EE105 Fall 2005 Microelectronic Devices and Circuits Lecture 6 Currents in PN Junction MOS Capacitor Announcements Homework 3 due next week Reading Chapter 3 3 7 3 9 2 1 Lecture Material Last lecture PN junction Diode capacitance This lecture Diode currents MOS capacitor 3 Diode under Thermal Equilibrium Minority Carrier Close to Junction Thermal Generation p type J p drift J n drift ND n type J n diff J p diff NA E0 Recombination q bi Carrier with energy below barrier height Diffusion small since few carriers have enough energy to penetrate barrier Drift current is small since minority carriers are few and far between Only minority carriers generated within a diffusion length can contribute current Important Point Minority drift current independent of barrier Diffusion current strong exponential function of barrier 4 2 Reverse Bias z z Reverse Bias causes an increases barrier to diffusion Diffusion current is reduced exponentially p type ND n type NA q bi VR z z Drift current does not change Net result Small reverse current 5 Forward Bias z z Forward bias causes an exponential increase in the number of carriers with sufficient energy to penetrate barrier Diffusion current increases exponentially p type ND n type NA q bi VR z z Drift current does not change Net result Large forward current 6 3 Diode I V Curve Id Is qVd I d I S e kT 1 I d Vd I S qVd kT 1 Diode IV relation is an exponential function This exponential is due to the Boltzmann distribution of carriers versus energy For reverse bias the current saturations to the drift current due to 7 minority carriers Minority Carriers at Junction Edges Minority carrier concentration at boundaries of depletion region increase as barrier lowers the function is minority hole conc on n side of barrier p n x xn p p x x p majority hole conc on p side of barrier e Barrier Energy kT p n x xn e q B VD kT NA Boltzmann s Law 8 4 Law of the Junction Minority carrier concentrations at the edges of the depletion region are given by pn x xn N Ae q B VD kT n p x x p N D e q B VD kT Note 1 NA and ND are the majority carrier concentrations on the other side of the junction Note 2 we can reduce these equations further by substituting VD 0 V thermal equilibrium Note 3 assumption that pn ND and np NA 9 Minority Carrier Concentration qVA pn 0 e kT p side n side qVA x qVA L pn x pn 0 pn 0 e kT 1 e p n p 0 e kT Minority Carrier pn 0 Diffusion Length np0 Wp xp xn Wn The minority carrier concentration in the bulk region for forward bias is a decaying exponential due to recombination 10 5 Steady State Concentrations Assume that none of the diffusing holes and electrons recombine get straight lines qVA pn 0 e kT p side n side n p 0e qVA kT pn 0 np0 xp Wp xn Wn This also happens if the minority carrier diffusion Ln p Wn p lengths are much larger than Wn p 11 Diode Current Densities qVA pn 0 e kT p side qVA dn p n side qVA n p 0 e kT x dx n p 0 e kT n p 0 x p W p pn 0 np0 np0 Wp xp xn Wn qVA Dn n p 0 e kT 1 dx x x Wp p qVA Dp dp qD p n q pn 0 1 e kT dx x xn Wn J ndiff qDn J pdiff ni2 Na dn p q Dp Dn J diff qni2 N dWn N aW p qVA e kT 1 12 6 Fabrication of IC Diodes p cathode annode p n p type n well p type Start with p type substrate Create n well to house diode p and n diffusion regions are the cathode and annode N well must be reverse biased from substrate Parasitic resistance due to well resistance 13 Diode Small Signal Model The I V relation of a diode can be linearized qVd qvd q Vd vd I D iD I S e kT 1 I S e kT e kT ex 1 x x 2 x3 L 2 3 q Vd vd I D iD I D 1 L kT iD qvd g d vd kT 14 7 Diode Capacitance We have already seen that a reverse biased diode acts like a capacitor since the depletion region grows and shrinks in response to the applied field the capacitance in forward bias is given by Cj A S X dep 1 4C j 0 But another charge storage mechanism comes into play in forward bias Minority carriers injected into p and n regions stay in each region for a while On average additional charge is stored in diode 15 Charge Storage pn 0 e p side n p 0e q Vd vd kT n side q Vd vd kT pn 0 np0 Wp xp xn Wn Increasing forward bias increases minority charge density By charge neutrality the source voltage must supply equal and opposite charge 1 qI d A detailed analysis yields Cd 2 kT Time to cross junction or minority carrier lifetime 16 8 Diode Circuits Rectifier AC to DC conversion Average value circuit Peak detector AM demodulator DC restorer Voltage doubler quadrupler 17 MOS Capacitor Oxide SiO2 ox 3 9 0 Gate n poly 0 Very Thin tox 1nm Body p type substrate x s 11 7 0 MOS Metal Oxide Silicon Sandwich of conductors separated by an insulator Metal is more commonly a heavily doped polysilicon layer n or p layer NMOS p type substrate PMOS n type substrate 18 9 P I N Junction Gate n poly Body p type substrate Under thermal equilibrium the n type poly gate is at a higher potential than the p type substrate kT N a ln n 550mV q ni No current can flow because of the insulator but this potential difference is accompanied with an electric field Fields terminate on charge p 19 Fields and Charge at Equilibrium Vox VB Body p type substrate Eox Xd0 At equilibrium there is an electric field from the gate to the body The charges on the gate are positive The negative charges in the body come from a depletion region 20 10 Good Place to Sleep Flat Band QG VGB VFB 0 VFB 0 Body p type substrate If we apply a bias we can compensate for this built in potential VFB n p In this case the charge on the gate goes to zero and the depletion region disappears In solid state physics lingo the energy bands are flat under this condition 21 Accumulation QG Cox VGB VFB VGB VFB QB QG Body p type substrate If we further decrease the potential beyond the flatband condition we essentially have a parallel plate capacitor Plenty of holes and electrons are available to charge up the plates Negative bias attracts holes under gate 22 11 Depletion VGB VFB Body …
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