Terahertz detection using the free-carrier absorption requires a small internal work function of the order of a few millielectron volts. A threshold frequency of $3.2\mathrm{THz}$ ( $93\mu \mathrm{m}$ or $\sim 13\mathrm{meV}$ work function) is demonstrated by using a $1\times {10}^{18}{\mathrm{cm}}^{-3}$ Si-doped GaAs emitter and an undoped ${\mathrm{Al}}_{0.04}{\mathrm{Ga}}_{0.96}\mathrm{As}$ barrier structure. The peak responsivity of $6.5\mathrm{A}∕\mathrm{W}$ , detectivity of $5.5\times {10}^8$ Jones, and quantum efficiency of 19% were obtained at $7.1\mathrm{THz}$ under a bias field of $0.7\mathrm{kV}∕\mathrm{cm}$ at $6\mathrm{K}$ , while the detector spectral response range spans from $3.2\text{to}30\mathrm{THz}$ .