Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.

Characteristic field (MV/cm)

Optional number in MV/cm. Characteristic tunneling field of the material. Must be a finite number greater than 0 MV/cm.

Electric field (MV/cm)

Required number in MV/cm. Electric field across the tunneling junction. Must be a finite number greater than 0 MV/cm.

Tunneling coefficient (nA/(MV/cm))

Optional number in nA/(MV/cm). Prefactor scaling the tunneling exponential. Must be a finite number at least 0 nA/(MV/cm).

The cited overview of P–n junction supplies background for the terminology and domain context used by this tool.^[1]

Estimate band-to-band tunneling current from the junction field through a field-driven exponential: I[nA]=coeff·E·exp(-E0/E) with E=electricFieldMVPerCm>0 MV/cm, E0=characteristicFieldMVPerCm>0 MV/cm, coeff=tunnelingCoefficient>=0 nA/(MV/cm). Defaults E0=40 MV/cm, coeff=1 nA/(MV/cm). Simplified Kane-like model; neglects barrier shape, temperature, and trap-assisted contributions; valid only for E comparable to E0 and for the fitted material. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

BTBT current (nA)

Returned number in nA. Band-to-band tunneling current (magnitude). At least 0 nA; underflow to 0 allowed.

• Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
• Characteristic field must be at least 5e-324.
• Electric field must be at least 5e-324.
• Tunneling coefficient must be at least 0.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Compare the estimate with measured process data, current device documentation, and a higher-fidelity circuit, field, thermal, quantum, or TCAD model when the decision requires it.

• Bandgap Narrowing Calculator

  Estimate heavy-doping bandgap narrowing in silicon relative to a 1e17 cm^-3 reference: ΔEg[meV]=max(0,18·log10(N/1e17)) where N is dopingPerCm3>0 cm^-3. Clamped to >=0 meV below reference. Empirical log-decade model for silicon; neglects temperature, compensation, and degeneracy beyond the fitted decade slope; invalid for N<=0.

• APD Breakdown Voltage Temperature Shift Calculator

  Shift an APD breakdown voltage to operating temperature using the linear temperature coefficient model V(T)=Vref·[1+0.0011·(T-25 °C)]. Valid for reference breakdown Vref>0 V defined at 25 °C and junction temperature T in [-55, 175] °C inclusive; outside this range the 0.11%/°C linear approximation degrades. Vref is the breakdown magnitude (positive, not signed). Result is the breakdown magnitude at temperature. Device-specific tempco may vary.

• Ballistic Mean Free Path Calculator

  Estimate the ballistic mean free path from low-field mobility using λ = (μ·Vt/vsat)·1e7 with thermal voltage Vt=0.02585 V (300 K) and saturation velocity vsat=1e7 cm/s (λ[nm]=μ·0.02585). Input mobility μ>0 cm²/V·s must be the low-field, non-degenerate value; rpm vs linear-velocity and per-area vs total distinctions do not apply. Model assumes Maxwell-Boltzmann statistics and constant vsat, valid only near 300 K as a quasi-ballistic estimate.