The Traveling Wave Laser Model (TWLM) accounts for self heating effects of the laser, and one key parameter to model this effect is the active layer to ambient thermal resistance, which is set with the “active-layer-to-ambient thermal resistance” parameter under “Waveguide/Self-heating Properties” of the TWLM element. To estimate this resistance, an analytical model based on the material parameters and the layer structure of the laser can be used, or a simulation can be used such as with Lumerical HEAT.
This article will detail how the specified parameter is applied during the simulation and discuss an example of estimating the thermal resistance using a simple analytic model based on the layer structure and material properties.
Active-to-Ambient Thermal Resistance Distribution
In the TWLM, the thermal resistance of the laser is modeled as follows, with \(R_{GA}\) in the diagram representing the active-layer-to-ambient thermal resistance for each discretized segment. For more information about discretizing TWLM into segments before numerically solving the TWLM equations, please see the Knowledge Base article INTERCONNECT as a Laser Design Platform.
Since the number of segments is automatically determined by the model, the value entered in with the “active-layer-to-ambient thermal resistance” parameter is the total thermal resistance. During the simulation, the value of \(R_{GA}\) assigned to each segment is calculated based on the relation for the parallel connection between thermal resistances as:
$$
R_{GA} = \mathrm{active\text{-}layer\text{-}to\text{-}ambient\ thermal\ resistance} \ast N
$$
where \(N\) is the total number of segments.
Estimating Active to Ambient Thermal Resistance by Material Parameters
To estimate the active layer to ambient thermal resistance, one method is to use the layer structure of the laser in conjunction with the thermal conductivity of each layer. To demonstrate this procedure, the thermal resistance of the device in [1] is estimated.
From [1] the device structure is an MQW laser, with a total quantum well thickness of 36 nm, and total quantum barrier thickness of 70 nm. The device is built on an n-doped InP substrate with a p-doped InGaAs contact. A heatsink is added to the bottom of the entire structure.
A diagram of the device is as follows:
Neglecting effects from MQW cross-plane thermal resistances, the total active-to-ambient thermal resistance can be estimated by the parallel combination of two paths between the MQW active layer to the ambient, through the top or the bottom of the device. Further neglecting the thermal resistance of the p-InGaAs contact, the active-layer-to-ambient resistance is estimated as follows:
$$
\mathrm{active\text{-}layer\text{-}to\text{-}ambient\ thermal\ resistance} = R_{GA,\text{top}} || R_{GA,\text{bot}} = \frac{R_{GA,\text{top}} \ast R_{GA,\text{bot}}}{R_{GA,\text{top}} + R_{GA,\text{bot}}}
$$
$$
R_{GA,\text{top}} = R_{\text{InP}} + R_{\text{AlInAs}} + R_{\text{AlGaInAs}}
$$
$$
R_{GA,\text{bot}} = R_{\text{InP,sub}} + R_{\text{AlInAs}} + R_{\text{AlGaInAs}} + R_{\text{heatsink}}
$$
Except for the thermal resistance of the heatsink, which is separately estimated in [1], the thermal resistance of each layer is calculated as:
$$
R_{\text{th}} = \rho_{\text{th}} \frac{L}{A}
$$
where \(\rho_{\text{th}} = 1 / \kappa_{\text{th}}\) is the thermal resistivity, which is the inverse of the thermal conductivity \(\kappa_{\text{th}}\), \(L\) is the layer thickness, and \(A\) is the area of the layer.
The attached script file runs through the calculation procedure described above using the thermal conductivity for each material. The total thermal conductivity to be entered as the “active-layer-to-ambient thermal resistance” parameter is 49.84 K/W.
References
- J. Piprek, J. K. White, and A. J. SpringThorpe, “What Limits the Maximum Output Power of Long-Wavelength AlGaInAs/InP Laser Diodes?,” IEEE J. Quantum Electronics, vol. 38, no. 9, pp. 1253 - 1259, Nov. 2002, doi: 10.1109/JQE.2002.802441.