A Simple Extraction Method of Thermal Resistance in Multifinger GaAs HBT

Abstract

A novel extraction method to estimate the thermal resistance (R th ) of a multifinger GaAs heterojunction bipolar transistor (HBT) device is presented based on the simplified Fourier's law. By calculating the thermal coupling resistance between the fingers on top of the self-heating thermal resistance, the values of R th of multifinger devices for various dimensions are accurately calculated while maintaining the simplicity of calculation. To verify the idea, the proposed method is compared with the measurement-based method as well as the analytic methods, such as the finite-element method and the solution of 3-D Laplace's equation. For four-finger HBT devices, the extracted R th results showed good agreements with the analytic methods within an error of 9% and the measurement-based results with a deviation of 7.4%, thus convincing the usefulness of the proposed method.

Static Thermal Coupling Factors in Multi-Finger Bipolar Transistors: Part I—Model Development

“…This temperature rise at the heating finger affects the operating temperature of the neighboring fingers through thermal coupling. Following [19], we assume circular isotherms for this structure having no-trench isolation as depicted in Figure 1 resulting into identical temperature profile in the vertical (z-) and lateral (x-) directions, i.e., T nt (z) = T nt (x). Therefore, temperature rise at the sensing finger-i due to the heat source at finger-j can be estimated directly from the z-dependent temperature profile of finger-j in (6) as ∆T ij,nt = T nt (x = z = |i − j|s) − T amb where s is the spacing between the adjacent fingers.…”

“…Although the results show good agreement with TCAD simulations, the model is not geometrically scalable due to its empirical nature. A particularly interesting work reported in [19] attempted to model the thermal coupling from the isothermal contours in GaAs multifinger HBT. Although the work provides an important insight that the coupling effect can be predicted from the modeling framework of self-heating, the application of the approach is limited only to structures without any trench isolation (see Figure 1).…”

“…Besides, the model does not consider the temperature dependent thermal conductivity of the semiconductor material yielding c ij values independent of dissipated power (P diss ). The model inaccuracy increases particularly for a smaller heat source area as shown in Figure 2a, with maximum error of around 22%, where we compared the c ij model of [19] with the corresponding 3D TCAD simulation data for multifinger HBTs having different emitter geometries but no-trench isolation between the fingers. Figure 2b shows that in case of shallow trench isolated (STI) multifinger structures, the model of [19] yields further erroneous results for c ij with maximum error of around 57% when compared with 3D TCAD simulation.…”

“…The model inaccuracy increases particularly for a smaller heat source area as shown in Figure 2a, with maximum error of around 22%, where we compared the c ij model of [19] with the corresponding 3D TCAD simulation data for multifinger HBTs having different emitter geometries but no-trench isolation between the fingers. Figure 2b shows that in case of shallow trench isolated (STI) multifinger structures, the model of [19] yields further erroneous results for c ij with maximum error of around 57% when compared with 3D TCAD simulation. Note that following the standard practice, c ij is represented in percentage which is obtained by multiplying Equation (2) by 100 [17,18,20].…”

“…In addition, the isotherms linking the heating finger and the sensing fingers are systematically shown. [19] (lines) compared with corresponding 3D TCAD simulation results (symbols) at different sensing fingers in five-finger transistor structures (a) without any trench isolation and (b) with only shallow trench isolated (STI). Finger spacing s = 2.5 µm.…”