6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-1Lecture 16 - The pn Junction Diode (II)Equivalent Circuit ModelApril 8, 2003Contents:1. I-V characteristics (cont.)2. Small-signal equivalent circuit model3. Carrier charge storage: diffusion capacitanceReading assignment:Howe and Sodini, Ch. 6, §§6.4, 6.5, 6.9Announcements:Quiz 2: 4/16, 7:30-9:30 PM, Walker (lectures #10-17)open book, must bring calculator6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-2Key questions• How does a pn diode look like from a small-signalpoint of view?• What are the leading dependences of the small-signalelements?• In addition to the junction capacitance, are there anyother capacitive effects in a pn diode?6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-31. I-V characteristics (cont.)Diode current equation:I = Io(expqVkT− 1)Physics of forward bias:npFnFp• potential difference across SCR reduced by V ⇒ mi-nority carrier injection in QNR’s• minority carrier diffusion through QNR’s• minority carrier recombination at surface of QNR’s• large supply of carriers available for injection⇒ I ∝ eqV/kT6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-4npFnFpPhysics of reverse bias:• potential difference across SCR increased by V⇒ minority carrier extraction from QNR’s• minority carrier diffusion through QNR’s• minority carrier generation at surface of QNR’s• very small supply of carriers available for extraction⇒ I saturates to small value6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-5I-V characteristics: I = Io(expqVkT− 1)IVlog |I|V000IoIolinear scalesemilogarithmic scale0.43qkT=60 mV/dec @ 300K6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-6Source/drain-body pn diode of NMOSFET:6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-7Key dependences of diode current:I = qAn2i(1NaDnWp− xp+1NdDpWn− xn)(expqVkT− 1)• I ∝n2iN(expqVkT−1) ≡ excess minority carrier concen-tration at edges of SCR– in forward bias: I ∝n2iNexpqVkT: the more carrierare injected, the more current flows– in reverse bias: I ∝−n2iN: the minority carrierconcentration drops to negligible values and thecurrent saturates• I ∝ D: faster diffusion ⇒ more current• I ∝1WQNR: shorter region to diffuse through ⇒ morecurrent• I ∝ A: bigger diode ⇒ more current6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-82. Small-signal equivalent circuit modelExamine effect of small signal overlapping bias:I + i = Io[expq(V + v)kT− 1]If v small enough, linearize exponential characteristics:I +i = Io(expqVkTexpqvkT−1) ' Io[expqVkT(1+qvkT)−1]= Io(expqVkT− 1) + Io(expqVkT)qvkTThen:i =q(I + Io)kTvFrom small signal point of view, diode behaves as con-ductance of value:gd=q(I + Io)kT6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-9Small-signal equivalent circuit model, so far:gdgddepends on bias. In forward bias:gd'qIkTgdis linear in diode current.6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-10Must add capacitance associated with depletion region:CjgdDepletion or junction capacitance:Cj=Cjos1 −VφB6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-113. Carrier charge storage: diffusion capaci-tanceWhat happens to the majority carriers?Carrier picture so far:log p, npopnonNdni2Ndx0Nani2NaIf in QNR minority carrier concentration ↑ but majoritycarrier concentration unchanged⇒ quasi-neutrality is violated.6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-12Quasi-neutrality demands that at every point in QNR:excess minority carrier concentration= excess majority carrier concentrationpnxxn0p(xn)p(x)Wnni2NdNdn(xn)n(x)n-QNRqNnqPnMathematically:p0(x)=p(x) − po' n0(x)=n(x) − noDefine integrated carrier charge:qPn= qA12p0(xn)(wn− xn)== qAwn−xn2n2iNd(expqVkT− 1) = −qNn6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-13Now examine small increase in V :pnxxn0p(xn)p(x)Wnni2NdNdn(xn)n(x)n-QNR∆qNn=-∆qPn∆qPn+-Small increase in V ⇒ small increase in qPn⇒ smallincrease in |qNn|Behaves as capacitor of capacitance:Cdn=dqPndV6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-14Can write qPnin terms of Ip(portion of diode currentdue to holes in n-QNR):qPn=(Wn− xn)22DpqAn2iNdDpWn− xn(expqVkT− 1)=(Wn− xn)22DpIpDefine transit time of holes through n-QNR:τTp=(Wn− xn)22DpTransit time is average time for a hole to diffuse throughn-QNR [will discuss in more detail in BJT]Then:qPn= τTpIpandCdn'qkTτTpIp6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-15Similarly for p-QNR:Cdp'qkTτTnInwhere τTnis transit time of electrons through p-QNR:τTn=(Wp− xp)22DnBoth capacitors sit in parallel ⇒ total diffusion capaci-tance:Cd= Cdn+ Cdp=qkT(τTnIn+ τTpIp)=qkTτTIwith:τT=τTnIn+ τTpIpI6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-16Complete small-signal equivalent circuit model for diode:CjCdgd6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-17Bias dependence of Cjand Cd:CV00CdCCj• Cjdominates in reverse bias and small forward bias(∼ 1/√φB− V )• Cddominates in strong forward bias (∼ eqV/kT)6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-18Key conclusionsSmall-signal behavior of diode:• conductance: associated with current-voltage charac-teristicsgd∼ I in forward bias, negligible in reverse bias• junction capacitance: associated with charge modu-lation in depletion regionCj∼ 1/rφB− V• diffusion capacitance: associated with charge storagein QNR’s to keep quasi-neutralityCd∼
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