EE5342 Semiconductor Device Modeling and CharacterizationLecture 11 - Spring 2005Professor Ronald L. Carterronc@uta.eduhttp://www.uta.edu/ronc/

Project 1Some 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

Additional Project 1 ActionsDevelop 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

SPICE Diode A.C. Parameters

SPICE Diode Static I-V

Small signal diodeZ-parameter**

SPICE Diode Re{Z}

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

SPICE Diode Temp. Eqs.1

Sheet1

IS(T) / IS =exp(T/Tnom-1)EG/(NVt)(T/Tnom)^(XTI/N )

ISR(T) / ISR =exp(T/Tnom-1)EG/(NRVt)(T/Tnom)^(XTI/NR )

IKF(T) / IKF =(1 + TIKF(T-Tnom))

BV(T) / BV =(1 + TBV1(T-Tnom) + TBV2(T-Tnom)^2)

RS(T) / RS =(1 + TRS1(T-Tnom) + TRS2(T-Tnom)^2)

VJ(T) / VJ =T/Tnom - 3Vtln(T/Tnom) - Eg(Tnom)T/Tnom + Eg(T)

Eg(T) =1.16 - .000702T^2/(T+1108)

CJO(T) / CJO ={1+M[4E-4*(T-Tnom)+(1-VJ(T)/VJ)]}

Sheet2

Sheet3

Corrections in some versions of SPICE

Sheet1

exp{[Eg(Tn)/Vtn - Eg(T)/Vt]/N}/*(T/Tnom)^(XTI/NR)

exp{[Eg(Tn)/Vtn - Eg(T)/Vt]/NR}/*(T/Tnom)^(XTI/NR)

Sheet2

Sheet3

SPICE Diode Temp. Pars.1PARAMETER definition and units default value

XTI IS temperature exponent 3.0TIKF ikf temperature coefficient (linear) C -1 0.0TRS1 rs temperature coefficient (linear) C -1 0.0TRS2 rs temperature coefficient (quadratic) C -2 0.0TBV1 bv temperature coefficient (linear) C -1 0.0TBV2 bv temperature coefficient (quadratic) C -2 0.0T_ABS absolute temperature CT_MEASURED measured temperature CT_REL_GLOBAL relative to current temperature CT_REL_LOCAL Relative to AKO model temperature C

Thermal Resistance

Self-Heating Effects

Self-Heating EffectsSPICE 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.

PiN DiodePiN: Na >> Nint (= N-) & Nint

PiN Diode Depletion Fields

PiN Diode Depletion Conditions

CV data and N(x) calculation

Chart2

76179474252496400

41575903140506600

25288919533076300

17996846674974400

15409254595284500

15711599253346500

18284166477075100

23021857866005000

30006134913259300

39359408496016100

51172745128483200

65521972580864800

82500668899263900

102161300757465000

124534413489029000

149736963828794000

177570539865575000

208046562807189000

241659667289905000

278109750566510000

316731141125134000

357825561061480000

403123623495584000

450263134192780000

499543654160092000

552501667434644000

607917750309954000

666598145228303000

727093155293900000

791190075201240000

857789767889100000

925195666733583000

991044494377849000

1066748322886010000

1146210801796520000

1218876504818400000

1301165103620520000

1382792175937530000

1475144221265380000

1564671215674230000

1648052671827040000

1740632560334500000

1844057575191250000

1936134437961230000

2037752113234020000

2150424088380240000

2243614647203310000

2345091174504050000

2456050131889530000

2577857689006500000

2666261722486660000

2760834643907930000

2915254014404290000

3028381935758780000

2972226718006310000

2865130720237540000

2352811682346180000

1433787944939490000

657746961118888000

249132341366454000

91511461412594600

37777054661100900

20265833256946600

14834063265768900

12906034553242000

10392320799894800

7173304950785510

5287554094372750

4554330881048940

3349742313706200

SRD_CV

A1. Develop extraction techniques on the data below for determining CJ0, VJ and M.

A2. Use these extraction techniques on the data below to determine estimates for

CJ0

VJ

M

B1. If the area of this junction is known to be 804 sq. microns, determine the

doping concentration on the lightly doped side as a function of

depletion width.

B2. Is the function determined in B1 consistent with the value of M determined in A2?

Why, and should a different model be used in SPICE for this diode?

epr =11.7

epso =8.85E-14

q =1.60E-19

A =8.04E-06

VextCjNx

-6.601.62E-135.14E-05

-6.501.62E-137.62E+165.13E-05

-6.401.63E-134.16E+165.11E-05

-6.301.64E-132.53E+165.07E-05

-6.201.66E-131.80E+165.01E-05

-6.101.69E-131.54E+164.92E-05

-6.001.72E-131.57E+164.84E-05

-5.901.75E-131.83E+164.75E-05

-5.801.78E-132.30E+164.69E-05

-5.701.80E-133.00E+164.63E-05

-5.601.81E-133.94E+164.59E-05

-5.501.83E-135.12E+164.56E-05

-5.401.84E-136.55E+164.54E-05

-5.301.84E-138.25E+164.52E-05

-5.201.85E-131.02E+174.50E-05

-5.101.85E-131.25E+174.49E-05

-5.001.86E-131.50E+174.48E-05

-4.901.86E-131.78E+174.47E-05

-4.801.87E-132.08E+174.46E-05

-4.701.87E-132.42E+174.46E-05

-4.601.87E-132.78E+174.45E-05

-4.501.87E-133.17E+174.45E-05

-4.401.87E-133.58E+174.44E-05

-4.301.88E-134.03E+174.44E-05

-4.201.88E-134.50E+174.44E-05

-4.101.88E-135.00E+174.43E-05

-4.001.88E-135.53E+174.43E-05

-3.901.88E-136.08E+174.43E-05

-3.801.88E-136.67E+174.42E-05

-3.701.88E-137.27E+174.42E-05

-3.601.88E-137.91E+174.42E-05

-3.501.88E-138.58E+174.42E-05

-3.401.89E-139.25E+174.42E-05

-3.301.89E-139.91E+174.42E-05

-3.201.89E-131.07E+184.41E-050.00000804

-3.101.89E-131.15E+184.41E-05

-3.001.89E-131.22E+184.41E-05

-2.901.89E-131.30E+184.41E-05

-2.801.89E-131.38E+184.41E-05

-2.701.89E-131.48E+184.41E-05

-2.601.89E-131.56E+184.41E-05

-2.501.89E-131.65E+184.41E-05

-2.401.89E-131.74E+184.41E-05

-2.301.89E-131.84E+184.40E-05

-2.201.89E-131.94E+184.40E-05

-2.101.89E-132.04E+184.40E-05

-2.001.89E-132.15E+184.40E-05

-1.901.89E-132.24E+184.40E-05

-1.801.89E-132.35E+184.40E-05

-1.701.89E-132.46E+184.40E-05

-1.601.89E-132.58E+184.40E-05

-1.501.89E-132.67E+184.40E-05

-1.401.89E-132.76E+184.40E-05

-1.301.89E-132.92E+184.40E-05

-1.201.89E-133.03E+184.40E-05

-1.101.89E-132.97E+184.40E-05

-1.001.89E-132.87E+184.40E-05

-0.901.89E-132.35E+184.40E-05

-0.801.89E-131.43E+184.40E-05

-0.701.90E-136.58E+174.39E-05

-0.601.90E-132.49E+174.39E-05

-0.501.90E-139.15E+164.38E-05

-0.401.91E-133.78E+164.36E-05

-0.301.93E-132.03E+164.30E-05

-0.201.98E-131.48E+164.21E-05

-0.102.03E-131.29E+164.10E-05

0.002.10E-131.04E+163.97E-05

0.102.20E-137.17E+153.79E-05

0.202.37E-135.29E+153.51E-05

0.302.67E-134.55E+153.12E-05

0.403.15E-133.35E+152.64E-05

0.504.41E-131.89E-05

4.41E-13

SRD_CV

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4.41E-13

MBD0006D92E.unknown

Chart1

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SRD_CV

A1. Develop extraction techniques on the data below for determining CJ0, VJ and M.

A2. Use these extraction techniques on the data below to determine estimates for

CJ0

VJ

M

B1. If the area of this junction is known to be 804 sq. microns, determine the

doping concentration on the lightly doped side as a function of

depletion width.

B2. Is the function determined in B1 consistent with the value of M determined in A2?

Why, and should a different model be used in SPICE for this diode?

epr =11.7

epso =8.85E-14

q =1.60E-19

A =8.04E-06

VextCjNx

-6.601.62E-135.14E-05

-6.501.62E-137.62E+165.13E-05

-6.401.63E-134.16E+165.11E-05

-6.301.64E-132.53E+165.07E-05

-6.201.66E-131.80E+165.01E-05

-6.101.69E-131.54E+164.92E-05

-6.001.72E-131.57E+164.84E-05

-5.901.75E-131.83E+164.75E-05

-5.801.78E-132.30E+164.69E-05

-5.701.80E-133.00E+164.63E-05

-5.601.81E-133.94E+164.59E-05

-5.501.83E-135.12E+164.56E-05

-5.401.84E-136.55E+164.54E-05

-5.301.84E-138.25E+164.52E-05

-5.201.85E-131.02E+174.50E-05

-5.101.85E-131.25E+174.49E-05

-5.001.86E-131.50E+174.48E-05

-4.901.86E-131.78E+174.47E-05

-4.801.87E-132.08E+174.46E-05

-4.701.87E-132.42E+174.46E-05

-4.601.87E-132.78E+174.45E-05

-4.501.87E-133.17E+174.45E-05

-4.401.87E-133.58E+174.44E-05

-4.301.88E-134.03E+174.44E-05

-4.201.88E-134.50E+174.44E-05

-4.101.88E-135.00E+174.43E-05

-4.001.88E-135.53E+174.43E-05

-3.901.88E-136.08E+174.43E-05

-3.801.88E-136.67E+174.42E-05

-3.701.88E-137.27E+174.42E-05

-3.601.88E-137.91E+174.42E-05

-3.501.88E-138.58E+174.42E-05

-3.401.89E-139.25E+174.42E-05

-3.301.89E-139.91E+174.42E-05

-3.201.89E-131.07E+184.41E-050.00000804

-3.101.89E-131.15E+184.41E-05

-3.001.89E-131.22E+184.41E-05

-2.901.89E-131.30E+184.41E-05

-2.801.89E-131.38E+184.41E-05

-2.701.89E-131.48E+184.41E-05

-2.601.89E-131.56E+184.41E-05

-2.501.89E-131.65E+184.41E-05

-2.401.89E-131.74E+184.41E-05

-2.301.89E-131.84E+184.40E-05

-2.201.89E-131.94E+184.40E-05

-2.101.89E-132.04E+184.40E-05

-2.001.89E-132.15E+184.40E-05

-1.901.89E-132.24E+184.40E-05

-1.801.89E-132.35E+184.40E-05

-1.701.89E-132.46E+184.40E-05

-1.601.89E-132.58E+184.40E-05

-1.501.89E-132.67E+184.40E-05

-1.401.89E-132.76E+184.40E-05

-1.301.89E-132.92E+184.40E-05

-1.201.89E-133.03E+184.40E-05

-1.101.89E-132.97E+184.40E-05

-1.001.89E-132.87E+184.40E-05

-0.901.89E-132.35E+184.40E-05

-0.801.89E-131.43E+184.40E-05

-0.701.90E-136.58E+174.39E-05

-0.601.90E-132.49E+174.39E-05

-0.501.90E-139.15E+164.38E-05

-0.401.91E-133.78E+164.36E-05

-0.301.93E-132.03E+164.30E-05

-0.201.98E-131.48E+164.21E-05

-0.102.03E-131.29E+164.10E-05

0.002.10E-131.04E+163.97E-05

0.102.20E-137.17E+153.79E-05

0.202.37E-135.29E+153.51E-05

0.302.67E-134.55E+153.12E-05

0.403.15E-133.35E+152.64E-05

0.504.41E-131.89E-05

4.41E-13

SRD_CV

4.41E-13

MBD0006D92E.unknown

Estimating Junction Capacitance ParametersFollowing L29 EE 5340 Fall 2003If CJ = CJO {1 Va/VJ}-MDefine y {d[ln(CJ)]/dV}-1A plot ofy = yi vs. Va = vi hasslope = -1/M, andintercept = VJ/MF

Derivatives DefinedThe 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)/2Equation 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)/2Equation A1.2

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.

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.

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

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)

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).

Additional Project 1 ActionsWhat 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?

2/24 and 3/1 classProject workday on 2/24 no classMeet on 3/1 in 212 ELBBe sure you have a gamma account and can access iccap. If problems, send questions to helpdesk@uta.eduWe will start using iccap and have a demonstration.Check project web page for updates

References1 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.