Double Diffused Silicon Mesa 1956 Verify Base Drift Field

# Verify the Base Drift-Field Profile: Measuring a Gradient Before Trusting It With an Emitter

## 1. Why a Field You Cannot Measure Is a Field You Cannot Rely On

Before any emitter diffusion is introduced on top of it, the base profile created by the drive-in step has to be measured directly, because the drift field this device depends on is a derivative of a dopant profile, and derivatives amplify small shaping errors into large field errors. A base that is slightly too shallow, too deep, or graded unevenly across the wafer will not simply shift the device's characteristics a little — it changes $dN/dx$ at exactly the point where the field matters most, the base-collector edge, where the emitter's injected carriers will later need the field's full assistance. Two measurements are taken at this step: sheet resistance, which integrates the total conductance of the diffused layer, and junction depth, found by sectioning and staining a sample wafer so the base-collector boundary is visible under a microscope. Together they let the actual profile be reconstructed and compared against the target:

$$R_s = \frac{1}{q \displaystyle\int_0^{x_j} \mu_p(x)\, N(x)\, dx}$$

where $R_s$ is the measured sheet resistance, $x_j$ the measured junction depth, and $\mu_p(x)$ the depth-dependent hole mobility. If $R_s$ and $x_j$ together imply a profile shallower or flatter than intended, the wafer is pulled before an emitter is ever diffused into it — correcting a base at this point is still possible; correcting it after the emitter exists is not.

Two Measurements Reconstruct One Profile neither alone tells you what the field actually is; together they do FOUR-POINT SHEET RESISTANCE diffused base layer Rₛ integrates total conductance of the layer a single number, not a shape SECTION AND STAIN FOR xᵀ stained base region, P-type unstained collector, N-type xᵀ measured directly under a microscope Rₛ and xᵀ together reconstruct N(x) — and therefore dN/dx, the field itself a profile wrong in either number is a field wrong in a way neither measurement alone would reveal

## 2. Real Diagram: What a Passing Profile Looks Like Against a Failing One

The diagram below overlays the target profile this step is checking against two kinds of failure: a drive-in run too long or too cool, which flattens the gradient toward the 1954-style uniform base this process is explicitly trying not to produce, and a drive-in run too short or too hot, which can leave the junction too shallow for the emitter step that follows to land correctly on top of it.

Target Profile vs. Two Named Failure Modes this step exists to catch both before an emitter is committed on top of either depth below surface target: steep, intended gradient too flat: drive-in ran too long/cool too shallow: drive-in ran too short/hot either failure is caught here, before the emitter step makes it permanent

## 3. Why This Checkpoint Did Not Exist in the Same Form in the 1954 Process

The 1954 diffused-base germanium process this project has already documented also measured sheet resistance and junction depth after its base diffusion, so the measurement techniques at this step are not new. What changes is what a failing measurement means: in the 1954 process, a profile slightly off target mainly risked a base width outside spec, a problem that degraded performance gradually. Here, because the device's entire advantage rides on a gradient steep enough to produce a usable drift field, a profile that drifts toward flat does not just degrade performance — it silently turns this device back into an ordinary diffused-base transistor with none of the speed advantage the rest of this process is built around, while still looking, by every other measure, like a successfully processed wafer. This step is the only point before the emitter is introduced where that silent failure can still be caught.

Step 5 does not change the base in any way; it decides, based on what the base actually turned out to be rather than what the furnace recipe intended, whether this wafer is still allowed to become a drift transistor.

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