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Silicon is doped with boron to a concentration of $4 \times 10^{17}$ atoms $/ \mathrm{cm}^{3}$. Assume the intrinsic carrier concentration of silicon to be $1.5 \times 10^{10} / \mathrm{cm}^{3}$ and the value of $\frac{k T}{q}$ to be $25 \; \mathrm{mV}$ at $300 \mathrm{~K}$. Compared to undoped silicon, the Fermi level of doped silicon

- goes down by $0.13 \; \mathrm{eV}$
- goes up by $0.13 \; \mathrm{eV}$
- goes down by $0.427 \; \mathrm{eV}$
- goes up by $0.427 \; \mathrm{eV}$