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 ronc@uta.edu http://www.uta.edu/ronc/ L10 February 17

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

Interpreting a plot of log(iD) vs. Vd In the region where iD ~ ISeff(exp (Vd/(NeffVt)) - 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)/(NVt) = 16.799 decades/V = 1decade/59.526mV L10 February 17

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

I-V data and ISeff estimation L10 February 17

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

RSeff and Neff estimation L10 February 17

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

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

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

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

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

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

Calculating the parameters (the data were generated using M = 0.389, thus we have a 0.77% error). VJ = yi(vi=0)/slope =1.6326/2.551 = 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

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

Doping Profile The data were equal-ly spaced (DV=0.1V), the central differ-ence was used, for -7.4V ≤ 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

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

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

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

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

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

CV data and N(x) calculation L10 February 17