Correlation Mechanics for Transferred Analog Block Yield Distributions across Secondary Wafer Foundries
Transferring analog blocks across secondary foundries requires mapping PCM covariance matrices to maintain targeted circuit yield distributions.
Bandgap Voltage Reference Stability
Meaning
Precision voltage sources in integrated circuits must provide a constant output regardless of operating conditions. The concept of bandgap voltage reference stability describes the ability of a circuit to maintain its nominal output voltage across specified thermal ranges and supply fluctuations.
Temperature Behavior
Negative and positive temperature coefficient voltages are summed in a specific ratio to achieve a flat response. When the circuit operates, the base-emitter voltage of a bipolar transistor decreases with temperature while the thermal voltage increases. The balance between these opposing effects establishes the overall temperature coefficient.
Silicon bandgap voltage reference stability remains bound by the non-linearities in the base-emitter voltage curve which create a residual curvature.
Qualification Test
Automated test equipment measures the output voltage at multiple discrete temperatures across the operating range to calculate the temperature coefficient. High-temperature operating life tests subject the silicon to sustained thermal stress for one thousand hours to verify long-term drift. Drift values exceeding the specified microvolt budget during these cycles trigger a redesign of the startup circuit or bias currents.
Degradation Mechanism
Mechanical stress from the plastic package of an integrated circuit alters the piezoresistive properties of the silicon die. When the package expands or contracts, it exerts pressure on the sensitive transistors of the bandgap circuit. This pressure shifts the reference voltage and degrades bandgap voltage reference stability over time.
Electromigration in the metal interconnects also introduces subtle resistance shifts that skew the temperature compensation loop.