Transparent conducting oxides (TCOs) used in the antireflection layer and current spreading layer of heterojunction solar cells should have excellent optical and electrical properties. Furthermore, TCOs need a high work function over 5.2 eV to prevent the effect of emitter band-bending caused by the difference in work function between emitter and TCOs. Sn-doped $In_2O_3$ (ITO) film is a highly promising material as a TCO due to its excellent optical and electrical properties. However, ITO films have a low work function of about 4.8 eV. This low work function of ITO films leads to deterioration of the conversion efficiency of solar cells. In this work, ITO films with various Zn contents of 0, 6.9, 12.7, 28.8, and 36.6 at.% were fabricated by a co-sputtering method using ITO and AZO targets at room temperature. The optical and electrical properties of Zn-doped ITO thin films were analyzed. Then, silicon heterojunction solar cells with these films were fabricated. The 12.7 at% Zn-doped ITO films show the highest hall mobility of 35.71 $cm^2$/Vsec. With increasing Zn content over 12.7, the hall mobility decreases. Although a small addition of Zn content increased the work function, further addition of Zn content over 12.7 at.% led to decreasing electrical properties because of the decrease in the carrier concentration and hall mobility. Silicon heterojunction solar cells with 12.7 at% Zn-doped ITO thin films showed the highest conversion efficiency of 15.8%.