課程名稱︰ 數位電子學 課程性質︰ 必修 課程教師︰ 歐陽彥正 開課學院： 電資學院 開課系所︰ 資工系 考試日期（年月日）︰ 2008.04.10 考試時限（分鐘）：150 分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(15%)Given a silicon material doped with ND = 10^15 cm^(-3), the resistivity of the semiconductor is given by σ=q(n*μn + p*μp)^(-1) When the temperature of the semiconductor is raised, will its resistivity increase or decrease based on the relation between the intrinsic carrier density of a semiconductor and the temperature shown in Fig.1(Note that the x-axis corresponds to reciprocal temperature) ? Please give your qualitative explantion. 2.(15%)Following problem(1), if the increase of temperature is from 250K to 300K, will the change of resistivity negligible, i.e. less than 1% ? 3.(20%)A silicon material is doped with ND' = 10^19 cm^(-3) and ND'' = 10^14 cm^(-3) in different regions Fig2. Given that the diffusion and drift current densities of electrons are equal to, jp(diff) = (+q)*Dp*(-dp/dx) = -q*Dp*dp/dx A/cm^2 jn(diff) = (-q)*Dn*(-dn/dx) = +q*Dn*dn/dx A/cm^2 jn(drift) = Qn*Vn = (-qn)(-μn*E) = qnμnE A/cm^2 jp(drift) = Qp*Vp = (qn)(μn*E) = qpμpE A/cm^2 what is the voltage change across the semiconductor material ? Please specify which side of the material, right or left, has a higher voltage. 4.(20%)Following problem(3), let the concentration of electrons at -x0 is 10^17 cm^(-3) and E(x) denote the magnitude of the electircal field at x. Given that the magnitude of electrical field at x is equal to the amount of charge in the region marked by the dot line divided by the permittivity of silicon, which is denoted by ε, can you figure out a closed form of E(x) within -x0 and 0 in terms of x0 and ε ? 5.(20%)Following problem(3), can you figure out which of the following 3 figures is the most accurate model of E(x) for x > 0 ? Please explain your reasons. 6.(20%)Following problem(3), let xd denote the width of the depletion region in x < 0. Can you write an equation about the concentration of electrons in x > 0 ? The equation may contain integration and differentiation terms and you do not need to obtain a closed form. --

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