Scattering parameters (S-parameters)

In the measurement of the RF or the microwave signals, it is prevalent to measure power directly because the measurements of the voltage and the electrical current are unrealistic.

In the measurement of the lossless transmission line, for example, the voltage and the electrical current are changed with the measured point among this lossless transmission line, but power is a constant anywhere, in this lossless transmission line. Another issue is that the voltage and the electrical current are difficult to define in a transmission line. So the power measurement is easier than the measurement of the voltage or the electrical current for the measurement of the RF and Microwave signal. Figure 3.2 shows the measurements of the two port network with S-parameters, which are measured by Network Analyzer, and definition of each S-parameter. The two-port matrix of S-parameters can be expressed as:

(3.19)

where a1 and a2 is signal traveling towards the two-port gate, b1 and b2 is signal reflected back from the two-port gate.S11 is equivalent to the input complex reflection coefficient or impedance of the DUT (Device Under Test), and S21 is the forward complex

transmission coefficient. S22 is equivalent to the output complex reflection coefficient or output impedance of the DUT, and S12 is the reverse complex transmission coefficient.

The characteristics of the VCSEL also can be measured as electromagnetic wave by Network Analyzer and DC Source/Monitor with the optical measurement set, which is described in the chapter 4. In the measurement and modeling of VCSEL, the S12 and S22

are undefined.

Figure 3.1 A small sinusoidal perturbation above threshold

Figure 3.2 Illustration of Scattering Parameters (S-parameters)

Reference

[1] H. Marcuse, “Classical derivation of the laser rate equation”, IEEE J. Quantum Electron., Vol. 19, No. 8, pp. 1228-1231, Aug. 1983.

[2] Renaud Stevens, “Modulation Properties of Vertical Cavity”, Doctoral Thesis, Laboratory of Photonics and Microwave Engineering, Department of Microelectronics and Information Technology, Royal Institute of Technology, Electrum 229, S-164 40 Kista, Sweden, 2001.

[3] R. Olshansky, P. Hill, V. Lanzisera and W. Powazinik, “Frequency response of 1.3µm InGaAsP high speed semiconductor laser”, IEEE J. Quantum Electron., Vol.

23, No. 10, pp. 1410-1418, 1987.

Chapter 4

VCSEL design and measurement setup

In this chapter, the fabrication systems and processes of an oxide-confined and an oxide-implant VCSEL will be presented briefly. The electrical and the optical measurement systems are also described here. The techniques for fabricating VCSEL, such as air-post, regrowth, proton-implantation and selective oxidation have been employed for the current path, gain region, carriers, and the optical confinement. The VCSEL fabricated by proton-implantation and selective oxidation has superior properties, such as simple and stable process. The fabrication systems and the design principles of VCSEL wafer structure are described in the section 4.1, 4.2, 4.3, and 4.4. The probe station system, spectrum measurement system, and the RF measurement system, which are used in our experiment, are described in the section 4.5 and 4.6.

4.1 Inductively coupled plasma reactive ion etching

The ICP etching equipment was a planar ICP-RIE system (SAMCO ICP-RIE 101iPH) as shown in Figure 4.1. The ICP main system is consisted of the source chamber and plasma chamber. The source chamber is constructed with RF generation and matching unit including vacuum pumping system, gas transportation system, and cooling water system.

4.1.1 Plasma source system

The ICP power and bias power source with RF frequency were set at 13.56 MHz.

The output RF power introduce into the tornado coil through impedance match and RF power transmission line. The high density plasma was formed by the tornado coil using the theory of inductively coupled plasma.

The tornado coil was fixed in the source chamber connecting with ground, and the

source chamber has the electromagnet field shielding effect. Between the source chamber and plasma chamber, there is the quartz window to be as the separation.

4.1.2 Vacuum pumping system

The vacuum pumping system was constructed with mechanical pump and turbo pump. There is a automatic pressure controller (APC) between the plasma chamber and pump. It could control the pumping rate by tuning the throttle inside the APC. The throttle and the pressure meter on the plasma chamber assemble a feedback control system.

4.1.3 Gas transportation system

Gas transportation system controls the flow rate of the gas source by the mass flow controller (MFC) and the entering of the gas source is decided by a control valve. The MFC and control valve can control the flux and time of the gas source. During the experiment, the pressure of the plasma chamber is set by tuning the APC and the MFC which control the flow rate of the gas source.

4.1.4 Cooling water system

During the experiment, some equipment must be continuously cooling and sure to be normal operating to prevent the damage, for example the RF generation and turbo pump. And the source chamber and plasma chamber should not be too hot; they also need to remove the heat by the circulating of the cooling water system.

4.1.5 Wafer transportation system

In the lab, the load lock chamber is set for keeping the high vacuum of the plasma chamber and enhances the convenience of the operation. The wafer transportation system contains the load lock chamber, the gate valve, the transportation arm.

4.2 Ion implantation system

The basic requirement for an ion-implantation system is to deliver a beam of ions of a particular type and energy to the surface of a wafer. Figure 4.2 shows a schematic view of a medium-energy ion implanter. Following the ion path, we begin with the left-hand-side of the system with the high-voltage enclosure containing many of the system components. A gas source feeds a small quantity of source gas such as BF3 into the ion source where a heated filament causes the molecules to break up into charged fragments. This ion plasma contains the desired ion together with many other species from other fragments and contamination. An extraction voltage, around 20 kV, causes the charged ions to move out of the ion source into the analyzer. The pressure in the remainder of the machine is kept below at 10^-6 Torr to minimize ion scattering by gas molecules. The magnetic field of the analyzer is chosen such that only ions with the desired charge to mass ratio can travel through without being blocked by the analyzer walls. Surviving ions continue to the acceleration tube, where they are accelerated to the implantation energy as they move from high voltage to ground. Apertures ensure that the beam is well collimated. The beam is then scanned over the surface of the wafer using electrostatic deflection plates. The wafer is offset slightly from the axis of the acceleration tube so that ions neutralized during their travel will not be deflected onto the wafer. A commercial ion implanter is typical 6m long, 3m wide, and 2m high, consumes 45 kW of power, and can process 200 wafers per hour (dose 10¹⁵ ions/cm²).

Three quantities define an ion implantation step: the ion type, energy, and dose.

Given an appropriate source gas, the ion type is determined by magnetic field of the analyzing magnet. In a magnetic field of strength B, ions of charge Q move in a circle of radius R, where

(4.1)

where V is the ion velocity and V is the source extraction voltage. The magnetic field is adjusted so that R corresponds to the physical radius of the magnet for the desired ion. It is possible for other ions to be accepted if they have a similar value for M1/Q, but since the source provides ions with decrease the beam current. The selected ions are accelerated to the implantation energy by the voltage applied to the acceleration tube.

The total number of ions entering the target per unit area is called the dose. If the current in the ion beam is I, then for a beam swept over an area A, the dose Φ is given by

(4.2)

where the integral is over time t. Completing the circuit between target and on source allows the current to be measured. For an accurate current reading, care must

be taken to recapture secondary electrons emitted from the target by incident ions. A Faraday cage around the target, at a small positive bias voltage collects this charge so that it can be included. Wafers frequently patterned surface layers of silicon dioxide, which is a good insulator. Implantation can charge up insulated regions of the surface high enough for dielectric breakdown to occur, which damages the materials. If the wafer is not well grounded, charging of the whole wafer can distort the ion beam. To avoid this effect, a low-energy election beam can be directed onto the target surface during implantation.

The electrons are drawn to charging regions where they neutralize the charge buildup.

Any implantation machine has design limits to its energy range. The minimum implantation energy is usually set by the extraction voltage, which cannot be reduced too far without drastically reducing beam current. Some special machines can operate in a deceleration mode, in which ions are extracted with a normal voltage but then slowed down in a reverse-biased "acceleration" tube resulting in energies as low as 5 KeV. A more common technique uses implants of molecular ions containing the required dopant,

for example, BF₂⁺ ions could be implanted at 30 KeV. When the molecule hits the target surface it immediately breaks up into its components, and the energy is divided according to the relative masses. In this case, we would have one 7 keV boron atom and two 11 keV fluorine atoms. The resulting profiles are the same as if 7 keV boron and 11 keV fluorine had been directly implanted, because the binding energy of the molecule is negligible compared to the implantation energy. If channeling is significant, the profiles will be different from that of 7 keV boron alone because the addition of fluorine will increase the lattice damage and reduce channeling. The fluorine distribution is shallower than the boron distribution, so ions can still enter channels when they have traveled past the fluorine peak. Fluorine has only a small effect on annealing and on electrical mobility in the final device.

The maximum implantation energy is set by the design of the high-voltage equipment. The only way to circumvent this is to implant a multiply-charged ion such as B⁺⁺. This ion would receive twice the energy of B⁺ from the same accelerating potential, effectively doubling the energy of the machine. The price paid is a reduced beam current since the number of B⁺⁺ ions in the source plasma is much smaller.

4.3 Fabrication of the oxide-confined VCSEL

A VCSEL consisted of two DBR mirrors and an active layer, which is usually multi-quantum-well sandwiched between two high reflectivity DBR mirrors. We study an 850nm GaAs / AlGaAs VCSEL that is grown by MOCVD on the Si-doped GaAs substrate in this paper. The bottom DBR mirrors has 32 pairs of alternate Al0.15Ga0.85As and Al0.9Ga0.1As layer with quarter-wavelength-thick. The active region consists of three GaAs / AlGaAs quantum wells and cladding layer. The top DBR has 22 pairs of alternate Al0.15Ga0.85As and Al0.9Ga0.1As layer. A three high Al-content selective oxidation layers, Al0.98Ga0.02As, are inserted between the active region and the top DBR. Figure 4.3 shows a cross sectional view of a ring-trenched VCSEL structure, which is one of the oxide-confined VCSEL. A ring trench is made from the top to the bottom DBR mirrors

including the active layer by mesa etching in order to perform the selective oxidation process, which can improve the current spreading effect in VCSEL. The insulated layer is formed by SiN_X to reduce the current leakage of the metal contact. The metallic bond pad is connected to the ring electrode by a bridge connection. This VCSEL structure not only provides an electrical confinement, but also has the optical confinement effect. The detail fabricated processes of this oxide-confined VCSEL structure are shown in Figure 4.4.

Figure 4.5 shows an oxidation process system setup. The wafer is placed in the center of the furnace and purged by N2. The wafer is annealed at 420^OC in the furnace, and then an invariable flow-rate of steam is imported into furnace for a fixed duration.

The duration of oxidation process is crucial to forming different oxide apertures. The oxide-extent is almost a linear proportion to the duration of the oxidation. Figure 4.6 shows the oxidation rate of 98% Al-content layer. We designed and a series of the oxide –confined VCSELs with different oxide apertures, which are 6, 7 and 8 um, by adopting different oxidation durations. The figure 4.7 shows photographs of oxide -confined VCSELs are taken by CCD camera.

4.4 Fabrication of the oxide-implant VCSEL

Figure 4.8 shows the fabricated processes for oxide-implant VCSEL. The most of processes are similar to oxide-confined VCSEL before the proton-implantation process.

The energy is 300-420K eV with the dosage of 10¹⁵ cm^-2 for implanting protons in the proton-implantation process. The purpose is that builds a partial rectangular insulated region under the P-metal for using different bombarding energies. Figure 4.9 shows the result of the simulation with Trim software. The implantation pattern is designed away from the oxide aperture in order to avoid the reliability issue caused. A series of VCSELs with different oxide aperture sizes are fabricated using same condition in implant process.

The characteristics of the static and the dynamic are presented in the chapter 5.

4.5 The probe station and the spectrum measurement systems

The probe station system is an essential instrument set for measuring the basic characteristics of VCSEL, such as I-L (current versus light output) and I-V (current versus voltage). Figure 4.10 shows a scheme of the probe station system, which includes a probe station, a current source, and a power-meter module. Keithley 238 is a current source that supplied a continuous current to the VCSEL and monitors the operation voltage of VCSEL simultaneously. The light output power of VCSEL is measured by Newport power-meter module (model 1835C). Then all of the measured data can be integrated by computer and plot the L-I-V trend of VCSEL on by the computer. For the measured accuracy of the light output power, an integration sphere is used to pick up whole light output from VCSEL. In the basic measurement, VCSEL device is placed on platform of probe station and injected a bias current through a microprobe. The threshold condition, slope efficiency, turn-on voltage, and differential resistance as L-I-V information can be observed by sweeping injected bias current. Distribution of transverse mode power is metered as near-field pattern. Near-field pattern (NFP) can be obtained by specific CCD and traced out by computer. Beam-view analyzer is useful software we used for taking NFP. We can obtain a NFP image of the spontaneous emission to define oxide aperture size while the VCSEL is operating under threshold. Emission spectrum is measured by Optical Spectrum Analyzer (OSA) from Advantec Inc. A multi-mode fiber is bundled on probe close to the focus of the emission aperture for taking spectra. The minimum spectrum resolution is 0.1nm the OSA provided. The lasing spectrum of VCSEL can be measured precisely by OSA. The spectrum measurement system has been combined with the probe station system in the Figure 4.10.

4.6 RF measurement system

We adopted the RF measurement system with powerful software from Agilent Inc.

Figure 4.11 shows a RF measurement system, which contains a network analyzer of Agilent 8720ES, a DC source/Monitor of Agilent 4156, an optical platform, and a RF probe. The software is Agilent 85190A IC-CAP 2002, which is used to extract the

parameters of the device, which can be a component, circuitry, or Integrated Circuit. The Agilent 8720ES network analyzer is a crucial instrument in the RF measurement system.

The output of the DC source/Moniter (Agilent 4156) is connected to the DC input at the rear panel of the network analyzer and provides a bias current through the internal circuit of the network analyzer for VCSEL operation. Transmitter of the network analyzer provides a -10dBm RF signal and a bias current to VCSEL directly. The benefit of this connection is that can perform RF measurement with DC sweep. All of the measured data will be sent back to computer via GPIB and plotted/recorded by IC-CAP 2002 software.

All of test conditions we wanted can be set in IC-CAP 2002. The extraction of the parameters can be executed by IC-CAP 2002 software after that all test conditions have been completed. The RF test signal from the network analyzer is injected into VCSEL, which is bonded on sub-mount substrate shown as Figure 4.12, through the coaxial cable and the coplanar RF probe. The coplanar RF probe has 700µm pitch, which is space from ground (G) to signal (S) tips, and maximum working frequency is up to 40 GHz. Signal probe is higher than ground tips. Fine probing is observed by signal probe skating on contact substrate.

Optical platform contains microscope, beam splitter, objective and fiber coupler etc.

We used a long work distance objective (20X, Mitutoyo), fixed in a triple-divide translation stage, to pick up the light output from VCSEL. Light is separated by beam splitter and received by CCD and another 10X objective (Olympus). One of splitting light is received by a simplified microscope, which is constructed by beam splitter and CCD to make probing easily. Another light path through 10X objective is coupled into multimode fiber by five-axis fiber aligner (Newport).

The collected light is transmitted into a 12 GHz Photodetector (Model 1580, NewFocus) that converts the light into electrical signal. The output of Photodetor is connected to the port 2 of the network analyzer. The characteristics of transmission and reflection can be expressed as vector (magnitude and phase), scalar (magnitude only), or phase-only quantities, that is, S-parameter. The theorem of S-parameter has been reviewed briefly in the chapter 3.

Figure 4.1 Schematic diagram of inductively coupled plasma reactive ion

Figure 4.2 Schematics diagram of a typical commercial ion-implantation

Figure 4.3 A cross sectional view of a ring-trenched VCSEL structure

(a) Epitaxial growth a VCSEL (b) Made a ring trench by mesa etching

(c) Passivation process (d) Metal contact coating for electrode

(f) Made electrical confinement by oxidation process.

Figure 4.4 The fabricated steps of a oxide-confined VCSEL

Figure 4.5 Illustration of an oxidation process system setup

Figure 4.6 The oxidation rate of 98% Al-content layer

Figure 4.7 OM-image of VCSEL with 6µm oxide-aperture

(a) Epitaxial growth a VCSEL (b) Made a ring trench by mesa etching

(c) Passivation process (d) Metal contact coating for electrode

(f) The oxidation process (g) The proton implantation process Figure 4.8 The fabricated steps of a oxide-implant VCSEL

Figure 4.9 Proton-implant depth with different energy simulating by Trim

Figure 4.10 Probe station measurement system

Figure 4.11 A RF measurement system

Figure 4.12 Sub-mount substrate design

Chapter 5

Measurement and modeling analysis

Most of VCSELs are fabricated to be an oxide-confined VCSEL, which can work with high frequency modulation. [1] [2]. But the highest modulation frequency that an oxide-confined VCSEL can reach is not enough to challenge the conventional Edge Emitting Laser due to parasitic effect in the oxide-confined structure. [3] A considerable parasitic capacitor, located between the bonding pad and the oxide-layer, is a crucial parameter for high speed modulation. There are many studies that reported about decreasing parasitic capacitance by the reduction of pad area [4], mesa implantation [5],

Most of VCSELs are fabricated to be an oxide-confined VCSEL, which can work with high frequency modulation. [1] [2]. But the highest modulation frequency that an oxide-confined VCSEL can reach is not enough to challenge the conventional Edge Emitting Laser due to parasitic effect in the oxide-confined structure. [3] A considerable parasitic capacitor, located between the bonding pad and the oxide-layer, is a crucial parameter for high speed modulation. There are many studies that reported about decreasing parasitic capacitance by the reduction of pad area [4], mesa implantation [5],