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Volume Charge Density & Space Charge Calculator

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### Semiconductor Physics, Poisson's Equation & Volume Charge Density Metrology Volume Charge Density is the quantity of electric charge per unit volume in a 3D continuum.

Reviewed by Sheraz Share · BSCS
Last updated:
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⚙ Input Values

ρ_q
mm

📊 Results

Converted Target Volume Charge
0.0016
density units
Volume Charge Density in SI (C/m³)
1,602
C/m³
Density in Coulombs per cm³
0.0016
C/cm³
Equivalent Ion Doping Density (N = ρ_q/e)
9,999,000,000,000,000
ions/cm³
Total Enclosed Sphere Charge (Q = ρ_q·V)
0
Coulombs (C)
Gauss's Law Surface Electric Field E(R)
60,310.44
kV/m
✦ Gauss's Law & Semiconductor Physics Summary
Space Charge & Semiconductor Profile (PN Junction Depletion Space Charge): Converted Volume Charge = 1.6020e-3 coulombs per cubic cm c cm3. Standard SI Value: ρ_q = 1.6020e+3 C/m³ (1.6020e-3 C/cm³). Equivalent Net Dopant Carrier Ionization: N = 9.999e+15 ions/cm³ (9.999e+21 m⁻³). Uniform Sphere Enclosure (R = 1.00 µm): Enclosed Charge Q = 6.7104e-15 Coulombs. Gauss's Law Surface Electric Field: E(R) = 60.31 MV/m (60,310,444 V/m). Solid-State Semiconductor Principle: In a reverse-biased PN junction diode or MOSFET space charge region, uncompensated ionized donor atoms (N_d⁺) create a fixed volume charge density (ρ_q = q·N_d). Poisson's equation (d²V/dx² = -ρ_q / ε_s) determines the junction peak electric field and breakdown voltage.
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📐 Formula

Equivalent Ion Carrier Density: N = rho / e (ions/m^3 -> ions/cm^3)
Total Enclosed Sphere Charge: Q = rho * (4/3 * pi * R^3)
Gauss's Law Surface Electric Field: E(R) = (rho * R) / (3 * eps_0)

💡 Practical Example

✅

A semiconductor device engineer measuring a space charge density $\rho_q = 1,602\text{ C/m}^3$ in a silicon diode depletion region calculates the active ionized donor density is $N_d = 1.0 \times 10^{16}\text{ atoms/cm}^3$, establishing the exact junction capacitance.

📖 About Volume Charge Density & Space Charge Calculator

Semiconductor Physics, Poisson's Equation & Volume Charge Density Metrology

Volume Charge Density is the quantity of electric charge per unit volume in a 3D continuum or plasma:

  • **
  • Universal Volume Charge Conversion Formulas (SI Standards)**:

1 C/cm^3 = 10^6 C/m^3 = 10^9 mC/m^3 = 10^12 µC/m^3

1 C/m^3 = 10^-6 C/cm^3 = 1,000 mC/m^3 = 10^6 µC/m^3

1 statC/cm^3 = 3.335641 × 10^-4 C/m^3

  • **
  • Ionized Dopant Carrier Density & Poisson's Equation**:

N_ions/cm^3 = ρ_q, C/m^31.602176634 × 10^-19 × 10^-6 (Active Doping Level in cm^-3)

^2 V = -(ρ_q) / (_r _0) (Poisson's Equation for Electric Potential)

E(R) = (ρ_q × R) / (3 _0) (Gauss's Law Surface Electric Field of Sphere)

  • **
  • Standard Semiconductor & Physical Benchmarks**:
  • Martian Dust Storm: 0.010 mC/m^3 = 10 nC/m^3 N ≈ 6.24 × 10^10 charges/m^3
  • Ionosphere Plasma: 1.0 µC/m^3 N = 6.24 × 10^12 electrons/m^3
  • PN Junction Depletion (10^16 cm^-3): 1,602.0 C/m^3 0.001602 C/cm^3
  • Atomic Nucleus Core: 1.0 × 10^25 C/m^3 1.0 × 10^19 C/cm^3 (Extreme density)

How to Use This Calculator

Enter your Volume Charge Density (ρ_q) (e.g. 1602 in ρ_q), From Volume Charge Density Unit — choose from Coulombs per Cubic Meter (C/m³ - SI Base Unit), Coulombs per Cubic Centimeter (C/cm³ = 10⁶ C/m³), Millicoulombs per Cubic Meter (mC/m³ = 10⁻³ C/m³), To Volume Charge Density Unit — choose from Coulombs per Cubic Centimeter (C/cm³), Coulombs per Cubic Meter (C/m³), Millicoulombs per Cubic Meter (mC/m³), Charged Sphere / Depletion Radius (R in mm) (e.g. 1.0 in mm), and Semiconductor & Plasma Benchmark — choose from Custom Volume Charge System, Silicon PN Junction Depletion Space Charge (1,602.0 C/m³ = 10¹⁶ ions/cm³) → 0.001602 C/cm³ | E(0.001mm) = 60.3 kV/cm, Ionosphere D-Layer Plasma (1.0 µC/m³) → 6.24 × 10¹² ions/m³ | Space plasma physics. Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Equivalent Ion Carrier Density: N = rho / e (ions/m^3 -> ions/cm^3)

Total Enclosed Sphere Charge: Q = rho (4/3 pi * R^3)

Gauss's Law Surface Electric Field: E(R) = (rho R) / (3 eps_0)

Worked Example

A semiconductor device engineer measuring a space charge density ρ_q = 1,602 C/m^3 in a silicon diode depletion region calculates the active ionized donor density is N_d = 1.0 × 10^16 atoms/cm^3, establishing the exact junction capacitance.

Understanding Your Result

Geometric calculations assume ideal shapes — real-world measurements should include a 5–15% tolerance for irregular shapes, cutting waste, and installation overlap. For construction applications: always verify calculated areas match your physical measurements before ordering materials. Standard practice is to measure the same dimension twice from different reference points and use the average. Express results in the units required by your supplier or building permit — conversions between cubic yards, cubic feet, and cubic meters must be precise for material orders.

💡 Methodological Standards & Calculation Accuracy

  • All calculations are performed client-side in your browser using verified, standards-compliant mathematical algorithms.
  • Results are provided for educational and informational analysis; verify critical applications with certified domain specialists.
  • Ensure input values are entered in consistent units matching the selector options to guarantee accurate outputs.
  • Periodic recalibration is recommended whenever baseline assumptions, operating parameters, or external conditions change.
Sources: NIST Standards · ISO International Standards

Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.

❓ Frequently Asked Questions

How do you calculate semiconductor dopant carrier density from volume charge density?
Divide volume charge density in C/m³ by the elementary charge e and convert to cm³: Doping Density = × 10^-6. For ρ_q = 1,602 C/m³, Doping = × 10^-6 = 1.0 × 10^16 ions/cm³.

How do you convert C/m³ to C/cm³?
Divide by 1,000,000 (10^6), since 1 m³ = 1,000,000 cm³. For example, 1,602 C/m³ = 0.001602 C/cm³.

What is space charge in a PN junction diode?
When p-type and n-type semiconductors join, free electrons and holes diffuse across the junction, leaving behind fixed uncompensated ionized donor (N_d⁺) and acceptor (N_a⁻) impurity atoms. This creates a charged 'depletion region' with a non-zero volume charge density ρ_q.

What is Poisson's equation for volume charge density?
Poisson's equation states that the spatial curvature of electric potential is directly proportional to local volume charge density divided by permittivity. Integrating this equation yields the built-in potential and electric field profile across electronic devices.

What is the electric field inside a uniformly charged sphere?
Under Gauss's Law, the radial electric field inside a uniform sphere of charge increases linearly with distance from the center: E(r) = /, reaching its maximum at the outer surface r = R.

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