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The existing surface-potential-based compact metal-oxide-semiconductor transistor models are based on the 1978 Brews delta-function charge-sheet approximation, which was derived empirically from the 1966 Pao-Sah drift-diffusion double integral formula. This paper provides a device physics-based derivation of a surface-potential-based compact model by analytical approximation of the double and single bulk-charge integrals of the four one-dimensional components of the six-component 1996 Sah two-dimensional formula. In this compact model development, the mobile carrier-space-charge-limited parabolic-drift and linear-diffusion current components are analytically represented by the surface potential without approximation, while the immobile-impurity bulk-space-charge-limited double-integral drift-current and single-integral diffusion-current components are evaluated analytically using three possible surface-potential compact model approximations. This paper calculates the accuracy of these approximate analytical bulk-charge-limited drift and diffusion current components in both the inversion and subthreshold ranges and discusses factors that affect the accuracy in the subthreshold range and near flatband.