IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 10, OCTOBER 2001 1049 Small-Signal Frequency Response of Long-Wavelength Vertical-Cavity Lasers K. A. Black, Member, IEEE, E. S. Björlin, Student Member, IEEE, J. Piprek, Senior Member, IEEE, E. L. Hu, Fellow, IEEE, and J. E. Bowers, Fellow, IEEE Abstract—The small-signal frequency response of long-wavelength vertical-cavity lasers (LW-VCLs) is of interest in determining the ultimate bandwidth of these devices for use in terrestrial networks. This letter analyzes two distinct device structures of double wafer-bonded vertical-cavity lasers operating at 1.5 m and compares their high-speed performance. We demonstrate the highest modulation bandwidth and the highest modulation current efficiency of an electrically pumped LW-VCL of 7 and 4.1 GHz/ mA, respectively. Index Terms—Frequency response, optical modulation, semiconductor lasers, vertical-cavity surface-emitting lasers, wafer bonding. I. INTRODUCTION M UCH of the current research activity surrounding longwavelength vertical-cavity lasers (LW-VCLs) is inspired by the growing need for sources aimed at high capacity wavelength-division-multiplexed (WDM) networks. Until recently, progress in the field has been slow as compared to shorter wavelength VCLs, mainly due to the lack of developed materials systems capable of achieving both high mirror reflectivity and long-wavelength emission. Extensive progress has been made in the static performance and high temperature characteristics through the uses of wafer bonding , antimonide-based structures , and GaInAsN . However, perhaps the greatest attribute of the vertical-cavity structure is its small active volume, which could potentially lead to large modulation bandwidths at low drive currents. This is extremely important as one moves toward OC-192 and 10-Gb Ethernet networks that demand inexpensive directly modulated sources. To date, the best reported LW-VCL performance has been demonstrated using wafer bonding. Previous transmission results at 1.5 m have demonstrated 2.5-Gb/s transmission over 200 km of single-mode fiber, as well as a small-signal modulation bandwidth of 4.7 GHz . This letter investigates two similar LW–VCL structures and their capacity to demonstrate high modulation bandwidths. Both devices were made by wafer bonding AlGaAs–GaAs-based mirrors onto an InP-based active region. Manuscript received March 28, 2001; revised June 18, 2001. K. A. Black was with the Electrical and Comuter Engineering Department, University of California at Santa Barbara, Santa Barbara, CA 93106 USA. She is now with Zaffire, San Jose, CA 95134 USA. E. S. Björlin, J. Piprek, E. L. Hu, and J. E. Bowers are with the Electrical and Comuter Engineering Department, University of California at Santa Barbara, Santa Barbara, CA 93106 USA (e-mail: [email protected]). Publisher Item Identifier S 1041-1135(01)08076-4. II. THEORY The modulation bandwidth of a laser is governed by inherent properties of the cavity and the materials used, drive current relative to threshold, as well as external parasitics associated with contact pads, current supplying leads, etc. The intrinsic bandwidth of the laser cavity is limited by the relaxation resonance frequency of the cavity, thermal constrictions, and at higher drive currents, by the damping rate. The square of the relaxation oscillation frequency ( ) is proportional to the drive current less the threshold current, and inversely proportional to the active volume of the device. The low threshold current and small active volume of VCLs, compared to in-plane lasers, yields high relaxation resonance frequency at relatively low drive currents, i.e., high modulation current efficiency factor (MCEF). Short wavelength VCLs have demonstrated modulation bandwidths of 21.5 GHz  and MCEF of 16.8 GHz/ mA . Modulation bandwidths up to 30 GHz have been achieved for in-plane lasers . However, the MCEF was in that case 1.2 GHz/ mA, clearly showing the advantage of the vertical-cavity design. The relaxation resonance oscillations of a laser cavity are damped by the loss of carriers to leakage and spontaneous emission, as well as photon losses. The damping rate increases with increased relaxation resonance frequency, eventually resulting in an over-damped system where the 3-dB rolloff occurs before the relaxation resonance frequency. The dependence of , where the damping on can be described by and are constants. depends on carrier transport effects and gain compression at higher photon densities. and can be extracted from modulation response measurements, and the intrinsic bandwidth can be calculated from these parameters. As the drive current above threshold increases, the photon density in the cavity, and thereby the rate of stimulated recombination increases. However, the laser cannot be driven infinitely hard. Problematic to LW-VCLs is the early onset of thermal rollover in the light output versus current versus voltage ( – – ) characteristics, at which additional injected current is dissipated as heat instead of generating more photons, limiting the maximum achievable resonance frequency. In practice, the modulation response of electrically pumped LW-VCLs is usually limited by external parasitics , . Contacts to the device add external capacitance, resulting in a three-pole filter behavior instead of the intrinsic (two-pole) RCL circuit behavior. The contact-pad capacitance can be reduced by decreasing the contact-pad area  or by increasing the distance between the p-contact and the ground . 1041–1135/01$10.00 © 2001 IEEE 1050 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 10, OCTOBER 2001 (a) (b) Fig. 3. Small-signal modulation response of device A. A 3-dB bandwidth of 3 GHz is achieved. The modulation bandwidth is limited by external parasitics. Fig. 1. Schematic of VCL structures with overlain equivalent circuit. Fig. 2. Room temperature L–I –V characteristics. III. EXPERIMENT The two analyzed device structures are shown in Fig. 1(a) and (b). Exact detail concerning the device design and processing can be found in . Both devices were fabricated using the same active region and mirror structures to eliminate inherent device differences from growth. The only material difference is in the top p-mirror doping close to the wafer bonded interface: device A uses a Be-doped surface layer (30 nm) at 8 10 /cm , whereas device B has a lower Be doping of 3 10 /cm . Both devices use oxide apertures for current confinement; the aperture opening is 7 m for device A and 4 m for device B. – – characteristics of both devices are shown in Fig. 2. The threshold currents of the devices are 2 and 1.1 mA, respectively, however the series resistance and operating voltage of device B is considerably higher. This difference, we attribute to an increased resistance across the wafer-bonded junction resulting from a lower doping of the GaAs-based mirror at the surface. Although this increase in operating voltage is most likely indicative of increased current spreading at the wafer bonded junction, it is estimated that the spreading will be no more than 1 m, effectively making the active volumes of device A and B similar. A quantitative analysis of the exact active volume of these devices is not necessary for the discussion of their frequency response, as the resonance relaxation frequency is not the limiting factor in either device. Also shown in Fig. 1, there are equivalent circuits overlain onto the structures. A resistance and capacitance in parallel ap- proximate the active region; the top DBR is modeled as a series resistance. The series capacitance across the oxide aperture has been neglected in this model, as in practice most currents, will be transported through the aperture opening due to the high parallel conductivity of the DBRs. Device A has a differential resistance of 138 and device B has a differential resistance of 153 . The major structural difference between the two devices is a reduction of the contact-pad capacitance in device B. In both devices, current is injected through the top (p) mirror. In device A, the p contact pad sits on the doped n-cladding, separated only by 400 nm of SiN. In device B, the doped cladding layer was removed and the contact pad is separated from ground by over 500 m of undoped material (Fig. 1), thereby practically eliminating the contact-pad capacitance. This structural difference does not affect the dc performance of the devices. All measurements were performed using a 20-GHz bandwidth HP8150 network component analyzer. A microwave frequency coplanar probe was used to contact the VCL contact pads. The optical response of the lasers was collected using a cleaved multimode fiber probe. Small-signal modulation response was measured for different drive currents. The measured data were fit to a general three-pole modulation transfer function where modulation frequency; parasitic rolloff frequency; resonance frequency; damping rate. A. Device A Fig. 3 shows the modulation response of device A. Measured data is shown by dots; the curve fits are shown by solid lines. (3 mA), a maximum 3-dB bandwidth of At a dc bias of 1.5 3 GHz is achieved. At larger biases, the response is limited by an initial low rolloff characteristic of external parasitic damping. The parasitic rolloff frequency associated with this device is found to be 1.2 GHz. Knowledge of the parasitic bandwidth allows one to extract the capacitance of the device from the RC . The differential resistance of time constant this device is measured to be 138 ; the calculated capacitance BLACK et al.: SMALL-SIGNAL FREQUENCY RESPONSE OF LW-VCLs 1051 damping, the relation between and is given by . In our case, occurs earlier than suggested by the above relation, a deviation that we attribute to damping. However, the linear dependence of to over the entire range of data suggests that this device is not limited by damping. Both the 3-dB rolloff frequency and relaxation oscillation frequency cease to increase with bias current above 5 mA. This is precisely the current at which thermal rollover in the – – characteristic occurs, suggesting that Device B is thermally limited. The calculated thermal limit to the maximum achievable bandwidth for this device, neglecting damping, is 8 GHz. IV. CONCLUSION Fig. 4. Small-signal response of device B. A modulation bandwidth of 7.0 GHz is demonstrated. Inset shows 3-dB bandwidth versus square root of current above threshold. A modulation current efficiency of 4.1 GHz/mA1/2. of the device is 2.6 pF. The maximum internal parasitic VCL capacitance is estimated to be less than 1 pF , indicating high external parasitic capacitance. reveals a -factor of Plotting the damping rate versus 0.48 ns. The intrinsic bandwidth, including carrier transport and gain compression, but neglecting heating effects and external parasitics, can be calculated using the experimentally derived -factor and the relation . The intrinsic bandwidth was found to be 18.4 GHz. This is a low value compared to those reported for short wavelength VCLs, due to the large -factor of this device. B. Device B Device B was fabricated with contact pads optimized to reduce the external parasitic capacitance of the VCL. The modulation response of device B is shown in Fig. 4. A record LW-VCL 3-dB bandwidth of 7 GHz at 5.5-mA bias is demonstrated. Immediately apparent, is the reduction in external parasitic capacitance as compared with device A. Indeed, the total capacitance calculated from the RC time constant was reduced to 0.92 pF, indicating that the contact-pad capacitance has been reduced significantly. The inset in Fig. 4 analyzes the modulation current efficiency of device B. A linear fit at low biases above threshold reveals a record LW-VCL MCEF of 4.1 GHz/ mA. The deviation from the fit at high bias is due to gain saturation and heating of the active region. The -factor of this device is determined to be 0.65 ns, implying a maximum intrinsic bandwidth of 13.8 GHz. The relatively large -factor of both device A and B can be attributed to their high differential resistance and current spreading under the oxide aperture. The fact that device B has a larger -factor than device A can be attributed to the lower doping close to the bonded interface in this device. 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