Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ EE5342 – Semiconductor Device Modeling and Characterization Lecture 11 - Spring 2005 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L11 February 22

Project 1 Some initial data and assignments for Project 1 are posted at http://www.uta.edu/ronc/5342/projects/Project_1/IVdata.xls and http://www.uta.edu/ronc/5342/projects/Project_1/CVdata.xls L11 February 22

Additional Project 1 Actions Develop the best least squares* static model (IS, N, ISR, NR, RS) for operating the diode in the range 700mV < vext < 1000mV *i.e. minimize Repeat for the range 300mV to 1V L11 February 22

SPICE Diode A.C. Parameters L11 February 22

SPICE Diode Static I-V Id,ext (A) Vd,ext (V) L11 February 22

Small signal diode Z-parameter** L11 February 22

SPICE Diode Re{Z} Re{Z} (Ohms) Frequency (Hz) (2pTT)-1 1 mA 10 mA CJ0 = 1E-12 VJ = 0.75 M = 0.5 TT = 1E-9 (2pTT)-1 1 mA 100 pA 1 nA 10 nA 100 nA 10 mA 100 mA L11 February 22

Small signal low and high freq. limits for Z-par.** L11 February 22

SPICE Diode Temp. Eqs.1 L11 February 22

Corrections in some versions of SPICE L11 February 22

SPICE Diode Temp. Pars.1 PARAMETER definition and units default value XTI IS temperature exponent 3.0 TIKF ikf temperature coefficient (linear) °C -1 0.0 TRS1 rs temperature coefficient (linear) °C -1 0.0 TRS2 rs temperature coefficient (quadratic) °C -2 0.0 TBV1 bv temperature coefficient (linear) °C -1 0.0 TBV2 bv temperature coefficient (quadratic) °C -2 0.0 T_ABS absolute temperature °C T_MEASURED measured temperature °C T_REL_GLOBAL relative to current temperature °C T_REL_LOCAL Relative to AKO model temperature °C L11 February 22

Thermal Resistance L11 February 22

Self-Heating Effects Id (A) Vd,ext = Vd + Id*RS 348K < TNOM < 300K 10 mW 20 mW 30 mW 40 mW 50 mW 60 mW 70 mW 80 mW Rth = 0 K/W , RS = 0.32 W Rth = 600 K/W, RS = 1 W L11 February 22

Self-Heating Effects SPICE models the IS, etc. the same for all power dissipations. The effect of diode self-heating is to increase the current at all voltages. In this case, an Rth of 600K/W gave nearly the same simulation as re-setting RS from 1 Ohm to 0.32 Ohm. The diode Tj is different at all curr. L11 February 22

PiN Diode PiN: Na >> Nint (= N-) & Nint << Nd Wi = Intrinsic region (metall.) width Em,P-T = Peak field mag. when xn = Wi Vbi = fi = Vtln(NaNd/ni2) Vbi,int = fi,int = Vtln(NaNint/ni2) VHL = Vtln(Nd/Nint), the offset at N+N- Vbi = Vbi,int + VHL VPT = applied voltage when xn = Wi L11 February 22

PiN Diode Depletion Fields Normalized Position, x’ = x/Wi Normalized Field, E/Em,P-T dx’p dx’n x’n -x’p L11 February 22

PiN Diode Depletion Conditions L11 February 22

CV data and N(x) calculation L11 February 22

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 L11 February 22

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 L11 February 22

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. L11 February 22

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. L11 February 22

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 L11 February 22

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) L11 February 22

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). L11 February 22

Additional Project 1 Actions What forward voltage range actually fits the standard CV model? Hint: this will be for Va > VPT. What auxiliary circuit would you add in order to model the diode for operation at Va < VPT? L11 February 22

2/24 and 3/1 class Project workday on 2/24 – no class Meet on 3/1 in 212 ELB Be sure you have a gamma account and can access iccap. If problems, send questions to helpdesk@uta.edu We will start using iccap and have a demonstration. Check project web page for updates L11 February 22

References 1 OrCAD PSpice A/D Manual, Version 9.1, November, 1999, OrCAD, Inc. 2 Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. L11 February 22