A method comprising: providing a substrate having a first region, second region, and third region that is between the first region and second region, wherein the third region abuts the first region at a first point along a first axis (z), and wherein the third region abuts the second region at a second point along the first axis; and providing a first layer of a first material disposed on the substrate, wherein the first layer has a first thickness in the first region and a second thickness in the second region, and wherein the thickness (h(z)) of the first layer in the third region changes in non-linear fashion from the first thickness at the first point to the second thickness at the second point, and wherein the first layer is provided by operations comprising: (i) forming the first layer with a first surface and a thickness equal to the second thickness; (ii) forming an accelerator layer on the first surface, the layer comprising a second material and a second surface; (iii) forming a mask layer on the second surface, the mask layer defining an opening having a first side and second side that define a shaped region having a first width Δ(z) that increases monotonically and non-linearly between the first point and second point, wherein the shape of each of the first side and second side is characterized by an etch-front angle function (Φ(z)) that is based on a first desired thickness profile (h(z)) for the first layer in the third region; and (iv) etching the first layer and the accelerator layer in a first etchant for a first time period, the first etchant being selected such that it etches the second material at a faster rate than the first material, wherein the first time period is selected based on the etch rate of the first material, the first thickness, the second thickness, and the distance between the first point and the second point. providing a substrate having a first region, second region, and third region that is between the first region and second region, wherein the third region abuts the first region at a first point along a first axis (z), and wherein the third region abuts the second region at a second point along the first axis; and providing a first layer of a first material disposed on the substrate, wherein the first layer has a first thickness in the first region and a second thickness in the second region, and wherein the thickness (h(z)) of the first layer in the third region changes in non-linear fashion from the first thickness at the first point to the second thickness at the second point, and wherein the first layer is provided by operations comprising: (i) forming the first layer with a first surface and a thickness equal to the second thickness; (ii) forming an accelerator layer on the first surface, the layer comprising a second material and a second surface; (iii) forming a mask layer on the second surface, the mask layer defining an opening having a first side and second side that define a shaped region having a first width Δ(z) that increases monotonically and non-linearly between the first point and second point, wherein the shape of each of the first side and second side is characterized by an etch-front angle function (Φ(z)) that is based on a first desired thickness profile (h(z)) for the first layer in the third region; and (iv) etching the first layer and the accelerator layer in a first etchant for a first time period, the first etchant being selected such that it etches the second material at a faster rate than the first material, wherein the first time period is selected based on the etch rate of the first material, the first thickness, the second thickness, and the distance between the first point and the second point. (i) forming the first layer with a first surface and a thickness equal to the second thickness; (ii) forming an accelerator layer on the first surface, the layer comprising a second material and a second surface; (iii) forming a mask layer on the second surface, the mask layer defining an opening having a first side and second side that define a shaped region having a first width Δ(z) that increases monotonically and non-linearly between the first point and second point, wherein the shape of each of the first side and second side is characterized by an etch-front angle function (Φ(z)) that is based on a first desired thickness profile (h(z)) for the first layer in the third region; and (iv) etching the first layer and the accelerator layer in a first etchant for a first time period, the first etchant being selected such that it etches the second material at a faster rate than the first material, wherein the first time period is selected based on the etch rate of the first material, the first thickness, the second thickness, and the distance between the first point and the second point.