One aspect of the present subject matter relates to a method for forming a
transistor. According to an embodiment of the method, a pillar of
amorphous semiconductor material is formed on a crystalline substrate,
and a solid phase epitaxy process is performed to crystallize the
amorphous semiconductor material using the crystalline substrate to seed
the crystalline growth. The pillar has a sublithographic thickness. A
transistor body is formed in the crystallized semiconductor pillar
between a first source/drain region and a second source/drain region. A
surrounding gate insulator is formed around the semiconductor pillar, and
a surrounding gate is formed around and separated from the semiconductor
pillar by the surrounding gate insulator. Other aspects are provided
herein.