Etching method, substrate processing apparatus, and substrate processing system

An etching method, comprising:

• providing a substrate having a layer to be etched and a mask on the layer and in direct contact with the layer, the mask having an opening which partially exposes the layer, the layer having an opening having a first depth, the substrate further including an underlying layer below the layer, with the underlying layer being composed of a different material than a material of the layer:
• forming a film on a top surface of the mask so that the mask is between the film and layer, the film being formed on at least one of a side wall of the opening of the mask or a portion of the layer exposed through the mask, and the film includes a same material as the material of the layer;
• and
• after the forming the film, etching the layer through the opening in the mask to etch the layer to a second depth deeper into the layer than the first depth.