bphet-143-solved-assignment-2024-ss-8e24e610-06c9-4b43-84f6-a5bf6ef5ab5c

1. a) Write the three processes responsible for charge carrier transport in a semiconductor. Calculate the resistivity of an intrinsic semiconductor sample of area $4{\mathrm{c}\mathrm{m}}^2$$4{\mathrm{c}\mathrm{m}}^2$4cm^(2)4 \mathrm{~cm}^2$4{\mathrm{c}\mathrm{m}}^2$, thickness $0.5\mathrm{c}\mathrm{m}$$0.5\mathrm{c}\mathrm{m}$0.5cm0.5 \mathrm{~cm}$0.5\mathrm{c}\mathrm{m}$ and carrier concentration of $5\times {10}^{16}{\mathrm{m}}^{-3}$$5\times {10}^{16}{\mathrm{m}}^{-3}$5xx10^(16)m^(-3)5 \times 10^{16} \mathrm{~m}^{-3}$5\times {10}^{16}{\mathrm{m}}^{-3}$. It is given that the electron and hole motilities are $0.35{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$$0.35{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$0.35m^(2)V^(-1)s^(-1)0.35 \mathrm{~m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$0.35{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and $0.2{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$$0.2{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$0.2m^(2)V^(-1)s^(-1)0.2 \mathrm{~m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$0.2{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ respectively.

1. Drift: When an electric field is applied to a semiconductor, the charge carriers (electrons and holes) experience a force in the direction of the field. This causes the carriers to drift toward the opposite charges, resulting in a current. The drift velocity of the carriers is proportional to the applied electric field.
2. Diffusion: In the absence of an electric field, charge carriers move from regions of high concentration to regions of low concentration due to the concentration gradient. This movement is called diffusion and is driven by the random thermal motion of the carriers.
3. Thermionic Emission: At elevated temperatures, some electrons in the semiconductor gain enough energy to overcome the potential barrier at a junction (e.g., a metal-semiconductor junction or a p-n junction) and are emitted into the adjacent region. This process is known as thermionic emission.

• $q$$q$qq$q$ is the elementary charge ($1.6\times {10}^{-19}\text{C}$$1.6\times {10}^{-19}\text{C}$1.6 xx10^(-19)” C”1.6 \times 10^{-19} \text{ C}$1.6\times {10}^{-19}\text{C}$),
• $n$$n$nn$n$ and $p$$p$pp$p$ are the electron and hole concentrations, respectively (which are equal in an intrinsic semiconductor),
• ${\mu }_n$${\mu }_n$mu _(n)\mu_n${\mu }_n$ and ${\mu }_p$${\mu }_p$mu _(p)\mu_p${\mu }_p$ are the mobilities of electrons and holes, respectively.

• $n=p=5\times {10}^{16}{\text{m}}^{-3}$$n=p=5\times {10}^{16}{\text{m}}^{-3}$n=p=5xx10^(16)” m”^(-3)n = p = 5 \times 10^{16} \text{ m}^{-3}$n=p=5\times {10}^{16}{\text{m}}^{-3}$,
• ${\mu }_n=0.35{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$${\mu }_n=0.35{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$mu _(n)=0.35″ m”^(2)”V”^(-1)”s”^(-1)\mu_n = 0.35 \text{ m}^2\text{V}^{-1}\text{s}^{-1}${\mu }_n=0.35{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$,
• ${\mu }_p=0.2{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$${\mu }_p=0.2{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$mu _(p)=0.2″ m”^(2)”V”^(-1)”s”^(-1)\mu_p = 0.2 \text{ m}^2\text{V}^{-1}\text{s}^{-1}${\mu }_p=0.2{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$.

1. Conventional $p-n$$p-n$p-np-n$p-n$ Junction Diode:
   • A conventional diode is designed to allow current to flow in one direction (forward bias) and block it in the opposite direction (reverse bias).
   • When reverse-biased, a conventional diode experiences a small leakage current until the reverse voltage reaches a critical value called the breakdown voltage. Beyond this voltage, the diode undergoes avalanche breakdown, which can cause permanent damage if the current is not limited.
2. Zener Diode:
   • A Zener diode is specifically designed to operate in the reverse breakdown region without being damaged.
   • It has a precisely controlled breakdown voltage, known as the Zener voltage ($V_Z$$V_Z$V_(Z)V_Z$V_Z$), at which it starts conducting in the reverse direction.
   • Zener diodes are used for voltage regulation and as reference voltages in circuits.

1. Zener Breakdown: This occurs in diodes with a low breakdown voltage (typically less than 5V). At the Zener voltage, the strong electric field in the depletion region causes a significant increase in the tunneling of electrons through the energy barrier, leading to a sharp increase in reverse current. This process is not destructive, and the diode can return to its normal state once the voltage is reduced.
2. Avalanche Breakdown: This occurs in diodes with higher breakdown voltages (typically above 5V). When the reverse bias voltage increases, it accelerates the minority carriers to high velocities. These carriers then collide with the lattice atoms, creating additional electron-hole pairs, leading to a chain reaction and a sudden increase in reverse current. Like Zener breakdown, avalanche breakdown is not destructive, and the diode can return to normal operation when the voltage is lowered.

2. a) Draw the structure of an n-channel JFET and explain the process of pinch-off when appropriate voltage bias is applied. Why is the depletion layer wider near the drain terminal?

1. Initial State: When no voltage is applied between the gate and source (V_GS = 0), the n-channel is wide open, and electrons can flow freely from the source to the drain.
2. Applying V_GS: As a negative voltage is applied between the gate and source (V_GS < 0), a depletion region forms around the p-n junctions, narrowing the n-channel. This reduces the current flow from source to drain.
3. Pinch-Off: As V_GS is made more negative, the depletion region extends further into the n-channel, eventually "pinching off" the channel near the drain. At this point, the JFET enters the saturation region, where the current becomes constant and independent of the drain-source voltage (V_DS). The pinch-off voltage (V_P) is the gate-source voltage at which the channel is completely pinched off.