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Bandgap references, packaged in plastic, have been known to shift in voltage, a pre-package to post-package voltage variation. This package shift has been analytically discussed and experimentally investigated in this paper. The culprits for such a variation are the package-induced stresses present once the reference is encapsulated. Systematic voltage shifts can range from -3 to -7 mV, and is closely related to package type and processing. Major emphasis has been placed on reducing the random package-shift component, since systematic package shift can be trimmed and its temperature coefficient compensated. The package shift is seen to have a systematic positive temperature coefficient; its effects are mitigated as temperature increases. In summary, results of the study show that die-surface planarization techniques and mechanically elastic compliant layers between the die and the package reduce random as well as systematic package shifts. In particular, systematic variations improved from -5 to -2 mV (0.4% to 0.17% bandgap error) and three-sigma (3σ) variations improved from 8 to 4 mV (0.67% to 0.33% bandgap error) when adding a 15-μm mechanically compliant layer between the die and the package.