Unit 3: Diode Voltage Quest

ECE120 — Basic Electronics Engineering Workshop 10 min read

I. Orientation

A PN junction diode is a two-terminal semiconductor device formed by joining p-type and n-type materials. Its principal electrical property is unidirectional conduction: it conducts substantial current when forward biased and only a very small leakage current when reverse biased. In this unit, the diode is studied under forward-bias conditions by relating the applied voltage (V_D) to the resulting current (I_D).

Governing principle: A forward voltage reduces the depletion-region barrier, allowing majority carriers to cross the junction.
Reference direction: Conventional current (I_D) is taken from the p-side, or anode, to the n-side, or cathode.
Voltage convention: The diode voltage is
[
V_D = V_A - V_K
]
where (V_A) is anode potential and (V_K) is cathode potential.
Forward-bias condition: The anode is at a higher potential than the cathode, so (V_D>0).
Characteristic curve: The forward V-I characteristic is a graph of (I_D) on the vertical axis against (V_D) on the horizontal axis.
Practical assumption: Temperature, device construction, and measurement polarity must be kept controlled because diode current is strongly temperature-dependent.
Important distinction: The commonly stated (0.7\text{ V}) for silicon is an approximate operating voltage, not a universal physical threshold.

II. PN Junction Diode — Structure and Forward Conduction

A PN junction diode consists of a p-type region containing holes as majority carriers and an n-type region containing electrons as majority carriers. At the junction, diffusion creates a depletion region and an internal electric field that oppose further carrier movement.

A. Definition and Operating Principle

The diode permits substantial current mainly in one direction because the junction barrier changes with the applied voltage.

P-type region: Acceptor impurities create holes as the majority carriers; electrons are minority carriers.
N-type region: Donor impurities create electrons as the majority carriers; holes are minority carriers.
Depletion region: Near the junction, electrons and holes recombine, leaving fixed charged ions and very few mobile carriers.
Built-in potential: The electric field in the depletion region establishes a barrier potential (V_{bi}), typically about (0.6\text{--}0.8\text{ V}) for silicon at room temperature, depending on doping and construction.
Equilibrium condition: With no external voltage, diffusion and drift currents balance, so the net diode current is approximately zero.
Forward voltage effect: Applying positive voltage to the p-side reduces the effective barrier and narrows the depletion region.
Carrier injection: Majority carriers cross the junction and become minority carriers in the opposite region, producing the external current.

B. Analysis of the voltage-current characteristics of a PN junction diode under forward-bias conditions

The forward-bias V-I characteristic shows that diode current remains small at low voltage and then rises rapidly after the junction begins conducting strongly.

Characteristic relation: The ideal diode current is described by the Shockley equation:
TEXT
```
  I_D = I_S [ exp(V_D / (η V_T)) - 1 ]
```
where:
- (I_D) = forward diode current in amperes,
- (I_S) = reverse saturation current in amperes,
- (V_D) = applied diode voltage in volts,
- (\eta) = ideality factor, usually approximately (1) for germanium and (2) for many practical silicon junctions,
- (V_T) = thermal voltage.
Thermal voltage: At absolute temperature (T),
TEXT
```
  V_T = kT / q
```
where (k=1.38\times10^{-23}\text{ J/K}) is Boltzmann’s constant and (q=1.6\times10^{-19}\text{ C}) is electronic charge. At (T=300\text{ K}), (V_T\approx25.9\text{ mV}).
Low-voltage region: When (V_D) is small, the exponential term is not large, so (I_D) is very small. The diode behaves as a high-resistance element.
Knee or cut-in region: As (VD) approaches the practical conduction voltage, current begins increasing noticeably. The knee voltage (V\gamma) is approximately (0.3\text{ V}) for germanium and (0.7\text{ V}) for silicon in simple circuit models.
Rapid-rise region: Once the junction is conducting, a small increase in (V_D) causes a large increase in (I_D). This is the exponential portion of the curve.
Silicon example: If a silicon diode operates at (I_D=1\text{ mA}) and its voltage changes from (0.65\text{ V}) to (0.67\text{ V}), the current can increase substantially because the change is applied inside an exponential relationship, not a linear one.
Nonzero current before the knee: The knee is a convenient engineering approximation; the actual current increases continuously according to the diode equation.
Temperature influence: For a constant forward current, a silicon diode’s forward voltage commonly decreases by approximately (2\text{ mV}/^\circ\text{C}) as junction temperature rises, although the exact value depends on the device and current.
Saturation-current influence: (I_S) increases strongly with temperature. Consequently, at the same applied voltage, a warmer diode generally carries more current.

C. Experimental Determination of the Forward V-I Curve

The characteristic is obtained by applying several forward voltages and recording the corresponding currents.

Test circuit: Connect a DC supply, a current-limiting resistor (R), an ammeter in series, and a voltmeter across the diode.
Protection requirement: The resistor limits current according to the approximate relation:
TEXT
```
  R = (V_S - V_D) / I_D
```
where (V_S) is supply voltage, (V_D) is diode voltage, and (I_D) is selected maximum current.
Polarity check: Connect the p-side or anode to the positive supply terminal and the cathode, usually marked by a band, toward the negative side.
Measurement sequence: Increase the supply gradually and record paired values ((V_D,I_D)), using small voltage steps near the knee where current changes rapidly.

Table format: A useful observation table contains:

TEXT

  Applied supply voltage | Diode voltage V_D | Diode current I_D

Graphing convention: Plot (V_D) horizontally in volts and (I_D) vertically in milliamperes. A nonuniform vertical scale may be useful because the current rises sharply.
Curve interpretation: The nearly flat initial part represents weak conduction; the bending portion identifies the knee; the steep part represents strong forward conduction.
Experimental precautions:
- Current limit: Never exceed the diode’s rated forward current.
- Temperature control: Allow readings to stabilize because self-heating changes the curve.
- Instrument connection: Place the ammeter in series and the voltmeter in parallel with the diode.
- Reading accuracy: Use appropriate meter ranges and avoid parallax error with analog instruments.
- Polarity safety: Reversed connections produce reverse bias and do not generate the intended forward characteristic.

D. Quantitative Parameters from the Characteristic

The plotted curve provides resistance and conduction information at a selected operating point.

DC or static resistance: The resistance represented by the operating point is:
TEXT
```
  R_DC = V_D / I_D
```
where (R_{DC}) is in ohms, (V_D) in volts, and (I_D) in amperes.
AC or dynamic resistance: The small-signal resistance is the local slope reciprocal:
TEXT
```
  r_d = ΔV_D / ΔI_D
```
where (\Delta V_D) and (\Delta I_D) are small changes around the operating point.
Diode-equation approximation: In the strong forward region:
TEXT
```
  r_d ≈ η V_T / I_D
```
Thus, for (T=300\text{ K}), (\eta=2), and (I_D=1\text{ mA}),
[
r_d\approx\frac{2(25.9\text{ mV})}{1\text{ mA}}\approx51.8\ \Omega.
]
Comparison of resistances: (R_{DC}) uses the line from the origin to the operating point, whereas (r_d) uses the tangent slope at that point; they are generally different.
Conductance: The incremental conductance is:
TEXT
```
  g_d = 1 / r_d
```
where (g_d) is measured in siemens.
Operating point: In a practical circuit, the intersection of the diode characteristic and the external circuit’s load line determines the actual (V_D) and (I_D).

E. Equivalent Models and Analytical Use

Simplified diode models make circuit calculations faster, but each model discards some detail from the exponential characteristic.

Ideal-diode model:
- Forward bias: The diode is treated as a short circuit, so (V_D=0).
- Reverse bias: The diode is treated as an open circuit, so (I_D=0).
Constant-voltage model:
- Silicon approximation: Use (V_D\approx0.7\text{ V}) during conduction.
- Germanium approximation: Use (V_D\approx0.3\text{ V}).
- Purpose: This model is convenient when an approximate current or voltage is required without solving an exponential equation.
Piecewise-linear model: Represent the diode by a threshold voltage (V_\gamma) in series with a small resistance (r_d):
TEXT
```
  V_D ≈ V_γ + I_D r_d
```
Exponential model: Use the Shockley equation when accurate current-voltage behavior, temperature effects, or small-signal analysis is important.
Model selection:
- Switching estimate: The ideal model is usually adequate.
- Bias calculation: The constant-voltage model is often sufficient.
- Amplifier analysis: The dynamic resistance (r_d) gives a more useful local approximation.
- Precision design: Use measured data or a detailed device model rather than assuming a fixed (0.7\text{ V}).

III. Forward-Bias Analysis — Interpretation and Limitations

Forward-bias analysis connects the physical operation of the junction with the measured curve and identifies where simple assumptions stop being reliable.

A. Analytical Dimension of the Forward Characteristic

The curve is useful because its slope, position, and shape reveal the diode’s operating behavior.

Slope meaning: A steep (I_D)-versus-(V_D) curve means a small dynamic resistance and strong sensitivity of current to voltage.
Barrier interpretation: The gradual reduction of the depletion barrier explains the curved transition into conduction; the diode does not suddenly switch from zero current to full current.
Bias-current relationship: Increasing the forward bias increases carrier injection, which increases recombination and diffusion current through the device.
Circuit consequence: A small voltage error can create a large current error in the steep region, so current limiting is essential during workshop measurements.
Logarithmic analysis: Rearranging the Shockley equation in strong forward bias, where the (-1) term is negligible:
TEXT
```
  ln(I_D) ≈ ln(I_S) + V_D / (η V_T)
```
A plot of (\ln(I_D)) against (V_D) is approximately linear, with slope (1/(\eta V_T)).

B. Applications and Limitations

The forward V-I characteristic supports practical diode selection and circuit design, but it must be interpreted within the device’s ratings.

Rectification: A forward-biased diode conducts one half-cycle of an AC waveform, while the opposite half-cycle is blocked by reverse bias.
Voltage reference and detection: The approximately fixed forward drop of a conducting diode can be used for signal detection or level shifting, but its value changes with current and temperature.
Switching circuits: The diode can be approximated as ON when forward biased beyond its conduction region and OFF when insufficiently biased.
Power limitation: The forward power loss is:
TEXT
```
  P_D = V_D I_D
```
where (P_D) is power in watts. For (V_D=0.7\text{ V}) and (I_D=100\text{ mA}), (P_D=70\text{ mW}).
Self-heating limitation: Increasing (P_D) raises junction temperature, which lowers forward voltage and can increase current further in a poorly controlled circuit.
Component variation: Two diodes of the same type may show different forward voltages because of manufacturing tolerances, current level, and temperature.
Measurement limitation: Meter resolution, resistor tolerance, supply fluctuations, wiring resistance, and thermal drift can distort the plotted characteristic.
Safe interpretation: The V-I curve should be used with the manufacturer’s maximum forward-current, power-dissipation, and junction-temperature ratings. A measured curve is valid for the particular diode and test temperature used.