6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-1 Lecture 6 - PN Junction and MOS Electrostatics (III) Electrostatics of pn Junction under Bias September 27, 2005 Contents: 1. electrostatics of pn junction under bias 2. depletion capacitance Reading assignment: Howe and Sodini, Ch. 3, §§3.5-3.66.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-2 Key questions • What happens to the electrostatics of a pn junction if a voltage is applied across its terminals? • Why does a pn junction behave in some way like a capacitor?6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-3 1. Electrostatics of pn junction under bias Bias convention for pn junction: p n +-V V>0 forward bias V<0 reverse bias6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-4 • Potential distribution across pn junction in thermal equilibrium: p -+ n p-QNR SCR n-QNR x φ φB 0 xno-xpoφmp φmn • Apply voltage to p-side with respect to n-side: V p -+ n +-p-QNR SCR n-QNR x φ φB 0 xno-xpo V Battery imposes a potential difference across diode6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-5 How does potential distribution inside junction change as a result of bias? V p -+ n +-p-QNR SCR n-QNR x φ V ? V=0V>0 Five regions where V can drop: • metal/p-QNR contact? • p-QNR? • SCR? • n-QNR? • metal/n-QNR contact? In which region does V drop most? Or, how is V distributed across diode?6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-6 Essentially, all applied voltage drops across SCR: V p -+ n +-p-QNR SCR n-QNR x φ V V=0 V>0 φB φB-V Potential difference across junction (potential ”barrier”): • in equilibrium: φB • in forward bias: φB − V< φB • in reverse bias: φB − V> φB (since V< 0) What happens to SCR electrostatics?6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-7 SCR electrostatics under bias: E(V) x x x ρ φ φB xn(V) qNd -xp(V) -qNa φB-V φB-V V=0 V>0 V<0 E forward bias: built-in potential ↓⇒|E|↓⇒xd ↓ reverse bias: built-in potential ↑⇒|E|↑⇒xd ↑� � � � � � � � � � � � � � � � � � � � � � � � � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-8 Fundamentally, • electrostatics of SCR under bias unchanged from ther-mal equilibrium • SCR dipole of charge modulated to accommodate mod-ified potential build up across junction Useful consequence: • Analytical formulation of electrostatics of SCR iden-tical to that of thermal equilibrium if: φB −→ φB − V Then, within depletion approximation: 2s(φB − V )Na 2s(φB − V )Nd xn(V )= xp(V )= q(Na + Nd)Nd � q(Na + Nd)Na 2s(φB − V )(Na + Nd) xd(V )= qNaNd 2q(φB − V )NaNd| E| (V )= s(Na + Nd)� � � � � � � � � � � � � � � � � � � � � � � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-9 Can all be rewritten as: � � � V xn(V )= xno 1 − φB V xp(V )= xpo 1 − φB V xd(V )= xdo 1 − φB V |E|(V )= |Eo| 1 − φB In strongly asymmetric junction, all changes take place in lowly doped side: E(V) xxx ρφ xn(V) qNd φB -qNa φB-V φB-V V=0 V>0 V<0 El6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-10 2. Depletion capacitance Apply smal signal on top of bias:small signalV ∆V x ρ xn(V) qNd x ∆ρ +Qj -Qj -∆Qj −∆Qj +∆Qj ∆Qj -qNa -xp(V) xn(V) -xp(V) ----------------------------++++++++++++++++++++++++p n ++++++++++++--------+-V V+∆V Change in ∆V across diode: ⇒ change of ∆Qj at −xp ⇒ change of −∆Qj at xn6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-11 Looks like parallel-plate capacitor: V ∆V x ρ +Q -Q -∆Q +∆Q εs tins +-x ∆ρ -∆Q +∆Q Capacitance per unit area: sC = tins� � � � � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-12 In analogy, in pn junction: V ∆V --------------++ + + + + + + + + + + p n + + + + + + ----+-x ρ xn(V) qNd x ∆ρ V V+∆V +Qj -Qj -∆Qj −∆Qj +∆Qj ∆Qj -qNa -xp(V) xn(V) -xp(V) Depletion capacitance per unit area (depletion approx.): � qsNaNd CjoCj (V )= sxd(V )= = 2(φB − V )(Na + Nd)1 − V φB� � � � � � � � � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-13 s � qsNaNd CjoCj (V )= = � = � xd(V ) 2(φB − V )(Na + Nd)1 − V φB Key dependencies of Cj : • Cj depends on bias (because xd depends on bias) Cj Cjo 0 φBV • Cj depends on doping: Na,Nd ↑⇒Cj ↑ • In strongly asymmetric junction (i.e. p+-n junction): � qsNdCj (V ) 2(φB − V ) capacitance dominated by lowly-doped side. 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-14 Relevance of capacitance-voltage characteristics of diode: 1. pn diode= variable capacitor (varactor): ⇒ useful for voltage-controlled oscillators (VCO) 2. Cj : important consideration in dynamics of pn diode 3. powerful characterization technique: i.e. 1/Cj 2 vs. V yields φB and Nd in strongly asym-metric p+-n junction: 1 2(φB − V ) Cj 2 qsNd 1 Cj2 V -2 εsqNd φB06.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-15 Experimental data [from Fortini et al., IEEE Trans. Electron Dev. ED-29, 1604 (1982)]: Appears in Fortini, A., A. Hairie, and M. Gomina. "Analysis and capacitive measurementof the built-in-field parameter in highly doped emitters." IEEE Trans on Electron Devices 29,no. 10 (1982): 1604 (© 1982 IEEE). Used with permission.� � � � � � � � � � � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-16 Alternative view of capacitance: depletion charge V ∆V --------------++ + + + + + + + + + + p n + + + + + + ----+-x ρ xn(V) qNd x ∆ρ V V+∆V +Qj -Qj -∆Qj −∆Qj +∆Qj ∆Qj -qNa -xp(V) xn(V) -xp(V) Within depletion approximation: 2qsNaNd(φB − V ) V Qj(V )= Na + Nd � = Qjo 1 − φB� � � � � � � � � � � � 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-17 2qsNaNd(φB − V ) V Qj(V )= � = Qjo 1 − Na + Nd � φB Qj Qjo V0 φB Cj Cj is slope of Qj vs. V characteristics: Cj = dQj dV but not: Cj = Qj V6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 6-18 Application of voltage to pn junction also
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