updating doping FAQ with custom doping

_faqs/how-can-i-define-doping-profile.md

@@ -4,12 +4,12 @@ date: 2025-08-26 10:06:59
 enabled: true
 category: "Charge"
 ---
-Doping is defined as a box with a specific doping profile and is added to a [`SemiconductorMedium`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.SemiconductorMedium.html){: .color-primary-hover} object.  
-Positive doping corresponds to the `N_d` (number of donors) parameter of the [`SemiconductorMedium`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.SemiconductorMedium.html){: .color-primary-hover}, while negative doping corresponds to the `N_a` (number of acceptors).
+Doping is defined as a box with a specific doping profile and is added to a [`SemiconductorMedium`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.SemiconductorMedium.html){: .color-primary-hover}{: .color-primary-hover} object.  
+Positive doping corresponds to the `N_d` (number of donors) parameter of the [`SemiconductorMedium`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.SemiconductorMedium.html){: .color-primary-hover}{: .color-primary-hover}, while negative doping corresponds to the `N_a` (number of acceptors).
 
 The doping profile can be:
 
-- Uniform, implemented using the [`ConstantDoping`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ConstantDoping.html){: .color-primary-hover} object:
+- **Uniform**, implemented using the [`ConstantDoping`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ConstantDoping.html){: .color-primary-hover}{: .color-primary-hover} object:
 
 <div markdown class="code-snippet">
 {% highlight python %}
@@ -34,7 +34,7 @@ constant_box2 = td.ConstantDoping.from_bounds(
 {% endhighlight %}
 {% include copy-button.html %}</div>
 
-- Gaussian, implemented using the [`GaussianDoping`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.GaussianDoping.html){: .color-primary-hover} object:
+- **Gaussian**, implemented using the [`GaussianDoping`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.GaussianDoping.html){: .color-primary-hover}{: .color-primary-hover} object:
 
 <div markdown class="code-snippet">
 {% highlight python %}
@@ -65,6 +65,47 @@ gaussian_box2 = td.GaussianDoping.from_bounds(
 {% endhighlight %}
 {% include copy-button.html %}</div>
 
+- **Arbitrary (user-defined)**, implemented by directly providing a [`SpatialDataArray`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.SpatialDataArray.html){: .color-primary-hover}{: .color-primary-hover} to the `N_d` or `N_a` arguments of the [`SemiconductorMedium`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.SemiconductorMedium.html){: .color-primary-hover}{: .color-primary-hover}.  
+This approach allows defining essentially any spatial doping profile (for example, Pearson-like implantation profiles derived from fab parameters).
+
+<div markdown class="code-snippet">
+{% highlight python %}
+import tidy3d as td
+import numpy as np
+
+# Define geometry
+geometry = td.Cylinder(radius=1, length=1)
+
+# Pearson-like doping profile
+def pearson_doping(z, P, R, T, S, offset=0):
+    z = z - offset
+    return P * (1 + ((z - R) / T)**2)**(S / 2 + 0.75) + offset
+
+# Create coordinates
+NUM_PTS = 300
+rmin, rmax = geometry.bounds
+x = np.linspace(rmin[0], rmax[0], NUM_PTS)
+y = np.linspace(rmin[1], rmax[1], NUM_PTS)
+z = np.linspace(rmin[2], rmax[2], NUM_PTS)
+X, Y, Z = np.meshgrid(x, y, z)
+
+# Mask geometry
+mask = geometry.inside(X, Y, Z)
+
+# Doping profile along z
+doping_profile = pearson_doping(
+    z, P=7.77e18, R=0.10384, T=0.07878, S=1.71, offset=z.min()
+)
+
+# Create SpatialDataArray
+doping_values = td.SpatialDataArray(
+    mask * np.tile(doping_profile, (len(x), len(y), 1)),
+    coords={"x": x, "y": y, "z": z}
+)
+{% endhighlight %}
+{% include copy-button.html %}</div>
+
 The unit for the free carrier concentration is 1/$\text{cm}^3$.
 
-It is important to note that doping boxes are additive; i.e., if two donor doping boxes overlap, the total concentration will be the sum of these two overlapping doping boxes.
+It is important to note that doping boxes are additive; i.e., if two donor doping regions overlap, the total concentration will be the sum of the overlapping contributions.
+

docs/faq/how-can-i-define-doping-profile.md

@@ -10,7 +10,7 @@ Positive doping corresponds to the `N_d` (number of donors) parameter of the [`S
 
 The doping profile can be:
 
-- Uniform, implemented using the [`ConstantDoping`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ConstantDoping.html) object:
+- **Uniform**, implemented using the [`ConstantDoping`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ConstantDoping.html) object:
 
 
 
@@ -37,7 +37,7 @@ constant_box2 = td.ConstantDoping.from_bounds(
 
 
 
-- Gaussian, implemented using the [`GaussianDoping`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.GaussianDoping.html) object:
+- **Gaussian**, implemented using the [`GaussianDoping`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.GaussianDoping.html) object:
 
 
 
@@ -70,6 +70,49 @@ gaussian_box2 = td.GaussianDoping.from_bounds(
 
 
 
+- **Arbitrary (user-defined)**, implemented by directly providing a [`SpatialDataArray`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.SpatialDataArray.html) to the `N_d` or `N_a` arguments of the [`SemiconductorMedium`](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.SemiconductorMedium.html).  
+This approach allows defining essentially any spatial doping profile (for example, Pearson-like implantation profiles derived from fab parameters).
+
+
+
+```python
+import tidy3d as td
+import numpy as np
+
+# Define geometry
+geometry = td.Cylinder(radius=1, length=1)
+
+# Pearson-like doping profile
+def pearson_doping(z, P, R, T, S, offset=0):
+    z = z - offset
+    return P * (1 + ((z - R) / T)**2)**(S / 2 + 0.75) + offset
+
+# Create coordinates
+NUM_PTS = 300
+rmin, rmax = geometry.bounds
+x = np.linspace(rmin[0], rmax[0], NUM_PTS)
+y = np.linspace(rmin[1], rmax[1], NUM_PTS)
+z = np.linspace(rmin[2], rmax[2], NUM_PTS)
+X, Y, Z = np.meshgrid(x, y, z)
+
+# Mask geometry
+mask = geometry.inside(X, Y, Z)
+
+# Doping profile along z
+doping_profile = pearson_doping(
+    z, P=7.77e18, R=0.10384, T=0.07878, S=1.71, offset=z.min()
+)
+
+# Create SpatialDataArray
+doping_values = td.SpatialDataArray(
+    mask * np.tile(doping_profile, (len(x), len(y), 1)),
+    coords={"x": x, "y": y, "z": z}
+)
+```
+
+
+
 The unit for the free carrier concentration is 1/$\text{cm}^3$.
 
-It is important to note that doping boxes are additive; i.e., if two donor doping boxes overlap, the total concentration will be the sum of these two overlapping doping boxes.
+It is important to note that doping boxes are additive; i.e., if two donor doping regions overlap, the total concentration will be the sum of the overlapping contributions.
+