Internal heating is a key issue for vertical cavity surface emitting lasers (VCSELs), a semiconductor micro laser diode that emits light in a cylindrical beam vertically from the surface of a fabricated wafer. They generally have higher thermal impedance than edge emitting lasers and are fairly efficient for optical devices, running at roughly 25% efficiency in contrast to light emitting diodes' (LEDs) typical 2% to 3%. For instance, they produce 10 mW of optical power from a 40-mW input; the remaining is dissipated as heat.
How easily a laser dissipates heat varies with the physical design. A buildup of heat in the active region can reduce device efficiency along with reliability and operating lifetime. Because VCSELs are narrow band devices, in this case generating energy at a wavelength of 850 nm, the length of the optical cavity changes as it heats up and the wavelength shifts at a rate of roughly 0.6 Å/°C.
A study was conducted to estimate the total temperature increase around the device's active region as a function of drive current. The study used a 350- µm VCSEL die made of gallium arsenide (GaAs) with a gold bonding pad on top to examine internal temperature distribution. Each die was bonded at its base to a ceramic pedestal with a silver epoxy. One of the main goals was to determine the effects of going from a die size of 350 µm on an edge to 220 µm. While this reduction would allow more devices per wafer and lead to lower manufacturing costs, the reduced cross section (through which heat escapes) would also lead to a higher thermal resistance.
Geometry was created and heat transfer by conduction was modeled using the 3D Heat Transfer Application Mode of the COMSOL Multiphysics mathematical modeling package. Figure 1 shows the result of the VCSEL cube. Note that the aperture through which the light leaves the device is located in the center of the gold pad on the top of the die. Following the rendering of the geometry, boundary conditions were defined based on several assumptions: the VCSEL is the only heat source; all surfaces in direct contact with air lose heat at a rate governed by Newton's law of cooling; and the coefficient of heat transfer h = 0.1 W/m2-K.
Conditions at the bottom face are also important because in a real application the die attaches to the physical package and provides a path for heat to flow. This model assumes that the package is attached to a large heat sink that can handle as much heat as the device can produce, so the base of the VCSEL die is set at a constant ambient temperature. To help set these boundary values, and verify the model's validity, researchers used an infrared camera to measure the actual temperature on the VCSEL's top face and sides, which were coated with India ink to make them highly emissive. Then, a miniature thermocouple was bonded onto the device base. The results from the camera and thermocouple agreed, confirming that the camera-based temperatures were valid on all device surfaces.
Next, the coefficients for the underlying heat equation were set to:
𝜌 C T / t - ∇ • (k ∇ T) = Q
This model considers only the steady state case, ignoring the first term. The model dealt with three different subdomains (the gallium arsenide, the gold, and the VCSEL itself), each with its own thermal conductivity. With the model set up, the software then generated a mesh for the entire geometry (see Figure 2).
A tighter mesh was applied in areas of greatest interest; in this case, the 1.5-µm thick gold pad on the top surface. The remainder of the model worked with a relatively coarse mesh to help conserve memory space and reduce the solution time. Figure 3 shows a graphical plot of the temperature distribution inside the VCSEL die. It also reads out the temperature at the same point that was previously read with the camera, again confirming the model's validity.
The study included roughly 20 models for each experiment involving a different geometry or material formulation, each with a different drive current. Findings showed that the difference in measured values of temperature and those obtained from modeling was ±0.2 °C. The experiments substantiated the original hypothesis, that most of the heat generated by the drive current goes through the substrate, and that only a small amount is radiated into the ambient air directly from the device. With this model, new design concepts, such as alternative doping profiles, aperture diameters, and levels of drive current, were tested and verified. Further studies showed that various types of solder and thermoconductive ceramic bases had little effect on the final results. It was concluded that a smaller die size could be used without any significant negative effects on device reliability.