The International Office provides the PROMOS programme to help students finance study visits abroad. This provides funding for visits of up to six months anywhere in the world. Further information is available from the programme website: PROMOS.
Another way of financing your semester abroad is the overseas Bafög (Federal Training Assistance Act). The overseas Bafög comprises travel costs and a monthly overseas allowance (half of each of which must be paid back) along with any tuition fees up to a maximum of 4,600 Euros. Applications should be submitted six months before the start of any visit abroad. Even if you are not eligible for assistance at home, it is possible that you will be eligible for the overseas Bafög due to the higher costs of study abroad. Further information is available from http://www.auslandsbafoeg.de/.
The DAAD offers other programmes to help fund your visit. The DAAD grants database allows you to search for suitable options.
A range of other foundations and organisations award support grants for study abroad. A few websites worth looking at are: