2006 INTERNATIONAL RF AND MICROWAVE CONFERENCE PROCEEDINGS, SEPTEMBER 12 - 14, 2006, PUTRAJAYA, MALAYSIA

Microwave Characterization of Silicon Wafer Using RectangularDielectric Waveguide

Kamariah Ismail1, Noor Hasimah Baba1, Zaiki Awang2 and Mazlina Esa3

'Faculty of Electrical Engineering, 2Microwave Technology Centre,Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

3 Department of Radio Communication Engineering, Faculty of Electrical Engineering,Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Darul Takzim, Malaysia

qamariah79@yahoo.com, hasimah6O84@yahoo.com, zaiki437@salam.uitm.edu.my, mazlina.esa@ieee.org

Abstract - A non-destructive and easy to use method ispresented to characterize p-type and n-type siliconsemiconductor wafers using a rectangular dielectricwaveguide measurement (RDWG) system. Themeasurement system consists of a vector networkanalyzer (VNA), a pair of coaxial cable, coaxial towaveguide adapter and dielectric-filled standard gainhorn antenna. In this method, the reflection andtransmission coefficients, Si, and S21, were measured forsilicon wafer sandwiched between the two Teflon, thedielectric that filled the standard gain horn antenna. Itwas observed that, the dielectric constant of the siliconwafers are relatively constant, varying slightly over thefrequency range of 9 to 12 GHz. The loss factor, losstangent and conductivity of the doped wafers are higherthan the undoped type.

Keywords: Microwave characterization, rectangulardielectric waveguide, silicon wafer.

1. Introduction

The advancement in the semiconductor processingand device development has led to the feasibility of themonolithic microwave integrated circuit (MMIC),where all passive and active components required for agiven circuit can be grown or implanted in thesubstrate. The substrate of an MMIC must be asemiconductor material to accommodate thefabrication of active devices [1]. The semiconductorcharacteristics such as permittivity, resistivity,conductivity and mobility must be evaluated since atmicrowave frequencies these properties may changesignificantly due to dielectric loss or other undesiredspurious effects such as electromagnetic coupling thusposing problems for high frequency IC designers. Thedielectric loss which contributed to the increase inpermittivity and conductivity value is associated withformation of dipoles due to electronic and ionicpolarization.

For this reason, silicon semiconductor wafer ischosen as the sample in this study. Silicon is one of themost common substrate for high frequency ICs. Inaddition, silicon wafer can be considered a perfect

planar sample due to its single-crystal property, whichhave a high degree of regular geometric periodicitythroughout the entire volume of material and arecapable of being cleaved at precise planes [2]. Thusthis technique is suitable which allows reflection andtransmission measurements for normal incidence.

To date, various techniques have been reported forcharacterizing semiconductors at microwavefrequencies. These include cavity and waveguidemethods. The microwave bridge with the dielectricwaveguide technique has been used by Coue et. al [3],Roy et. al [4] and Datta et. al [5]. The disadvantage ofthese methods is that it is necessary to machine thesample so as to fit the waveguide cross section withnegligible air gap.

The research presents a RDWG method formeasurement of scattering parameters ofsemiconductor wafers at microwave frequencies usingreflection and transmission techniques. The values ofthe complex permittivity, loss tangent, conductivity,skin depth and other electrical properties of the deviceunder test (DUT) can be extracted from thesemeasured scattering parameters.

This technique provides an alternative techniquefor measuring scattering parameters and complexpermittivity where other methods may subject todifficulties due to sample dimensions and positioningproblems.

2. Theory

Every material has a unique set of electricalcharacteristics that are dependent on its dielectricproperties. Permittivity is a quantity used to describedielectric properties of materials under the influence ofelectromagnetic waves with reflection at interfaces andthe attenuation of wave energy within those materials.In frequency domain, the complex relative permittivityE*of a material to that of free space can be expressedas follows [6]: -

8* = 8' - jg" F-E

(1)

0-7803-9745-2/06/$20.00 (©)2006 IEEE. 411

8* YS I£ = Ys0

YoIk+ r) (5)

where

E relative permittivity of the material,g, dielectric constant,E =-loss factor,co the permittivity of free space,cy the conductivity of the material,o angular frequency ofthe field,D electric flux density or displacement andE electric field intensity.

The real part, E is referred to as the dielectricconstant and represents stored energy when thematerial is exposed to an electric field, while thedielectric loss factor, , which is the imaginary part,determine the energy absorption and attenuation.

When a linearly polarized, uniform plane wave isnormally incident on the sample of thickness, ds as

shown by Figure 1, the incident wave is partiallyreflected, transmitted and absorbed by the sample.The reflected signal and transmitted signal are

comprised of an infinite number of components due tomultiple reflections between the air/sample. The DUTis assumed to be planar of infinite extent laterally so

that diffraction effects at the edges can be neglected,thus the total reflected signal, SI I and transmittedsignals, S21 are given respectively by [7]:

Sl1 S21

d,

Figure 1: Schematic diagram of planar sample

and

Sl1

S21 =

F- Fexp( - 2y5d,)1 F2 exp( 2y5d,)

(1 - F2)exp( - y5d,)F2exp(-2y5d,)

where y = 02(j/,) represents the propagation constantof free space, and Xo is the free-space wavelength. Theequations (1) to (5) will be the basis to the calculationof complex permittivity of silicon wafer in thisresearch. By using equations (3) through (5),calculated S'lI and SC2l can be expressed in terms of £but £ cannot be expressed explicitly in terms of SI,and S21, so it is necessary to find it iteratively byassuming a guess value for the complex permittivity ofthe sample. This is done by using a zero findingtechnique which finds the zeros of the error function.The error function is defined as;

E= Sn l-Sc + s M-SC (6)

where Sm and S' are the measured and calculated valuesof the complex transmission coefficients, respectively.The Muller method with deflation is used forcalculation of zeros of the error function [8].

3. Measurement System

The RDWG measurement system based on

transmission and reflection measurement is as shownin Figure 2. It consists of a Wiltron 37269B vectornetwork analyzer (VNA), a pair of coaxial cables,coaxial to waveguide adapter, standard metallicwaveguide (WR-90) and dielectric filled standard-gainhorn antennas. The WR-90 carrying TEBo mode is usedas a launcher and for launching electromagnetic wave

purposes into RDWG, it is double-tapered at one endand inserted into the WR-90 waveguide throughstandard-gain horn antennas. The dielectric materialused for RDWG is made of poly-tetra-fluoro-ethylene(PTFE) and its length beyond the horn antenna is 4.5cm. Its cross-sectional area is 22.86 mm x 10.16 mm,which is of the same cross-sectional area as themetallic waveguide. The PTFE material is chosenbecause it has low dielectric constant and very lowloss.

(3) In evaluating the measurement results, it isassumed that the phase velocity of a wave propagatingin a dielectric waveguide is equal to the velocity of a

plane wave in unbounded dielectric medium and thedielectric constant of the device under test (DUT) is

(4) greater or at least equal to the dielectric constant of thethe dielectric that filled the waveguide [9].

where y, is the propagation constant in the sample andis the reflection coefficient of the sample/air

interface. Both are functions of the complexpermittivity ofthe sample, F* and given by: -

412

F- =a=c/oi°

(2)

Computer

VNA L zz Printer

DUT

dielectric filled horn antenna

Figure 2: RDWG Measurement Setup.

3.1 CalibrationThe internal TRL (through, reflect, line)

calibration model ofVNA is used for calibration of theRDWG measurement system. The through standard isrealized by keeping the distance between the twoRDWGs equal to zero. Reflect standards for port 1and port 2 are obtained by mounting a metal platebetween transmit and receive RDWGs. The linestandard is achieved by separating two RDWGs by adistance which is approximately equal to quarterwavelength at the mid-band frequency. After TRLcalibration, the through standard was measured. Theamplitude and phase of S21 (or S12) was within 0.00 +0.06 dB and 0.00 + 0.8°, respectively. For the metalplate, the amplitude and phase of S11 (or S22) were 0.00+ 0.06 dB and 180 + 1.90 respectively.

3.2 ValidationValidation of measurement system was done by

measuring complex permittivity of commonly usedreference samples. Modelling and simulation of themeasurement system was also carried out using CSTMicrowave Studio software package.

4. Results and Discussion

The DUT used in this experiment are doped three-inch-diameter n-type, p-type of 0.60 mm thickness and(100) orientation and an undoped two-inch-diametersilicon wafers.

Figure 3 shows the measured values of dielectricconstant at 9 to 12.0 GHz, for the n-type, p-type andundoped silicon wafers. The values are between 10.85to 12.20, 11.43 to 12.26 and 11.43 to 12.03respectively. These compare favourably to thosereported by Roy et al. [4] who obtained valuesbetween 11.01 to 11.77 for p-type samples, whilePozar [1] quoted figures of 1 1.9-jO.004 for theundoped type. Differences in our values and thosequoted in literature are due to the errors in themagnitude and phase of the S11 and S21, and the air-gapeffect of the sample assembly.

Figure 4 shows the loss factor with valuesbetween 20.71 to 26.98 for the n-type, 12.44 to 16.23for the p-type and 0.02 to 0.11 for the undoped siliconwafer. The presence of the doping material caused theincrease in values of the loss factor, whereby the lossfactor of the n- type is higher than the p-type. Hencethe loss tangent of n-type is higher than the p-type andan undoped wafer as illustrated by the Figure. 5

From the measured results, the conductivity of thesilicon wafers can be obtained by the followingrelationship: -

a = CO£o£ = 27Zf&£o (8)

where E0 is 8.854 x 10-12 Farad/meter and E " is theimaginary part of the complex permittivity. Thepresence of the doping material is the contributingfactor to the high conductivity values. Theconductivities in the wafer are caused by the rotationof the dipoles as they attempt to align with the appliedfield when its polarity is rotating [10]. For the case ofsilicon wafers, both electrons and holes contribute tothe electrical conduction, the conductivity ofsemiconductor can be expressed as [11]: -

c = enCle + eP/h (9)

where e =1.60xlO-19C and n and p are the electron andholes concentration and t =1350 cm2/V-s and th =480cm2/V-s are the mobility of the electron and holesrespectively [11] - [12]. Table 1 illustrates the dopingconcentration for the two wafers and it shows that thep-type has more doping concentration than the n-typewafer.

Table 1: Doping concentration of silicon wafers.

Silicon Wafer Type DopingConcentration/cm3

3-inch n-type 6.375 x 10143-inch p-type 1.08 x 1015

Figure 6 is a plot of the conductivity whichexhibits a trend of increase conductivity with increasefrequency. The values were between 8.13 to 8.31 S/mfor the p-type and 13.51 to 13.83 S/m for the n-type.The presence of the doping material is the contributingfactor to this high conductivity.

Figure 7 gives the depth of skin effect for thesilicon wafers. The skin depth, 6 is defined as thedepth at which the amplitude of the electric field isreduced to 36.79% of the original value and isdetermined from the following equation [6],

a + j8 = j(2;r I e) (9)

413

where 6 is given by the inverse of the attenuationconstant (1/oc). It is observed that 6, at 10 GHz, forthe p-type was 2.52mm while the n-type was reducedto 2.12mm because of higher loss tangent.

5. Conclusion

A non-destructive and easy to use measurementmethod which gives accurate values of complexpermittivity of silicon wafers at microwave frequencyis developed. From the values of complex permittivity,the electrical characteristics such as resistivity,conductivity and skin depth could be obtained. Theresults agree well with that measured by otherconventional method and also with the values given bythe wafer manufacturer.

This approach and set-up can be applied to othersamples in the form of solid and liquid.

Cu40,000

0C.)

C.)

12.512.011.511.010.510.0

en4-

F-

2.52.01.51.00.50.0

9.0 10.0 11.0 12.0Frequency in GHz

-- Silicon-n-type Silicon-p-typeSilicon-undoped

Figure 5: Plot of loss tangent versus frequency.

E

.15.0

Z 10.0.2Z 5.0o0o 0.00)

9.0 10.0 11.0 12.0

Frequency in GHz

, * _, * .

9.0 10.0 11.0 12.0Frequency in GHz

-- Silicon-n-type

Undoped Silicon>Silicon-p-type -+ Silicon-n-type

Silicon-undopedSilicon-p-type

Figure 3: Plot of dielectric constant versus frequency.

30.00O 20.0U-u) 10.00,0-J

0.0

Figure 6: Plot of conductivity versus frequency.

EE._

sQ*0'a._

cn9.0 10.0 11.0 12.0

Frequency in GHz-* Silicon-n-type + Silicon-p-type

Undoped-Silicon

3.02.52.01.51.00.50.0

9.0 10.0 11.0 12.0

Frequency in GHz

- Silicon-n-type Silicon-p-type

Figure 4: Plot of loss factor versus frequency. Figure 7: Plot of skin depth versus frequency.

414

*. --*=7*--#-

-01

References

[1] D. M. Pozar, Microwave Engineering, ThirdEdition, U.S.A, Wiley, 2005.

[2] G. S. Brady, H. R. Clauser and J. A. Vaccari,Materials Handbook, Fifteenth Edition, McGraw-Hill, U.S.A, 2002.

[3] E. Coue and J.P Chausse, "Microwave Method forElectrical Measurements of Semiconductors:Theory and Measurements," in SemiconductorScience and Technology, vol. 15, No.2, pp.178-183, Feb. 2000.

[4] P.K. Roy and A. N. Datta, "Application ofQuarter-Wave Transformers for PreciseMeasurement of Complex Conductivity ofSemiconductors," in IEEE Trans. on MicrowaveTheory and Techniques, vol. 37, pp.l144-146, Feb.1974.

[5] A.N. Datta and B.R Nag, "Techniques for theMeasurement of Complex MicrowaveConductivity and the Associated Errors," IEEETrans. on Microwave Theory and Techniques, vol.MTT-18, No.3, pp.162-166, March 1970.

[6] A. von Hippel, Dielectric and Waves, NewEdition, Artech House, London, 1995.

[7] D.K Ghodgaonkar,and V.V. Varadan, "Free SpaceMeasurement of Complex Permittivity andComplex Permeability of Magnetic Materials atMicrowave Frequencies," in IEEE Transaction onInstrumentation and Measurement, vol. 19, pp 387- 394, April 1990.

[8] R. J. Schilling and S. L. Haris, Applied NumericalMethods for Engineers, Brooks/Cole PublishingCompany, USA, pp212-215,2000.

[9] Z. Abbas, R.D. Pollard and R.W. Kelsall,"Complex Permittivity Measurements at Ka-BandUsing Rectangular Dielectric Waveguide," inIEEE Transaction on Microwave Theory andTechniques, vol. 50, pp 1334-1342, Oct. 2001.

[10] S.O. Kasap, Principles of Electronics Materialsand Devices, Second Edition, McGraw-Hill,U.S.A., 2002.

[11] B.G. Streetman, Solid State Electronic Devices,Prentice Hall, U.S.A, pp83, 1980.

[12] D.A. Neamen, Semiconductor Physics andDevices, McGraw-Hill, U.S.A., pp 713, 2003.

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