MICROELECTRONICS and NANOTECHNOLOGY (MN)

Question 2: Junction Devices

August 2009

## Questions

All questions are in this link

# Solutions of all questions

1) a) Zinc blend crystal. 8 atoms/unit cell. b) $1.12 eV$

c) $\sim10^4 V/cm (??)$

d) Chemistry exam question. (some other language) ??

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2) a) $n = N_Ce^{(E_F-E_C)/kT} p = N_Ve^{(E_V-E_F)/kT}$

b) If $E_F = E_i$ then $n = n_i, p = n_i$ \begin{align*} n_i &= N_Ce^{(E_i-E_C)/kT} =n\\ n_i &= N_Ve^{(E_V-E_i)/kT} =p\\ \therefore n_p&=n_i^2=N_CN_Ve^{-E_g/kT} \end{align*}

c)

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3) a)

\begin{align*} p &=\frac{1}{q\mu_nN_D}\\ \implies\mu_n&=\frac{1}{qp\cdot N_D}\sim 1.5\times10^3cm^2/V\cdot s \text{ (chk)} \end{align*}


b)

$\mu_p=\frac{1}{qp\cdot N_A}\sim 0.5\times10^3cm^2/V\cdot s \text{ (chk)}$
$\mu_p<\mu_n$ as  $p_p>p_n$


because $m_p^*>m_n^*$

c) Ionized impurity

$\tau_n\sim\frac{T^{3/2}}{N_D}$


Photon scattering

$\tau_n\sim T^{-3/2}$
$\mu_n = \frac{q\tau_n}{m^*}\sim\tau_n$


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4) a) ??



b) Depletion mode device is ON without applied $V_{GS}$. So, $V_{GS}$ is lower for Dep. mode device. Hence low current.

c) $I_D = \frac{1}{2}\mu_nC_{ox}\frac{W}{L}(V_{GS}-V_{th})^2$ $g_m = \frac{\partial I_D}{\partial V_{GS}} = \mu_nC_{ox}\frac{W}{L}(V_{GS}-V_{th})$ If W=L then; $\mu_n=\frac{g_m}{C_{ox}(V_{GS}-V_{th})}$

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