Question

A constant electric field is maintained inside a semiconductor. As the temperature is lowered, the magnitude of the current density inside the semiconductor a) increases. c) decreases. b) stays the same. d) may increase or decrease.

Short answer

Answer: decreases

Step-by-step solution

Understanding the Terms

Semiconductors are special materials that have electrical properties lying between conductors and insulators. The current density (J) inside a semiconductor is the amount of electric current flowing through a unit cross-sectional area perpendicular to the direction of the electric field. With a constant electric field inside the semiconductor, the current density depends on various factors such as charge carrier concentration, the charge of the carriers, and their mobility.

Electric Field and Temperature in Semiconductors

In a semiconductor, the current density is directly related to the charge carrier concentration, which further depends on the temperature of the material. As the temperature increases, the number of charge carriers available (both electrons and holes) also increases, leading to a higher current density within the semiconductor.

Evaluating the Options

Now let's evaluate the given options: a) As the temperature is lowered, the charge carrier concentration decreases, which would ultimately lead to a decrease in the current density. So, this option is incorrect. b) Since the current density depends on the temperature, it cannot stay the same when the temperature is lowered. So, this option is also incorrect. c) Decreasing the temperature leads to a decrease in the charge carrier concentration, which in turn decreases the current density. This option is correct. d) As we have determined, lowering the temperature always results in a decrease in the current density, so this option is incorrect.

Conclusion

Therefore, when the temperature of a semiconductor is lowered while maintaining a constant electric field inside it, the magnitude of the current density inside the semiconductor decreases. So, the correct answer is option c) decreases.

Key concepts

Semiconductor Current Density

When discussing the electrical properties of semiconductors, an essential parameter to consider is semiconductor current density. Current density, denoted often as J, refers to the amount of electric current flowing through a specific cross-sectional area in a semiconductor. It's formulated as J = nqv, where n is the charge carrier concentration, q is the charge of the carriers, and v is the drift velocity of the carriers.

An increase in any of these variables will result in a higher current density. For instance, if we introduce more charge carriers into the semiconductor material, which could be done through doping, the current density will likely increase. Similarly, if we could somehow increase the charge on the carriers or their drift velocity possibly by increasing the electric field, we would again observe an increase in current density. However, other factors such as scattering events due to impurities or lattice vibrations can negatively affect the drift velocity and consequently the current density.

Understanding how temperature, impurities, and intrinsic properties of the semiconductor material influence the current density is crucial in designing devices like transistors and diodes that heavily rely on controlled current flow.

Temperature Effect on Semiconductors

Temperature plays a crucial role in the behavior of semiconductors. As the temperature of a semiconductor material changes, so does its ability to conduct electricity. This is often counterintuitive as we're used to conductors where resistance increases with temperature.

At lower temperatures, semiconductors behave more like insulators; their charge carrier concentration, and consequently their current density, is relatively low. This occurs because fewer thermally generated charge carriers are available to participate in conduction. As temperature increases, more electron-hole pairs are thermally excited across the band gap, and thus the semiconductor becomes more conductive; this translates to an increased current density.

However, at extremely high temperatures, the material may start to exhibit intrinsic conduction, where virtually every atom contributes charge carriers, making it difficult to control or use this conductivity for practical purposes. This delicate balance is why temperature management is critical in semiconductor devices, such as ensuring proper heat dissipation in computer chips.

Charge Carrier Concentration

In the realm of semiconductors, charge carrier concentration is a term that refers to the density of freely moving charged particles within the material. These carriers, which include electrons and holes, are integral to the semiconductor's ability to conduct electricity.

The concentration of these charge carriers is not fixed; it can be affected by many factors, including temperature and the level of doping. Doping involves adding impurities to the semiconductor to either increase free electrons (n-type doping) or holes (p-type doping), thus modifying its electrical properties.

Exercise improvement advice suggests understanding the intricacies of how doping affects the concentration as it is key to tailoring the electrical properties of semiconductors for specific applications.Ultimately, the number of charge carriers available for conduction directly impacts the current density and overall electrical performance. Therefore, in semiconductor technology, meticulous control over the charge carrier concentration is vital to achieving the desired operation in semiconductor-based devices.