Chapter 2 VCSEL structure
2.3 Optical and Electrical confinement
In the DBR section, we mentioned the diffraction of light in DBR mirrors reduces the reflectivity of DBR mirror. It is necessary to confine the electrical current and optical region in order to obtain high performance VCSEL. The Figure 2.6 shows five main types of electrical confinement and described below.
(a) Ring electrode type:
This structure restricts the electrical current in the vicinity of the ring electrode.
The light output is taken out from the central aperture of the ring electrode.
This structure is easy to fabricate, but the electrical current can not be confined completely in a small area due to the electrical current diffusion.
(b) Proton-implant type:
This structure usually uses proton (H+) to implant top DBR mirrors surrounding the desired optical region above active layer. The proton-implant builds a non-conductive region surrounding the desired optical region to confine the injection carriers into the opening of the electrical current aperture formed by the implanted area. Since proton-implant is a rather simple and low-cost technique and is simplified for further processing and packaging by the planarity, most commercialized VCSELs are fabricated by this scheme.
(c) Regrowth Buried-Heterostructure (BH) type:
This structure uses mesa etching to etch from top to bottom DBR mirrors including the active layer. After mesa etching, a wide-gap semiconductor is formed to restrict the electrical current in the VCSEL. The refractive index will be small in the surrounding optical region, leads to an index-guiding structure is formed. This is one of ideal structures in terms of the electrical current and the optical confinement. But the essential processes are rather complex for fabricating this structure.
(d) Air-post type:
A circular or rectangular air post is used to achieve the electrical current confinement. This structure is the simplest to fabricate, but non-radiative recombination at the outer wall may degrade the performance of VCSEL.
(e) Selective AlGaAs oxidation type:
A high Al content AlGaAs layer is made by oxidation process in the DBR mirrors. The Al-oxide formed a non-conductive layer during the oxidation process. This non-conductive layer has a lower refractive index than AlGaAs, acts as both an electrical current aperture and an optical waveguide. This effect leads to high conversion efficiency for converting electrical current to
optical output. By carefully monitoring the speed of the oxidation, the current aperture as small as a few µm can be reached, creating a waveguide that supports only the fundamental optical mode. The disadvantage of this structure is that the reproducibility is more difficult than the proton-implant type. Since the oxidation of the high Al content AlGaAs layer is very sensitive to material and process parameters, the speed of oxidation is highly dependent on the Al concentration and the temperature of the furnace in which the oxidation takes place. [4]
Figure 2.1 A typical structure of the VCSEL
Figure 2.2 How to achieve the reflection of light by DBR mirrors
Figure 2.3 Stop band effect in DBR mirrors
Figure 2.4 A GaAs/AlGaAS quantum well
Figure 2.5 A typical multi-quantum wells structure
(a) Ring electrode type (b) Proton implant type
(c) Regrowth Buried-Heterostructure type (d) Air-post type
(e) Selective AlAs oxidation
Figure 2.6 The electrical confinement schemes
Reference
[1] G.M. Yang, M.H. MacDougal and P.D. Dapkus, “Ultralow threshold current vertical-cavity surface-emitting lasers obtained with selective oxidation”, Electron. Lett., Vol. 31, pp. 886-888, 1995.
[2] Rainer Michalzik and Karl Joachim Ebeling, “Operating Principles of VCSELs”, University of Ulm, Optoelectronics Department, D-89069 Ulm, Germany.
[3] L.A. Coldren and S.W. Corzine, “Diode Lasers and Photonic integrated Circuits”, John Wiley & Sons, Chapter 4, 1995.
[4] K.D. Choquette, K.M. Geib, C.I.H. Ashby, R.D. Twesten, O.Blum, H.Q. Hou, D.M. Follstaedt, B.E. Hammons, D. Mathes and R.Hull, “Advances in selective wet oxidation of AlGaAs alloys”, IEEE J. Select. Topics Quantum Electron., Vol.3, pp. 916-926, 1997.
Chapter 3
VCSEL dynamics
For digital communication, the maximum bit-rate, which the information can be sent, depends on how fast the laser can be modulated. The constantly increasing demand for bandwidth requires faster lasers. Therefore, It is important to understand the mechanisms occurring in a VCSEL under modulation, to identify the limiting factors and ultimately to minimize them. This chapter presented the small signal analysis based on the rate equations. In this chapter we presented the small signal analysis first. Second, we presented three main factors of bandwidth-limitation, damping, thermal and parasitic effects. Third we presented a part of S-parameters, which are used in our experiment.
3.1 Small signal analysis
Figure 3.1 shows a small sinusoidal perturbation above threshold current (Ith). In the small signal analysis with time dependence e jωt is assumed to initiate only small changes in the steady state values of carrier and photon densities. The Equations 3.1 and 3.2 expresses the rates of change of carriers and photons numbers, which are rate equations.
(3.1)
where (dN/dt) states that the temporal increase of the number of carriers in the cavity. N is the number of carriers in the cavity, Iin is the injection rate of carriers, Isp is the rate of carriers dissipated through spontaneous recombination, and the RstS is the stimulated emission.
(3.2)
The Equation 3.2 is derived from the wave equation. [1] (dS/dt) states that the temporal increase of the number of photons. S is the net increase of the number of
photons, Rsp is the rate of the generated photons through spontaneous emission, RstS is stimulated emission, γi is the internal loss rate of the photons due to the absorption of photons through scattering and free carrier absorption. The γm is the loss rate of the photons in DBR mirrors. The output coupling is represented by the term γmS. The term Rsp is the amount of spontaneous emission that is resonant with the cavity and within the same longitudinal mode as the coherent light. The spontaneous recombination current Isp
describes the recombination of the electrons in the conduction band with holes in the valence band.
In the small signal analysis, the Equations 3.1 and 3.2 can be linearized by neglecting the quadratic and higher power of ∆S and ∆N, and can be written in the following matrix form [2]
Rst is the stimulated emission rate while the spontaneous emission is neglected above threshold. The subscripts S and N denote the partial derivatives with respect to the photon and carrier numbers and the subscript 0 denotes the steady state solutions of the rate equations. By solving ∆N and ∆S from the above equation system, the following solutions are obtained:
(3.4)
(3.5) where Q0(ω) = - ω2 + jω(A + D0) + (B0C + AD0) (3.6)
The term (B0C+AD0) represents the resonance frequency ωR2, and (A+D0) governs the damping γ. Therefore the modulation intrinsic response of a laser is
(3.7)
In addition to the two complex conjugated poles of the intrinsic response, the measured response often contains a third real pole. This parasitic-like roll-off is due to the electrical capacitance of the metallic contact and the high conductive layers connected to the metallic contact. However, slow diffusion limited carriers transport through undoped layers can also cause parasitic-like effects due to the charge pile.
From above discussion, the theoretical transfer function describing the modulation response of a laser can be written a function of the frequency f:
(3.8) γm
where C1 = 4π 2C fP ——— (3.9)
γm + γi
C1 is a coefficient that depends on the coupling efficiency and the quantum efficiency. fr
and γ are the resonance frequency and damping rate of the relaxation peak, fP is the parasitic-like roll-off frequency.
The angular resonance frequency can be written as follows:
(3.10)
where vg is the group velocity, a is the differential gain, Np is the photon density (ΓS/V) and τP is the photon lifetime in the cavity. This equation shows the importance of the differential gain in the modulation response of a laser.
The damping rate of the resonance peak, γ, can be written
(3.11)
where ε is the gain compression factor and τ∆N is the spontaneous differential lifetime.
The first two terms can be interpreted as the inverse differential stimulated carrier lifetime and the third term is the excess damping associated with gain compression. The damping rate of the resonance peak is also affected by spontaneous emission rate, carrier transport effects and spatial hole burning effects but they are neglected here for simplicity.
Using Equation 3.10 the damping rate γ can then be expressed as function of the resonance frequency fr
γ = Kfγ2 + γ0 (3.12)
1 ε where K = 4π [τ + —— ] and γ = —— P 0
vga τ∆N
K is called the K-factor and it describes the damping of the response for high bias currents. γ0 is the damping factor offset and determines the laser bandwidth at threshold.
These two parameters can be extracted from the result of the RF measurement which is described in the chapter 5. Because the damping increases in proportion to fr2, the response becomes flatness while the laser is driven at high current. At some points, the damping is large enough that drops the response below the 3dB cut-off at frequencies smaller than fr. As a result, there is a maximum bandwidth that can be achieved.
By taking into account the steady state solution of the rate equations for the photon density, and assuming that all injected carriers are converted to photons above threshold current, Ith. The photon density, Np, can be written:
(3.13)
where q is the electron charge, Γ is the confinement factor and V is the active region volume. I and Ith are measured in Amperes.
By plugging Equation 3.13 into Equation 3.10, we can then obtained
(3.14)
where D is called the D-factor and has been defined as
(3.15)
3.2 Bandwidth limitations
At high relaxation frequencies the linear relation between γ and fr2 implies a maximum possible bandwidth, the damping limit given by [3]
(3.16)
The modulation bandwidth of the laser may be limited by thermal effects that gives a maximum relaxation frequency fr,max, that occurs at a current Imax , before the damping limit is reached.
(3.17)
The parasitic and transport effects lead to a low-pass filtering with a cut-off at ω=1/τpar
where τpar is the time constant for the RC -like roll-off. The maximum 3dB frequency corresponding to the parasitic limit is
(3.18)
where fpar = 1 / (2 π τpar)
Because the resonance peak raises the response at high frequency, so that the maximum 3dB frequency corresponding to the parasitic is larger than the frequency associated with the RC-constant.
For the equations 3.16, 3.17 and 3.18, the true maximum 3dB bandwidth of the VCSEL is dominated by any equation, which provides the 3dB bandwidth is much lower than the other two equations provided. By comparing those 3dB bandwidths provided by equations 3.16, 3.17 and 3.18, it is possible to identify the physical mechanism that is the main factor of the bandwidth limitation.
3.3 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
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