ee5342 – semiconductor device modeling and characterization lecture 10 - spring 2005
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L10 February 17 1
EE5342 – Semiconductor Device Modeling and CharacterizationLecture 10 - Spring 2005
Professor Ronald L. Carterronc@uta.edu
http://www.uta.edu/ronc/
L10 February 17 2
vD=Vext
ln iD
Data
ln(IKF)
ln(IS)
ln[(IS*IKF) 1/2]
Effect
of Rs
t
a
VNFV
exp~
t
a
VNRV
exp~
VKF
ln(ISR)
Effect of high level injection
low level injection
recomb. current
Vext-
Va=iD*Rs
t
a
VNV
2exp~
L10 February 17 3
Interpreting a plotof log(iD) vs. VdIn the region where
iD ~ ISeff(exp (Vd/(NeffVt)) - 1)
For N = 1 and Vt = 25.852 mV, the slope of the plot of log(iD) vs. Vd is evaluated as
{dlog(iD)/dVd} = log (e)/(NVt) = 16.799 decades/V = 1decade/59.526mV
L10 February 17 4
Static Model Eqns.Parameter ExtractionIn the region where
iD ~ ISeffexp (Vd/(NeffVt) )
{diD/dVd}/iD = d[ln(iD)]/dVd = 1/(NVt)
so N ~ {dVd/d[ln(iD)]}/Vt Neff,
and ln(IS) ~ ln(iD) - Vd/(NVt) ln(ISeff).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
L10 February 17 5
I-V data and ISeff estimation
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
0.4 0.6 0.8 1.0
Vext (V)
Id (
A)
1.E-16
1.E-15
1.E-14
1.E-13
1.E-12
0.4 0.6 0.8 1.0
Vext (V)
ISef
f
L10 February 17 6
Hints for RS and NFparameter extractionIn the region where vD > VKF. Defining
vD = vDext - iD*RS and IHLI = [ISIKF]1/2.
iD = IHLIexp (vD/2NVt) + ISRexp (vD/NRVt)
diD/diD = 1 (iD/2NVt)(dvDext/diD - RS) + …
Thus, for vD > VKF (highest voltages only)
plot iD-1 vs. (dvDext/diD) to get a line with
slope = (2NVt)-1, intercept = - RS/(2NVt)
L10 February 17 7
RSeff and Neff estimation
y = 0.0275x + 2.311
R2 = 1
y = 0.0287x + 1.9049
R2 = 0.9998
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
0.0 500.0 1000.0
1/Ia (1/Amp)
RS
eff
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
0.4 0.6 0.8 1.0
Vext (V)
Nef
f
L10 February 17 8
Application of RS tolower current dataIn the region where vD < VKF. We still have
vD = vDext - iD*RS and since.
iD = ISexp (vD/NVt) + ISRexp (vD/NRVt) Try applying the derivatives for methods
described to the variables iD and vD (using RS and vDext).
You also might try comparing the N value from the regular N extraction procedure to the value from the previous slide.
L10 February 17 9
Estimating Junction Capacitance Parameters
• Following L29 – EE 5340 Fall 2003• If CJ = CJO {1 – Va/VJ}-M
• Define y {d[ln(CJ)]/dV}-1
• A plot ofy = yi vs. Va = vi has
slope = -1/M, andintercept = VJ/MF
L10 February 17 10
Derivatives Defined
The central derivative is defined as (following Lecture 14 and 11)
yi,Central = (vi+1 – vi-1)/(lnCi+1 – lnCi-1), with vi = (vi+1 + vi-1)/2 Equation A1.1
The Forward derivative (as applied to the theory in L11 and L14) is defined in this case as
yi,Forward = (vi+1 – vi)/(lnCi+1 – lnCi), with vi,eff = (vi+1 + vi-1)/2 Equation A1.2
L10 February 17 11
Data calculationsTable A1.1. Calculations of yi and vi for the Central and Forward derivatives for the data in Table 1. The yi and vi are defined in Equations A1.1 and A1.2.
Va (V) Cj (Fd) viCentral Forward
0.40 2.51E-12 derivative derivative0.35 0.585
0.30 2.11E-12 0.30 0.8160.25 1.347
0.20 1.96E-12 0.20 1.1520.15 1.007
0.10 1.78E-12 0.10 1.3250.05 1.938
0.00 1.69E-12 -0.20 2.231-0.25 2.300
-0.50 1.36E-12 -0.50 2.946-0.75 4.096
-1.00 1.20E-12 -1.00 4.132
yi = (dlnc/dv)^-1
L10 February 17 12
y = -2.551x + 1.6326
R2 = 0.9977, Central
y = -2.9965x + 1.7788
R2 = 0.9517, Forward
0
1
2
3
4
5
-1.0 -0.5 0.0 0.5 1.0
Vi (Volts)
yi (V
olts^-1
)
Central
Forward
Linear (Central)
Linear (Forward)
y vs. Va plotsFigure A1.3. The yi and vi values from the theory in L11 and L14 with associa-ted trend lines and slope, intercept and R^2 values.
L10 February 17 13
Comments on thedata interpretationIt is clear the Central derivative gives the more reliable data as the R^2 value is larger. M is the reciprocal of the magnitude of the slope obtained by a least squares fit (linear) plot of yi vs. ViVJ is the horizontal axis intercept (computed as the vertical axis intercept divided by the slope)Cj0 is the vertical axis intercept of a least squares fit of Cj-1/M vs. V (must use the value of V for which the Cj was computed). The computations will be shown later.The results of plotting Cj-1/M vs. V for the M value quoted below are shown in Figure A1.4
L10 February 17 14
Calculating theparametersM = 1/2.551 = 0.392
(the data were generated using M = 0.389, thus we have a 0.77% error).
VJ = yi(vi=0)/slope =1.6326/2.551 = 0.640
(the data were generated using fi = 0.648, thus we have a 1.24% error).
Cj0 = 1.539E30^-.392 = 1.467 pF (the data were generated using Cj0 =
1.68 pF, thus we have a 12.6% error)
L10 February 17 15
Linearized C-V plotFigure A1.4. A plot of the data for Cj^-1/M vs. Va using the M value determined for this data (M = 0.392).
y = -1.539E+30x + 1.058E+30
R2 = 9.976E-01
0.00E+00
1.00E+30
2.00E+30
3.00E+30
-1.0 -0.5 0.0 0.5 1.0Va (Volts)
Cj^
-1/M
L10 February 17 16
Doping ProfileThe data were equal-ly spaced (V=0.1V), the central differ-ence was used, for -7.4V ≤ V ≤ 0.4V, which for Cj = /x, corresponds to a range of 2.81E-5 cm ≤ x ≤ 8.99E-5 cm. These data are shown. The trend line is also shown for a linear fit. Since R^2 = 1.000, a linear N(x) relationship can be assumed.
y = 1.888E+20x + 1.861E+15
R2 = 1.000E+00
6.0E+15
8.0E+15
1.0E+16
1.2E+16
1.4E+16
1.6E+16
1.8E+16
2.0E+16
2.0E-05 4.0E-05 6.0E-05 8.0E-05 1.0E-04
Depletion depth, x (cm)
Dop
ing
Con
cent
ratio
n (c
m^-
3)
dV
CdqA
xN n )(
2)(
22
L10 February 17 17
PARAMETER definition and units default value
TT transit time sec 0.0CJO zero-bias p-n capacitance farad 0.0M p-n grading coefficient 0.5FC forward-bias depletion capacitance coeff 0.5VJ p-n potential volt 1.0
SPICE Diode Capacitance Pars.1
L10 February 17 18
Cd = Ct + area·CjCt = transit time capacitance = TT·GdGd = DC conductance = area * d (Inrm Kinj + Irec Kgen)/dVdKinj = high-injection factor
Cj = junction capacitanceIF: Vd < FC·VJ Cj = CJO*(1-Vd/VJ)^(-M) IF: Vd > FC·VJ Cj = CJO*(1-FC)^(-1-M)·(1-FC·(1+M)+M·Vd/VJ)
SPICE Diode Capacitance Eqns.1
L10 February 17 19
Junction Capacitance
• A plot of [Cj]-1/M vs. Vd hasSlope = -[(CJO)1/M/VJ]-1
vertical axis intercept = [CJO]-2 horizontal axis intercept = VJ
Cj-1/M
VJVd
CJO-1/M
L10 February 17 20
Junction Width and Debye Length
• LD estimates the transition length of a step-junction DR (concentrations Na and Nd with Neff =
NaNd/(Na +Nd)). Thus,
bi
efft
dabia
dDaD
VFC12
NV
N1
N1
VFCVWNLNL
*
• For Va=0, & 1E13 < Na,Nd < 1E19 cm-3
13% < < 28% => DA is OK
pnqVL tD / , qNVVW effdbi /
L10 February 17 21
Junction CapacitanceAdapted from Figure 1-16 in Text2
Cj = CJO/(1-Vd/VJ)^M
Cj = CJO/(1-FC)^(1+M)*(1-FC·(1+M)+M·Vd/VJ)
VJFC*VJ
L10 February 17 22
CV data and N(x) calculation
1.E+15
1.E+16
1.E+17
1.E+18
1.E+19
2.0E-05 3.0E-05 4.0E-05 5.0E-05
0.00E+00
1.00E-13
2.00E-13
3.00E-13
4.00E-13
5.00E-13
-7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00
C
Ax
dVdCqA
C)x(N
n
2
3
n
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