Since you want it to appear a bit modern while still using farmhouse style, then you need to consider using something with simple lines that is neutral but still have dramatic contrast on the detail. Use element that can be define to make the backsplash appear more beautiful.
For example, you can try to use subway tiles which is very simple but still have modern and classic appearance at the same time. It is also very easy to maintain as it is made from tile so it is suitable for those who want something easy to take care for their farmhouse kitchen backsplash.
If you are not really concern about maintenance, then you can always use wooden material for the backsplash. This material will give great texture to the kitchen and it will also make the whole appearance more unite with the farmhouse theme. Just make sure it does not used anywhere near fire source.
If you are going for more rustic look then you might want to try using exposed brick which is very suitable for the farmhouse theme that you like. It will also give more unique appearance to the kitchen with the exposed look that make it look raw.
Or you can actually create unique pattern with tile material that have suitable design for your farmhouse theme. Try to go with neutral color that suitable with the color scheme you use in your kitchen. You can give some contrast if you want but make sure the farmhouse kitchen backsplash ideas is suitable with the other color you have.
image source : pinterest.com