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Collection of Excel Formulas SB
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etch
thickness by weight
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density of silicon is
2.328 g/cm3
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100 cm² square
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100mm round
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for a 1 inch sample
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weight (g)
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t (µm)
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t(µm)
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Start Weight (g)
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End Weight (g)
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weight diff (g)
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t (cm)
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t (µm)
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Resistivity
Measurements
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Thickness
(cm)
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Current (mA)
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Voltage- (mV)
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Voltage+ (mV)
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Resistivity
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Thickness (um)
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Average
change in thickness for lots of wafers
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Start
Weight
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End Weight
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Wafers
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weight (g)
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t (µm)
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S
from W, teff, tb
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W (um)
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D (cm2/s)
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teff (µsec)
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tb (µsec)
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ts (µsec)
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S (cm/s)
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tb
from teff, S, W
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W (um)
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D (cm2/s)
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teff (µsec)
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S
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ts (µsec)
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tb (µsec)
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teff
from tb, S, W
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W (um)
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D (cm2/s)
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tb (µsec)
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S
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ts (µsec)
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teff (µsec)
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Lifetime
at limit
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D (cm2/s)
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W (cm)
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taus (s)
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Seff
from J0 and minority carrier density (unverified)
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J0 (A/cm²)
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delta n
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Seff (cm/s)
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Seff
from J0 and base doping at 25C (PC1D uses 300K)
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J0 (A/cm²)
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N (cm-3)
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S (cm/s)
300K
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S (cm/s)
25 K
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1.00e-013
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1.00e+015
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Calculation
of n and Jo from two light intensities
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Sample id
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Isc (A)
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Area (cm²)
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Jsc (A/cm²)
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Voc (mV)
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n from shaded
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J0 (A/cm²)
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Shading Fraction
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shaded
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unshaded
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Calculation
of Optimum Shading Level
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Isc (Shaded)
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Isc (Full)
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Optimum shading
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92.993
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102.24
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Diffusivity
from Mobilty
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Mobility (Vcm2/s)
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D (cm2/s)
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20.0
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Diffusion
Length from Lifetime
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For 1 ohm cm material
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D (cm2/s)
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tb (µsec)
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L (um)
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tb (µsec)
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L (um)
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11
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1000
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30
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Lifetime
From Diffusion Length
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D (cm2/s)
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L (um)
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tb (µsec)
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26.88
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400
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Leff
from S and L
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W (um)
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D (cm2/s)
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L (um)
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S (cm/s)
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S.L/D
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tanh(W/L)
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Leff (um)
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200
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26.9
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1400
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Calculation
of n and Jo from two light intensities in PC1D. Rshunt can ruin the
measurements so turn it off!
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Batch run
from:two light levels.txt
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PriInsySS
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PriInsyTR1
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PriInsyTR2
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BaseIsc
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BasePmax
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BaseVoc
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Area (cm²)
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Jsc (mA/cm²)
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Voc (mV)
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n from shaded
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J0 (A/cm²)
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0.1
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0.1
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0.1
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-3.1474
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1.61321
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0.617331
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1
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0.01
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0.01
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0.01
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-3.15e-001
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0.14469
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0.557211
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Using
PC1D to calculate n and J0 in the dark. Make sure all light, Rs, Rshunt are
off
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Batch run
from:two light levels.txt
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PriInsySS
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PriInsyTR1
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PriInsyTR2
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BaseIsc
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BasePmax
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BaseVoc
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Area (cm²)
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Jsc (mA/cm²)
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Voc (mV)
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n
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J0 (A/cm²)
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0.1
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0.1
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1.00e-001
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-3.1474
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1.61
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6.17e-001
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100
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0.01
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0.01
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1.00e-002
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-3.15e-001
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0.14469
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0.557211
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Calculation
of mobility etc. Use solve to find at a particular resistivity
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Doping
(cm-3)
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7.00e+014
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resistivity for p-type
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max
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min
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Nref
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a
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Mobility
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Diff
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Resistivty
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target
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diff
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1417
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60
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9.64e+016
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0.664
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Electron Majority
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n-type
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1
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1417
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160
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5.60e+016
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0.647
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Electron Minority
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470
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37.4
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2.82e+017
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0.642
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Hole Majority
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p-type
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0.78
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470
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155
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1.00e+017
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0.9
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Hole Minority
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Polynomial
fits to find doping from resistivity boron doped Si
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res (ohm
cm)
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doping (cm-3)
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7
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fit for 0.2 to 200 ohm cm
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1.47
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fit for 0.2 to 200 ohm cm
using simpler cubic
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1.47
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fit for doping 1e12 1e21
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Determination
of bulk lifetime from emitter sat. current plus LLI lifetime
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NA
(cm-3)
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J0
(A/cm²)
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W
(cm)
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J0term
(s-1)
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1/J0term (s)
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tau eff (µs)
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tau bulk (µs)
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1.50e+016
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Find
Voc from the excess carrier (Implied Voc)
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NA
(cm-3)
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delta n
(cm-3)
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Implied Voc
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1.40e+016
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1.79e+016
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Calculation
of Voc from Effective Lifetime
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Suns
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Optical Coeff
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Jph
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tau eff (s)
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W (cm)
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delta n
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Doping
(cm-3)
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Implied Voc
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1.00e+000
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1
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Calculation
of Optical Correction Factor for QSS-PC
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Jsc (mA/cm²)
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Optical
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Generation (/s)
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Generation (/s)
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Jsc (mA/cm²)
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Optical Constant
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40
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Reflactivity
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Optical Trans
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0.22
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Effect
of Rsh on Voc
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Jsc (A/cm²)
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Rsh (Ocm²)
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delta Voc (mV)
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0.034
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100
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Effect
of J02 and J01 on Voc
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Jsc
(A/cm²)
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Vt (V) 25°C
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J01 (A/cm²)
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J02 (A/cm²)
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Voc J01 only (V)
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Voc J01 & J02 (V)
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delta Voc (V)
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0.033
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0.02568
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1.52e-012
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2.80e-008
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Using
Leff to get Voc
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Diffusivity
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Base Doping
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ni
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Jsc
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Leff
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Constant
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Job
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Joe
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max Voc
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cm²/s
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/cm³
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/cm³
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A/cm²
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µm
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for J0b
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A/cm²
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A/cm²
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volts
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3.00e-013
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Voc
from J0 and Jsc
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Jsc
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J0
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max Voc
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A/cm²
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A/cm²
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volts
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Auger
Lifetime
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n
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p
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n0
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p0
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delta_n
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1.00e+017
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5.00e+013
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2.00e+006
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1.00e+017
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Calculation
of Job
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Jb
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V
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4.20e-009
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0.2237
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ni
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Base Doping
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Jb
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/cm³
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n
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/cm³
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2.89e+007
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Simple
Auger lifetime
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n
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C
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tb (µsec)
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1.00e+015
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1.66e-030
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Surface
Recombination velocity at HLI
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S
from W, teff, tb
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W (um)
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D (cm2/s)
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teff (µsec)
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tb (µsec)
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ts (µsec)
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S (cm/s)
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1.00e+004
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Conductivity
in LLI
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un + up
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deltaN
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deltaS
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Rons
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1514
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1.00e+015
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0.251
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Termperature
Sesitivity
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Vgo
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gamma
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Voc
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1.2
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3
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0.7
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popular probes 0.635 and 1.588
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Four
Point Probe (simple sheet resistivity)
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Voltage (V)
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Current (Amps)
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Rsheet (ohm/sqr)
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Wafer Thickness (cm)
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Wafer Resistivity (ohm cm)
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Probe Spacing (cm)
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Corrected Resistivity
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Anti-Reflection
Coatings
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Wavelength
(nm)
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ARC thickness (nm)
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Substrate Refractive Index
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surrounding refractive index
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ARC Refractive Index
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Theta
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R2
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R1
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Reflection
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Absorption
from the Extinction Coefficinet
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k
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Wavelength (nm)
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absorption coefficient (/m)
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absorption coefficient (/cm)
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0.43331
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300
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Ideality
Factor from Light and Shaded Curves
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Jsc
(mA/cm²)
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Voc (mV)
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n from shaded
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J0 (A/cm²)
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Shading
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0.72
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552
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10.50
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562.5
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Series
Resistance from Light and Shaded Curve
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Current
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Vshaded
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Vcurve
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22.4
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512
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485
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Series
Resistance Losses in a Finger
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Length
(cm)
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Current Density (A/cm2)
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Finger Spacing (cm)
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Metal Resistivity (ohm cm)
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Radius of Wire (cm)
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Wire Resistivity (ohm/cm)
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Resistive Loss in Wire(W)
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Ideal Power Output
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Fraction of Power Lost (%)
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1.7
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0.02
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0.1
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5.00e-006
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0.0723197373901
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Series
Resistance Losses in a Finger
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Length
(cm)
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Current Density (A/cm2)
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Finger Spacing (cm)
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Metal Resistivity (ohm cm)
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Width of Wire (cm)
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Thickness (cm)
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Wire Resistivity (ohm/cm)
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Resistive Loss in Wire(W)
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Ideal Power Output
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Fraction of Power Lost (%)
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0.8
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0.03
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0.2
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4.00e-006
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0.1
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2.00e-005
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Intrinsic
Carrier Concentration
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Nc (cm-3)
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Nv (cm-3)
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Eg (eV)
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ni(300K)
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2.86e+019
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3.10e+019
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1.12
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Density
of States in the Conduction Band
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Temperature (K)
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Nc (cm-3)
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300
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Density
of States in the Valence Band
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Temperature (K)
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Nv (cm-3)
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300
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Area
of a Quadralateral
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x1
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y1
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x2
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y2
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x3
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y3
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x4
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y4
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Area
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226
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181
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192
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705
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1058
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755
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1096
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235
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n
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p
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n0
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p0
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Dn
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R Auger
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QSS
Lifetime
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Thickness
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delta_n (cm-3)
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G (s-1)
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3.93e+015
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Effect
of amorphous layer conductivity on cell
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Thickness (cm)
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Conductivity (S/cm)
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current (A/cm2)
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Vdrop (V)
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3.00e-002
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1.00e-006
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0.05
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Effect of
conductivity of base
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Thickness (cm)
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Resistivity (ohmcm)
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current (A/cm2)
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Vdrop (V)
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3.00e-002
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2.00e+000
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0.05
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Intrinsic
Lifetime of Silicon
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Dn
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NA
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1/t
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t (sec)
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t (µsec)
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1.00e+013
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1.00e+016
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Dp
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ND
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1/t
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t (sec)
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t (µsec)
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1.00e+015
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3.50e+015
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