Chapter 1. Introduction
1.2 Outline of the thesis
This thesis is mainly presented by four parts as a diagram shown in Fig. 1.4, including QW design, materials, device characteristics, and waveguide coupler design.
For QW design, the principle to determine important material quantities for the band lineup and effective mass of strained layer is presented in appendix-A, along with an introduction of achievable materials in appendix-B, which both appendices can be regarded as the preparation for QW design. In order to prevent those basic parameters confusing reader, this thesis directly looks in more detail at the design of 1.55 μm transition wavelength InGaAlAs/InP strained-balanced QW structure, along with whole p-i-n laser/SOA’s ones in Chapter 2. Additional, in Chapter 6, six samples having similar structure to λ = 1.55 μm ones but different MD distribution inside barriers with reduced QW layer thickness for blue shifting transition wavelength to 1.48 μm are prepared for investigating the relations between Δn, Δα, and MD distribution.
For materials, after introducing the method for calibrating flux of source materials, those analytic results of MBE-grown epitaxial wafers including DCXRD, PL and TEM are discussed in chapter 3. Besides, a brief description for molecular beam epitaxy (MBE) machine using in this study and the growth process combing with growth conditions are separately exposed in appendix C and appendix D.
For device characteristics, the lasing properties of ridge waveguide and electro-absorption characteristics of mesa diode, including current vs. voltage (I-V), light vs.
current (L-I), lasing spectrum, photocurrent, EL, and EA measurements are separately discussed in Chapter 4 and 5 as well as their fabrication process.
Moreover, based on the same laser/SOA’s structure, a novel new design concept to reduce the device length more than 32% for conventional multi-mode interference (MMI) couplers, to have couplers with new power splitting ratio of 0.07, 0.64, 0.80, and 0.93, even to realize couplers with freely chosen power splitting is also presented in Chapter 6. Finally, several conclusions with a developing integrated device exposed as the future work are given in Chapter-7.
Fig. 1.4. A diagram for showing the outline of this thesis including four parts: QW design, materials, device characteristics, and waveguide coupler design.
Reference
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Chapter 2
Design of N-type Modulation-Doped InGaAlAs/InP Strained-Balanced MQWs Laser/SOA’s
In this thesis, we present the designs and MBE growth of epitaxial structures on InP containing n-type modulation-doped (MD) QW’s. They are designed to incorporate all the attractive features discussed in chapter 1. In section 2.1, important issues for designing TE-polarized laser/SOA’s wafer with lower transparency current density and higher differential gain are discussed by considering how to do a trade-off to have a narrow QW but still keep the wavefunction overlap integral squared (OIS) between conduction- and valance-band high for strained QW layers. After understanding what we concern given in section 2.1, a compact strained-QW with a high value OIS of 0.94 is exposed in section 2.2 with an introduction how to strain balance the strained-QW totally. In order to have a ridge waveguide with low loss, more circular intensity distribution in far field, and larger mode confinement factor, a frame for making our p-i-n laser/SOA’s structures completely is detailed in section 2.3; also, its n-type modulation doping distribution is involved in this section.
2.1 Important issues for TE-polarized laser/SOA’s QW
Considering a ternary InGaAs single QW with 1eV InGaAlAs (M) barriers for 1.55 μm wavelength emission, the calculated quantized energy states (e1, hh1, and lh1) and wavefunction overlap integral squared related to the needed QW thickness in different in-plane strain are separately indicated in Fig. 2.1(a) and (b). As mentioned previously, strain effect causes a separation between band edges of heavy- and light-hole. Compressive
strain moves up the heavy-hole band edge and moves down the conduction band edge; it will benefit the pure TE-polarized light emission because the energy transition of e1-hh1 will be more exposed by enlarging conduction- and valance-band offset. The larger band offsets also help to reduce the necessary QW width for 1.55 μm operation. Additionally, in order to make QWs having low-transparency carrier density (for low lasing threshold) and high differential gain (for high-speed modulation), two major issues for multiple-QWs (MQWs) design should be considered: (1) the first one is how to reduce in-plane effective mass inside QWs as low as possible that is because the step-like density of states are directly proportional to its effective mass, in other word, keeping the in-plane effective mass low will follow a lower density of states; (2) the other is how to have a closely matched density of states between the valance and conduction bands.
See dash-line in Fig. 2.1(c), because the out-off-plane electron effective mass is about 8 times smaller than heavy-hole one, it usually exists only one electron subband but not for heavy hole one. A narrower QW width further enlarges the separation between the lower hole subbands (i.e. hh1-hh2). And, a larger separation between these subbands has a positive influence on the gain [2.1]. In addition, according to Fig. 2.1(d), the another advantage of a closely matched density of states between conduction and valance bands from a compressive strain QW is contributed to which in-plane heavy-hole effective mass is reduced significantly and more closed to electron one. However, a QW with thinner thickness cause another problem: more asymmetric wavefunction distribution and a lower value of OIS between electron and hole.
In brief, in order to lower transparency current density and have a higher differential gain, trade-off to have a narrow QW but still keep the OIS high for a compressive strained-QW is the very important issue in the design of TE-polarized laser/SOA’s QWs structures.
Fig. 2.1. Strain dependent bandgap parameters for the strained InGaAs single QW with lattice-matched InGaAlAs (Eg = 1eV) barrier and the well width is set such that the energy transition wavelength of e1-hh1 (ε|| < 0) or e1-lh1 (ε|| > 0) is 1.55 μm: (a) quantized energy position (e1, hh1, and lh1), (b) QW thickness and wavefunction overlap integral squared, (c) the inverse out-of-plane effective mass, and (d) the inverse in-plane effective mass.
2.2 Laser/SOA’s QW design for active devices
In this thesis, our QW’s design is based on those achievable materials mentioned in appendix-B. Fig. 2.2 shows the wavefunction and the band diagram (conduction and heavy-hole valance bands) of six different QW designs for 1.55-μm TE-polarized laser/SOA’s. The simple QW as shown in Fig. 2.2(a) uses a lattice-matched InGaAs in the QW core and lattice-matched InGaAlAs (1eV) in the barriers. Although its ΔEc/ΔEg = 0.65 and the value of wavefunction OIS between e1 and hh1 states is quite high at 0.95, the required QW thickness of 9-nm is rather large to introduce the living of undesired first excited electron state (e2), which is not indicated inside Fig. 2.2(a). In Fig. 2.2(b), we change the QW core from lattice-matched InGaAs to compressive-strained In0.67Ga0.33As (ε||
= - 0.94 %). In this case of ΔEc/ΔEg = 0.57, the 3.5-nm QW is much more compact, but the wavefunction OIS decreases to 0.84. In Fig. 2.2(c), we use tensile-strained In0.438Ga0.386Al0.176As (ε|| = 0.63 %) as the barriers to compensate the strained stress between the QW core and barriers. In this case of ΔEc/ΔEg = 0.49, the 3.5-nm thick QW is still compact but the wavefunction OIS decreases significantly to 0.78. This is because the electron wavefunction extends much wider than the heavy-hole wavefunction. In Fig. 2.2(d), we obtain a compromise by using a thin 1.8-nm lattice-matched InGaAs as the QW core and 1.5-nm compressive-strained In0.67Ga0.33As as the QW padding beside the QW core. The wavefunction OIS improves to 0.87 with a little extended QW thickness of 4.8-nm. In Fig.
2.2(e), the design is optimized by using a thin 2.2-nm lattice-matched InGaAs as the QW core and 1.5-nm compressive-strained In0.67Ga0.33As as the QW padding on both sides of the QW core. We further use 1.6-nm wavefunction-adjustment layers of compressive-strained In0.714Al0.286As (ε|| = - 1.28 %) and thin 1.2-nm tensile-strained In0.438Ga0.386Al0.176As spacer layers to form the barrier structure, to balance the strain, and to enhance the electron confinement. With this design, we are able to achieve a high value OIS of 0.94 for a 5.2-nm-thick compact QW.
Considering how to design a strain-balanced QW by strain-compensated skills, we know two strained layers will be strain compensated if one is compressively strained with Nc monolayers (ML’s) while the other one is tensile strained with Nt ML’s and simultaneously matched to llowingfo rela ion t
N a N a N N a
(2.1)
where a and a are the out-of-plane lattice constant for compressively and tensile strained layers, respectively. a is the lattice constant of substrate. Eq. (2.1) can be transferred as
where dc and dt are the thicknesses for compressively and tensile strained layers, respectively. By using Eq. (2.2) and assuming the thickness of the most outside barriers in case of Fig. 2(e) is “d”, a symmetric strain-compensated QW structure with thicknesses of
“d(T)-1.6(C)-1.2(T)-1.5(C)-2.2(M)-1.5-1.2-1.6-d (nm)” can be calculated as
d 1.6 1.2 1.5 d
to obtain d = 4.3-nm, which out-of-plane lattice constant of strained layers are according to Table B-2. Additionally, n-type modulation doping (Si: 1x1018cm-3) is incorporated inside the half thickness of tensile-strained In0.438Ga0.386Al0.176As barrier layers and amounting to a sheet density of 4.3 x 1011 cm-2 per QW. The purpose of modulation doping is to help low the transparency current, to enhance the spontaneous-emission factor [2.2], [2.3] and to provide large Δn under reverse bias. This is the basis of our triple-QW’s laser/SOA’s structure which is labeled MD3QW. Its internal one-period structure for this strain-balanced
QW structure is detailed in Table 2-1. Moreover, it has a 3-nm-thick tensile-strained In0.305Ga0.417Al0.278As (ε|| = 1.55 % and Egu = 1.33 eV) as hole-stopping barrier, incorporated at the end of the n-region of the p-i-n layer structure immediately next to the InAlAs wavefunction-adjustment layer of the first QW as indicated in Fig. 2.2(f). The hole-stopping barrier is away from the first QW with 1.2-nm spacer layer and 1.6-nm wavefunction-adjustment layer. According to our simulation, it does not affect the value of wavefunction OIS between e1 and hh1. Also, it is expected to reduce the penetration of holes into the n-layer and to enhance the injected hole density inside the QW’s.
On the other hand, trade-off between threshold current, differential gain and refractive index change (Δn) is another important issue at SOA-based devices. Usually, we can get the lowest threshold current by single QW design but higher differential gain will carry out from more QW’s. The Δn simulation relative to the number of QW’s by Chin et al.[2.4]
points out that Δn does not have significant increase even at large reverse bias if the number of QW’s is more than three. In this study, we use triple-QW’s design as a compromise between threshold current, differential gain and Δn.
Fig. 2.2. Wavefunction and the band diagram of six different QW designs for 1.55 μm laser/SOA’s.
Table 2-1 Details of one fundamental period structure for 1.55-μm strain-balanced QW’s
Besides designing the active MQW’s structure, a frame for making p-i-n laser/SOA’s structure completely is also introduced with a schematic diagram incorporated with its band diagram of conduction- and valance-band as shown in Fig. 2.3(a) and (b); simultaneously detailed layer by layer in Table 2-2. Because growing InP is not possible presented in our MBE system, a 20-nm quaternary InGaAlAs (M) is used immediately as the smoothing layer in the beginning of epitaxy growth. Then, a following lower cladding layer is formed by a 100-nm InAlAs (M) sandwiched in between two pair of thin strain-balanced layers.
These two strain-balanced layers are composed of a 2.6-nm In0.714Al0.286As (C) and a 4.4-nm In0.416Ga0.205Al0.379As (T) and functioned as the conduction band grading steps. A 40-nm InGaAlAs (M) in the n-side and a 49.5-nm one in the p-side are applied beside the MQW’s to form the separate-confinement-heterostructure (SCH). In the p-side, we use a 1.82 μm InAlAs (M) as the upper cladding layer, a 30-nm InGaAlAs (M) as the p-contact grading step and a 60-nm InGaAs (M) as the final p-contact layer. In order to avoid p-type impurities penetrating into the MQW’s and ease to achieve the ohmic contact, the
Be-doping concentration in the p-side is stepped distributed and increased from 1 × 1018 cm-3 to 8 × 1018 cm-3; incorporated with a 75-nm undoped region. Further, the left 4.5-nm p-side and whole 40-nm n-side SCH layers are Si-doped with the same density as used inside MD-MQW’s barriers, 1 × 1018 cm-3; besides, the other layers in the n-layer is kept in a uniform doping distribution of 2 × 1018 cm-3.
Fig. 2.3. Schematic diagram for (a) p-i-n laser/SOA’s structure and (b) band diagram.
According to B.W. Wessels [2.5], we can estimate critical thickness (hc) at different in-plain strain (ε||) as indicated in Fig. 2.4. With this design, which strained-layer thicknesses presented in the structure of “MD3QW” shown in Table 2-2 are all controlled below the predicted critical layer thickness.
Because the refractive index (n) of InGaAlAs material system, special for strained ones, is less discussed in early; therefore, which refractive index values of quaternary and ternary
alloys listed in Table 2-2 for λ = 1.55 μm are deduced from Mondry et al [2.6] and estimated by assuming that each layer is like as an unstrained bulk material and its bandgap is corresponding to one of possible lattice-matched InGa(Al)As material. But the refractive index of InGaAs (M) and n+-InP are referred to Nojima et al [2.7] and Martin et al [2.8], respectively.
In order to make the optical mode calculation more easily in a p-i-n laser/SOA structure and considering the electric field of lasing mode is almost parallel to the epitaxial layer (TE-polarized mode), a method to obtain an effective average refractive index for active MQW region is given by nav(||) = ∑ d n d [2.9], where d is the layer thickness in the QW’s. Thus, for structure of “MD3QW”, the resulted value of nav(||) = 3.421 is applied to the following optical mode simulation.
In Fig. 2.5, we show the refractive index distribution of MD3QW in the transverse direction (y, perpendicular to epi-layers) combining with its related E-field expansion of fundamental slab TE-polarized mode (TE0); the effective index of slab (neff) TE0 is 3.2125.
Considering the single-mode-operation ridge laser is desirable in application, a 2-μm wide ridge is simulated to exist only one cross-section (xy) fundamental TE-mode when the etching-depth is 1.79 μm, which is very closed to the InAlAs-InGaAlAs interface; its ridge cross-section profile with the TE0-mode (neff = 3.196) near-field map is illustrated in Fig.
2.6(a). By using fast Fourier transform (FFT) method to transfer the near-field mode pattern, a far-field mode pattern is obtained and shown in Fig. 2.6(b). The simulated result indicates the far-field pattern is still kept in a quite symmetric angle divergence with a FWHM = 35.11o in the lateral direction (x) and a FWHM = 34.4o in the transverse direction (y) as shown in Fig. 2.6(c) and (d), respectively.
Table 2-2 Structure details of MD3QW
Fig. 2.4. Calculated critical thickness (soild-line) and the strained-layer thickness presented in structure of MD3QW (circle) as shown in Table 2-2 at different in-plain strain.
Fig. 2.5. The refractive index distribution of MD3QW in the transverse direction (y, perpendicular to epi-layers) and its E-field expansion of fundamental slab TE-mode.
(a) (b)
(c) (d)
Fig. 2.6. Ridge waveguide laser with width = 2 μm and etching depth = 1.79 μm; (a) the near-field map of fundamental cross-section TE-mode, and (b) its far-field pattern; (c) the divergence of far-field mode pattern in the lateral direction, and (d) in the transverse direction.
Reference
[2.1] J. C. L. Yong, J. M. Rorison, and I. H. White, “1.3- m Quantum-Well InGaAsP, AlGaInAs, and InGaAsN Laser Material Gain: A Theorectical Study,” IEEE J.
Quantum Electron., vol. 38, pp. 1553-1564, 2002.
[2.2] T. Mukai, Y. Yamamoto and T. Kimura: Semiconductors and Semimetals, ed. W. T.
Tsang (Academic Press, New York, 1985) vol. 22, Part E.
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[2.9] P. Bhattacharya, Semiconductor Optoelectronic Devices (2nd, Prentice-Hall, New Jersey, 1994), Appendix 18.
Chapter 3
MBE Growth of InGa(Al)As Materials and Laser/SOA’s Structures
The most important thing toward achieving our complicated QW’s designs is based on high quality MBE-grown materials. Fortunately, the reliable MBE techniques nowadays with helping by various powerful materials characterization skills provide us more opportunities to realize our designs than before. In order to introduce MBE-growth skills to newcomer interesting in this topic, the relevant issues will be focused on the growth-procedures, temperature conditions, molecular beam flux controller, and calibration
The most important thing toward achieving our complicated QW’s designs is based on high quality MBE-grown materials. Fortunately, the reliable MBE techniques nowadays with helping by various powerful materials characterization skills provide us more opportunities to realize our designs than before. In order to introduce MBE-growth skills to newcomer interesting in this topic, the relevant issues will be focused on the growth-procedures, temperature conditions, molecular beam flux controller, and calibration