1ECE 410, Prof. F. Salem/Prof. A. Mason with updates Lecture Notes 6.1Conduction in Semiconductors -Review• Intrinsic (undoped) Semiconductors– intrinsic carrier concentration ≡ ni= 1.45x1010cm-3, at room temp.– n = p = ni, in intrinsic (undoped) material•n ≡ number of electrons, p ≡ number of holes– mass-action law, np = ni2=1.45E10, applies to undoped and doped material• Extrinsic (doped) Semiconductors– dopants added to modify material/electrical propertiesPBPB++++--group Velementgroup IIIelementionelectronholen-type Donorp-type Acceptorionfreecarrierfreecarrier•n-type (n+), add elements with extra an electron–Nd≡ conc. of donor atoms [cm-3]–nn= Nd, nn≡ conc. of electrons in n-type material–pn= ni2/Nd, using mass-action law, –pn≡ conc. of holes in n-type material–always a lot more n than p in n-type material•p-type = p+, add elements with an extra hole–Na≡ concentration of acceptor atoms [cm-3]–pp= Na, pp≡ conc. of holes in p-type material–np= ni2/Na, using mass-action law, –np≡ conc. of electrons in p-type material–always a lot more p than n in p-type material2ECE 410, Prof. F. Salem/Prof. A. Mason with updates Lecture Notes 6.2Conduction in Semiconductors• doping provides free charge carriers, alters conductivity • conductivity, σ, in semic. w/ carrier densities n and p– σ = q(μnn + μpp), q ≡ electron charge, q = 1.6x10-19[Coulombs]• μ≡mobility [cm2/V-sec], μn≅ 1360, μp≅ 480 (typical values)• in n-type region, nn>> pn– σ≈qμnnn• in p-type region, pp>> np– σ≈qμpnp•resistivity, ρ = 1/σ• resistance of an n+ or p+ region–R = ρl , A = wt• drift current (flow of charge carriers in presence of an electric field, Ex)– n/p drift current density: Jxn = σnEx= qμnnnEx, Jxp = σpEx= qμpppEx–total drift current densityin x direction Jx = q(μnn + μpp) Ex= σ Exmobility = average velocity per unit electric fieldμn> μpelectrons more mobile than holes⇒conductivity of n+ > p+ltwA3ECE 410, Prof. F. Salem/Prof. A. Mason with updates Lecture Notes 6.3pn Junctions: Intro• What is a pn Junction?– interface of p-type andn-type semiconductor– junction of two materials forms a diode• In the Beginning…– ionization of dopantsat material interface•Diffusion -movement of charge to regions of lower concentration– free carriers diffuse out– leave behind immobile ions– region become depleted offree carriers– ions establish an electric field• acts against diffusiondonor ion and electron free carrieracceptor ion and hole free carrierp-typehole diffusionhole currentelectron diffusionelectron currentN acceptors/cmA3N donors/cmD3n-type-+-+-+-+-+-+-+-++-+-+-+-+-+-+-+-+-+-+-Edepletion regionimmobile acceptor ions(negative-charge)immobile donor ions(positive-charge)electric fieldxpWxn--------++++++++p-typeN acceptors/cmA3N donors/cmD3n-typep-type Si waferpn diodejunctiondepletion regionboundariesdielectricinsulator(oxide)contactto p-sidecontactto n-sidep+n+n “well”p-type n-type4ECE 410, Prof. F. Salem/Prof. A. Mason with updates Lecture Notes 6.4pn Junctions: Equilibrium Conditions• Depletion Region– area at pn interface void of free charges–charge neutrality• must have equal charge on both sides•q A xpNA= q A xnND, A=junction area; xp, xndepth into p/n side• ⇒ xpNA= xnND• depletion region will extend further into the more lightly doped side of the junction• Built-in Potential– diffusion of carriers leaves behind immobile charged ions– ions create an electric field which generates a built-in potential• where VT= kT/q = 26mV at room temperatureEdepletion regionimmobile acceptor ions(negative-charge)immobile donor ions(positive-charge)electric fieldxpWxn--------++++++++p-typeN acceptors/cmA3N donors/cmD3n-typeNAND⎟⎟⎠⎞⎜⎜⎝⎛=Ψ20lniDATnNNV5ECE 410, Prof. F. Salem/Prof. A. Mason with updates Lecture Notes 6.5pn Junctions: Depletion Width•Depletion Widthuse Poisson’s equation & charge neutrality–W = xp+ xn• where VRis applied reverse bias• One-sided Step Junction–if NA>>ND(p+n diode)• most of junction on n-side–if ND>>NA (n+p diode)• most of junction on p-sideEdepletion regionimmobile acceptor ions(negative-charge)immobile donor ions(positive-charge)electric fieldxpWxn--------++++++++p-typeN acceptors/cmA3N donors/cmD3n-typeNAND⎟⎟⎠⎞⎜⎜⎝⎛=Ψ20lniDATnNNV()()2102⎥⎦⎤⎢⎣⎡++Ψ=ADADRpNNqNNVxε()()2102⎥⎦⎤⎢⎣⎡++Ψ=ADDARnNNqNNVxε()2102⎥⎦⎤⎢⎣⎡++Ψ=ADADRNNNNqVWε()2102⎥⎦⎤⎢⎣⎡+Ψ=≅ARpqNVxWε()2102⎥⎦⎤⎢⎣⎡+Ψ=≅DRnqNVxWεε is the permittivity of Siε = 1.04x10-12F/cmε = KSε0, where ε0 = 8.85x10-14F/cmand KS= 11.8 is the relative permittivity of silicon6ECE 410, Prof. F. Salem/Prof. A. Mason with updates Lecture Notes 6.6pn Junctions - Depletion Capacitance• Free carriers are separated by the depletion layer• Separation of charge creates junction capacitance–Cj = εA/d ⇒ (d = depletion width, W)– A is complex to calculate in semiconductor diodes• consists of both bottom of the well and side-wall areas– Cj is a strong function of biasing• must be re-calculated ifbias conditions change– CMOS doping is not linear/constant• graded junction approximation•Junction Breakdown– if reverse bias is too high (typically > 30V) can get strong reverse current flow()⎟⎟⎠⎞⎜⎜⎝⎛+Ψ⎥⎦⎤⎢⎣⎡+=RDADAjVNNNNqAC02112εε is the permittivity of Siε = 11.8 ε0= 1.04x10-12F/cmVR= applied reverse bias⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛Ψ+=01RjojVCC()2102⎥⎦⎤⎢⎣⎡+Ψ=DADAjoNNNNqACε⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛Ψ+=301RjojVCC7ECE 410, Prof. F. Salem/Prof. A. Mason with updates Lecture Notes 6.7• Forward Bias; VD> Ψ0– acts against built-in potential– depletion width reduced– diffusion currents increase with VD• minority carrier diffusion• Reverse Bias; VR= -VD> 0– acts to support built-in potential–depletion width increased– electric field increased– small drift current flows• considered leakage• small until VRis too high and breakdown occursDiode Biasing and Current Flow+ V -DVDVf+ V -DIDIDIDpn()1−=TDVVSDeII⎟⎟⎠⎞⎜⎜⎝⎛+∝ADSNNAI118ECE 410, Prof. F. Salem/Prof. A. Mason with updates Lecture Notes 6.8MOSFET Capacitor• MOSFETs move charge from drain to source underneath the gate, if a conductive channel exists under the gate• Understanding how and why the
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