A phase change memory with a very limited area of contact between the lower electrode and the phase change material may be formed by defining a closed geometric structure for the lower electrode. The lower electrode may then be covered. The covering may then be opened in a very narrow strip extending across the closed geometric shape using phase shift masking. A phase change material may be formed in the opening. Because the opening effectively bisects the closed geometric structure of the lower electrode, two very small contact areas may be created for contacting the lower electrode to the phase change material.