Size depth tradeoffs for monotone arithmetic circuits

Are there any size depth trade-offs known for monotone arithmetic circuits that compute permanent and determinant?

• there are no monotone circuits that compute the determinant because the determinant is not a monotone function. May 9 '13 at 20:43
• I meant sum of monotone ( I am unsure if there is a separate name for it). May be something like this sciencedirect.com/science/article/pii/S0020019097000690 May 10 '13 at 11:28