  We present a Spitzer/IRAC survey of H-faint ($H_{160} \gtrsim 26.4$,
$<5\sigma$) sources in 101 lensing cluster fields. Across a CANDELS/Wide-like
survey area of $\sim$648 arcmin$^2$ (effectively $\sim$221 arcmin$^2$ in the
source plane), we have securely discovered 53 sources in the IRAC Channel-2
band (CH2, 4.5 $\mathrm{\mu m}$; median CH2$=22.46\pm0.11$ AB mag) that lack
robust HST/WFC3-IR F160W counterparts. The most remarkable source in our
sample, namely ES-009 in the field of Abell 2813, is the brightest H-faint
galaxy at 4.5 $\mathrm{\mu m}$ known so far ($\mathrm{CH2}=20.48\pm0.03$ AB
mag). We show that the H-faint sources in our sample are massive (median
$M_\mathrm{star} = 10^{10.3\pm 0.3}$ $M_\odot$), star-forming (median star
formation rate $=100_{-40}^{+60}$ $M_\odot$yr$^{-1}$) and dust-obscured
($A_V=2.6\pm0.3$) galaxies around a median photometric redshift of
$z=3.9\pm0.4$. The stellar continua of 14 H-faint galaxies can be resolved in
the CH2 band, suggesting a median circularized effective radius
($R_\mathrm{e,circ}$; lensing corrected) of $1.9\pm0.2$ kpc and $<1.5$ kpc for
the resolved and whole samples, respectively. This is consistent with the sizes
of massive unobscured galaxies at $z\sim4$, indicating that H-faint galaxies
represent the dusty tail of the distribution of a wider galaxy population.
Comparing with the ALMA dust continuum sizes of similar galaxies reported
previously, we conclude that the heavy dust obscuration in H-faint galaxies is
related to the compactness of both stellar and dust continua
($R_\mathrm{e,circ}\sim 1$ kpc). These H-faint galaxies make up
$16_{-7}^{+13}$% of the galaxies in the stellar mass range of
$10^{10}-10^{11.2}$ $M_\odot$ at $z=3\sim5$, contributing to $8_{-4}^{+8}$% of
the cosmic star formation rate density in this epoch and likely tracing the
early phase of massive galaxy formation.

Astrophysics of Galaxies