Perfect absorbers with broadband absorption of terahertz (THz) radiation are promising for applications in imaging and detection to enhance the contrast and sensitivity, as well as to provide concealment. Different from previous two-dimensional structures, here we put forward a new type of THz absorber based on sawtooth-shape doped-silicon with near-unit absorption across a broad spectral range. Absorbance over 99% is observed numerically from 1.2 to 3 THz by optimizing the geometric parameters of the sawtooth structure. Our absorbers can operate over a wide range of incident angle and are polarization insensitive. The underlying mechanisms due to the combination of an air-cavity mode and mode-matching resonance on the air-sawtooth interface are analyzed in terms of the field patterns and electromagnetic power loss features.