EE2 Applications

# EE2 Applications - E lectron and Hole Concentrations:...

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3/1/11 Electron and Hole Concentrations: Application Calculate the electron and hole concentrations in intrinsic silicon at room temperature ( Eg = 1.12 eV, me* = 1.18mo, mh* = 0.81mo) * We begin by calculating the position of the FERMI ENERGY

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3/1/11
3/1/11

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3/1/11 Carrier Drift in an Electric Field: Application 1 3 31 12 19 ms 176 10 10 1 . 9 10 10 6 . 1 - - - - = × × × = = E v m q d τ 1 31 23 2 kms 117 10 1 . 9 300 10 38 . 1 3 3 2 3 2 1 - - - = × × × × = = = m T k v T k mv B Th B Th IF WE USE QUANTUM  STATISTICS vTh WILL BE  EVEN BIGGER !  For simplicity consider the case of  FREE  electrons at room temperature (300 K). If the relaxation time of the  electrons at this temperature is 10-12 s, estimate their  DRIFT  and  THERMAL  velocities in the presence of an  applied electric field of 10 Vcm-1.  Since we are in the  LINEAR  regime we may estimate the drift velocity as h  To estimate the thermal velocity we recall that in a  CLASSICAL  gas the  AVERAGE  thermal energy associated with each particle is 3kBT/2
3/1/11  The electron mobility in intrinsic silicon is 1350 cm2/Vs at room temperature while the corresponding hole mobility  is 480 cm2/Vs. Given this information compute the resistivity of intrinsic silicon at this temperature. Also compute  the resistivity with a donor doping density of 1017 cm-3, assuming an electron mobility of 800 cm2/Vs. Resistivity: Application cm 08 . 0 10 800 10 6 . 1 1 1 : cm 10 4 . 3 10 ) 480 1350 ( 10 6 . 1 1 ) ( 1 K 300 @ cm 10 : 17 19 5 10 19 3 10 = × × × = = - × = × + × × = + = = = - - - D n i i p n i i N q doping type n heavy For n q n p n have we silicon rinsic int For μ ρ

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3/1/11  An intrinsic Si sample is doped with donors from one side such that ND = Noexp(-ax). Find an expression for Ex at  equilibrium over the range for which Nd >> Ni. Also evaluate Ex when a = 1 (mm)-1.  The Einstein Relation: Application V/cm 259 10 10 6 . 1 300 10 38 . 1 ) μm 1 ( 4 19 23 1 = × × × = = = - - - a q T k a E B x ) 13 . 6 ( ) ( x nE T k q dx dE T k n dx dn B i B - = - = a q T k n ae N q T k x E B ax o B = = - ) ( NOTE THAT THE ELECTRIC FIELD IS  POSITIVE  SINCE THE ELECTRONS LEAVE BEHIND  POSITIVELY-CHARGED IONIZED  DONORS  WHEN THEY DIFFUSE!
3/1/11  Since the electric field developed due to the concentration gradient is  CONSTANT  the   energy bands will exhibit a  CONSTANT  tilt as discussed in Subject_04 The Einstein Relation: Application

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3/1/11 The Einstein Relation: Application  Consider a silicon sample at 300 K that is doped with acceptors at a concentration of 1015 cm-3. A stream of  minority carriers is injected at x = 0 and the distribution of these carriers is assumed to be linear, decreasing from  1011 cm-3 at x = 0 to the equilibrium value at x = 10 μm. Determine the diffusion current density of electrons.  2 4 5 11 23 2 3 5 2 3 15 3 10 mA/cm 54 . 0
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## This note was uploaded on 02/28/2011 for the course EE 2 taught by Professor Vis during the Winter '07 term at UCLA.

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EE2 Applications - E lectron and Hole Concentrations:...

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