So-called n-type silicon has a resistivity given by = (q NDn)1 , where ND is the volume

Chapter 2, Problem 50

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So-called “n-type” silicon has a resistivity given by \(ρ = (−qN_D \mu_n)^{−1}\), where \(N_D\) is the volume density of phosphorus atoms \((atoms/cm^3)\), \(\mu_n\) is the electron mobility \((cm^2/V \cdot s)\), and \(q = −1.602 \times 10^{−19}\ C\) is the charge of each electron. Conveniently, a relationship exists between mobility and \(N_D\), as shown in Fig. 2.39. Assume an 8 inch diameter silicon wafer (disk) having a thickness of \(300\ \mu m\). Design a \(10\ \Omega\) resistor by specifying a phosphorus concentration in the range of \(2 \times 10^{15}\ cm^{−3}\ \leq\ N_D\ \leq\ 2 \times 10^{17}\ cm^{−3}\), along with a suitable geometry (the wafer may be cut, but not thinned).