1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
EE5342 – Semiconductor Device Modeling and Characterization Lecture 10 - Spring 2005
Professor Ronald L. Carter
L10 February 17

2. ln iD ln(IKF) ln[(IS*IKF) 1/2] ln(ISR) ln(IS) vD= Vext VKF
Vext-Va=iD*Rs
low level injection
ln iD
ln(IKF)
Effect of Rs
ln[(IS*IKF) 1/2]
Effect of high level injection
ln(ISR)
Data
ln(IS)
vD=
Vext
recomb. current
VKF
L10 February 17

3. Interpreting a plot of log(iD) vs. Vd
In the region where
iD ~ ISeff(exp (Vd/(NeffVt)) - 1)
For N = 1 and Vt = mV, the slope of the plot of log(iD) vs. Vd is evaluated as
{dlog(iD)/dVd} = log (e)/(NVt)
= decades/V
= 1decade/59.526mV
L10 February 17

4. Static Model Eqns. Parameter Extraction
In the region where
iD ~ ISeffexp (Vd/(NeffVt) )
{diD/dVd}/iD = d[ln(iD)]/dVd = 1/(NVt)
so N ~ {dVd/d[ln(iD)]}/Vt  Neff,
and ln(IS) ~ ln(iD) - Vd/(NVt)  ln(ISeff).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
L10 February 17

5. I-V data and ISeff estimation
L10 February 17

6. Hints for RS and NF parameter extraction
In the region where vD > VKF. Defining
vD = vDext - iD*RS and IHLI = [ISIKF]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
L10 February 17

8. Application of RS to lower current data
In 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 of
y = yi vs. Va = vi has
slope = -1/M, and
intercept = 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 calculations
Table 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.
L10 February 17

12. y vs. Va plots
Figure 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 the data interpretation
It 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. Vi
VJ 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 the parameters
(the data were generated using M = 0.389, thus we have a 0.77% error).
VJ = yi(vi=0)/slope =1.6326/ = 0.640
(the data were generated using fi = 0.648, thus we have a 1.24% error).
Cj0 = 1.539E30^-.392 = pF
(the data were generated using Cj0 = 1.68 pF, thus we have a 12.6% error)
L10 February 17

15. Linearized C-V plot
Figure A1.4. A plot of the data for Cj^-1/M vs. Va using the M value determined for this data (M = 0.392).
L10 February 17

16. Doping Profile
The data were equal-ly spaced (DV=0.1V), the central differ-ence was used, for V ≤ V ≤ 0.4V, which for Cj = e/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.
L10 February 17

17. SPICE Diode Capacitance Pars.1
PARAMETER definition and units default value
TT transit time sec 0.0
CJO zero-bias p-n capacitance farad 0.0
M p-n grading coefficient 0.5
FC forward-bias depletion capacitance coeff 0.5
VJ p-n potential volt 1.0
L10 February 17

18. SPICE Diode Capacitance Eqns.1
Cd = Ct + area·Cj
Ct = transit time capacitance = TT·Gd
Gd = DC conductance
= area * d (Inrm Kinj + Irec Kgen)/dVd
Kinj = high-injection factor
Cj = junction capacitance
IF: 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)
L10 February 17

19. Junction Capacitance
A plot of [Cj]-1/M vs. Vd has Slope = -[(CJO)1/M/VJ]-1 vertical axis intercept = [CJO]-2 horizontal axis intercept = VJ
Cj-1/M
CJO-1/M Vd VJ
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,
For Va=0, & 1E13 < Na,Nd < 1E19 cm-3
13% < d < 28% => DA is OK
L10 February 17

21. Junction Capacitance Adapted 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)
FC*VJ VJ
L10 February 17

22. CV data and N(x) calculation
L10 February 17