In a semiconductor characteristics experiment, the relationship between the voltage applied to a semiconductor device and the current flowing through it is measured to confirm nonlinear electrical characteristics that differ from those of metallic resistors.
A typical experiment measures the current-voltage characteristics of silicon or germanium diodes. A diode is a semiconductor device that allows current to flow easily in one direction while strongly restricting it in the opposite direction.
Under forward bias, the current increases rapidly above a certain voltage. Under reverse bias, only a very small leakage current flows. This difference can be explained by the depletion region and built-in potential formed at the pn junction.
This article assumes an experiment measuring the forward- and reverse-bias current-voltage characteristics, temperature dependence, and rectifying behavior of a pn-junction diode, and presents the introduction, precautions, result items, sample experimental values, calculations, sources of error, example results, and discussion examples in that order.
Note:
This article is a study reference for discussing results obtained in physics experiments at schools, universities, and similar institutions. The experimental conditions and measured values shown here are examples for explanation and are not actual measurement results.
Excessive forward current through a diode can cause heating or damage. Always connect a current-limiting resistor and do not exceed the maximum ratings of the device. For reverse voltage as well, make measurements below the breakdown voltage. Turn off the power before changing wiring, and follow the laboratory manual and the instructions of your instructor or teaching assistant for actual operation.
- What Is a Semiconductor?
- Forward Characteristics of a Diode
- Reverse Characteristics of a Diode
- Changes with Temperature
- Main Items to Record in the Results
- Sample Experimental Conditions
- Sample Experimental Values
- Calculation Methods
- Main Sources of Error
- Example of How to Write the Results
- Points to Connect the Results to the Discussion
- Discussion Example
- Summary
What Is a Semiconductor?
A semiconductor is a material with electrical conductivity intermediate between that of a conductor and an insulator. Silicon and germanium are representative examples.
By adding a small amount of impurity to a pure semiconductor, an n-type semiconductor, in which electrons are the main carriers, or a p-type semiconductor, in which holes are the main carriers, can be produced.
When p-type and n-type semiconductors are joined, a pn junction is formed. Near the junction, electrons and holes recombine, producing a depletion region containing few mobile carriers.
Forward Characteristics of a Diode
The connection in which the p-type side is connected to the positive terminal of the power supply and the n-type side to the negative terminal is called forward bias.
Applying a forward voltage narrows the depletion region and lowers the built-in potential barrier. As a result, once the voltage becomes sufficiently large, many carriers cross the junction and the current increases rapidly.
Ideally, the diode current is expressed by the following equation.
I = IS{exp(qV/nkT) − 1}
Here, IS is the reverse saturation current, q is the elementary charge, V is the diode voltage, n is the ideality factor, k is the Boltzmann constant, and T is the absolute temperature.
For a silicon diode, the current generally begins to increase rapidly around 0.6–0.7 V. This voltage is called the threshold voltage, turn-on voltage, forward voltage, or similar terms.
Reverse Characteristics of a Diode
The connection in which the p-type side is connected to the negative terminal and the n-type side to the positive terminal is called reverse bias.
Applying a reverse voltage widens the depletion region, making it difficult for majority carriers to cross the junction. Therefore, normally only a very small reverse leakage current flows.
If the reverse voltage is increased further, breakdown occurs at a certain voltage and the current rises rapidly. In basic experiments with ordinary rectifier diodes, measurements are generally not taken into the breakdown region in order to protect the device.
Changes with Temperature
The electrical characteristics of semiconductors are affected by temperature.
For a silicon diode, the forward voltage required to produce the same forward current tends to decrease as temperature rises. As a general guideline, the temperature coefficient of forward voltage is approximately −2 mV/℃.
Meanwhile, reverse leakage current increases as temperature rises.
Main Items to Record in the Results
- Type of semiconductor device used
- Diode model number
- Forward- or reverse-bias connection
- Power-supply voltage
- Series resistance
- Voltage across the diode
- Forward current
- Reverse current
- Current-voltage characteristic graph
- Threshold voltage
- Forward voltage at a specified current
- Static resistance
- Dynamic resistance
- Rectification ratio
- Measurement temperature
- Forward voltage at each temperature
- Temperature coefficient
- Instrument resolution
- Change in device temperature during measurement
Sample Experimental Conditions
| Item | Sample Condition |
|---|---|
| Device used | Silicon diode |
| Series resistance | 1.0 kΩ |
| DC power supply | 0–10 V |
| Maximum forward current | 10 mA or less |
| Maximum reverse voltage | 5 V or less |
| Voltmeter resolution | 0.001 V |
| Ammeter resolution | 0.01 mA |
| Measurement temperatures | 20, 30, 40, 50 ℃ |
| Room temperature | 23 ℃ |
Sample Experimental Values
Forward Characteristics of a Silicon Diode
| Diode Voltage VF (V) | Forward Current IF (mA) | Static Resistance V/I (Ω) |
|---|---|---|
| 0.40 | 0.01 | 40000 |
| 0.45 | 0.04 | 11250 |
| 0.50 | 0.15 | 3333 |
| 0.55 | 0.48 | 1146 |
| 0.60 | 1.35 | 444 |
| 0.65 | 3.20 | 203 |
| 0.70 | 6.80 | 103 |
| 0.73 | 9.60 | 76 |
Reverse Characteristics
| Reverse Voltage VR (V) | Reverse Current IR (μA) |
|---|---|
| 0.5 | 0.02 |
| 1.0 | 0.03 |
| 2.0 | 0.04 |
| 3.0 | 0.05 |
| 4.0 | 0.06 |
| 5.0 | 0.07 |
Temperature and Forward Voltage
The following are sample values when the forward current is held constant at 5.0 mA.
| Temperature (℃) | Forward Voltage VF (V) |
|---|---|
| 20 | 0.682 |
| 30 | 0.662 |
| 40 | 0.642 |
| 50 | 0.622 |
Example of Repeated Measurements
| Measurement | Forward Voltage at 5.0 mA (V) |
|---|---|
| 1 | 0.674 |
| 2 | 0.676 |
| 3 | 0.675 |
| 4 | 0.673 |
| 5 | 0.677 |
Calculation Methods
Calculating Current from the Series Resistor
If the supply voltage is 5.00 V, the diode voltage is 0.70 V, and the series resistance is 1.0 kΩ, the circuit current is calculated as follows.
I = (VS − VF)/R
= (5.00 − 0.70)/(1.0 × 103)
= 4.30 × 10−3 A
= 4.30 mA
Calculating Static Resistance
For a forward voltage of 0.65 V and a forward current of 3.20 mA, the calculation is as follows.
Rstatic = V/I
= 0.65/(3.20 × 10−3)
= 203 Ω
Calculating Dynamic Resistance
Using two points on the forward characteristic, 3.20 mA at 0.65 V and 6.80 mA at 0.70 V, the dynamic resistance is calculated as follows.
rd = ΔV/ΔI
= (0.70 − 0.65)/{(6.80 − 3.20) × 10−3}
= 13.9 Ω
Static resistance is the ratio V/I from the origin to the measurement point, whereas dynamic resistance is the local slope ΔV/ΔI near the measurement point, so the two are different.
Calculating the Rectification Ratio
The ratio of currents when voltages of the same magnitude are applied in the forward and reverse directions is taken as the rectification ratio.
If the forward current is 3.20 mA and the reverse current is 0.05 μA, the calculation is as follows.
Rectification ratio = IF/IR
= (3.20 × 10−3)/(0.05 × 10−6)
= 6.4 × 104
Calculating the Temperature Coefficient
If the forward voltage is 0.682 V at 20 ℃ and 0.622 V at 50 ℃, the calculation is as follows.
Temperature coefficient = ΔVF/ΔT
= (0.622 − 0.682)/(50 − 20)
= −0.00200 V/℃
= −2.00 mV/℃
Average Forward Voltage
Vavg = (0.674 + 0.676 + 0.675 + 0.673 + 0.677)/5
= 0.675 V
Calculating Relative Error
If the measured temperature coefficient is −2.00 mV/℃ and the reference value is −2.10 mV/℃, the relative error using absolute values is calculated as follows.
Relative error (%) = |experimental value − reference value|/|reference value| × 100
= |−2.00 − (−2.10)|/2.10 × 100
= 4.76%
Main Sources of Error
| Source of Error | Effect on Measurement | Likely Effect on Results | Improvement |
|---|---|---|---|
| Diode self-heating | Junction temperature rises | Forward voltage decreases with time | Use a small current and measure quickly |
| Change in room temperature | Semiconductor characteristics change | I-V characteristics shift during measurement | Record temperature and measure under constant conditions |
| Contact resistance | Voltage drops occur in wiring and terminals | Diode voltage is overestimated | Secure contacts and measure directly across the diode |
| Internal resistance of the ammeter | Circuit conditions change | Actual current deviates from the ideal value | Take internal resistance into account |
| Input resistance of the voltmeter | A small current flows through the voltmeter | Error becomes larger in the low-current region | Use a voltmeter with high input resistance |
| Instrument resolution | Small currents or voltages cannot be resolved | Low-current and reverse-bias regions become coarse | Select an appropriate measurement range |
| Zero-point offset | A constant bias is added to all measurements | The I-V curve shifts | Perform zero adjustment before measurement |
| Error in series resistance | Calculated current is incorrect | A systematic error occurs in all current values | Measure the actual resistance value |
| Power-supply voltage fluctuation | Operating point changes | Repeated measurements vary | Use a regulated power supply |
| Individual variation among diodes | Characteristics differ even for the same model | Threshold voltage differs from the reference value | Measure and compare multiple devices |
| Incorrect polarity connection | Forward and reverse directions are swapped | Almost no current flows | Check the anode and cathode |
| Too few measurement points | The turn-on region is not represented sufficiently | Threshold voltage and dynamic resistance become inaccurate | Measure the rapid-current-rise region at finer intervals |
| Voltage increments are too large | Changes in the I-V curve are difficult to capture | The turn-on point becomes ambiguous | Measure in increments of 0.01–0.05 V |
| Very small reverse current | Susceptible to noise and leakage current | Measurements become unstable | Use a microammeter and improve insulation |
| Nonuniform temperature | Measured temperature differs from junction temperature | Temperature coefficient deviates from the reference value | Measure after sufficient thermal equilibrium is reached |
Why Current Increases Rapidly under Forward Bias
When a forward voltage is applied, the depletion region of the pn junction narrows and the built-in potential barrier that carriers must overcome is reduced.
As a result, holes on the p-type side and electrons on the n-type side can cross the junction more easily, causing the forward current to increase exponentially.
Why Almost No Current Flows under Reverse Bias
When a reverse voltage is applied, the depletion region widens and majority carriers are driven away from the junction.
Therefore, almost no current due to majority carriers flows, and only a very small leakage current due to minority carriers remains.
Why a Diode Does Not Obey Ohm’s Law
In a metallic resistor, voltage and current are approximately proportional when temperature is constant.
In contrast, diode current changes exponentially with voltage, so the resistance V/I is not constant. Therefore, a diode is a non-ohmic device.
Why Forward Voltage Decreases as Temperature Rises
As temperature rises, the number of thermally excited carriers in the semiconductor increases, making it easier for carriers to cross the junction.
Therefore, the voltage required to produce the same forward current decreases.
Example of How to Write the Results
The forward- and reverse-bias current-voltage characteristics of a silicon diode were measured.
Under forward bias, the current was small below approximately 0.55 V, but began to increase rapidly around 0.60 V. The forward current at 0.70 V was 6.80 mA.
Under reverse bias, even when the voltage was increased to 5.0 V, the current remained at or below 0.07 μA, which was extremely small compared with the forward current.
At a forward current of 5.0 mA, the forward voltage was 0.682 V at 20 ℃ and 0.622 V at 50 ℃. The temperature coefficient was calculated to be −2.00 mV/℃.
Points to Connect the Results to the Discussion
- Was the forward current proportional to voltage, or did it increase rapidly?
- What was the approximate threshold voltage?
- Was the reverse current sufficiently smaller than the forward current?
- What was the rectification ratio?
- Were the static and dynamic resistances different?
- Could you confirm that the diode is a non-ohmic device?
- Did the forward voltage decrease as temperature increased?
- Was the temperature coefficient close to the reference value?
- Was there any self-heating during measurement?
- Were there enough measurement points in the rapid-current-rise region?
- Was the voltage measured directly across the diode?
- Was the reverse current sufficiently above the detection limit of the instrument?
Discussion Example
In this experiment, forward and reverse voltages were applied to a silicon diode and its current-voltage characteristics were measured.
Under forward bias, almost no current flowed at low voltages, but the current increased rapidly from approximately 0.60 V. It was 3.20 mA at 0.65 V and 6.80 mA at 0.70 V, showing that a small increase in voltage produced a large change in current.
This result is consistent with the fact that diode current is not proportional to voltage but ideally increases exponentially.
A depletion region with few carriers and a built-in potential are formed at a pn junction. Applying a forward voltage narrows the depletion region and lowers the built-in potential barrier, making it easier for electrons and holes to cross the junction.
Under reverse bias, on the other hand, the current remained at or below 0.07 μA even when 5.0 V was applied. This is because the reverse voltage widened the depletion region and inhibited the movement of majority carriers.
The forward current and reverse current differed by tens of thousands of times or more, confirming that the diode has a rectifying action that allows current to flow much more easily in one direction.
The static resistance at 0.65 V and 3.20 mA was 203 Ω. In contrast, the dynamic resistance calculated over the range from 0.65 to 0.70 V was 13.9 Ω, which was smaller than the static resistance.
This is because the I-V characteristic of a diode is not a straight line. Static resistance corresponds to the slope of the line connecting the origin and the measurement point, whereas dynamic resistance corresponds to the local slope of the tangent near the measurement point.
Therefore, a diode cannot be treated as a device with a constant resistance; it is a non-ohmic device whose electrical resistance changes with the operating point.
In the temperature measurement, when the forward current was fixed at 5.0 mA, the forward voltage was 0.682 V at 20 ℃ and 0.622 V at 50 ℃. The temperature coefficient was −2.00 mV/℃, showing a tendency for the forward voltage to decrease as temperature increased.
As temperature rises, the carrier concentration in the semiconductor increases and more carriers can cross the junction, so the voltage required to produce the same current is considered to decrease.
One source of error is self-heating of the diode. If forward current continues to flow, the junction temperature rises and the forward voltage decreases. Therefore, measuring from high to low voltage may produce different I-V characteristics from measuring from low to high voltage.
To reduce this effect, it is effective not to use unnecessarily large current, to make each measurement quickly, and to wait for the device temperature to stabilize at each measurement point.
The internal resistance of the voltmeter and ammeter, contact resistance in the wiring, and the difference between the nominal and actual values of the series resistor are also sources of error.
In particular, because the reverse current is extremely small, it is easily affected by instrument resolution, insulation resistance, wiring leakage current, and electrical noise. Accurate measurement of reverse characteristics requires equipment suitable for measuring very small currents.
The threshold voltage is not a strict boundary at which the current suddenly changes from zero to a finite value. Because diode current increases continuously and exponentially, the determined threshold voltage depends on the current chosen as the criterion or on the method of drawing a tangent to the I-V curve.
Therefore, the method used to determine the threshold voltage should be stated in the experimental results.
In conclusion, the silicon diode showed a rapid increase in current above a certain forward voltage and only a very small current under reverse bias. The forward voltage also decreased as temperature increased, demonstrating that semiconductor characteristics depend strongly on temperature.
Discussion Example When the Threshold Voltage Was Higher Than the Reference Value
Possible reasons why the threshold voltage was higher than the reference value include including voltage drops in wiring or contacts in the measured diode voltage, a low device temperature, defining the threshold using a relatively large current, and individual variation among diodes.
Discussion Example When the Threshold Voltage Was Lower Than the Reference Value
Possible reasons why the threshold voltage was lower than the reference value include an increase in junction temperature due to self-heating during measurement, a voltmeter zero-point offset, and determining the threshold using a small current value.
Discussion Example When the Reverse Current Was Large
Possible reasons why the reverse current was larger than expected include increased device temperature, leakage current through wiring or the surface of the circuit board, instrument zero-point offset, diode degradation, and an excessively high reverse voltage.
Discussion Example When the I-V Characteristics Showed Large Variation
Possible reasons for large variation in repeated I-V measurements include self-heating during measurement, fluctuations in power-supply voltage, changes in contact resistance, differences in device temperature caused by the measurement order, and measurement intervals that were too coarse in the rapid-current-rise region.
Summary
A semiconductor diode has the property that current increases rapidly above a certain voltage under forward bias, whereas only a very small leakage current flows under reverse bias.
Because current and voltage are not proportional, a diode is a non-ohmic device. Static resistance and dynamic resistance differ, and the electrical characteristics change with the operating point.
Semiconductor characteristics also depend on temperature, and the forward voltage of a silicon diode decreases as temperature rises.
In the discussion, it is important to relate rectification due to the pn junction and depletion region, self-heating, instrument internal resistance, contact resistance, temperature changes, and the definition of threshold voltage to the changes observed in the measured values.
