Unit 3: Diode Voltage Quest - Subjective Questions

Forward biasing is the condition in which the P-type terminal of a PN junction diode is connected to the positive terminal of a supply, while the N-type terminal is connected to the negative terminal.

• The applied electric field opposes the built-in electric field of the junction.
• The barrier potential decreases as the applied forward voltage increases.
• The depletion-region width becomes narrower.
• Majority carriers move toward the junction:
  • Holes move from the P-region toward the N-region.
  • Electrons move from the N-region toward the P-region.
• When the applied voltage becomes sufficiently large, majority carriers cross the junction and a significant forward current flows.

For a silicon diode, noticeable conduction generally begins near , while for a germanium diode it begins near .

The forward voltage-current characteristic is a graph of forward diode current against forward diode voltage .

• Below the knee voltage: The current is extremely small because the applied voltage has not sufficiently reduced the junction barrier.
• At the knee voltage: The current begins to increase rapidly. The knee voltage is approximately for silicon and for germanium.
• Above the knee voltage: A small increase in voltage produces a large increase in current. The diode behaves like a low-resistance conducting device.
• At high current: The curve becomes more nearly linear because the bulk and contact resistances of the diode become significant.

A labeled sketch should place on the horizontal axis and on the vertical axis, showing very little current before the knee and a steep rise after it.

The cut-in voltage, also called the knee voltage or threshold voltage, is the approximate forward voltage at which the diode current begins to rise rapidly.

Typical values are:

• Silicon diode: approximately
• Germanium diode: approximately

Its physical significance is as follows:

• The applied voltage reduces the effective potential barrier of the junction.
• Below the knee voltage, only a very small forward current flows.
• Near and above the knee voltage, majority carriers cross the junction in large numbers.
• The knee voltage is not an exact switching voltage because diode current changes exponentially rather than abruptly.
• Its value varies with diode material, current level, temperature, and device construction.

1. Ideal diode model

• A forward-biased diode is treated as a perfect short circuit.
• Its voltage drop is .
• It is useful for quick and simple circuit analysis.

2. Constant-voltage model

• The diode is assumed to have a fixed voltage drop while conducting.
• Typical values are for silicon and for germanium.
• It provides better practical accuracy than the ideal model.

3. Exponential model

• The current is calculated using the Shockley diode equation:

• This model represents the nonlinear characteristic more accurately.
• It requires the saturation current , ideality factor , and thermal voltage .

Thus, model selection depends on the required accuracy and complexity of analysis.

The Shockley diode equation is

where:

• is the diode current.
• is the voltage across the diode.
• is the reverse saturation or scale current.
• is the ideality factor, commonly between and .
• is the thermal voltage, given by

• is Boltzmann's constant.
• is absolute temperature in kelvin.
• is the electronic charge.

At room temperature, . Under appreciable forward bias, , so the equation may be approximated as

This equation shows that the forward current increases exponentially with forward voltage. Therefore, a small change in voltage can produce a very large change in current.

DC or static resistance is the ratio of the total voltage across the diode to the total current through it at an operating point:

It is represented graphically by the slope of a line drawn from the origin to the operating point on the characteristic.

AC or dynamic resistance describes the response to a small change around the operating point:

For the exponential diode model, it is approximately

Key distinction:

• Static resistance uses total voltage and current.
• Dynamic resistance uses small changes in voltage and current.
• Dynamic resistance is the reciprocal of the local slope of the forward characteristic.
• The two values are generally different because the diode characteristic is nonlinear.

Using the Shockley equation under forward bias,

For :

Therefore,

For :

Therefore,

The voltage increased by only , but the current increased by a factor of approximately

This demonstrates the strong exponential relationship between forward voltage and diode current.

Temperature significantly affects the forward characteristic of a PN junction diode.

• As temperature rises, the reverse saturation current increases strongly.
• At a fixed forward voltage, the forward current therefore increases.
• At a fixed forward current, the required forward voltage decreases.
• For a silicon diode, the forward voltage has a typical temperature coefficient of approximately

near normal operating current.

Graphically, the forward characteristic shifts to the left as temperature increases. This means the same current can be obtained at a lower forward voltage.

Temperature effects are important because excessive current can raise junction temperature, which may further increase current. Without current limiting or proper thermal design, this positive feedback may cause thermal runaway and damage the diode.

The practical forward characteristic can be divided into three main regions:

1. Low-voltage region

• The applied voltage is below the knee voltage.
• The junction barrier is only partly reduced.
• A very small forward current flows.
• The diode offers relatively high resistance.

2. Exponential conduction region

• The voltage is around or above the knee voltage.
• The current increases approximately according to

• A small increase in voltage produces a large increase in current.

3. High-current region

• Internal bulk resistance, lead resistance, and contact resistance become significant.
• The curve becomes less exponential and more linear.
• Power dissipation and junction heating become important.

A current-limiting component is required to prevent the diode from entering a destructive high-current condition.

Apparatus required:

• PN junction diode
• Variable DC power supply
• Series current-limiting resistor
• Ammeter or milliammeter
• Voltmeter
• Breadboard and connecting wires

Circuit connection:

• Connect the diode in forward bias.
• Connect the P-side to the positive supply through a series resistor.
• Connect the N-side to the negative supply.
• Place the ammeter in series and the voltmeter across the diode.

Procedure:

1. Set the supply voltage to zero before switching on.
2. Increase the supply voltage in small steps.
3. Record the diode voltage and current at each step.
4. Use smaller voltage increments near the knee because current changes rapidly there.
5. Do not exceed the rated current or power of the diode.
6. Plot on the vertical axis against on the horizontal axis.

Result: The graph shows a small current below the knee voltage followed by a rapid rise in current above it.

Estimating the knee voltage:

• Observe the point where the forward-current curve changes from a nearly flat region to a rapidly rising region.
• Extend the steep portion of the curve backward toward the voltage axis if necessary.
• The approximate voltage at this transition is taken as the knee voltage.

Estimating dynamic resistance:

• Select an operating point on the forward curve.
• Choose two nearby points around it: and .
• Calculate the small voltage and current changes:

• The dynamic resistance is

The points must be close together because dynamic resistance represents the local slope. Since the curve becomes steeper as current increases, the dynamic resistance generally decreases with increasing current.

Silicon diode:

• Typical knee voltage is approximately .
• Reverse saturation current is relatively low.
• It has better thermal stability.
• It can generally operate at higher temperatures.
• Silicon diodes are widely used in practical electronic circuits.

Germanium diode:

• Typical knee voltage is approximately .
• It begins conducting at a lower forward voltage.
• Reverse saturation current is higher.
• It is more sensitive to temperature changes.
• It may be useful in low-level signal detection because of its lower forward drop.

Both devices have nonlinear forward characteristics, but the germanium curve begins its rapid rise at a lower voltage. Silicon is normally preferred where low leakage and thermal stability are important.

A series resistor limits the forward current and protects the diode from excessive current and power dissipation.

For a supply , resistor , and forward-biased diode, Kirchhoff's voltage law gives

Rearranging,

This is the load-line equation.

The intercepts are:

• When ,

• When ,

A straight line joining these intercepts is drawn on the diode characteristic. The point at which the load line intersects the diode curve is the operating point or Q-point. Its coordinates give the actual diode voltage and diode current.

The resistor makes the current stable because an increase in diode current produces a larger resistor voltage drop, leaving less voltage across the diode.

The ideal Shockley equation assumes that the diode current is controlled mainly by junction carrier diffusion. At high forward current, additional practical effects become important:

• Bulk resistance: The P-type and N-type semiconductor regions have finite resistance.
• Contact resistance: Metal-semiconductor contacts produce voltage drops.
• Lead resistance: Device leads and connections add small series resistance.
• High-level injection: The injected carrier concentration becomes comparable with the normal doping concentration, changing the transport process.
• Self-heating: Large current increases the junction temperature and alters the diode parameters.

The practical diode may be modeled as an ideal junction in series with resistance :

At high current, the term becomes significant. Therefore, the characteristic becomes more linear, and a larger voltage increase is required for a given current increase.

The reverse saturation current, represented by , is a very small current produced mainly by thermally generated minority carriers in a PN junction.

It appears in the Shockley equation:

Under appreciable forward bias,

Therefore:

• A larger produces a larger forward current at the same forward voltage.
• Germanium diodes generally have a larger than silicon diodes.
• rises strongly with temperature.
• Device area and semiconductor material affect its value.
• Differences in cause apparently identical diodes to have slightly different forward voltage drops at the same current.

Although called reverse saturation current, acts as the scale factor for both forward and reverse diode behavior.

For appreciable forward bias, the Shockley equation is approximated as

Differentiate current with respect to voltage:

Since

we obtain

The dynamic resistance is the reciprocal of the small-signal conductance:

Therefore,

At room temperature, , so

This expression shows that dynamic resistance decreases as the DC forward current increases.

The power dissipated by a forward-biased diode is

where is the forward voltage and is the forward current.

For example, if a diode carries at ,

Precautions:

• Keep below the maximum rated forward current.
• Keep below the maximum power-dissipation rating.
• Use a correctly selected series current-limiting resistor.
• Avoid excessive junction temperature.
• Use suitable heat sinking for power diodes.
• Observe the manufacturer's derating specifications at high ambient temperatures.
• Ensure that measurement instruments are connected correctly.

Excessive power raises the junction temperature and may lead to thermal runaway, permanent parameter changes, or junction failure.

Common experimental errors include:

• Meter loading: The voltmeter has finite resistance and the ammeter has internal resistance, which can affect the circuit.
• Contact resistance: Loose wires, breadboard contacts, and leads introduce additional resistance.
• Temperature variation: Diode heating changes the forward voltage and current during measurement.
• Large voltage steps: The knee region may not be recorded accurately if the supply is varied in large steps.
• Supply fluctuations: An unstable DC source causes inconsistent readings.
• Incorrect polarity: Reverse connection prevents the intended forward characteristic from being measured.
• Instrument resolution: Low-resolution meters may not detect small currents below the knee.
• Reading errors: Parallax errors may occur with analog instruments.

To improve accuracy, use calibrated digital meters, stable connections, small voltage increments, a current-limiting resistor, and sufficient time for temperature stabilization.

Forward bias:

• The P-side is connected to the positive terminal and the N-side to the negative terminal.
• The depletion layer becomes narrower.
• The barrier potential is reduced.
• A substantial current flows after the knee voltage is reached.
• The diode has relatively low resistance in its conducting region.
• Current is mainly due to majority carriers.

Reverse bias:

• The P-side is connected to the negative terminal and the N-side to the positive terminal.
• The depletion layer becomes wider.
• The barrier potential increases.
• Only a small reverse saturation current flows before breakdown.
• The diode has very high resistance before breakdown.
• Current is mainly due to minority carriers.

Thus, the diode conducts strongly in forward bias but blocks current in reverse bias under normal operating conditions.

For a silicon diode, take the forward voltage as

The resistor voltage is

The series current is

Therefore,

The diode power is

The resistor power is

Hence:

• Diode current:
• Resistor voltage:
• Diode power:
• Resistor power: