Vertical Cavity Surface Emitting Laser (VCSEL)

Microwave Extraction Method of Radiative Recombination and Photon Lifetimes up to 85 o C on 50 Gb/s Oxide- Vertical Cavity Surface Emitting Laser (VCSEL) C. Y. Wang, M. Liu, M. Feng, and N. Holonyak Jr. Department of Electrical and Computer Engineering and Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, 208 N. Wright St., Urbana, Illinois 61801 USA Abstract Optical modulation bandwidth for a semiconductor diode laser is governed by the thermally limited spontaneous radiative recombination lifetime, rec, photon lifetime, p, and cavity photon density for stimulated recombination. Thus, temperature dependent recombination lifetime is a critical parameter for the limitation of photonic device operations. Here, we develop a microwave extraction method to accurately determine the radiative recombination and photon lifetimes over a temperature range up to 85 C through the equivalent circuit modeling based on the measured microwave scatteringparameters. For an 850 nm oxide-vcsel with error free data transmission capability over 50 Gb/s, the extracted lifetimes are rec = 0.1778 ns and p = 4.2 ps at 25 C and rec = 0.2445 ns and p = 4.8 ps at 85 C. 1

1. Introduction Optical modulation bandwidth for a semiconductor diode laser is fundamentally governed by the thermally limited spontaneous radiative recombination lifetime, rec, photon lifetime, p, and cavity photon density. The radiative recombination lifetime of electron-hole pairs in quantum-wells (QWs) can be considered as an electrical delay and the photon lifetime inside the cavity can be treated as an optical delay which limits the frequency response of a diode laser. Thus, it is important to accurately determine these lifetimes in order for us to further improve the bandwidth of directly modulated laser (DML) optical links for energy efficient error-free data transmission. Previous experiments have been performed to measure the radiative recombination lifetime of GaAs and InGaAs. The methods of experimental conduction vary from optical transmission excitation [1], photoluminescence phase shift [2, 3], and time-resolved photoluminescence decay employing sub-picosecond/femtosecond pulses [4]. However, the determined recombination lifetimes range widely from 50 ns to 190 ps for the active region of double hetero-structures such as AlGaAs-GaAs-AlGaAs layers [1, 2, 5-7]. Recently, the heterojunction bipolar transistor with insertion of quantum-wells in the base is fabricated to characterize the radiative recombination lifetimes from 134 to 35 ps via the measurement of the collector current gain and optical output as a function of doping and QW size [8]. Therefore, a more accurate way of determining recombination lifetime is of great interest. The most direct technique for accurately determining radiative recombination lifetime is to measure the optical frequency response of the LED [9, 10] and semiconductor laser [11, 12] with microwave frequency input signal. 2

Nowadays, short-haul optical links based on 850 nm emission wavelength optical transceivers and multimode fibers (MMFs) are widely deployed in data centers, high performance computing and Ethernet applications because of their high speed and high data transmission efficiency. Vertical cavity surface emitting lasers (VCSELs) are the predominant devices used in the optical transceivers due to their high modulation bandwidth and low threshold capability. The electrically pumped VCSELs were first demonstrated with metal cavities [13]; however, the threshold current was too high for practical uses. Later, distributed Bragg reflector (DBR) cavities [14] were adopted to improve the optical cavity loss. Yet, it was not until the discovery of the native oxide of AlGaAs to provide simultaneous current and optical confinement, the low threshold VCSELs were finally realized for energy-efficient optical links [15-18]. A high Alcontent AlGaAs layer in the top DBR mirror stack can be oxidized to become Al x O y and form an aperture. The oxide is electrically insulating and thus can confine the flow of electrical carriers into the active region [16]. The low threshold 850 nm oxide-confined VCSELs opened up a new era for energy-efficient data transmission. Also, the refractive index contrast between the oxide and the surrounding semiconductor forms an optical aperture. Hence, by controlling the depth of the oxidation of the high Al-content AlGaAs layer, the aperture dimensions and the active region volume of a VCSEL can be tuned [16-18]. Currently, high speed VCSELs, without the usage of external error correction circuitry, with error-free (bit error ratio, BER, 10-12 ) data transmission capability 40 Gb/s have been demonstrated up to 85 C in both wavelengths of 850 nm and 980 nm [19-21]. However, the 850 nm VCSELs are much more widely use in the high speed 3

datacom application. Data rate up to 57 Gb/s error-free transmission have been reported for 850 nm oxide-vcsels at room temperature [22, 23]. For practical use, considerable efforts have been invested into the design of the active region and the DBR stacks to improve the thermal limited bandwidth up to 85 C for error-free data transmission [24]. We have recently reported an oxide-confined 850 nm VCSEL capable of achieving 50 Gb/s error-free transmission up to 85 C [25]. Table I sums up the state of the art high speed data transmission results for oxide-confined 850nm VCSELs. In this work, we developed a microwave extracting method on 850 nm oxide- VCSEL with a modulation bandwidth, f -3dB = 29 GHz, and an error-free transmission up to 57 Gb/s to accurately determine the recombination and photon lifetimes through the equivalent circuit modeling based on the measured microwave scattering-parameters (Sparameters) up to 85 C. With the formation of microwave equivalent circuit model, we are able to extract electrical parasitic parameters, intrinsic optical modulation bandwidth, and the recombination and photon lifetimes via de-embedding the bias dependent transfer functions obtained from optical bandwidth measurement and photodetector calibration. So far, very few efforts have been reported on microwave equivalent circuit modeling on high speed oxide-vcsels [12, 26]. 2. High-Speed 850 nm Oxide-VCSEL Epitaxial Structure The microwave equivalent circuit model is developed based on the physical structure and epitaxial layering of the oxide-vcsel. Hence, a brief introduction on the device structure and epitaxial design is needed to illustrate the equivalent circuit model. 4

The 850 nm oxide-vcsel material is grown by metalorganic chemical vapor deposition (MOCVD). From bottom to top, the epitaxial layer structure starts with the bottom n- doped DBR mirror consisting of 26 pairs of AlAs/Al 0.12 Ga 0.88 As and 3 pairs of Al 0.9 Ga 0.1 As/Al 0.12 Ga 0.88 As, followed by a 0.5-λ InGaAs multiple quantum-well (MQW) active region with 5 In 0.072 Ga 0.928 As strained QWs separated by Al 0.37 Ga 0.63 As barrier layers. The photoluminescence (PL) peak is at 839 nm and the fundamental mode, etalon, wavelength is at 848.7 nm at 25 C. Above the MQW active region is a p-dbr stack including 2 Al 0.98 Ga 0.02 As layers, 4 Al 0.96 Ga 0.04 As layers, and a total of 20 pairs of high/low graded index Al 0.9 Ga 0.1 As/Al 0.12 Ga 0.88 As layers, and finally a heavily p-doped GaAs contact layer. The binary AlAs layers in the bottom DBR mirror are designed to facilitate heat transfer out of the active region. In the top DBR mirror, the 2 Al 0.98 Ga 0.02 As layers are used for lateral oxidation to form oxide apertures for both electrical and optical confinement, and the 4 Al 0.96 Ga 0.04 As layers are for parasitic capacitance reduction to improve the high speed performance. The device fabrication steps are similar to the ones reported [21]. 3. Oxide-VCSEL DC Characteristics The DC characteristics, such as light-current-voltage (L-I-V) and optical emission spectrum, of the device are shown before the discussion of equivalent circuit model and the microwave characteristics. The device is mounted on a temperature-controlled stage and probed with 50 GHz bandwidth ground-signal-ground (GSG) probes. The device under test is biased with DC current, and the optical light output is collimated and coupled into a 50 μm core diameter OM4 MMF through a lens package constructed with 5

anti-reflection (AR) coating. The temperature-dependent, from 25 to 85 C, light-currentvoltage (L-I-V) characteristics of the device are shown in Figure 1. The threshold current increases from I = 0.8 ma at 25 C to 0.86 ma at 45 C, to 0.95 ma at 65 C, and finally to 1.08 ma at 85 C. The VCSEL threshold current (I ) as a function of the temperature (T) can be modeled by the following empirical formula [27], EEL (, ) (, ) exp / I T F T I F T I T T, (1) 0 0 EEL where I ( T ) describes the edge-emitter like behavior, exponential fitting, and FT (, is the factor that accounts for the gain-cavity wavelength detuning resulted from the narrow emission wavelength range of the top DBR mirror stacks. We assumed the detuning factor FT (, 1 since our VCSEL QW emission spectrum is closely match with that of the DBR mirror cavity as we have demonstrated good threshold EEL current fitting solely with I ( T )[12]. The fitted data of threshold current with respect to temperature for the VCSEL is shown in the inset of Figure 1, and the fitted 0 C threshold current and characteristics temperature are I o = 0.69 ma and T o = 195 C respectively. Derived from the slope of the L-I curves, the slope efficiency of the device is ~ 0.58 W/A at room temperature and ~ 0.5 W/A at 85 C. Figure 2 shows the optical spectrum of the device under the bias of I = 2.5 ma (25 C) and I = 3.6 ma (85 C). The biasing points correspond to a ratio of I I ~3for the respective ambient temperatures. A redshift of 3.98 nm is observed when the bias and temperature condition changes. From the optical mode spacing, (1,1) (2,1) 0.86 nm at room temperature, the optical modal diameter of the device can be determined to be d o ~ 5 μm by solving the Helmholtz equation [12]. 6

4. Equivalent Circuit Model and Parasitic Parameters Extraction In order to accurately represent the VCSEL, a physical model is needed as the basis for the equivalent circuit model. Previously we have constructed a physical schematic of microcavity VCSEL to model the electrical parasitic parameters [12]. A modified version of the physical schematic for the improved epitaxial structure is shown in Figure 3. The physical meaning of each parameter is described in the annotation of Figure 3. In regards of the two port S-parameter theory, if the mirror resistance is partially attributed to terminate the output port, the reflection coefficient, ( f ), is equivalent to S11 ( f ) and can be expressed as, itot ( f) itot ( f) itot ( f) ( f) S11, (2) i ( f) i ( f) tot tot where i ( f) tot is the transmitted modulation current wave and i ( f) tot is the reflected modulation current wave. The total modulation current injected to the VCSEL at frequency f can be defined as i ( f) i ( f) i ( f) at the input node. The electrical tot tot tot parasitic transfer function can be expressed as, id( f) id( f) Hpar ( f) (1 S11), (3) i ( f) i ( f) tot tot where id ( f ) is the portion of the transmitted small signal modulation current that goes through the diode intrinsic active region. By fitting both the magnitude and the phase of the S 11 ( f ) measurement data, the electrical parasitic parameters can be extracted and be used to formulate the electrical parasitic transfer function. Figure 4 (a) and (b) shows that 7

the modeled S 11 ( f ) results are well fitted with the measurement data at various biasing points at both RT and 85 C. The fitted electrical parasitic parameters are summarized in Table II. One way to verify the accuracy of the fitting parameter is to compare the fitted DBR mirror resistance to the derived differential resistance from the I-V curves in Figure. 1. The DBR mirror resistance is the most dominant resistance element since an ideal diode should intrinsically have very low resistance after turn on, especially at higher biasing current. The differential resistances at various biasing points are summarized in Table II as well. 5. Intrinsic Bandwidth Extraction and Lifetimes Determination The optical microwave small signal analysis is performed on the device using an Agilent 50 GHz Parametric Network Analyzer (PNA) with 2-port calibration. The electrical microwave signal from port 1 of the PNA is combined with the DC bias through an Agilent 50 GHz bias Tee, and the coupled optical output is relayed into a New Focus 25 GHz Photodetector. The converted electrical signal is fed into port 2 of the PNA. Therefore, the optical modulation response data, S ( ) 21,data f, obtained from the PNA, consists of the following superimposed microwave responses: photodetector module transfer function, HPD ( f ), laser intrinsicoptical response, S 21,int ( f ), and electrical parasitic transfer function, H par ( f ). The relationship of these three responses and the measurement data can be expressed as, db( S ( f )) db( H ( f )) db( S ( f )) db( H ( f )). (4) 21, data PD 21,int par 8

In order to extract the laser intrinsic optical response, S 21,int ( f ), H ( f ) and ( ) PD H par f need to be de-embedded out of measured S 21,data ( f ) as inferred from Eqn. 4. It is well verified that by solving the Statz and demars rate equation [28], the laser intrinsic transfer function can be obtained as followed, S A ( f) 1 ( 2 ), (5) 21,int 2 2 2 f fr j f fr where A is magnitude fitting parameter, f R is the resonance frequency and γ is the damping rate of the optical modulation response. The intrinsic laser optical response, S ( f ), can be fitted with Eqn. 5 by de-embedding measured 21,int S 21,data ( f ) at various biasing current points over the frequency range of 0.1 to 35 GHz. Figure 5 (a) to (d) shows the overall and intrinsic small signal optical modulation response of the modeled VCSEL at various biasing points at both RT and 85 C. The damping rate,, in this context is related to ability of the VCSEL device to convert carriers into photons. If the carrier injection rate is faster than the electron-to-photon conversion rate, excess carrier concentration in the QWs will build up and choke the optical modulation response as indicated from the laser resonant frequency effect shown in Figure 5. At higher I I, the cavity optical field intensity increases and expedites the stimulated recombination process, and hence the carrier choking effect reduces and resonance peak amplitude decreases. The extracted intrinsic optical modulation response shows a higher -3 db bandwidth than the overall optical modulation response. This increase of bandwidth can be attributed to the reduction of damping limitation imposed by the electrical parasitic transfer function at high frequency. 9

By fitting the intrinsic optical bandwidth with the 2 pole laser transfer function shown with Eqn. 5, the parameters, namely f R and γ, can be used to estimate both the recombination lifetime, rec, and photon lifetime, p. The -3 db bandwidth of a VCSEL is proportional to the resonance frequency. Resonance frequency of VCSELs at biasing current higher than I is closely approximated as, 1 vgn g p 1 vg g fr i ( I I ) D ( I I ) 2 2 qv, (6) p p where v g is the group velocity of the photons, g is the differential gain, N p is the photon density in the cavity, p is the photon lifetime, V p is the optical modal volume and i is the carrier injection efficiency. The D-factor is related to the slope of resonance frequency, f R, vs. the diode current, I I. It can be interpreted as the conversion efficiency from electrical input modulation to optical modulation output since higher resonance frequency corresponds to higher modulation bandwidth. By re-writing Eqn. 6 in terms of more fundamental parameters and under the assumption that no spontaneous modes are coupled into stimulated laser emission mode, the relationship between the resonance frequency and the lifetimes, rec and p, can be shown more clearly. The re-written Eqn. 6 is illustrated as, where 1 vg g 1 gn 1 fr i( I I) ( I 1), (7) 2 qv 2 g I p rec p N is the threshold carrier concentration, g is the material differential gain at laser threshold, and g is the material laser threshold gain. As shown in Eqn. 7, resonance frequency is inversely proportional to the square root of recombination and photon lifetimes. This makes physical senses because the lifetimes fundamentally are 10

microwave modulation delays as f 12. The photon lifetime can be seen as optical signal output delay from the DBR mirror cavity and the recombination lifetime is the fundamental limitation on the input electrical to output optical conversion delay. It has been demonstrated that the modulation bandwidth can be enhanced around 30% by increasing the mirror loss (reduce the cavity Q) resulted in reducing the photon lifetime and increasing the optical output power [29]. On the other hand, the modulation bandwidth can be further improved considerably toward 10 from the reduction of recombination lifetime which can be realized in a transistor laser (TL) [30]. By plotting of intrinsic f R against I I, the D-factor of the VCSEL can be extracted and is shown in Figure. 6. At high biasing current, damping rate of the optical response is one of the factors that limit the increase of the resonance frequency and hence the modulation bandwidth. The relationship between and f R can be expressed as, 1 1 Kf 4 f, where (8) 2 2 2 R p R rec rec N K 4 [1 ] 4. (9) 2 2 p p N p The K-factor, K, relates the damping rate, to the resonance frequency, f R. By plotting the microwave modelling of against 2 f R, the photon lifetime, p, and recombination lifetime, rec, can be extracted. Two assumptions were made so the estimated value of p can be extracted from the modelling data. According to Eqn. 9, the K-factor is also dependent on, the optical confinement factor, and N dnp. The assumption that the optical modal volume, V p, is larger than the electrical carrier injection volume, V, in the 11

active region is made so the confinement factor, VVp, is negligible. Furthermore, the assumption that the change of carriers in the active region is comparable to the change of photons is made and therefore, N dn p 1. With these two assumptions, the approximation in Eqn. 9 is reached. Figure 7 shows that the K-factor, and the photon lifetime, of the VCSEL can be determined from the linear slope and the recombination lifetime can be determined from intercept of the plot vs. 2 f R. The extracted recombination and photon lifetimes at RT, 45 C, 65 C and 85 C are summarized in the inset table of Figure. 7. Both of the recombination and photon lifetimes increase as temperature increases from RT to 85 C. The increase of recombination lifetime is expected. As temperature increases, the carriers on average have higher thermal kt energy and therefore there is a higher chance for carriers to either skip through the quantum wells without being captured or escape out of the quantum well after being captured [31, 32]. These physical phenomena will, hence, result in higher recombination lifetime. On the other hand, the increase of photon lifetime is likely associated with the change of refractive index in the high/low alternating index Al x Ga 1-x As p-dbr mirror stack. The refractive index in semiconductor materials can be altered by carrier-induced change. From experimental data and theoretical calculation, the refractive index of semiconductor decreases as the carrier concentration increases [33, 34]. For a p-dbr stack with more than 20 pairs of high/low Al content Al x Ga 1-x As layers (Al 0.9 Ga 0.1 As/Al 0.12 Ga 0.88 As), there are more deep trap levels in the high Al content layers (Al 0.9 Ga 0.1 As) and, on top of it, there are interface trap levels between the high/low Al content transition thin layers. As temperature increases, the hole carriers in the deep trap 12

levels may gain enough thermal energy to escape the trap levels and become free carriers adding to the hole carrier concentration, p. This is reflected on the increase of conductivity, qp, and, therefore, the reduction of resistance, R L A, at higher p temperature. Although the hole mobility,, decreases, hence conductivity, at higher temperature due to lattice scattering (~T -3/2 ), the increase of hole concentration is significant and consequently the resistance decreases. The photon lifetime is related to photon loss rate out of the optical cavity; longer photon lifetime at higher temperature indicates less photon loss. The less photon loss rate can be attributed to the reduction of material absorption ( i ) and the decrease of the mirror loss ( m ). In this case, the decrease of the mirror loss is related to the increase of the contrast of refractive index of the p-dbr stack. The decrease of refractive index in high Al content of Al 0.9 Ga 0.1 As layers at higher temperature can be attributed to more thermally induced carriers from the deep and interface trap levels contributing to a higher hole concentration. Therefore, the contrast of refractive index between the high/low content Al x Ga 1-x As layers increases. p The effect of thermally induced increase of carrier concentration in the low Al content can be neglected as deep level concentration is insignificant for Al content below 0.3 [35]. Therefore, it can be assumed that only the refractive index of the high Al content decreases and this leads to a larger contrast of refractive indexes between the alternating Al content p-dbr mirror layers. Resulting from the further refractive index contrast, the optical cavity provides a better photon confinement, Q factor, and hence the average time that takes a photon to leave the p-dbr mirror stack, p, increases. 13

To gain more insights into the fitted parameters such as rec, and p, a comparison between f R for different temperatures at approximately the same I I can be made. According to Eqn. 7, f is proportional ( I I 1) and inversely proportional to R. Therefore, at the same I I rec p, f R should be lower for higher temperature as both recombination and photon lifetimes are longer at higher temperature. Figure 8 shows f R against I I at RT, 45 C, 65 C and 85 C. At I I 7, f R at the four different temperatures are close to each other; within 10% of highest value. The similarity in value can be attributed to temperature dependent material parameters, such as differential gain and threshold carrier concentration, and f R fitting uncertainty errors. After I I > 7, the fr difference between each temperature becomes more pronounced. The increasing difference can be attributed to the larger and earlier, with respect to I I, thermal roll off limitation of f R. From f R fitted value and extracted rec and p, the product of g' N g can be further extracted according to Eqn. 7. Calculated differential gain, g, threshold carrier concentration, N, and threshold gain, g of an active region that is similar to the described structure in section 2 can be found in ref [24]. The extracted product of material parameters is 1.21 at RT. Compared to the calculated value, 1.43, the two values are in very good agreement. Comparison is not made at 85 C because we believe the threshold carrier concentration is temperature dependent whereas in ref [24] it is assumed to be independent of temperature. 6. Data Transmission Performance 14

In this section, the bit error ratio test (BERT) results and the corresponding eye diagrams at the data transmission rate are shown at both RT and 85 C. The highest error free (BER 10-12 ) data transmission rates achieved by this VCSEL are 57 Gb/s and 50 Gb/s at RT [23] and 85 C [25] respectively. The transmission interconnect setup consists of a SHF 12103A Bit Pattern Generator (BPG) that provides the modulation bit sequence, the same light collimation module used for DC and RF measurement, a 2 m OM4 optical fiber that collects the coupled light from the light collimation module and a New Focus 1484-A-50 22 GHz high-gain photoreceiver that converts the collected optical signal back into electrical signal. The test bit sequence used is an non-return-to-zero (NRZ) 2 7 1 pseudorandom binay sequence (PRBS7) with a peak-to-peak voltage swing V pp = 0.65 V generated by the SHF BPG. An Agilent Oscilloscope with 70 GHz bandwidth sampling module is used to capture the eye diagrams. Figure 9 (a) shows eye diagrams at the data rate of 46, 48, and 50 Gb/s of the device biased at I = 10 ma at 85 C. The VCSEL under test is able to exhibit open eyes at each data rate under the bias and temperature condition. To further validate the transmission performance of the device, the converted electrical signal from the photoreceiver is sent to the SHF 11104A Error Analyzer for BER testing. A free space neutral density filter is used to attenuate the received optical power into the optical fiber to characterize the BER as a function of optical power. Figure 9 (b) shows the BER measurement, and the device is able to demonstrate error-free (BER < 10-12 ) transmission at 46 and 50 Gb/s at received optical power greater than 0.54 and 1.95 mw, respectively at 85 C. The power penalty is therefore 5.6 dbm when the data rate increases from 46 Gb/s to 50 Gb/s. Previously reported data on single 15

device 850 nm oxide-confined VCSEL, without using equalization, has shown error-free transmission at 40 Gb/s up to 85 C [36] and 50 Gb/s up to 57 C [37]. This reported 50 Gb/s error-free transmission oxide VCSEL is the highest speed to date for any 850 nm oxide-confined VCSEL at 85 C without the uses of equalization. At the bias I = 10 ma at 85 C, the device s differential resistance is ~ 58 Ω, derived from the I-V characteristics. Due to the better impedance match to standard 50 Ω of testing instruments, no external amplification was implemented to acquire the errorfree transmission results. Higher speed error-free transmission could possibly be achieved if amplifications were utilized. With the electrical power consumption of the device PElectrical I V, the energy/data efficiency at 50 Gb/s is calculated 456 fj/bit at 85 C. 7. Conclusion In summary, we have developed a microwave extraction method for accurate determination of radiative recombination lifetime and demonstrated a microwave equivalent circuit modeling technique used to de-embed the electrical parasitic transfer function and obtain the intrinsic optical response for diode lasers or VCSELs. For a 5 m aperture oxide-confined VCSEL, The extracted intrinsic modulation bandwidth is 31.86 GHz and 26.19 GHz at RT and 85 C. With the same technique, we have also illustrated a method to empirically extract the recombination and photon lifetimes of VCSEL. The extracted rec and p are 0.1778 ns and 4.2 ps at RT and 0.2445 ns and 4.8 ps at 85 C. Additionally, at the biasing condition of I = 10 ma and V pp = 0.65 V, the same VCSEL is able to achieve record high error-free (BER < 10-12 ) data transmission at bit rates of 46 Gb/s and 50 Gb/s at 85 C. The energy/data efficient at the bit rate of 50 Gb/s is 456 16

fj/bit. 17

References [1] P. D. Dapkus, N. Holonyak, J., R. D. Burnham, D. L. Keune, J. W. Burd, K. L. Lawley, and R. E. Walline, "Spontaneous and Stimulated Carrier Lifetime (77 K) in a High Purity, Surface Free GaAs Epitaxial Layer," J. Appl. Phys., vol. 41, pp. 4194-4199, 1970. [2] D. L. Keune, N. Holonyak, Jr., R. D. Burnham, D. R. Scifres, H. R. Zwicker, J. W. Burd, M. G. Craford, D. L. Dickus, and M. J. Fox, "Optical Phase Shift Measurement of Carrier Decay Times (77 K) on Lightly Doped Double Surface and Surface Free Epitaxial GaAs," J. Appl. Phys., vol. 42, pp. 2048-2053, 1971. [3] C. J. Hwang, "Doping Dependence of Hole Lifetime in n Type GaAs," J. Appl. Phys., vol. 42, pp. 4408-4413, 1971. [4] T. C. Damen, M. Fritze, A. Kastalsky, J. E. Cunningham, R. N. Pathak, H. Wang, and J. Shah, "Time resolved study of carrier capture and recombination in monolayer Be δ doped GaAs," Appl. Phys. Lett., vol. 67, pp. 515-517, 1995. [5] G. B. Lush, H. F. MacMillan, B. M. Keyes, D. H. Levi, M. R. Melloch, R. K. Ahrenkiel, and M. S. Lundstrom, "A study of minority carrier lifetime versus doping concentration in n type GaAs grown by metalorganic chemical vapor deposition," J. Appl. Phys., vol. 72, pp. 1436-1442, 1992. [6] R. J. Nelson and R. G. Sobers, "Minority carrier lifetimes and internal quantum efficiency of surface free GaAs," J. Appl. Phys., vol. 49, pp. 6103-6108, 1978. [7] Fouquet, J. and Burnham, R., "Recombination dynamics in GaAs/Al x Ga 1- x As quantum well structures," IEEE J. Quantum Electron., vol. 22, pp. 1799-1810, 1986. [8] H. W. Then, M. Feng, N. Holonyak, Jr., and C. H. Wu, "Experimental determination of the effective minority carrier lifetime in the operation of a quantum-well n-p-n heterojunction bipolar light-emitting transistor of varying base quantum-well design and doping," Appl. Phys. Lett., vol. 91, p. 033505, 2007. [9] G. Walter, C. H. Wu, H. W. Then, M. Feng, and N. Holonyak, Jr., "Tilted-charge high speed (7 GHz) light emitting diode," Appl. Phys. Lett., vol. 94, p. 231125, 2009. [10] C. H. Wu, G. Walter, H. W. Then, M. Feng, and N. Holonyak, J., "4-GHz Modulation Bandwidth of Integrated 2 x 2 LED Array," IEEE Photon. Technol. Lett., vol. 21, pp. 1834-1836, 2009. [11] C. H. Wu, H. W. Then, M. Feng, and N. Holonyak, Jr., "Microwave determination of electron-hole recombination dynamics from spontaneous to stimulated emission in a quantum-well microcavity laser," Appl. Phys. Lett., vol. 96, p. 131108, 2010. [12] C. H. Wu, F. Tan, M. K. Wu, M. Feng, and N. Holonyak, Jr., "The effect of microcavity laser recombination lifetime on microwave bandwidth and eye-diagram signal integrity," J. Appl. Phys., vol. 109, p. 053112, 2011. [13] H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, "GaInAsP/InP Surface Emitting Injection Lasers," Jpn J. of Appl. Phys, vol. 18, pp. 2329-2330, 1979. [14] D. R. Scifres and R. D. Burnham, "Distributed feedback diode laser," vol. U.S. Patent 3983509, 1976. [15] J. M. Dallesasse, N. Holonyak, Jr., A. R. Sugg, T. A. Richard, and N. El Zein, "Hydrolyzation oxidation of Al x Ga 1 x As AlAs GaAs quantum well heterostructures and superlattices," Appl. Phys. Lett., vol. 57, pp. 2844-2846, 1990. [16] J. M. Dallesasse and N. Holonyak, Jr., "Native oxide stripe geometry AlxGa1 xas GaAs quantum well heterostructure lasers," Appl. Phys. Lett., vol. 58, pp. 394-396, 1991. [17] C. C. Hansing, H. Deng, D. L. Huffaker, D. G. Deppe, B. G. Streetman, and J. Sarathy, "Low-threshold continuous-wave surface emitting lasers with etched void confinement," IEEE Photon. Technol. Lett., vol. 6, pp. 320-322, 1994. 18

[18] D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, "Native oxide defined ring contact for low threshold vertical cavity lasers," Appl. Phys. Lett., vol. 65, pp. 97-99, 1994. [19] P. Wolf, P. Moser, G. Larisch, H. Li, J. A. Lott, and D. Bimberg, "Energy efficient 40 Gbit/s transmission with 850 nm VCSELs at 108 fj/bit dissipated heat," Electron. Lett., vol. 49, pp. 666-667, 2013. [20] P. Westbergh, R. Safaisini, E. Haglund, J. S. Gustavsson, A. Larsson, M. Geen, R. Lawrence, and A. Joel, "High-Speed Oxide Confined 850-nm VCSELs Operating Error- Free at 40 Gb/s up to 85 o C," IEEE Photon. Technol. Lett., vol. 25, pp. 768-771, 2013. [21] F. Tan, M. K. Wu, M. Liu, M. Feng, and N. Holonyak, Jr., "850 nm Oxide-VCSEL With Low Relative Intensity Noise and 40 Gb/s Error Free Data Transmission," IEEE Photon. Technol. Lett., vol. 26, pp. 289-292, 2014. [22] P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsso, and A. Larsson, "High-speed 850 nm VCSELs operating error free up to 57 Gbit/s," Electron. Lett., vol. 49, pp. 1021-1023, 2013. [23] M. Liu, C. Wang, M. Feng, and N. Holonyak, Jr., "Advanced Development of 850 nm Oxide-Confined VCSELs with a 57 Gb/s Error-Free Data Transmission," GOMACTech- 2016 (Session 27: Digital Photonics (Paper No. 27.4), Thursday 3-17-(2016). [24] S. B. Healy, E. P. O' Reilly, J. S. Gustavsson, P. Westbergh, Haglund, A. Larsson, and A. Joel, "Active Region Design for High-Speed 850-nm VCSEL," IEEE J. Quantum Electron., vol. 46, pp. 506-512, 2010. [25] M. Liu, C. Y. Wang, M. Feng, and N. Holonyak, Jr., "850 nm Oxide-Confined VCSELs with 50 Gb/s Error-Free Transmission Operating up to 85 C," in Conference on Lasers and Electro-Optics, San Jose, California, 2016, p. SF1L.6. [26] Y. Ou, J. S. Gustavsson, P. Westbergh, A. Haglund, A. Larsson, and A. Joel, "Impedance Characteristics and Parasitic Speed Limitations of High-Speed 850-nm VCSELs," IEEE Photon. Technol. Lett., vol. 21, pp. 1840-1842, 2009. [27] S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, "Temperature sensitivity of the threshold current of long-wavelength InGaAs- GaAs VCSELs with large gain-cavity detuning," IEEE J. Quantum Electron., vol. 40, pp. 453-462, 2004. [28] H. Statz and G. demars. New York, N. Y.: Columbia University Press, 1960. [29] P. Westbergh, J. S. Gustavsson, B. Kögel, Å. Haglund, and A. Larsson, "Impact of Photon Lifetime on High-Speed VCSEL Performance," IEEE J. Selected Topics in Quantum Electron., vol. 17, pp. 1603-1613, 2011. [30] M. Feng, H. W. Then, N. Holonyak, Jr., G. Walter, and A. James, "Resonance-free frequency response of a semiconductor laser," Appl. Phys. Lett., vol. 95, p. 033509, 2009. [31] Y. Arakawa, H. Sakaki, M. Nishioka, J. Yoshino, and T. Kamiya, "Recombination lifetime of carriers in GaAs GaAlAs quantum wells near room temperature," Appl. Phys. Lett., vol. 46, pp. 519-521, 1985. [32] T. Matsusue and H. Sakaki, "Radiative recombination coefficient of free carriers in GaAs AlGaAs quantum wells and its dependence on temperature," Appl. Phys. Lett., vol. 50, pp. 1429-1431, 1987. [33] D. D. Sell, H. C. Casey, and K. W. Wecht, "Concentration dependence of the refractive index for n and p type GaAs between 1.2 and 1.8 ev," J. Appl. Phys., vol. 45, pp. 2650-2657, 1974. [34] J. Manning, R. Olshansky, and S. Chin, "The carrier-induced index change in AlGaAs and 1.3 m InGaAsP diode lasers," IEEE Journal of Quantum Electronics, vol. 19, pp. 1525-1530, 1983. [35] M. Razeghi, The MOCVD Challenge: A survey of GaInAsP-InP and GaInAsP-GaAs for photonic and electronic device applications. Boca Raton, FL: CRC Press, 2011. 19

[36] P. Westbergh, R. Safaisini, E. Haglund, J. S. Gustavsson, A. Larsson, M. Geen, R. Lawrence, and A. Joel, "High-Speed Oxide Confined 850-nm VCSELs Operating Error- Free at 40 Gb/s up to 85C," IEEE Photon. Technol. Lett., vol. 25, pp. 768-771, 2013. [37] D. M. Kuchta, A. V. Rylyakov, C. L. Schow, J. E. Proesel, C. W. Baks, P. Westbergh, J. S. Gustavsson, and A. Larsson, "A 50 Gb/s NRZ Modulated 850 nm VCSEL Transmitter Operating Error Free to 90 C," J. Lightwave Technol., vol. 33, pp. 802-810, 2015. 20

Figure Captions Figure 1. L-I-V characteristics of the 850 nm oxide-confined VCSEL from room temperature (~25 C) to 85 C. The inset shows the measured data and fitting of the threshold current versus temperature to obtain I o = 0.69 ma and T o = 195 C, under the assumption that FT (, 1. Figure 2. The optical spectrum of the 850 nm oxide-confined VCSEL at two biasing and temperature conditions: the black curve represents room temperature measurement at I = 2.5 ma ( I I ~3) and the red curve represents 85 C measurement at I = 3.6 ma ( I I ~3). The optical aperture is determined to be 5 m. Figure 3. Physical model with equivalent circuit including the parasitic parameter identified as follows: C p and R p, the p-pad capacitance and resistance; R m,p and R m,n, the p-dbr and n-dbr mirror series resistance; C diff, diffusion capacitance at the active region; R j, junction resistance at the active region; C ox and C dep, the lumped oxide capacitance and depletion capacitance. C a is the total parasitic capacitance resulted from C ox and C dep. Figure 4. Measurement S ( ) 11 f data and fitting of the electrical reflection coefficient of the 5 m optical aperture VCSEL at both RT and 85 C. The fitting curves are generated from the equivalent circuit shown in Figure 3. Electrical parasitic parameters at various biasing points are listed in Table II. Figure 5. (a) & (c) The overall optical frequency response of the 5 m optical aperture VCSEL at RT and 85 C. (b) & (d) The intrinsic optical response of the 5 m optical aperture VCSEL. The highest 3 db modulation bandwidth of the overall optical response is 29.15 GHz and 24.53 GHz at RT and 85 C whereas it is 31.86 GHz and 26.19 GHz for the intrinsic optical response at RT and 85 C. Figure 6. Fitted resonance frequency, f R, vs. I I graph at RT, 45 C, 65 C and 85 C. The fitted slope of the data points in the linear region corresponds to the D-factor, which is 8.2 GHz/ (ma 1/2 ) and 7.8 GHz/ (ma 1/2 ) at RT and 85 C. Figure 7. Fitted damping rate,, vs. fitted resonance frequency squared, f 2 R, at RT, 45 C, 65 C and 85 C. The extracted K-factor, recombination lifetime, rec, and photon lifetime, p are listed in the inset table. Figure 8. Fitted resonance frequency, f R, vs. I I at RT, 45 C, 65 C and 85 C. I I. Notice the difference between each temperature becomes more obvious when 7 21

Figure 9. (a) Eye diagrams at 46 Gb/s and 50 Gb/s under the bias of I = 10 ma and V pp = 0.65 V at 85 C for the 5 μm optical aperture VCSEL. (b) BER (46 Gb/s and 50 Gb/s) versus received optical power for the optical link based on the 5 µm optical aperture VCSEL at 85 C. The power penalty is 5.6 dbm when the data rate increases from 46 Gb/s to 50 Gb/s under the same biasing condition. 22

Fig. 1 23

Fig. 2 24

Fig. 3 25

Fig. 4 26

Fig. 5 27

Fig. 6 28

Fig. 7 29

Fig. 8 30

Fig. 9a Fig. 9b 31

Table I. Summary of State of Art High Speed Results of 850 nm Oxide-Confined VCSELs Institution Chalmers UIUC f -3dB @ RT 30 GHz 29 GHz Highest Error-Free @ RT 57 Gb/s 57 Gb/s f -3dB @ 85 C 21 GHz 24.5 GHz Highest Error-Free @ 85 C 40 Gb/s 50 Gb/s Table II. Electrical Parasitic Parameters at Various Biasing Points at Both RT and 85 C RT I C p R p R m,n + R m,p dv/di C a C diff R j f -3dB, overall f -3dB,intrinsic (ma) (ff) (Ω) (Ω) (Ω) (ff) (ff) (Ω) (GHz) (GHz) I = 0.8 ma 1.6 106 11.3 111 133 98 332.57 34 11.09 11.97 2.4 103 11.1 99 108.4 98 372 26 15.11 16.07 3.2 102 11 92 94.6 98 422 20 17.81 19.03 4.8 97 11.1 83.5 77.4 98 512 12.3 21.91 22.96 12 88 10.6 63.9 51 98 812 6.5 29.15 31.86 85 C I C p R p R m,n + R m,p dv/di C a C diff R j f -3dB, overall f -3dB,intrinsic (ma) (ff) (Ω) (Ω) (Ω) (ff) (ff) (Ω) (GHz) (GHz) I = 1.08 ma 2 96 12 85 101.4 98 502 22 11.79 12.4 2.4 95 11.9 82 94.5 98 522 19 13.8 14.58 3.6 91 11.7 75.5 81.7 98 562 14 17.99 18.86 5.5 88 11.2 69 70.6 98 632 10.3 21.74 22.44 9.6 84 10.3 61 59.3 98 772 7.5 24.53 26.19 32

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9a Fig. 9b