Internal Bandgap Voltage Error Reduction in High Gradient Layouts
Internal bandgap voltage errors in high gradient layouts are reduced by common-centroid matching, thermal isolation trenching, and package stress mitigation.
Substrate Isotherms
Thermal Mapping
Imaginary contour lines connecting points of identical temperature across a silicon chip trace the heat distribution resulting from power-dissipating elements. Mapping substrate isotherms is essential for locating matched analog components where local temperature differences must be kept to an absolute minimum.
Gradient Mitigation
Uneven temperature distributions create thermal gradients that cause differences in transistor thresholds and resistor values. By aligning matched components along the same isotherm, these devices experience identical temperatures, which cancels out the gradient-induced drift. This technique is especially important in high-power mixed-signal chips where heat sources are close to sensitive analog inputs.
Simulation Tooling
Thermal simulation software calculates the position of these contours based on the power dissipation of each block and the thermal conductivity of the package. Designers use these simulated maps to plan the layout, ensuring that critical matched pairs are oriented parallel to the isotherms rather than perpendicular to them. This layout methodology prevents thermal mismatch and reduces the need for complex compensation circuitry.
The simulated results are validated against physical thermal measurements during the prototype phase.
Temperature Verification
Physical verification is performed using infrared thermography on uncovered die or by monitoring built-in temperature diodes distributed across the substrate surface. These measurements confirm that the actual thermal profiles match the simulated isotherms under different power levels. The data are used to refine the layout rules.