半导体物理学 - 4

SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing第四章平衡和偏置状态下的PN结特性PNJunctionatEquilibriumandUnderBiasingSemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingPN结是半导体样品中P型区域和N型区域间的界面。PN结相关的现象乃是包括所有集成电路在内的半导体器件的基础。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingPN结基本的概念BasicPNJunctionConcepts由于杂质分布不同，存在着各种各样的PN结，但只要掌握基本的物理和数学概念，不同PN结的分析处理并不困难。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing这一章我们将通过最简单的PN结，引出一些与平衡和偏置状态相关的重要结论。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing对称突变结示意电中性N区ND=1016/cm3电中性P区NA=1016/cm3X0冶金结位置SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing我们曾描绘过P型和N型半导体样品的能带，那么掺杂浓度相当的P型半导体和N型半导体构成对称突变结时，样品的能带将会如何呢？SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing仍以费米能级作基准，因为费米能级无论对P型半导体，还是N型半导体应该是统一的，所以，PN结的能带图可按下图所示次序来绘制。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingPN的能带图BandDiagramofJunctionP型和N半导体单独样品的能带图导带价带-ψC(x)φ=0-ψi(x)-ψV(x)导带价带-ψC(x)φ=0-ψi(x)-ψV(x)SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing构成PN结的能带图电中性N区电中性P区x0ψφ=0ψC(x)ψV(x)Ψi(x)△ψ空间电荷区SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing导带价带-ψC(x)φ=0-ψi(x)-ψV(x)导带价带-ψC(x)φ=0-ψi(x)-ψV(x)电中性N区电中性P区x0ψφ=0ψC(x)ΨV(x)Ψi(x)△ψ空间电荷区SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing耗尽近似TheDepletionApproximation由于PN结空间电荷区内静电势、电场、电荷和载流子密度相关的微分方程都是非线性方程，分析PN结问题并不容易。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing耗尽近似却给我们提供了处理和分析PN结问题的可能性。对称突变结采用耗尽近似绘于下图：SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingn(x)，p(x)n(x)p(x)x0两侧分别为电子和空穴的密度分布，带正、负符号的圆圈分别代表施主和受主离子。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingxρ(x)0空间电荷的实际分布SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingqND-qNA-x0/2+x0/2xρ(x)0采用耗尽近似后的空间电荷分布SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingn(x)，p(x)n(x)p(x)ρ(x)ρ(x)qND-qNA-x0/2+x0/2x0x0x0SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing我们看到：–X0/2和+X0/2处存在电荷密度分布突变的边界，对称突变结空间电荷区的总厚度为X0SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing空间电荷区内载流子完全耗尽，故无载流子分布，为此，空间电荷区也称耗尽区；电中性区内电荷保持平衡，亦无电荷分布。这就是所谓的耗尽近似SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing图中各区的电荷密度为：x–X0/2，ρ(x)=0：电中性N型区–X0/2≤x≤0，ρ(x)=qND；正空间电荷区0≤x≤+X0/2，ρ(x)=–qNA：负空间电荷区x+X0/2，ρ(x)=0：电中性P型区SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing分别求解泊松方程：在电中性N型区SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing在正空间电荷区SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing由于SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing故SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing据对称性，x=0处，ψ（0）=0,则因此SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing在负空间电荷区SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing考虑到对称突变结ND=NA，我们同样可以得到恰与正空间电荷区反向对称的负空间电荷区中的电势函数。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingEmqND-qNAρ(x)x0E(x)-x0/2+x0/2x0SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingΔψ0Em-x0/2+x0/2ψn=-qNDX02/8ε0E(x)xxΨ0SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing+x0/2-x0/2xΨ0Ψ0xSemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing-qNAxρ(x)qND0EmxE(x)0-x0/2+x0/2x0ψn=-qNDX02/8εΔψ0Ψ+x0/2x0-x0/2ΨSemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing接触势ContactPotential结两侧存在的电势差Δψ0称为接触势。任何材料相互接触，并发生电荷交换时都会形成接触势。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing接触势有时也称自建电势（Built-inPotential）扩散电势（DiffusionPotential）SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing对称突变结接触势的数值为2ψN式中N=ND=NASemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing空间电荷区的宽度为实际上，根据布尔兹曼关系，就能导出接触势的独立表示式。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing可得由SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingn0P=ni2/p0p，求上式的逆函数考虑到对称突变结，N=n0N=n0P，则SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingPN结的偏置TheBiasingofaJunction至此，我们讨论的仅是处于平衡状态，不加任何偏置，也称零偏置PN结的性状。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing外电压正极接PN结P侧，负极接PN结N侧，称为给PN结加正向偏置或正偏。外电压负极接PN结P侧，正极接PN结N侧，称为给PN结加反向偏置或反偏。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingPN结施加正偏时，接触电势减小，耗尽区减薄；施加反偏时，接触电势增大耗尽区加厚。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing正、反偏结两侧的电势差和耗尽层宽度示意PΔψ0ΔψRUFURNUNPΔψFxx0Fx0Rx0x0SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing耗尽区厚度与电压的关系DepletionLayerThicknessVersusVoltage图示为反向偏压增加，空间电荷区厚度由x0扩展到x时，电荷密度及对应的电场分布。SemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasingρEmNPEm0-X0/2X0/2E0xx0xx0-x/2x/2qND-qNASemiconductorPhysicsChapter4PNJunctionatEquilibriumandUnderBiasing假定外电压完全施于PN结区，N型和P型电中性区不承受任何电压，并把UNP标为结两端施加的结电压。不难求出UNP为Semiconduct