# An Efficient Thermal Model for Multifinger SiGe HBTs Under Real Operating Condition

## Summary (2 min read)

### Introduction

- Therefore, it has been a common practice to partition a large emitter into smaller fingers each having small enough emitter width (WE) leading to a multi-finger transistor.
- This makes the straightforward application of superposition to include both the self-heating and thermal coupling effects in calculating the overall finger temperature questionable.
- Section II presents the elaborate model formulation with a hint towards model implementation.

### II. MODEL FORMULATION

- Electrothermal effect in HBTs causes heat generation at the base-collector junction.
- Cross sectional view of (a) two-finger and (b) three-finger transistor structure with no trench isolation showing heat source, heat sink, isothermal lines and the imaginary boundaries.
- In case of a system with three heat sources as shown in Fig. 2(b), the thermal boundaries of heat source in the middle are governed by two adjacent heat sources.
- In order to accurately predict the temperature at each finger, an effective heat spreading angle (θ1) has to be defined between the adjacent heat sources as shown by the dashed lines in Fig. 2(b).
- While testing against TCAD simulation (as presented in the next section) the authors have found that in most of the geometries θ = 46◦ yields excellent accuracy.

### A. Comparison with 3D TCAD simulation

- First, the authors test their proposed model against 3D TCAD thermal simulation results of multifinger SiGe HBT structures having no trench isolation.
- Fig. 6(a) compares their modeling results for the T (z) variation with the 3D TCAD simulation data corresponding to the corner fingers in case of multifinger structures with STI.
- As a next step, the authors test their model for multifinger transistor system where each finger is individually surrounded by STI and the whole transistor is housed within a deep trench isolation (DTI).
- Since the heat flow volume inside the DTI region is equally shared among the fingers, this assumption leads to the prediction of the same temperature at the bottom of DTI and identical T (z) for all fingers.
- The proposed model (solid lines) demonstrates an excellent agreement with the TCAD results .

### IV. CONCLUSION

- The authors have presented a simple, analytical, thermal model for multifinger SiGe HBTs.
- The proposed model is highly accurate as it considers the temperature dependence of thermal conductivity of silicon and at the same time requires no extra circuit node to account for the thermal coupling effects between nearby fingers.
- Other than the dissipated power, the input for the model are the dimensions and relative locations of emitter fingers and different trenches in order to compute the temperature at each finger.
- The model is implemented within the framework of existing self-heating sub-circuit of the main electrical model of bipolar transistor.
- The model is found to simulate 40% faster than the stateof-the-art thermal coupling model while tested for transient simulation.

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##### Frequently Asked Questions (7)

###### Q2. What is the effect of the temperature insensitive bias technique in a multi-finger transistor?

The modern application circuits such as power amplifiers are equipped with temperature insensitive bias techniques to ensure a near constant operating current [6]–[9].

###### Q3. What is the geometry factor for the heating finger?

In the present work, since the authors have computed the geometry factor (fG) for each heating finger, the corresponding thermal resistance is easily obtained and can be used within the already existing self-heating network.

###### Q4. What is the way to estimate the temperature at each finger?

In order to accurately predict the temperature at each finger, an effective heat spreading angle (θ1) has to be defined between the adjacent heat sources as shown by the dashed lines in Fig. 2(b).

###### Q5. What is the speed improvement of the model?

In order to quantify the speed improvement of their model over the stateof-the-art thermal model for multifinger transistor [2], quasistationary and transient simulations of a 5-finger SiGe HBT are carried out for both the models using QucsStudio.

###### Q6. What is the geometry factor for the STI and DTI?

The corresponding geometry factor fG(z) is evaluated with a symmetric lateral spread of θ (=46◦) or by a simple depth/area ratio (as applicable in different sections) and eventually the T (z) profile is obtained using (1).

###### Q7. What is the simplest way to capture the thermal effect of a transistor finger?

In practice, each transistor finger is to be modeled using separate electrical model where a thermal sub-circuit is available in order to capture the self-heating effect.