  Semi-detached binaries are in the stage of mass transfer and play a crucial
role in studying mass transfer physics between interacting binaries.
Large-scale time-domain surveys provide massive light curves of binary systems,
while Gaia offers high-precision astrometric data. In this paper, we develop,
validate, and apply a pipeline that combines the MCMC method with a forward
model and DBSCAN clustering to search for semi-detached binary and estimate its
inclination, relative radius, mass ratio, and temperature ratio using light
curve. We train our model on the mock light curves from PHOEBE, which provides
broad coverage of light curve simulations for semi-detached binaries. Applying
our pipeline to TESS sectors 1-26, we have identified 77 semi-detached binary
candidates. Utilizing the distance from Gaia, we determine their masses and
radii with median fractional uncertainties of ~26% and ~7%, respectively. With
the added 77 candidates, the catalog of semi-detached binaries with orbital
parameters has been expanded by approximately 20%. The comparison and
statistical results show that our semi-detached binary candidates align well
with the compiled samples and the PARSEC model in Teff-L and M-R relations.
Combined with the literature samples, comparative analysis with stability
criteria for conserved mass transfer indicates that ~97.4% of samples are
undergoing nuclear-timescale mass transfer, and two samples (GO Cyg and TIC
454222105) are located within the limits of stability criteria for dynamical-
and thermal-timescale mass transfer, which are currently undergoing
thermal-timescale mass transfer. Additionally, one system (IR Lyn) is very
close to the upper limit of delayed dynamical-timescale mass transfer.
