Experimental and theoretical thermal analysis of a Hybrid Silicon Evanescent Laser

: In this work we present both experimental and theoretical thermal analysis of an electrically pumped hybrid silicon evanescent laser. Measurements of an 850 µ m long Fabry-Perot structure show an overall characteristic temperature of 51 o C, an above threshold characteristic temperature of 100 o C, and a thermal impedance of 41.8 o C/W. Finite element analysis of the laser structure predicts a thermal impedance of 43.5 o C/W, which is within 5% of the experimental results. Using the overall characteristic temperature, above threshold characteristic temperature, and the measured thermal impedance, the continuous wave output power vs. current from the laser is simulated and is in good agreement with experiment.


I. Introduction
Recently, there has been significant interest in developing a laser source that is compatible with silicon based optics and electronics. A laser that can be integrated with silicon optical and electrical components has the potential to utilize the low cost, high volume manufacturing that has been developed in the CMOS microelectronics industry. Several optical sources that could fulfill this requirement have been proposed and demonstrated. These include optically pumped Raman lasers [1], nano-crystalline Si structures [2], and rare-earth doped Si rich oxides [3]. Of these integrated solutions, one of the most attractive is a wafer bonded hybrid silicon laser. In this approach, a III-V active region is wafer bonded onto a pre-patterned silicon on insulator (SOI) wafer. Lasers fabricated in this manner do not require aligned bonding steps since the optical waveguides are defined in the silicon. Furthermore, these lasers can be integrated with additional passive and active components such waveguide splitters, waveguide combiners, evanescent photodetectors, and amplifiers. Using the wafer bonded approach, Fabry-Perot (FP) and ring lasers have demonstrated output powers greater than 20 mW, threshold currents of < 75 mA and operating temperatures up to 60 o C [4]. Unfortunately, one of the drawbacks to fabricating integrated lasers using an SOI substrate deals with the ability of the device to dissipate heat. While crystalline silicon is a good thermal conductor (thermal conductivity, k Si ~ 130 W/m/K), the oxide in the SOI substrate has poor thermal conductivity (k SiO2 ~ 1.3 W/m/K). The poor thermal properties of the buried oxide layer represent an issue for high temperature laser performance.
In this work, we present experimental and theoretical thermal analysis of a hybrid silicon evanescent Fabry-Perot (FP) laser. For an 850 µm long device, measurements show an overall characteristic temperature (T 0 ) of 51 o C, an above threshold characteristic temperature (T 1 ) of 100 o C, and a thermal impedance (Z T ) of 41.8 o C/W. Simulations of the thermal impedance in the hybrid laser using a finite element modeling technique predicts a Z T of 43.5 o C/W, which is within 5% of the experimental results. Using the theoretical model it is shown that the buried oxide in the SOI substrate accounts for 25.2 o C/W of the total device thermal impedance. Combining the experimental T 0 , T 1 , and Z T , the relationship between the continuous wave (CW) output power from the laser and applied current at various backside temperatures is predicted. For temperatures of 15 o C, 25 o C, and 35 o C, the agreement between the theoretical and experimental laser characteristics is good, but the agreement is worse at higher temperatures for reasons discussed in Section VI.

II. Device overview
The hybrid silicon evanescent laser consists of a III-V InGaAlAs/InP active region that is wafer bonded to a pre-patterned SOI wafer. A cross section of the device is shown in Fig. 1.
Device fabrication begins by patterning a set of rib waveguides on an SOI wafer. The rib etch depth is 0.5 µm and the waveguide with is 2 µm. Following the silicon patterning, a plasma assisted wafer bonding process is performed to bond an InGaAlAs/InP active region to the SOI wafer. No alignment steps are required in the bonding process. Following the bonding, additional fabrication steps are performed including removal of the InP substrate, dry etch definition of the III-V mesas, proton (H+) implantation of the p-InP cladding (for current confinement), and definition of the p and n contact regions. A detailed description of the fabrication process can be found in [4]. For testing, the FP lasers were diced into bars of 32 devices (bar dimension 850 µm x 8 mm) and facets were polished.

III. Hybrid laser characteristic temperatures
The threshold current and differential efficiency of the hybrid laser at elevated temperatures can be characterized using an overall characteristic temperature (T 0 ) and an above threshold characteristic temperature (T 1 ) [5]. These characteristic temperatures are described in Eq. (1) and Eq. (2), where I 0 and I PO are fitting parameters. To extract the two characteristic temperatures, a set of pulsed output power vs. applied current (LI) measurements (1 kHz repetition rate, 0.1% duty cycle) were performed with the device placed on a temperature controlled stage. The pulsed measurement ensures that there is limited additional heating from power dissipation in the laser other than that provided by the stage. Thermal paste was used for efficient heat conduction between the lasers and the stage. LI results from these measurements are shown in Fig. 2 for stage temperatures ranging from 20 to 45 o C. Using Eqn. (1), T 0 and I 0 can be extracted by fitting the natural log of threshold current vs. the stage temperature. Results are shown in Fig. 3(a) and give an overall characteristic temperature of 51 o C and an I 0 of 48 mA. Fitting the difference in current between threshold and that required for 1 mW of output power allows the above characteristic temperature to be determined. Results are shown in Fig. 3(b) and yield a T 1 of 100 o C with an I p0 of 10.65 mA.

IV. Experimental thermal impedance
The thermal imepdance of the laser is measured using a combination of two experiments. The first set of measurements is used to establish a baseline for the shift in lasing wavelength as a function of active region (stage) temperature (dλ/dT). Similar to the characteristic temperature measurement above, this experiment is performed pulsed to ensure that there is minimal device heating other than what is provided by the temperature controlled stage. The second measurement is performed CW, and is used to measure the shift in wavelength as a function of applied electrical power to the laser (dλ/dP). Z T is then given by Eq. (3): The experimental shift in wavelength as function of stage temperature for the pulsed measurements, along with the output spectrum from the FP laser at 15 o C and 30 o C are shown in Fig. 4(a). For the CW measurements, the experimental shift in lasing wavelength is shown in Fig. 4(b). In all experiments, a single longitudinal mode in the laser spectrum is monitored. Combining the results in Fig. 4(a) and 4(b) results in a thermal impedance of 41.8 o C/W.

V. Theoretical thermal impedance
The thermal performance of the hybrid laser depends on several factors. These include the amount and location of heat that is generated, the thermal conductivity of the layers surrounding the heat sources, and the operating temperature of the laser active region. To model the temperature rise as a function of applied bias we have employed a two dimensional finite element modeling technique. For the hybrid laser cross section shown in Fig. 1, there are six major sources of thermal energy. These include resistive heating in the p-cladding, the n-contact layer, the active region, and the p and n contacts, along with heat generated by the diode drop associated with the active region. Although for shorter devices the contact resistance in the hybrid laser would be problematic, for an 850 µm long FP laser, the n and p contact resistance is not significant compared to that of the p-cladding and n-contact layers. Hence it is neglected in the model.
For the resistive heating, the resistances of the various laser regions (p-cladding, n-InP contact layer, etc.) have been extracted using transmission line measurements (TLM). Based on these measurements, an 850 µm long FP structure has a p-cladding resistance of 3.3 Ω and an n-contact layer resistance of 2.9 Ω. For the active region, the total resistance was calculated to be 0.3 Ω, and is based on the material resistivity for the average composition between the wells and barriers [6], the thickness of the active layer (0.1 µm), and the width of the unimplanted region (4 µm). The dissipated electrical power associated with resistive heating in the model is calculated by simply taking the product of the square of the current in a particular layer and the resistive contribution in each device section. For the dissipated power in the n-InP contact layer, the current is reduced by a factor of two since the double sided n-contact shown in Fig 1 acts as a current divider. For the active region diode drop, the dissipated power is simply the turn on voltage multiplied by the current.
The dimensions of the hybrid laser used in the model are shown in Fig. 5. The thermal conductivity in each of the various regions is k InP = 130 W/m/K, k Si = 130 W/m/K, k SiO2 = 1.3 W/m/K, and k QWs = 5 W/m/K (active QWs) [6].
A two dimensional temperature profile of the hybrid laser operating with a bias current of 500 mA is shown in Fig. 6(a). The predicted temperature rise in the laser active region as a function of applied current, is shown in Fig. 6(b). Results show that for applied bias currents greater than 250 mA, the largest source of power dissipation is the p-cladding region, followed by the active region, then the n-InP layer. Using the simulated temperature rise and dissipated electrical power, the thermal impedance of the laser is 43.5 o C/W, which is within 5% of our initial experimental results.
To show the effect of the buried oxide on the thermal impedance, Fig. 6(b) also includes a simulation of the temperature rise in the device when the buried oxide has been removed. Although removal of the BOX has adverse effects on the optical guiding characteristics of the laser, replacing this layer with silicon would result in a thermal impedance of 18.3 o C/W.

VI. Continuous wave LI experiments and theory
The characteristic temperatures in combination with the experimental and theoretical predictions of thermal impedance can be used to predict the CW LI properties of the laser as a function of stage temperature [7]. Combining Eqn. 1 and Eqn. 2 [5], the output power (P out ) from the 850 µm long hybrid laser is given by Eq. (4).
In Eqn. 4, P D is the total electrical power dissipation in the laser, I is the applied bias current, I 0 is the fitting parameter from Eqn 1, and η i , α m , hν, q and <α i > have their typical definitions. Given an injection efficiency of 70%, a modal loss of 10 cm -1 , and an estimated mirror loss of 11.4 cm -1 (facet reflectivity 38%), Fig. 7(a) shows the predicted and experimental single sided laser output power (measured into an integrating sphere) at various backside temperatures. A set of residuals along with an R 2 value for each of the theoretical fits are shown in Fig. 7(b).
For operating temperatures of 15 o C and 25 o C, R 2 values of 0.983 and 0.982 along with small residuals (<+/-1 mW) over >95% of the data indicates a good fit between theory and experiment. For temperatures of 35 o C and 45 o C, the decrease in the R 2 (0.895 and 0.311 respectively) and increase in residuals at high bias currents are most likely caused by thermal runaway effects that are not included in Eq. (4), but are described in [8].

VII. Conclusions
We have experimentally and theoretically investigated the thermal performance of a FP hybrid silicon evanescent laser. Experiments show a T 0 of 51 o C, T 1 of 100 o C, and a Z T of 43.5 o C/W. Simulations of the laser using finite element analysis show a Z T of 41.5 o C/W, which is within 5% of our experimental results. Using a combination of T 0 , T 1 , and Z T , the laser output power vs. current characteristics are predicted and compared with experiment. At stage temperatures of 15 o C and 25 o C, there is good agreement between theory and experiment. At temperatures of 35 o C and 45 o C, degradation between the experimental and theoretical predictions occurs due to thermal runaway.