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# MICROELECTRONICS TECHNOLOGY ECSE 2210

RPI

GPA 3.52

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This 19 page Class Notes was uploaded by Miss Damien Crooks on Monday October 19, 2015. The Class Notes belongs to ECSE 2210 at Rensselaer Polytechnic Institute taught by E. Schubert in Fall. Since its upload, it has received 68 views. For similar materials see /class/224773/ecse-2210-rensselaer-polytechnic-institute in ELECTRICAL AND COMPUTER ENGINEERING at Rensselaer Polytechnic Institute.

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Date Created: 10/19/15

Chapter 31 Carrier action Topics to be covered in this chapter Response of carriers holes and electrons under perturbed conditions Drift Diffusion Recombinationgeneration Equations of state Thermodynamic equilibrium vs steady state Thermodynamic equilibrium Thermodynamic or thermal equilibrium refers to the condition in which a specimen is not subjected to external excitations except a uniform temperature That is no voltages electric fields magnetic fields illumination etc are applied Under thermal equilibrium conditions ever process is balanced in detail by an opposing process This is called the principle of detailed balance Example A semiconductor in the dark at T 300 K with no excitation is in thermal equilibrium Thermal generation is exactly balanced by recombination i e principle ofa eiailed balance is fulfilled Steady state Steady state refers to a nonequilibrium condition in which all processes are constant in time Example A LED driven at a constant current is in the steady state Note that the principle ofa eiailed balance does not apply Carrier drift Drift by de nition is charged particle motion in response to an applied electric eld Because of collisions with ionized impurity atoms and thermally agitated lattice atoms the carrier acceleration is frequently interrupted called scattering D Z gtd 3 v 0 G gt i j a Legs a b C Figure 31 Drift velocity vi and thermal velocity 12m The net result is carrier motion generally along the direction of E eld The resultant motion of each carrier type under the in uence of E eld can be described in terms of a constant drift velocity vd Thermal Motion Note that the carrier thermalvelocity is very large 107 cms at 300 K but 7 this does not contribute to current transport Why 3 Random thermal motion m vtzh 3 kT of carriers vth x3kTm Drift current Drift current is the current owing Within a semiconductor as a result of carrier drift By definition 1 current the charge per unit time crossing an arbitrarily chosen plane of observation oriented normal to the direction of current ow Q t Ampere Coulomb second J current density current per unit area I A Drift current Consider a ptype semiconductor Figure 33 WWW plane in a time t vth A11 holes in this volume will cross the plane in a time t pvd tA Holes crossing the plane in a time t Wangwossuig mplmemaumet Drift current q p vdA is the charge crossing the plane per unit time and by de nition is the hole drift current Idrift By inspection the current density associated with hole drift is Jp drift 2 W9 Va Since drift current arises in response to Efield we need to find the relationship between drift current and E eld At low electric field it is found that drift velocity is proportional to E eld Jpldriftqu pf Where up is the proportionality constant called hole mobility Drift velocity vs electric eld in Si vdcmsec 107 106 105 I I IIIIII I IIIIIIII III IITTII I IIIIII E vdzvsat g Electrons Holes E E d cc6 1111111 1 1111111l 11111111 1 1111111 102 103 104 105 106 C6Vcm Figure 34 Hole and electron drift current density JPldrift Iluvpf6 34a JNIdrift 511 quot 5 34b Resistivity Q The resistivity is a measure of a material s inherent resistance to current ow The total current density in a semiconductor due to drift is given by JdriftJpldrift ndriftqp Hp qn Mn E IJAVRVplAVZgtltAp z A I I lt V gt Comparing the above equations we get Mobility vs donant concentration for Si at 300 K Silicon T 300 K 1000 8 1 E 3 ll 1 8 NA or ND cm c1112 V sec 1 1x1014m 1358 6 H 2 1357 460 O 1 100 5 1352 L 1x1015 1345 2 1332 5 1298 1x1016 1248 2 1165 5 986 1x1017 801 10 1014 1015 1016 1017 1018 NA or ND cm3 a Mobility versus doping concentration for G6 and GaAs at 300 K 1014 1015 1016 1017 1015 N A or ND cm3 b Figure 35 Temperature dependence of electron mobility T K a Temperature dependence of hole mobility b Figure 37 Silicon Si resistivity VS p ohm cm 1014 1015 1013 doping concentration at 300K 1016 1017 1018 1019 1020 NA or ND cm 3 a Figure 38 15 Resistivity vs doping concentration at 300K Other semiconductors 102 TmmK ntype ptype 101 p ohmcm 5 3 0 N 103 4 10 1014 1015 1016 1017 1018 1019 1020 1021 NA 0139 ND CHI 3 Figure 38 b 16 Resistivity measurement a 4point probe b eddycurrent apparatus D Figure 39 Example 1 Calculate the resistivity of intrinsic Ge at room temperature First find n and p at room temperature Since intrinsic from page 34 n p r21 2 x1013 cm 3 Then estimate up and an at room temperature From Fig 35 extending the curve to N A ND 0 we get up 2000 cmzVs and un 4000 cmzVs Calculate p from the equation pi qpup qnun 391 Note One summand in the denominator of the above equation may or may not be neglected when calculating p Explain Example 2 Calculate the resistivity of 1013 cm 3 phosphorousdoped Si at room temperature First nd n and p at room temperature Since phosphorous is a donor n ND 1013 cm 3 Note ND gtgt Hi and N AO npni2 gt p107cm 3 Then estimate up and an at room temperature From Fig 35 extending the curve to N A ND 1013 cm 3 we get um 1350 cmzVs and up 450 cmzVs Calculate p from the equation 51 p I QPH P gnun

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