Comparisons

A comparison of the stress-induced with the liquid crystal based switchable gratings is listed in table 3-2. Among the four characteristic items, the stress-induced switchable grating requires higher driven voltage and produces fewer beams. But its size is smaller by 2 orders. Its process compatibility with other optical components is also better.

For the large driven voltage issue, the structure can be further optimized to reduce its driven voltage. For example, the tip height (1250 μm) is above the requirement (800 μm). By reducing the tip height, the driven voltage is lessened. The thickness of the stress beam can be reduced from 2μm to 1.5 μm to induce the spring constant and thus the driven voltage. Besides, the coupling length between the movable and fixed comb fingers can be increased to reduce the driven voltage according to [35]:

² 2

1 V

dZ L dC N

F_E = ∗ ∗ _c∗ ∗ (3-1)

where N is the number of the comb fingers, Lc is the coupling length of comb fingers, dC/dZ is the gradient of capacitance of comb fingers in z direction, and V is the applied driven voltage. According to formula (3-1), the driven voltage can be lowered from 80 volts to 60 volts if the coupling length increases from 180 µm to 300 µm.

For the few diffraction beam issue, a 7-beam grating can be designed to replace the current 3-beam grating, but the width tolerance would be reduced from ±0.4μm to ± 0.1μm. Another solution is to use a cascaded grating array, as shown in Fig. 3-7.

Table 3-2: Comparison of liquid crystal and stress-induced switchable gratings

Fig. 3-7. Schematic of a cascaded grating array to produce seven diffraction beams of equal intensity.

3.6 Summary

Using a two-layer poly-silicon and one-layer low stress silicon nitride surface micromachining process, a switchable micro-grating composed of a binary phase grating and a bimorph actuator was demonstrated. The optical pattern area of the grating was 500 µm in diameter. The voltage required to switch the grating was 80 volts.

The measured diffraction angle was 4.51°. The normalized measured diffraction intensities of the -1^PstP order beam, 0^PthP order beam and the +1^PstP order beam were 0.93, 1, and 0.91. The optical performance of the dynamic grating shows its potential for integration with other micro-optical elements for multibeam optical pickups application

Chapter 4

Polarization Beam Splitter

High-extinction-ratio micro polarizing beam splitters (micro PBS) are required in micro optical systems for sensing and signal processing when the polarization state is a concern. For example, in an optical storage system, a high-extinction-ratio micro PBS is required to divide the incident light into a highly reflected TE mode and a highly transmitted TM mode to reduce the optical noise. The reflected TE mode is used to monitor the light intensity; the TM mode is used to read and write the data on the disk. A surface micromachined poly-silicon PBS was first proposed by Pu et al.

and demonstrated to operate well for near IR^P[46]P. For short wavelength applications, such as 405nm for blue light storage system, the poly-silicon based PBS is not suitable due to its high absorption. Among the materials used in polysilicon based surface micromachining, silicon nitride and silicon dioxide have high transparency in the visible spectrum range^P[47]P. However, silicon dioxide is usually used as the sacrificial layer. Therefore, silicon nitride was investigated as the optical material.

Employing the polarization sensitive characteristic of the dielectric film, a silicon nitride film at the Brewster angle incidence can serve as a PBS. To achieve higher polarization extinction ratio, multilayer coating on the PBS surface or cascading several PBS’s in tandem are required. The former method is limited by the materials available in surface micromachining, while the latter requires large area and operates only for the transmitted waves. To overcome the constraints of available materials and die size, a SiN/Air/SiN stack operating at the Brewster angle incidence is first

two silicon nitride layers (as high-refractive-index layers) separated by an air gap (as a low-refractive-index layer). At the Brewster angle incidence, the reflectivity of the TM mode will be nominally zero. By choosing specific thicknesses of the silicon nitride layers and the air gap, the reflectivity of the TE mode can be higher than 90%, leaving the transmitted light almost TM mode.

When combined with poly-silicon structures, a high-extinction-ratio pop-up micro PBS can be fabricated and easily integrated with other micro optical elements, such as a cylindrical lens to shape the incident beam, a grating to form tracking beams, a micro astigmatic lens to slightly alter the horizontal and vertical focal distances of the resulting spot on the photodiode array and mirrors as the reflectors, to form a micro optical pickup for short wavelength optical storage applications.

4.1 Transmittance, reflectance, and absorptance

For a single homogeneous and isotropic layer bounded by isotropic and homogeneous layers, the structure can be described by^P[48]P

⎪⎩

As shown in Fig. 4-1, if the plane wave propagates from the left, the electric field vector E(x) can be described using the form:

⎪⎩

where M,N,C,D, and F are the complex amplitudes.

x

n1 n2 n3

x=0 x=d

Fig.4-1 A thin homogenous layer of dielectric material

Assume the electric field vector is TE(s) polarized (the electric field is perpendicular to the plane of incidence), and then the complex amplitudes of the incident wave and the reflected and transmitted waves M, N, F are constant. k_ix is the x components of the wave vectors:

k_ix = ⁱ n_{i i} is the speed of light in vacuum. The magnetic field can be obtained from the equation:

H = ∇×Ε wu

i . (4-4)

From the boundary conditions of Maxwell’s equations, the tangential component of the electric and magnetic vectors are continuous across a discontinuity surface^P[49]P, so that the electric vector has the same value in each dielectric layer. Using the conditions and Snell’s law, the Fresnel reflection and transmission coefficients of the dielectric interfaces for TE wave can be written as^P[50-52]P:

r₂₃=

And the transmission and reflection coefficients can be written as

t= _φ and is proportional to the thickness d and index n₂of the layer.The expression for the transmission and reflection coefficients of the TM(p) wave are the same, except the coefficients t ,₁₂ t and ₂₃ r ,₁₂ r must be those associated with the TM waves. ₂₃

If media 1 and 3 are no absorbing, reflectance (R) defined as the energy reflected from the dielectric structure and transmittance (T) are given by

R= r², (4-12)

Regardless of whether the layer (medium 2) is absorbive, both Eqs. (4-12) and (4-13) can be used. Absorptance (A )defined as the fraction of energy dissipated is given by

A = 1 – R - T. (4-14) Under different angle of incidence, TE and TM states do not behave in the same way, In particular, if the incident angle is at a specific angle, so-called Brewster angle, the reflection coefficient of the TM mode will vanish completely, leaving the reflected light to be TE mode. The Brewster angle, noted asθ , is given by

tanθ_B =n /_t n_i (4-15) where n is the refractive index of the thin film and _t n is the material/air index _i from the incident side.

4.2 2 x 2 matrix formulation for a thin film

The proper thickness of TE mode can be determined by the matrix formulation. As shown in Fig. 4-2, the electric field E(x) consists of a right-propagating and left-propagating waves can be expressed as the form:

E(X) ≡ A(x) + B(x), (4-16)

Fig.4-2 A thin layer of dielectric material

Let A(x) represent the amplitude of the right right-traveling wave and B(x) be that of the left-traveling one. To illustrate the matrix method, we define

A1=A(0^-), B1=B(0^-), A2’=A(0⁺), B2’=B(0⁺), A2=A(d^-), B2=B(d^-), A3’=A(d⁺), and B3’=B(d⁺),

where 0^- represents the left side of the interface, x=0, and 0⁺ represents the right side of the same interface. Similarly, d^- and d⁺ are defined for the interface at x=d.

The transmission matrices that link the amplitudes of the waves on the two sides of the interfaces, noted D and D , can be expressed by

D₁₂=

The expression for D₂₃ is similar to those of D₁₂, except that the subscript indices have to be replaced with 2 and 3. Equations (4-17) and (4-18) can be written formally as where t and ₁₂ r are the Fresnel transmission and reflection coefficients, ₁₂ respectively, and are given by

⎪⎪

Then the amplitudes A₁, B₁ and A^'₃ , B^'₃^BBare related by and P is the so-called propagation matrix, which accounts for propagation through ₂ the bulk of the layer The column vectors representing the plane-wave amplitudes in each layer are related by a product of 2×2 matrices in sequence. A dynamical and propagation matrix can represent each side of an interface and the bulk of each layer, respectively.

We now recall the scheme of Fig. 4-2, with a collimated incident light of wavelength λ，according to Equation (4-23), the characteristic matrix of a thin dielectric film of thickness x is given by

M[x] =

where θ is the incident angle inside the film, p_{f f} =

(

ε_f /µ_f

)

cos(θ_f) for TE, p_f = µ_f /ε_f cos(θ_f) for TM, and µ ，_f ε are the permeability and permittivity of _f the thin film, respectively.

The reflectance R and transmittance T can be determined from M(x). From (4-28), R and T are periodical function of x with the period

f

nf

x θ

λ cos

= 2

∆ (4-29)

4.3 Simulation

The optical design of the SiN/Air/SiN stack is performed by using the characteristic matrix. Each layer is described by a 2×2 matrix according to equation (4-28), which relates to the components of the electric (or magnetic) field along the direction of propagation. The reflectivity, transmissivity and absorption of the stack can be derived from multiplication of the matrix of each layer together.

Fig. 4-3. Propagation of an electromagnetic wave through a stack of films of thickness d^Bi^B and refractive index N^Bi^B.

The characteristic matrix of the stack is given by^[51]:

(4-30)

The reflectivity R, transmissivity T and absorption A of the incident light for both polarizations can be derived from Eqs. (4-30)~(4-35):

(4-36)

If R^BTE^B and T^BTE^B are the reflectivity and transmissivity for the TE mode, and R^BTM^B and

T^BTM^B for the TM mode, respectively, the optical characteristics of the micro PBS can be evaluated by two extinction ratios σ^BT^B (for transmission) and σ^BR^B (for reflection) defined as

(4-37)

Our target is to design a PBS with extinction ratios for the transmitted light to be

)

calculated the optical performance of the stack at Brewster angle incidence as a function of d^B1^B, d^B2^B and d^B3^B, which were the thicknesses of the first silicon nitride layer, the air gap and the second silicon nitride layer, respectively. At Brewster angle incidence, the nominal reflectivity of the TM mode is zero. Therefore, to achieve high polarization extinction ratios, the reflectivity to transmissivity ratio of TE should be as high as possible. Besides, to reduce the fabrication complexity of the micro optical pickup, the thickness, d^B1^B, of the first silicon nitride layer is fixed to be 384 nm, which is the thickness of other micro optical elements. For example, the diffraction efficiency ratio of the 0th^{P P}order beam and the ±1st^{P P}order beams could be well controlled within 4~10 at this thickness for a micro-grating in the optical pickup using the three beam tracking method. The index of refraction of low-stress silicon nitride is n=2.189+0.095i at wavelength=405 nm. (The fabrication and optical characteristic of current low-stress silicon nitride will be described in section 4-4.)

Fig. 4-4. Calculated reflectivity to transmissivity ratio of the TE mode

as a function of d^B2^B and d^B3^B at the Brewster angle incidence.

As shown in Fig. 4-4, the reflectivity to transmissivity ratio of the TE mode can be over 50 around the points: (d^B2^B, d^B3^B) = (210 nm, 52 nm), (210 nm, 158 nm), (210 nm, 216 nm), (210 nm, 360 nm), (700 nm,52 nm), (700 nm, 158 nm), (700 nm, 216 nm), and (700 nm, 360 nm). If d^B3^B was selected to be 52 nm, the mechanical strength of the second silicon nitride film would be too low. On the contrary, if d^B3^B was selected to be thicker, the absorption for the transmitted light would increase.

Therefore, d^B2^B and d^B3^B were selected to be 700 nm to effectively minimize stiction and 158 nm to have adequate mechanical strength, respectively. The calculation also shows that σ^BT ^B=15±5 and σ^BR ^B=infinity can be achieved at d^B1^B=384±10 nm, d^B2^B=700±100 nm and d^B3^B=152 ± 30 nm. The process margin is also practical in current fabrication technology.

4.4 Silicon nitride film for 405 nm

Silicon nitride can be deposited by the chemical vapor deposition with plasma enhancement (PECVD) or at low pressure (LPCVD). A stress-free PECVD silicon nitride film with high transparency at short wavelength can be obtained by a proper choice of process parameters, such as temperature and gas mixture, etc.^P[53]P The most serious concern of PECVD silicon nitride is its poor chemical durability in HF solution, which is used to remove the sacrificial silicon dioxide layers^P[54]P. The process results in high surface roughness and thickness variation, which will induce distorted waterfronts. As compared with PECVD silicon nitride, LPCVD silicon nitride has higher chemical durability against HF solution. To apply for short wavelength, LPCVD silicon nitride has to possess other two characteristics: lower stress to reduce

curvature and lower absorption to enhance the optical utilization efficiency.

To reduce the thermal stress on silicon based materials, the LPCVD silicon nitride (SiN^Bx^B) can be silicon-rich by controlling the gas flow ratio, SiH^B2^BCl^B2^B:NH^B3,^B to be over 5^P[55]P. Our measurement shows that the transparency of LPCVD silicon-rich SiN^Bx^B is rather lower for its extinction coefficient k at 405 nm is as high as 0.07. According to Gardeniers’ study^P[56]P, the mechanical and optical characteristics of the LPCVD SiN^Bx^B

films are related to the following parameters, in decreasing order of importance: the gas flow ratio of Si and N containing precursors, temperature and pressure, etc.

Since the silicon content is related to the high absorption at short wavelength, the effects of gas flow ratio and annealing condition on the residual stress and optical transmission of SiN^Bx^B films were studied in our experiment. All SiN^Bx^B films were deposited by LPCVD at 850℃ and 180 mTorr with various SiH^B2^BCl^B2^B/NH^B3^B ratio (η) under constant total flow rate of 102 sccm. The deposited films were then annealed at 1050℃ in nitrogen gas.

The dependence of the residual stress on the reaction gas ratio, η, for various annealing time is shown in Fig. 4-5(a). The film stress shows a general decreasing trend with increasing SiH^B2^BCl^B2^B/NH^B3^B ratio due to the increased silicon content. After annealing, the stress can be either increased or decreased by two competing mechanisms: the stress relaxation within the grain of the film and the film shrinkage due to dehydrogenation^P[57]P.

The dependence of the complex refractive index, n + i k, on the reaction gas ratio for various annealing time is shown in Fig. 4-5(b). The n increases nearly linearly with increasing η while the k shows a sharp increase for η> 3, due to the increased content of silicon with high index and high absorption. For the SiN^Bx^B film to be used in the micro PBS, it should be low stress and low absorption. Since higher SiH^B2^BCl^B2^B/NH^B3

Bratios decrease the stress but increase the absorption, a trade-off is required. Therefore, a SiH^B2^BCl^B2^B/ NH^B3^B ratio = 3 with two-hour annealing was selected to fabricate the lower stress (585 MPa) and lower absorption (n = 2.189+i0.0095) micro PBS.

(a)

Fig. 4-5. Dependence of (a) residual stress and (b) complex refractive index, n + ik, on the reaction gas ratio for various annealing times.

4.5 Summary

The optical theory of thin films has been briefly described in this chapter. We presented the fundamental theory and basic design of our stacked PBS. To reduce the fabrication complexity, the PBS consisted of a novel stack of two silicon nitride layers separated by an air gap. The simulation showed that if the thicknesses of the first silicon nitride, air gap and the second silicon nitride were selected to be 384 nm, 700 nm and 158 nm, respectively, the extinction ratios of the PBS would be above 10 for the transmitted light and above 20 for the reflected light.

The development of the low stress silicon nitride film with low absorption at 405 nm was also described. The result showed that using the recipe SiH^B2^BCl^B2^B/ NH^B3^B ratio = 3 with two-hour annealing produced a silicon film with lower stress (585 MPa) and low absorption (n = 2.189+i0.0095).

Chapter 5

Fabrication and Measurement of a Polarization Beam Splitter

5.1 Structure design and device fabrication

The stack of two silicon nitride layers separated by an air gap can be fabricated by surface micromachining. The structure is shown in Fig. 5-1. A poly silicon capping ring is used to mount a stack of silicon dioxide and silicon nitride layers, which^BBare deposited alternatively on the poly silicon frame. After HF solution releasing, the silicon dioxide layers are removed, leaving an air gap, whose height can be controlled by dimples.

Fig. 5-1. Schematic of the micro PBS: (a) cross-sectional and (b) top view.

As compared with the previous surface micromachining, which we use to make the multi-beam optical pickup, there are some differences. First, there are two silicon nitride layers and one silicon dioxide sacrifical film after the first poly-silicon structural layer. Besides, there is no metal layer in the fabrication of the micro-PBS.

The surface micromachining we use to make a pop-up type micro PBS is illustrated in Figure 5-2. The three-dimensional micro PBS consists of two layers of SiN^Bx^B optical film mounted in a poly-Si supporting frame. The support frame is held perpendicular to the substrate by locking with a micro-spring latch. To fabricate the device, a sacrificial silicon dioxide (SiO^B2^B) layer was first deposited on the silicon substrate.

Dimples and first anchors were then patterned in the sacrificial layer (Fig. 5-2a). The first structural poly-Si was deposited by LPCVD and patterned to form a micro-frame.

(Fig. 5-2b). A SiO^B2^B layer and the first optical SiN^Bx^B layer were deposited and patterned (Fig. 5-2c).. After depositing a SiO^B2 ^Blayer, a^BB0.7-um-deep dimple array was etched to

control the air gap after releasing. The second optical SiN^Bx^B layer was deposited and patterned before depositing a SiO^B2 ^Blayer (Fig. 5-2d).. Both SiN^Bx^B layers were deposited aiming for a thickness slightly greater than the target value. The thickness was further reduced to the target value at the HF releasing step. After patterning another anchors, the second structural poly-Si layer was deposited and patterned to implement the micro-spring latches and the micro-frame (Figure 5-2e). The wafer was annealed for two hours at 1050℃ in nitrogen to reduce the residual film stress. After releasing in HF solution (Fig. 5-2f), the micro PBS was then lifted to its vertical position by using a micro-probe, (Fig. 5-2g). The SEM micrographs of a pop-up micro PBS with a central aperture of 500 µm in diameter is shown in Fig. 5-3(a). Using the same process, the micro PBS was integrated with other components to form a micro optical pickup as shown in Fig. 5-3(b).

(a)

(g)

(d)

(e)

(b)

(c)

(f)

Fig. 5-2. Cross section of the processing sequence for fabricating the micro PBS: (a) definition of dimples and anchors, (b) definition of the first poly-silicon layer.

(c) definition of the first silicon nitride layer, (d) definition of the second silicon nitride and the second poly-silicon layer, (e) the structure after HF release, (f) the pop-up micro-structure.

(a)

(b)

Fig. 5-3. SEM photographs of (a) the micro pop-up PBS and (b) a micro optical pickup, including a cylindrical lens, a grating, a PBS a folded mirror and an astigmatic lens.

5.2 Experimental results and discussions

To measure the optical characteristic of the micro PBS, a GaN semiconductor laser at λ=405 nm was used as the light source. A retarder and a polarizer were used to adjust the polarization state of the light. An aperture of a diameter 200 µm was used to yield the beam size comparable with the micro PBS at Brewster angle incidence. The beam profile was measured by a CCD camera positioned at 10 mm from the micro PBS. The configuration used for measuring optical properties of micro-PBS is depicted in Fig.5-4.

Fig. 5-4 Configuration of the measurement system

In the fabrication of the three-layered optical structure, it is difficult to precisely control the thickness of each layer. One of the cause is the difference of boundary conditions for the first (upper) and the second (lower) silicon nitride layers, as shown in Fig. 5-5. The upper silicon nitride is between air and the silicon dioxide, while the

In the fabrication of the three-layered optical structure, it is difficult to precisely control the thickness of each layer. One of the cause is the difference of boundary conditions for the first (upper) and the second (lower) silicon nitride layers, as shown in Fig. 5-5. The upper silicon nitride is between air and the silicon dioxide, while the

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