Chapter 2 Theory
2.3 V-parameter
where fp is the cutoff frequency of the low pass filter characterizing the extrinsic limitations. It is crucial for microwave applications that the modulation bandwidth of the VCSEL is sufficiently large so that efficient modulation is achieved as the modulation frequency.
2.3 V-parameter
Lateral-mode control of vertical-cavity surface-emitting lasers (VCSELs) is one of the key issues in realizing high performance optical communication systems, in which single-mode operation is necessary for long and short wavelength regions.
High-power single-mode operation is also required for free-space data communication applications. Recently, a two-dimensional photonic crystal (2-D PhC) structure formed on a VCSEL surface has been investigated as a lateral-mode control method. The most attractive feature of this structure is the enlargement of the emission area, thereby permitting higher power output. The large area can be realized because of strong wavelength dependence of the refractive index in the 2-D
photonic crystal structure, analogous to the situation in a photonic crystal fiber.
Although good single mode operation has been reported for a specific structure, the optimized design of 2-D photonic crystal structure was not clear, especially when considering a finite etching depth. Since the mode control mechanism utilized in this technology is the effective refractive index control achieved by forming a 2-D photonic crystal structure, a parameter representing this control must have a strong dependence on the etching depth. We have investigated the etching depth dependence, both theoretically and experimentally, of the effective index change in a VCSEL structure.
The 2-D photonic crystal structure with finite etching depth incorporating a single point or a seven-point defect is formed in the top DBR. It is known that the normalized frequency or V-parameter is useful in evaluating the number of guided modes in cylindrical wave guides, an important example being step index optical fibers. The cutoff condition of the first higher mode leads to Veff = 2.405, and thus a wave guide with Veff < 2.405 is considered to be single mode. In a photonic crystal VCSEL, the effective V-parameter can be expressed by
2 2 2 (2-23)
( )
eff eff eff
V πr n n γ
= λ − − n∆
where λ is an operating wavelength, r is an equivalent defect radius, neff is the effective refractive index of the VCSEL cavity [6] without a photonic crystal structure present, Dn is the refractive index reduction introduced by the photonic crystal structure, and gis the hole depth dependence factor that accounts for finite etching depth of the photonic crystal holes in actual photonic crystal VCSELs. The γ factor can be understood qualitatively as proportional to the spatial overlap between the photonic crystal structure and the longitudinal optical power distribution inside the VCSEL structure. Thus, γ = 0 for vanishing etching depth, γ = 1 for infinite etching depth, and γ = 0.5 for holes reaching the middle of the cavity. In the following discussion, the equivalent defect radii of a single point defect and seven-point defect structures are assumed to be Λ-d/2 and 3 Λ-d/2, respectively, where L is a lattice constant and d is the hole diameter of a circular hole of the 2-D photonic crystal
structure. Since we need to investigate larger d/L ratios than those of PCFs,[5] Veff is slightly modified from its appearance in Ref. 5, with the introduction of the Veff - parameter and the modified r in Eq. (2-23). The refractive index variation Dn can be obtained from the photonic band diagram of an out-of-plane propagation mode,[7,8]
calculated by assuming that the photonic crystal structure is infinite both in lateral and vertical directions.
Electron
SCH MQW SCH Cladding Cladding
Photon
Hole
Figure 2-1 Band diagram of active region of VCSEL
Rth
Ggen=ηi(I/qV)
Rnr
Rl
Current leakage
I/qV
Rsp
(a)
Rth
Rst
Ggen=ηi(I/qV)
Rsp
Rnr
Rl
Current leakage
I/qV
(b)
Figure 2-2 Reservoir analogy (a) under threshold (b) above threshold
Hole Electron
Photon
Ec
Ev
Ec
Ev
(b) Stimulated generation (absorption) (a) Spontaneous emission
Ec
Ev
(c) Stimulated recombination (emission)
Ec
Ev
(d) Nonradiative recombination
Figure 2-3 Basic electronic recombination/generation mechanism
Light output
Mirror 2 Mirror 1
Active region: N, Np, V Cavity: Vp
Z
Y
Figure 2-4 Schematic of VCSEL illustrating active region and cavity volumes
Light wer (mW
po )
Optical signal
Injection current (mA) Modulating
small signal
t
Figure 2-5 Conversion from electrical small signal train into optical signal
Frequency (Hz) Relaxation frequency
Cutoff frequency -3
0 Response
(dB)
Figure 2-6 Small signal modulation response of a VCSEL
Chapter 3
VCSEL fabrication and measurement setup
In this chapter, we presented the fabrication method of VCSEL, instrument setup for electrical and optical characteristics measurement. The fabrication techniques for VCSEL such as air-post, regrowth, proton-implantation, selective oxidation and reactive ion etch (RIE) had been employed to define the current path, gain region, carrier and the optical confinement. With in these techniques, the VCSEL fabricated by proton-implantation and reactive ion etch (RIE) had some superior properties such as simple and stable process. The design principles of VCSEL wafer structure were based on the method described as follow section. Finally, probe station system, spectrum measurement system , the establishments of eye diagram measurement system and far field pattern measurement system were described as follows.
3.1 Fabrication of tapered and blunt oxide VCSEL
A vertical cavity surface emitting laser consisted of multi-quantum-well sandwiched between two highly reflective distributed Bragg reflectors (DBRs). The 850nm GaAs / AlGaAs VCSEL devices studied here were grown by MOCVD on the Si-doped GaAs substrate. The bottom DBR had 39.5 pairs of alternating Al0.15Ga0.85As / Al0.9Ga0.1As pairs with quarter-wavelength-thick layer. The active region was consisted of three GaAs / AlGaAs quantum wells and cladding layer. The top DBR had 22 pairs of alternating Al0.15Ga0.85As / Al0.9Ga0.1As layer. A high Al-content selective oxidation layer, Al0.98Ga0.02As, was inserted just three layers above the active region. The VCSEL structure was trenched a ring of mesa, indicated in Figure 3-1, in order to execute oxidation process, which still improved current spreading effect. A bridge connected with contact ring and bond pad for current injection. Mesa structure benefited reducing current path and inducing optical confinement. Passivation layer coating, used of SiNx, formed an isolation layer reducing leakage current below metal contact. The detailed process of oxide-implant VCSEL was desired as Figure 3-2.
was placed into center of furnace and purge by N2. The furnace annealed approach 420oC then imported the invariable flow-rate of steam into furnace for fixed time.
Oxidation time was crucial for the process for forming different oxide apertures. The oxide-extent was almost linear relative to oxidation time, shown in Figure 3-4. For blunt oxide VCSELs, a 30-nm-thick Al0.98Ga0.02As layer was placed in node position.
For tapered oxide VCSEL, the tapered oxide layer was formed of a 10-nm-thick Al0.99Ga0.01 layer adjacent to a 200-nm-thick Al0.98Ga0.02As layer, which is similar to Ref. [9]. Multiple proton implantations with a dose in the range of 1013 ~ 1015 cm-2 and four different proton energy ranges between 200 to 420 keV were adapted according to simulation results of the stopping and range of ions in matter (SRIM). The implantation region was kept away from the mesa to prevent damage to the active region and consequent voiding of triggering reliability issues. A series VCSELs with different type of oxide layer were fabricated in the same implant process condition and their static and dynamic characteristics in were presented in chapter 4.
3.2 Fabrication of photonic crystal VCSEL
3.2.1 Fabrication of oxide photonic crystal VCSEL
The epitaxial layers of the PC-VCSEL’s wafer structure were grown on the n+-GaAs substrate by metal-organic chemical vapor deposition (MOCVD). The bottom distributed Bragg reflector (DBR) consists of a 30.5-pair n-type (Si-doped) quarter-wave stack of Al0.12Ga0.88As/AlAs. The top DBR consists of 22-period p-doped (carbon-doped) Al0.12Ga0.88As/AlAs quarter-wave stack. Above that is a heavily doped p-type GaAs contact layer. The graded-index separate-confinement heterostructure (GRINSCH) GaAs/AlGaAs active region has an undoped three-quantum-well (3QWs) GaAs/Al0.3Ga0.7As, a lower linearly-graded undoped AlxGa1-xAs (x = 0.6->0.3) waveguide layer and an upper linearly-graded undoped AlxGa1-xAs (x = 0.3->0.6) waveguide layer.The process was similar to oxide-confined VCSEL. After that, hexagonal lattice patterns of photonic crystal with a single-point defect were defined within the p-contact ring using photolithography and etched through the p-type DBR by using a reactive ion etch (RIE). The lateral index around a single defect can be controlled by the hole diameter (a) to lattice constant (Λ) ratio
and etching depth [10]. This ratio (a/Λ) is 0.5; the lattice constant Λ is 5 mm in the PC-VCSEL and the etching depth of the holes is about 17 pairs out of 22 pairs of the top DBR layers. The device structure, top view image of the PC-VCSEL, and the scanning electron microscope image of an etched hole were shown in Figure 3-5.
And the detailed process of oxide photonic crystal VCSEL was desired as Figure 3-6.
A series oxide photonic crystal VCSELs with different (a/Λ) ratio were fabricated in the same implant process condition and their static characteristics in were presented in chapter 4.
3.2.2 Fabrication of implant photonic crystal VCSEL
The process was similar to oxide photonic crystal VCSEL. The proton (H+)-implanted VCSEL was fabricated before combination with photonic crystal holes.
First, the p-contact ring with an inner diameter of 24 to 46 mm was deposited on the top of the p-contact layer and an n-contact was deposited on the bottom of an n+-GaAs substrate. The device was annealed at 430 oC under N2 ambient. The current confinement of the device, with a diameter of 10 mm, was then defined by proton implantation. The implantation energy was 270 keV, with a dosage of 6*1014 cm2. After that, the follow-up process was the same with the oxide photonic crystal VCSEL. The device structure is shown in Figure 3-7.
A series implant photonic crystal VCSELs with different (a/Λ) ratio were fabricated in the same implant process condition and their static characteristics in were also presented in chapter 4.
3.3 Probe station and spectrum measurement system
Probe station system was essential instrument for basic characteristics measurement such as I-L (current versus light output), I-V (current versus voltage).
Scheme of probe station system, illustrated in Figure 3-8, contained probe station, current source, and power-meter module. Keithley 238 as current source supplies continuous current for diode laser and receives relative voltage synchronously. Laser output power is measured by Newport power-meter module (model 1835C). With these data, we could plot the trend of L-I-V associated with computer. For accuracy
power measurement, an integration sphere was used to pick up whole light output from VCSEL.
For basic measurement, VCSEL device was placed on platform of probe station and injected bias current with microprobe. We could observe threshold condition, slope efficiency, turn-on voltage and differential resistance as L-I-V information by sweeping bias current injection. Distribution of transverse mode power is metered as near-field pattern. Near-field pattern (NFP) is still obtained by specific CCD and traces out results with computer. Beam-view analyzer is useful software we used in taking NFP. We could obtain NFP image under threshold, as spontaneous emission, to define oxide aperture size.
Emission spectrum was measured by Advantec optical spectrum analyzer (OSA). We served a multi-mode fiber bundle on probe close to emission aperture in focus for taking spectra. OSA had small spectrum resolution as 0.1nm for accurately measuring VCSEL lasing spectrum. Scheme of spectrum measurement system was combined with probe station as Figure 3-8.
3.4 Far field pattern measurement system
Distribution of divergence angle is metered as far -field pattern. We used a long work distance objective (20X,Nikon), fixed in a triple-divide translation stage, to pick up the laser output from VCSEL. Light was received by CCD(coherent 4800 )。
Far-field pattern (FFP) is still obtained by specific CCD and traces out results with computer. Beam-view analyzer is useful software we used in taking FFP. We could obtain FFP image under threshold, to define divergence angle illustrated with Figure 3-9.
3.5 Microwave test and eye diagram measurement system
The experimental setup for measuring eye diagrams is illustrated in Figure 3-10.
The VCSELs were probed using a high-frequency coplanar microwave probe (Picoprobe Model 40A) had 700µm pitch (ground (G) to signal (S) tip spacing) and
suitable frequency range was up to 40 GHz. Signal probe was higher than ground tips. Fine probing was observed by signal probe skating on contact substrate. Laser diode drivers (Newport, model 525) provided direct current signal to set the laser above the threshold. Bias-Tee combined AC and DC signal transmission through the same coaxial cable. A bias current was combined with a pseudorandom bit sequence of 231-1 from a 12.5-Gb/s pattern generator (Anritsu MP1764C). Optical platform contained 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 laser output from VCSEL. Light was separated by beam splitter and received by CCD and another 10X objective (Olympus). One of splitting light was received by a simplified microscope, which was constructed by beam splitter and CCD to make probing easily. Another light path trough 10X objective coupling into multimode fiber by five-axis fiber aligner (Newport).The laser output was focused using two object lenses into a 62.5 micore-diameter graded index multimode fiber and transmitted a short distance to a 12-GHz photoreceiver (New Focus 1580-LF).
The lenses serve to capture all the different modes despite their different divergence.
The electrical signal was amplified by the receiver before entering the 12.5-GHz digital oscilloscope (Agilent 86100A), triggered by the pattern generator.
3.6 Experimental guidelines
Special attention must be paid to the modulation depth of the single applied to the lasers. High modulation amplitude increases the signal to noise ratio but can introduce distortions of the response dues to nonlinerities and cause an artificial compression of the resonance frequency peak, especially with structures operating at very low bias currents such as oxidized VCSEL with sub-milliampere threshold.
For accurate parameter extraction it is also important to have a large signal-to-noise ratio. This can be achieved by using large temporal averaging factors during measurements. Averaging in the frequency domain, so-called smoothing is not recommended; it will reduce the frequency resolution of the signal and often corrupt the phase information.
A good rule is to measure the modulation response at 5 – 10 bias current until a maximum current is reached where the resonance frequency peak saturates or starts
At high frequency the signal to noise ratio is often poor. This noise in the high frequency region is in general not only caused by ordinary amplifier noise but also noise due to calibration problems of the measurement set-up. Even slight movement of the measurement cables will change the phase of distant reflections, which can give a noisy appearance of the measurement curve. Crosstalk can give similar effects. This type of noise is not uncorrelated at different measurement points and is difficult to distinguish from the signal. Hence, it is preferable to omit the highest frequency parts of the measurements where the signal where the signal-to-noise ratio is very poor.
The VCSEL chip has to be mounted on a module for commercial applications.
The package has limitations at high frequencies and the measured bandwidth can be strongly decreased by the package parasitics. Resonance and filtering effects introduced by the inherent package parasitics can be significant sources of error. The inductive and capacitive elements associated with the physical geometry of the package will result in small parasitic LC circuits, which will in turn cause voltage or current peaking at the resonace frequencies and low pass or band rejection filtering effect at other frequencies.
Figure 3-1 Cross section structure of tapered oxide implant VCSEL structure
Al0.98Ga0.02As layer
MQW: GaAs/AlGaAs
Al0.12Ga0.88As/Al0.90Ga0.10As 39.5 pairs (99.8%)
GaAs substrate
Au/Ge/Ni/Au n-contact Ti/Pt/Au p-contact
Al0.12Ga0.88As/Al0.90Ga0.10As 22 pairs (99.6%)
Figure 3-2 Steps of oxide-implant VCSEL process
(1) VCSEL structure epitaxy Substrate
(2) Mesa etching – ring-trench
(3) Passivation process PR
(4) Contact coating – electrode
(5) Oxidation process H2O 420oC
dosage: 1013~1015, 200~420keV
(6) Proton bombing
Figure 3-3 Illustration of oxidation process system setup
Thermal coupler
Furnace
N2
Heater
Boat VCSEL
H2O / H2 Purge
Figure 3-4 Oxidation rate of 98% Al-content layer
Al0.98Ga0.02As layer MQW: GaAs/AlGaAs
Al0.12Ga0.88As/AlAs 30.5 pairs (99.8%)
n+ GaAs substrate Al0.12Ga0.88As/AlAs 22 pairs (99.6%)
Figure 3-5 (a) Cross section structure of oxide photonic crystal VCSEL structure (b) top view image of the PC-VCSEL;(c) scanning electron microscope image of an etched hole.
60µm
(a)
(b)
(c)
Figure 3-6 Steps of oxide photonic crystal VCSEL process
(1) VCSEL structure epitaxy Substrate
(2) Mesa etching – ring-trench
(3) Passivation process PR
(4) Contact coating – electrode
R
Reeaaccttiivvee IIoonn EEttcchhiinngg ((AArr ,, CCll22 ))
(6) Etching air hole (5) Oxidation process
H2O 420oC
Implant region
MQW: GaAs/AlGaAs
Al0.12Ga0.88As/AlAs 30.5 pairs (99.8%)
n+ GaAs substrate Al0.12Ga0.88As/AlAs 22 pairs (99.6%)
Figure 3-7 Cross section structure of implant photonic crystal VCSEL
Probe Station Keithley 238
CW Current Source
Beam view analyzer
Objective nikon 20x NA 0.45 Computer
Objective nikon 20x NA 0.45 Computer
CCD mirror
Objective nikon 20x NA 0.45 Computer
CCD mirror
Computer Computer
CCD mirror
Figure 3-9 Far field pattern measurement system
Figure 3-8 Probe station measurement instrument setup
CCD
Bias-Tee
Photo detector Laser driver
Monitor
Lens CCD
Objective
Objective Fiber coupler
Beam splitter
Microwave probe
bonding wire
VCSEL (Device Under Test) substrate
Pattern generator
Bias-Tee
Photo detector Laser driver
Monitor
Lens CCD
Objective
Objective Fiber coupler
Beam splitter
Microwave probe
bonding wire
VCSEL (Device Under Test) substrate
bonding wire
VCSEL (Device Under Test) substrate
Pattern generator
Figure 3-10 eye diagram measurement instrument setup
Chapter 4
Result and discussion
Oxidation process was regular process for VCSEL fabrication. Most high speed VCSEL was also made by the same method. In our study, we chose different type of oxide implant VCSELs to compare with their high speed characteristics in first section.
In second section, we was according to the static and high speed characteristics of these VCSELs to modeling the equivalent circuit. Equivalent circuit modeling was investigated in section 4-2. With VCSEL modeling, the equivalent components were extracted and observe the modulation limitation caused by structure. In third section, we chose different type of photonic crystal VCSELs to compare with their static characteristics of these VCSELs
4.1 Oxide-implant VCSELs DC and AC characteristics
Tapered oxide VCSEL and blunt oxide VCSEL had same process structure, shown in Figure 4-1. Process structure was described in Chapter 3. Both VCSEL had the same oxide aperture as 5.5 µm and mesa as 30 µm.
The static characteristics of both VCSEL were shown in Figure 4-2. The threshold current is ~ 1 mA (0.9 mA) for tapered (blunt) type VCSELs with the same slope efficiency of ~ 0.35 mW/mA. The similar static performance is not surprising since 1. the oxide apertures here have the same size of 5~6µm and 2. the blunt oxide don’t incur excess scattering except at very small oxide size (< 3µm ). The maximal output power exceeds 3 mW at room temperature and output power rollover occurs as the current increases above 12 mA.
The measured modulation response curves for tapered oxide VCSEL and blunt oxide VCSEL were shown in Figure 4-3(a) and 4-3(b), respectively. The maximum modulation bandwidth of both VCSEL was 13 and 9.5 GHz. At low bias currents, the bandwidth increased in proportion to the square root of the current above threshold, as expected from the rate equation analysis. For blunt oxide VCSEL, low frequency rollover was observed and the modulation response became gradually overdamped
as the bias current increasing. In contrast, no rollover was observed in low frequency for tapered oxide VCSELs and the 3-dB bandwidth reached a maximum value of 13 GHz before fully overdamped. The observations coincide with the simulation results for blunt oxide VCSEL in which a significant overdamping was reported in the
as the bias current increasing. In contrast, no rollover was observed in low frequency for tapered oxide VCSELs and the 3-dB bandwidth reached a maximum value of 13 GHz before fully overdamped. The observations coincide with the simulation results for blunt oxide VCSEL in which a significant overdamping was reported in the