16
Figure 4.16 Dispersion diagram for TE like mode forГ1 case
For the band-edge Г1, there are four cavity mode frequencies, two are degenerated. T The cavity mode frequency can be obtained via simple transform of the normalized frequency which derived from R-soft. The normalized frequency values from lower to higher are 0.4482, 0.4595, 0.4704, and 0.4930. Once the cavity mode frequency at the
Г1
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individual band-dges can be obtained, we can derive the coupling coefficientsκ1, κ2, and κ3 from eqn (2.41) and its values are 17480 cm-1,11240 cm-1 and 11248 cm-1, respectively. Therefore, for Г1, the lasing oscillation forms a hexagonal cavity which provided the major significant contribution to support the lasing action.
K2 numerical results
The design for lasing action at K2 device which parameters are described as follows:
r/a=0.26, a=220nm, nb=2.63, na=2.0, neff=2.495
put these parameters in R-soft software and plot the dispersion diagram for TE-like mode as shown in Fig 4.17
Figure 4.17 Dispersion diagram for TE like mode forK2 case
For the band-edge K2, there are two cavity mode frequencies, one is degenerated. The cavity mode frequency can be obtained via simple transform of the normalized frequency which derived from R-soft. The normalized frequency values from lower to
K2
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higher are 0.5326 and 0.5413. Once the cavity mode frequency at the individual band- edges can be obtained, we can derive the coupling coefficientsκfrom eqn (2.45) is 4089 cm-1. Therefore, for K2, the lasing oscillation forms a triangular cavity which provided energy to support the lasing action
M3 numerical results
The design for lasing action at M3 device which parameters are described as follows:
r/a=0.266, a=247nm, nb=2.64, na=2.01, neff=2.495
put these parameters in R-soft software and plot the dispersion diagram for TE-like mode as shown in Fig 4.18
Figure 4.18 Dispersion diagram for TE like mode forM3 case
For the band-edge M3, there are four cavity mode frequencies. The cavity mode frequency can be obtained via simple transform of the normalized frequency which derived from R-soft. The normalized frequency values from lower to higher are
M3
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0.60898, 0.60943, 0.61409, and 0.62335. Once the cavity mode frequency at the individual band-edges can be obtained, we can derive the coupling coefficientsκ1, κ2, and κ3 from eqn (2.49) and its values are 1241 cm-1,1356 cm-1 and 2683 cm-1, respectively. Therefore, we know the lasing oscillation back and forth provided the major significant contribution to support the lasing action.
The threshold gain is determined by two factors, one is the gain medium and the other is coupling coefficient. It is expected that the lasing action occurs at Г1 band edge should have the lowest threshold gain due to the largest coupling coefficient.
Therefore, we analyze the threshold gain of PCSELs with its r/a, ranges from 0.25 to 0.26, as a function of normalized frequency as shown in Fig 4.19. It is obvious to see the Г1 indeed has the lowest threshold gain and M3 has highest threshold gain which correspond with our expectation. In the future, for the electrical pump PCSELs fabrication, one can follow this rule and design for Г1 group to achieve lasing action.
Figure 4.19 The threshold power versus normalized frequency for Г1 K2 M3 groups
0.4 0.5 0.6 0.7
0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
Threshold power (mW)
Normalized frequency (a/λ)
Г1
K2
M3
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References
1. M. Imada, A. Chutinan, S. Node, and M. Mochizuki, Phy. Rev. B, 65, 195306 (2002)
2. S. L. Chuang, Physics of Optoelectronic Devices, John Wiley & Sons, Inc (1995) 3. C. C. Kao, T. C. Lu, H. W. Huang, J. T. Chu, Y. C. Peng, H. H. Yao, J. Y. Tsai, T.
T. Kao, H. C. Kuo, IEEE Photon. Tech. Lett., 18 (2006)
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Chapter 5 Conclusion
The GaN-based 2D photonic crystal surface emitting lasers are fabricated and measured in this thesis. The lasing action is achieved under the optical pumping system at the room temperature with a threshold pumping energy density of about 3.5mJ/cm2. Moreover, the laser emits one dominant wavelength of 424.33nm with a linewidth of about 1.1Å. All normalized frequency of investigated PC lasing wavelength can correspond to three band-edge frequencies (Γ1, K2, M3), which indicates the lasing action can only occur at specific band-edges. Polarization states confirm the existence of lasing modes at different band-edge (Γ1, K2, M3). The degree of polarization and divergent angle of the laser emission is about 53% and smaller than 10o, respectively. The characteristic temperature is about 148K. The coupling coefficient at different band-edge (Γ1, K2, M3) can be obtained based on 2D couple-wave model. Furthermore, the threshold gain at Γ1 is the lowest which corresponds to the highest coupling coefficient. All the experiment results indicate that GaN-based PCSELs could be the highly potential optoelectronic device for the next generation lasers.