effective reflector

L

n

substrate

n

L

L

n

n

1 2 .. .. .. .. .. .. .. .. .. m

effective reflector

L

n

substrate

n

Figure 2. 3 A schematic diagram of DBRs

25

Multiple reflections at the interface of the DBR and constructive interference of the multiple reflected waves increase the reflectivity with increasing number of pairs. The reflectivity has a maximum at the Bragg wavelength λB. The reflectivity of a DBR with m quarter wave pairs at the Bragg wavelength is given by

where the no and ns are the refractive index of incident medium and substrate.

The high-reflectivity or stop band of a DBR depends on the difference in refractive index of the two constituent materials, ∆n (nH - nL). The spectral width of the stop band is

where n_eff is the effective refractive index of the mirror. It can be calculated by requiring the same optical path length normal to the layers for the DBR and the effective medium.

The effective refractive index is then given by

1 1 ¹ The length of a cavity consisting of two metal mirrors is the physical distance between the two mirrors. For DBRs, the optical wave penetrates into the reflector by one or several quarter-wave pairs. Only a finite number out of the total number of quarter-wave pairs are effective in reflecting the optical wave. The effective number of pairs seen by the wave electric field is given by

1

For very thick DBRs (m→∞) the tanh function approaches unity and one obtains 1 Also, the penetration depth is given by

^{1 2}tanh(2 )

26

where r = (n1-n2)/ (n1+n2) is the amplitude reflection coefficient.

For a large number of pairs (m→∞), the penetration depth is given by

^{1 2 1 2} number of periods seen by the electric field whereas L_pen applies to the optical power. The optical power is equal to the square of the electric field. The effective length of a cavity consisting of two DBRs is thus given by the sum of the thickness of the center region plus the two penetration depths into the DBRs.

2-2.2 Reflectance simulation of Ta2O5/SiO2 and nitride-based DBRs

The simulation of nitride-based DBRs

To determine how many pairs DBRs are required for a VCSEL, the realization of reflectivity spectra of DBR is inevitable and necessary. In the following, we simulate and discuss the reflectance of bottom and top reflectors we used, AlN/GaN and Ta2O5/SiO2

DBRs, to understand the DBR pairs we required at least to deposit for a VCSEL.

Reflectivity spectra of DBR structures here were simulated using the transfer matrix method. The incident angle of illumination and wavelength of the reference light were set to be 0^o (the direction normal to the sample surface) and 410nm, respectively.

[8]

The refractive index of GaN and AlN at wavelength of 410 nm, used as the parameters in the simulation, were nGaN = 2.45 and nAlN = 2.05.

AlN/GaN DBRs

Figure 2. 4 shows the reflectance spectrum of 5, 10, 15, and 25 pairs of AlN/GaN DBR. The reflectivity value at center wavelength rapidly rises with the increasing of used pairs. As the pairs of DBR were 25 pairs, AlN/GaN DBR could theoretically achieve a high reflectivity of 99% at 450 nm and a wide stop-band about 46nm. The superiority of the AlN/GaN DBR also

27

could be further confirmed using the simulation. Figure 2. 5 shows the reflectivity spectra of three different nitride-based DBRs, AlN/GaN DBR, Al0.25Ga0.75N/GaN DBR, and Al_0.35Ga_0.65N/GaN DBR, with high reflectivity larger than 99% at 450 nm. Other two DBRs with low aluminum contents both show large required pairs (>50 pairs) and small stop-band (<20 nm). Compared to those nitride reflectors, the AlN/GaN DBR obviously reveals relatively wide stop-band and high reflectivity with relatively few pairs.

400 425 450 475 500

0 20 40 60 80 100

99% 25 pairs

15 pairs

10 pairs 5 pairs

R e fl e ct ivi ty ( % )

Wavelength (nm)

Figure 2. 4 Simulated reflectivity spectra of 5, 10, 15, and 25 pairs of AlN/GaN DBRs

28

Figure 2. 5 Simulated reflectivity spectra of three different nitride-based DBRs with high reflectivity

Ta2O5/SiO2 DBRs

Dielectric mirror has the advantage of the large refractive index contrast between two different dielectric materials so it only needs a few pairs of DBR to form high reflectivity mirror. In most dielectric DBRs, SiO₂ is usually used as the low refractive index material due to its some advantaged characteristics such as relative low refractive index than many other dielectric materials. It is easy and cheap to get, hard to decompose, and high transparent window from the wavelength of 180 nm to 8 µm. As to the high refractive index material, Ta2O5 is a proper selection owing to benefits of low absorption and high transparency in visible to IR ray. The refractive index of SiO2 and Ta2O5 at wavelength of 450 nm, used as the parameters in the simulation, are n SiO2 = 1.463 and n

Ta2O5 = 2.15.

[9,10]

Figure 2. 6 shows the reflectance spectrum of 3, 5, and 8 pairs of Ta2O5/SiO2

DBR. The 8 pairs of Ta2O5/SiO2 mirror can have a high reflectivity of 99% and the wide stop band about 128 nm. Therefore, we use at least 8 pairs of Ta2O5/SiO2 DBR as the top mirror in the following experiments.

29

300 350 400 450 500 550 600 0

20 40 60 80 100

99% 8 pairs

5 pairs 3 pairs

R efl ec ti vi ty (% )

Wavelength (nm)

Figure 2. 6 Simulated reflectivity spectra of 3, 5, and 8 pairs of Ta2O5/SiO2 DBRs.

2-3 Design of GaN-based VCSELs ^[11-13]

The design of a typical VCSEL structure should consider three dominant components: the micro-cavity length, the location of active region, and how many pairs of DBR layers we should coated. To achieve lasing action of VCSEL, a careful evaluation and design for the active region and the DBRs are quite important. In this section, we discuss the design of nitride-based VCSEL with hybrid cavity. The hybrid cavity is a cavity sandwiched by an epitaxial grown AlN/GaN DBR and a Ta₂O₅/SiO₂ dielectric DBR. The design for each component in our VCSEL structure is determined by considering the analysis of the reflectance of DBRs and the electric field distribution inside our structure. The cavity length was designed to be seven-lambda in optical length (λ~410 nm). In addition to the consideration of high-reflectivity mirror, the location of active region, usually in the form of MQWs, is also an important issue to the fabrication of GaN-based VCSEL. The active region plays a role of the gain medium. How to effectively make photons to oscillate with active medium is an important consideration. If we put the gain medium at the node of optical field, the interaction between light and

30

electrons would be very weak, therefore, the gain medium couldn’t efficiently provide gain for lasing action. On the contrary, the lasing threshold would be significantly lowered if the active region was put at anti-node of optical field. The same mechanism can be applied in other component of the cavity.

For the electrical pumped VCSEL structure, the ITO layer as a current spreading layer should be considered as one important part of the whole cavity because it would increase the absorption when light resonates in the cavity region. In order to reduce the absorption of the ITO layer, there are two methods can achieve the effect. The first one is using the thinner ITO layer to reduce the absorption in the whole cavity. The second one is designed at the node of optical field, shows opposite views of the MQWs. Then we would introduce the simulation results of these two methods to achieve the better design in our VCSEL structure.

Before proceeding with the experiment, we first simulate the reflectance spectra with different thickness of ITO layer.

The reflectance and quality factor simulation with different ITO thickness

Figure 2. 7 shows the simulation cavity structure with different ITO layer thickness from 0 nm, 30 nm, 120 nm, 210 nm, and 225 nm. Here, the 225nm-thick ITO layer stands for one optical wavelength thickness at 440nm. Owing to DBR reflectivity symmetry, then we chosen 18-pair AlN/GaN DBR. Figure 2. 8 is the simulated reflectance spectra under different ITO thickness. The dip positions in the reflectance spectra represent the cavity modes with different ITO thickness and the quality factor can be estimated from the linewidth of the dip. In Figure 2. 9, the cavity mode wavelength is the function of different ITO thickness. The cavity mode wavelength shifts to longer wavelength because of the longer cavity length, but the cavity mode wavelength would turn back to shorter wavelength when ITO thickness is thicker than 120nm due to the exceeding of the stop band region of the lower DBR. In this case, the cavity mode would jump to the (m+1)th mode from the mth mode. Furthermore, the cavity mode also changes to multimode owing to longer cavity length and smaller mode spacing when ITO thickness is larger than 30nm. In Figure 2. 10, the quality factor is about 700 using the cavity with a 225nm-thick ITO layer, but this value is much lower than that without ITO layer of about 3300. If we consider the qualify factor of the cavity with a

31

30nm-thick ITO layer, the value of about 3100 is a little smaller than that with a 0nm-thick ITO layer but the structure with a ITO layer can be efficiently injected current in our electrical pumped VCSEL devices. Based on the simulation results and reality device requests, we can expect the 30nm ITO layer can efficiently reduce the loss and threshold current density of our VCSEL devices.

Figure 2. 7 The simulation cavity structure

32

420 430 440 450 460

70 80 90 100

0nm 30nm 120nm 210nm 225nm

R ef lect a n ce( % )

Wavelength(nm)

Figure 2. 8 The simulated reflectance spectra with different thickness of