Chapter 10, High-Frequency, High-Power and Nanoelectronic Devices Video Solutions, Solid State Electronic Devices

Problem 1

Sketch the band diagram for an abrupt junction in which the doping on the p side is degenerate and the Fermi level on the $\mathrm{n}$ side is aligned with the bottom of the conduction band. Draw the forward- and reverse-bias band diagrams and sketch the $I-V$ characteristic. This diode is often called a backward diode. Can you explain why?

Chai Santi

Numerade Educator

00:59

Problem 2

What determines the peak tunneling voltage $V_{p}$ of a tunnel diode? Explain. If a large density of trapping centers is present in a tunnel diode (Fig. $\mathrm{P} 10-2$ ), tunneling can occur from the $\mathrm{n}$ -side conduction band to the trapping level (A-B). Then the electrons may drop to the valence band on the $\mathrm{p}$ side $(\mathrm{B}-\mathrm{C})$, thereby completing a two-step process of charge transport across the junction. In fact, if the density of trapping centers is large, it is possible to observe an increase in current as the states below $E_{F n}$ pass by the trapping level with increased bias. In Fig. P10-2, the trapping level $E_{t}$ is located $0.3 \mathrm{eV}$ above the valence band. Assume that $E_{g}=1 \mathrm{eV}, E_{F_{n}}-E_{c}$ on the $\mathrm{n}$ side equals $E_{v}-E_{F_{p}}$ on the p side, and both $E_{F n}-E_{c}$ and $E_{v}-E_{F p}$ equal $0.1 \mathrm{eV}$.

Chai Santi

Numerade Educator

04:42

Problem 3

(a) Write down the complete continuity equation and solve it. Find the excess minority hole concentration as a function of time $(t)$ for $t \geq 0 .$ Assume that there is no applied field but recombination is present. Consider an n-type Si sample with donor concentration as $10^{16} / \mathrm{cm}^{3}$ at $T=300 \mathrm{~K}$. Due to uniform illumination of light at $t=0$, EHPs are generated at a rate of $10^{29} / \mathrm{cm}^{3} .$ If minority carrier lifetime is $10 \mathrm{nsec}$, find the excess hole concentration at $t=5 \mathrm{msec}$.
(b) When the steady state excess hole concentration is $2 \times 10^{14} / \mathrm{cm}^{3}$ as $t \longrightarrow \infty$, estimate the minority carrier lifetime
(c) Determine the time at which the excess minority carrier concentration becomes one third of the steady state value obtained in part (b).

Chai Santi

Numerade Educator

04:42

Problem 4

Chai Santi

Numerade Educator

02:56

Problem 5

We wish to estimate the d-c power dissipated in a GaAs Gunn diode. Assume that the diode is $5 \mu \mathrm{m}$ long and operates in the stable domain mode.(a) What is the minimum electron concentration $n_{0} ?$ What is the time between current pulses?
(b) Using data from Fig. $10-9 \mathrm{a}$, calculate the power dissipated in the sample per unit volume when it is biased just below threshold if $n_{0}$ is chosen from the calculation of part (a). In general, does operation at a higher frequency result in greater power dissipation?

Chai Santi

Numerade Educator

01:32

Problem 6

(a) Calculate the ratio $N_{L} / N_{\mathrm{T}}$ of the effective density of states in the upper
(L) valleys to the effective density of states in the lower ( $\Gamma$ ) valley of the GaAs conduction band (Fig. $10-6$ ).
(b) Assuming a Boltzmann distribution $n_{L} / n_{\Gamma}=\left(N_{L} / N_{\Gamma}\right) \exp (-\Delta E / k T)$, calculate the ratio of the concentration of conduction-band electrons in the upper valley to the concentration in the central valley in equilibrium at $300 \mathrm{~K}$.
(c) As a rough calculation, assume that an electron at the bottom of the central valley has kinetic energy $k T$. After it is promoted to the satellite $(L)$ valley, what is its approximate equivalent temperature?

Chai Santi

Numerade Educator

00:39

Problem 7

Explain why two separate transistors cannot be connected as in Fig. $10-11$ to achieve the $\mathrm{p}-\mathrm{n}-\mathrm{p}-\mathrm{n}$ switching action of Fig. $10-10 .$

Manish Kumar

Numerade Educator

03:14

Problem 8

In the $\mathrm{p}-\mathrm{n}-\mathrm{p}-\mathrm{n}$ diode (Fig. $10-12 \mathrm{a})$, the junction $j_{3}$ is forward biased during the forward-blocking state. Why, then, does the forward bias provided by the gateto-cathode voltage in Fig. $10-13$ cause switching?

Chai Santi

Numerade Educator

00:59

Problem 9

(a) Sketch the energy-band diagrams for the $\mathrm{p}-\mathrm{n}-\mathrm{p}-\mathrm{n}$ diode in equilibrium, in the forward-blocking state, and in the forward-conducting state.
(b) Sketch the excess minority carrier distributions in regions $n_{1}$ and $p_{2}$ when the $\mathrm{p}-\mathrm{n}-\mathrm{p}-\mathrm{n}$ diode is in the forward-conducting state.

Chai Santi

Numerade Educator

03:14

Problem 10

Use schematic techniques such as those illustrated in Fig. $7-3$ to describe the hole flow and electron flow in a p-n-p-n diode for the forward-blocking state and for the forward-conducting state. Explain the diagrams and be careful to define any new symbols (e.g., those representing EHP generation and recombination).

Chai Santi

Numerade Educator

01:35

Problem 11

In a coupled transistor model in presence of avalanche multiplication, the multiplication factor for the electrons is two times larger than that for the holes. The emitter to collector current transfer ratio and the collector saturation current for the $\mathrm{n}$ -p-n transistor is four times than that for the $\mathrm{p}-\mathrm{n}$ -p transistor. Find the expression for the total current flowing through the device.

Varsha Aggarwal

Numerade Educator