When a $p$-$n$ junction diode is forward biased, the flow of current across the junction is mainly

Figure shows two $p$-$n$ junction diodes along with a resistance $R$ and a DC battery $E$. The path of flow of appreciable current in the circuit is

A semiconductor $X$ is made by doping a germanium crystal with arsenic $\left(Z=33\right)$. A second semiconductor $Y$ is made by doping germanium with indium $\left(Z=49\right)$. The two are joined end to end and connected to a battery as shown in the figure. Which of the following statements is correct?

The diode in the circuit as shown in the figure has constant voltage drop of  $0.5 \mathrm{V}$ at all currents and maximum power rating of $100 \mathrm{mW}$ (milliwatt). What should be the value of resistance $R$, connected in series with the diode for obtaining maximum current?