Google uses the favicon to display the site logo in search results.

Favicons must be a square image with a size that is a multiple of 48 pixels (e.g., 48x48, 96x96, 144x144).

It must also be in a supported image format, such as ICO, PNG, or GIF.

Favicons under 48 pixels are not shown in Google listings anymore - so upgrade them.

At Organicwebs, we use png files, 144x144 size. This is our icon link code:

<link rel='icon' href='media/templates/site/organic/images/favicon.png'>