LAB III. CONDUCTIVITY & THE HALL EFFECT

Transcription

1 LA III. CONDUCTIVITY & THE HALL EFFECT. OJECTIVE In this lab, we will emirically calculate the resistivity (using the Van der Pauw Methd), alng with the ding density and tye (using the Hall effect) f a small square iece f ded silicn. Frm these quantities the cnductivity and the mbility will be determined. These quantities frm a art f the descritin f a ded iece f single-crystalline silicn, and they are essential quantities t knw when designing devices based these secialied materials. 2. OVERVIEW In this lab, we have built a fur-rbe bard that hlds a square iece f ded silicn wafer. The wafer has metal cntacts laced near its fur crners, each wired u t a lead (see Figure 3.) Tw SMUs will be used via LabVIEW. One is used as a current surce, t drive current thrugh the wafer. Anther is used as a vltmeter t measure vltage between tw cntacts f the wafer. In the first art f the lab, this setu is used t erfrm the van der Pauw Methd f measuring the resistivity, ρ, f the samle. In the secnd art, a similar setu - alng with tw bar magnets - are used t create the Hall effect and determine the Hall vltage and Hall cefficient. These measurements will be used t find the ding density, dant tye, and the majrity carrier mbility (Hall mbility) f the silicn samle. Infrmatin essential t yur understanding f this lab:. An understanding f cnductivity using the cncets f current density and electric field (i.e. a versin f Ohm s Law.) 2. Hw the Van Der Pauw Methd wrks. 3. Hw the Hall Effect wrks. 4. Hw ne can calculate characteristic arameters f a samle f silicn using these methds. Materials necessary fr this Eeriment:. Standard testing statin 2. Tw anana Plug leads 3. One fur-rbe bard with ded Si wafer 4. Tw bar magnets ~ Weber / m 2 ( Weber = V-s) Lab III: Cnductivity and Hall Effect Page

2 3. ACKGROUND INFORMATION 3. CHART OF SYMOLS Table. Symbls used in this lab. Symbl Symbl Name Units h + Hle Psitive charge article e - electrn Negative charge article q magnitude f electrnic charge C hle cncentratin (number h + / cm 3 ) n electrn cncentratin (number e - / cm 3 ) ni intrinsic carrier cncentratin ND Dnr cncentratin (number dnrs / cm 3 ) NA Accetr cncentratin (number accetrs / cm 3 ) kb ltmann's cnstant jules / K T temerature K Eg Energy ga f semicnductr ev J Current density A / cm 2 E Electric field V / cm cnductivity ( - cm) - resistivity - cm mbilities cm 2 / V-sec vd drift velcity cm / sec magnetic field Weber / m 2 Nv valence band effective density f states cm -3 Nc cnductin band effective density f states cm -3 Lab III: Cnductivity and Hall Effect Page 2

3 3.2 CHART OF EQUATIONS Table 2. Equatins used in this lab. Equatin Name Frmula Intrinsic carrier equatin 2 ( Eg / 2kT ) n i N c N v e 2 Charge Neutrality + ND = n + NA 3 Law f Mass Actin n = ni 2 (T) 4 Current density J J J E E 5 Cnductivity due t n n 6 Cnductivity due t n n q n q n 7 Cnductivity f a material q n n q t ln 2 8 Resistivity frmula fr the van der Pauw,34 23,4 F R 2 2 R 9 Resistivity frmula in terms f sheet resistance R s t 0 Current density J E Drift velcity v E 2 Lrent frce (y-directin) F = qv 3 Induced Hall Field ( E y ) qe y qv 4 E-field equatin fr the semicnductr samle E y J q 5 Hall cefficient R H q Lab III: Cnductivity and Hall Effect Page 3

4 6 Induced E-feild E R y H J 7 Hall vltage V E w 8 Current density J I tw H y / 9 Derivatin f the carrier density in a -tye material q I t V H 20 Derivatin f Hall cefficient R H VHt I 2 Derivatin f the mbility q R H 3.3 CONDUCTIVITY OF A SEMICONDUCTOR One f the mst basic questins asked in semicnductr devices is what current will flw fr a given alied vltage?, r equivalently what is the current density fr a given electric field? fr a unifrm bar f semicnductr (See Figure.) The answer t this questin is a frm f Ohm's law (see Sectin 3.4 in Streetman and anerjee): J = J n + J = σ n*e + σ *E (4) Here, J is the current density (A/cm 2 ), r net charge ging thrugh the crsssectinal area f the bar, er unit time. E is the alied electric field (V/cm), r vltage acrss the length f the bar. Sigma, σ, the rrtinality factr between J and E, is tyically measured in units f ( -cm) -. One can read σ as J/E r hw much current asses thrugh a material fr a given a vltage acrss it. We can see the term σ is a measure f hw well a material cnducts electric charge. It means that fr a given E, a material with a higher σ cnducts mre current. Naturally, σ is called cnductivity, and is an intrinsic rerty f a material. Lab III: Cnductivity and Hall Effect Page 4

5 Crss-sectinal area thrugh which net current flws, J= I/A. Length acrss which vltage is alied; V/L = E. Figure. ar f semicnductr. The n and subscrits refer t cntributin t the current density frm electrns and hles, resectively. This equatin tells us that the ttal current density J is equal t the sum f the electrn and hle current densities. Thse are given by the electrn cnductivity * E lus the hle cnductivity * E. Nte that the cnductivity increases as the numbers f electrns and hles increases, due t: σ n = q*n* μ n (5) σ = q** μ (6) σ = σ n + σ = q*n* μ n + q** μ (7) Remember q = Culmbs and n and are electrn and hle densities (number er cm 3.) The quantities μ n and μ are called the electrn and hle mbilities resectively (cm 2 /V-sec). Mbilities describe the average velcity (m/s) er unit electric field that electrns r hles eerience as they ragate thrugh the lattice f the semicnductr. In fact, we write that the electrn and hle average velcities are defined as v n = μ n*e and v = μ *E. Nte that the cnductivity f a semicnductr deends un bth the carrier densities and their mbilities. Cnsequently, it seems that a measurement f the cnductivity can nly be used t find n and if μ n and μ are already knwn. (Nte: The values f n and are related by the law f mass actin (n* = n i2 ) and s we nly need t knw either n r t knw them bth.) It wuld be nice if the mbilities were simle cnstants, but they are nt. μ n and μ are functins f temerature as well as the ding cncentratins (N A and N D) and therefre functins f n and! Frtunately, we knw these functins frm many rir calibratin measurements dne by scientists wrldwide. S a simle measurement f cnductivity still can be used t give us an estimate f n and rvided we at least knw the semicnductr tye (n-tye r -tye). We use the Irwin curves t make the cnnectin between the semicnductr cnductivity and its ding density (N A r N D). Nte that fr -tye material N A ~ and n ~ n i2 /N A; fr n-tye material N D ~ n and ~ n i2 /N D. Figure 2 shws the Irwin curves. It is a lt f Lab III: Cnductivity and Hall Effect Page 5

6 the silicn cnductivity as a functin f either N A r N D assuming that the ther is equal t er. Yu shuld familiarie yurself with it. There are many measurement methds t find the cnductivity f a samle. One f the mst cmmn methds is called the fur-int rbe methd. We will be ding a variant f the fur-int rbe methd called the van der Pauw methd in this lab. It is a measurement methd fr arbitrarily-shaed samles. The van der Pauw methd is cmmnly used t measure the cnductivity f semicnductrs, articularly fr thin eitaial layers grwn n semi-insulating substrates. Using this methd, yu will measure the cnductivity f yur samle. Once yu find the resistivity f the samle, yu can use the Irwin curves t estimate the values f n r. Nte: the van der Pauw methd des nt allw yu t determine the tye f yur semicnductr samle, yu ll have t use the Hall Effect t determine tye, then find the ding density. Fr eamle, if yu calculated a cnductivity f 0. mh/cm (frm resistivity is 0 hm-cm) using van der Pauw methd, and fund ut the samle was -tye frm Hall Effect results, then frm the Irwin curves yu can say N A wuld be arimately cm -3. Yu will cmare the values f ding density and cnductivity frm the van der Pauw methds with the values derived frm the Hall Effect measurements. Lab III: Cnductivity and Hall Effect Page 6

7 Resistivity N-tye Resistivity P-tye Resistivity.E+04.E+03.E+02 Resistivity (Ohm-cm).E+0.E+00 n-tye -tye.e-0.e-02.e-03.e+2.e+3.e+4.e+5.e+6.e+7.e+8.e+9.e+20 Dant Cncentratin (cm -3 ) Figure 2. Irwin curve fr singly ded silicn at 300K. Lab III: Cnductivity and Hall Effect Page 7

8 3.4. THE VAN DER PAUW METHOD L. J. van der Pauw rved that the resistivity f an arbitrarily shaed samle culd be estimated frm measurements f its resistance rvided the samle satisfied the fllwing cnditins: ) cntacts are at the bundary; 2) cntacts are small; 3) the samle is unifrmly ded and unifrmly thick; 4) there are n hles in the samle. He derived a crrectin factr, f, t use in that estimatin. In the van der Pauw methd, and in all 4-int rbe methds, a current is frced between tw cntacts (call them cntacts A & ) while the vltage is measured between tw different cntacts (C & D); See Figure 3. It is ften the case that UG students wnder why the vltage is NOT measured between cntacts A &. The thught is: Wuldn t yu get the resistance by simly dividing V A by I A? The answer is: Yu wuld get a resistance, but it wuld be the WRONG resistance. The resistance that is crrect is V CD/I A. V A/I A gives t large a resistance because it always includes smething called the cntact resistance t. The cntact resistance is a resistance that sits eactly at the cntact between the metal rbe (the cntact) and the semicnductr. This resistance has a vltage dr acrss it whenever there is current flwing thrugh it (V cntact=i A*R cntact.) The rblem is that this cntact resistance has nthing t d with the semicnductr cnductivity! Therefre, we d nt want t have V cntact be art f ur measured vltage. We want nly the vltage caused by the cnductivity f ur samle t be divided by I A. Figure 4 shws a schematic diagram f this rblem. y measuring V CD n cntacts with er current flwing thrugh them, we get n vltage dr acrss R cntact and as a result we measure nly the vltage due t the resistivity. Lab III: Cnductivity and Hall Effect Page 8

9 A A Cntacts N Mag. Field D C Thickness t f samle Vltmeter a) b) Figure 3. a) a t view f the samle used in the lab; b) a 3-D view f the ded silicn material t be tested in the lab. I A V CD A C D R cntact ρ R cntact R cntact ρ ρ ρ ρ R cntact Figure 4. Cntact resistances and the resistivity f the silicn samle. The current flwing between cntacts A& causes a vltage dr due t the cntact resistances there, but the fact that n current flws thrugh cntacts C&D allws them t measure just t the vltage due t the resistivity. Lab III: Cnductivity and Hall Effect Page 9

10 Cnsider a ded flat semicnductr samle with an arbitrary shae, with cntacts A,, C, and D alng the erihery as shwn in Fig. 5. The resistance is R A, CD = V CD/I A, where the current I A enters the samle thrugh cntact A and leaves thrugh the cntact and V CD = V C V D is the vltage difference between cntacts C and D. The van der Pauw methd then tells us that the resistivity f the arbitrarily shaed samle is given by: t ln 2 f RA, CD RC, DA (8) where f is a crrectin factr which is a functin f the rati R r = R A,CD/R C,DA. (f is ltted in Fig. 6.) 2 A 3 C 2 4 D Figure 5. Arbitrarily-shaed samle with fur cntacts at the erihery. Fr a symmetrical samle we wuld get R r = and the crrectin factr f =. In rder t measure the resistivity f the samle mre accurately, tyical measurement cnsists f a series f measurement using different current values and different current injectin directin. Lab III: Cnductivity and Hall Effect Page 0

11 Figure 6. f vs. (L. J. van der Pauw, Philis Res. Rrts, 3, -9 (958).) 3.5. HALL EFFECT MEASUREMENTS The Hall Effect yields a direct measure f the majrity carrier density. In the Hall measurement, a unifrm magnetic field,, is alied nrmal t the directin f a current flw (I ). The magnetic field induces a frce n the mving charged articles ushing them in a directin erendicular ( nrmal ) t bth the article flw and. This induces a vltage at the facets where the charges cllect called the Hall vltage as well as infrmatin abut the carrier density. In rder t elain hw the Hall Effect arises, we shall assume a -tye semicnductr having the gemetry shwn in Fig. 7. A vltage V is alied t the hmic cntacts n the frnt and back ( & D) which causes hles t flw in the sitive directin under the field E = V /l. The current is given by J = I / (w t) = σ E ~ σ E = qμ E = qv (0) Lab III: Cnductivity and Hall Effect Page

12 Where σ ~ σ because >> n in -tye materials. The average hle drift velcity is: v E () I + Ey - A C y E t D l I w Figure 7. The fields and vltage larities in -tye silicn fr the Hall effect measurement. In the absence f a magnetic field, the hles flw in the sitive directin. In a magnetic field,, shwn in Fig. 7 t be in the + directin, the hles eerience an additinal frce. F qv (2) MAGNETIC Lab III: Cnductivity and Hall Effect Page 2 that ushes the hles in the negative y directin. The hles thus cllect at the left side f the structure, n surface A and leave behind negatively charged accetrs at the right cntact C. These charges induce an electric field directed in the +y directin that creates an electric field induced frce site t the magnetic frce. N current can flw in the y directin, because nthing is cnnected t cntacts A and C. N current flw, means that the semicnductr must have n net frce in that directin. Therefre, the tw site frces (induced by and E y) must have equal magnitudes and qe y qv r (3)

13 E y J because v = J /q (4) q The Hall cefficient is defined as: R H q (5) S equatin (4) may be re-written as: E y R H J (6) The induced vltage between A & C is called the Hall vltage, V H: V H E y w (7) y using equatins (5), (6) and (7) we can slve fr the carrier density : q I t V H (9) and R H VHt I (20) Thus, can be fund frm a measurement f the Hall vltage, V H, at a current I in a magnetic field, as shwn in Fig. 7. The Hall mbility may be calculated using equatin (6) and the definitin f the Hall cefficient, equatin (5): q R H (2) Net we eamine the effects btained when an n-tye samle is measured. Fr the alied current I shwn in Fig. 6, the electrns will mve in the - directin. The frce due t will ush the electrns in the -y directin t cntact A leaving sitively charged accetrs n the right side (cntact C). Lab III: Cnductivity and Hall Effect Page 3

14 In this case the electric field will int in the -y directin, and the +y cntact C will be sitive relative t the -y terminal A. Thus the larity f the Hall vltage fr and n materials is site. Frm Eq. (9), the sign f the Hall cefficient is als negative fr n-tye material in this gemetry. y understanding these cncets yu shuld be able t identify any unifrmly ded semicnductr s carrier density and tye based n the sign f the Hall vltage. Yu will need this knwledge t successfully cmlete the Lab. If the samle was ideal, Hall vltage shuld be linearly increased with the alied current (Fig. 8). The Hall vltage shuld be linearly increased with the alied magnetic field as well. Mrever, if the samle was ideal (i.e., there is n asymmetry in the samle), there shuld be n hmic dr and the measured vltage is true Hall vltages. Hwever, if the samle was nn-ideal, deending n the asymmetry f the samle, the measured vltages may be shifted due t hmic dr. In this case, the measured vltage is NOT true Hall vltages. Yu must calculate the differences between the vltages measured with and withut the magnetic fields t calculate true Hall vltages. +ve mag. field -tye; -ve mag. field n-tye N mag. field V y -ve mag. field -tye; +ve mag. field n-tye SHIFT DUE TO NON-IDEAL SAMPLE Hall Vltages I Ideal Cnditin, when samle is symmetric and has lw hmic dr alng X directin Practical cnditin, when samle is asymmetric Figure 8. Measured vltages as a functin f the alied currents fr ideal (n hmic dr ) and nn-ideal samle. Lab III: Cnductivity and Hall Effect Page 4

15 4. PREPARATION Please read sectin 3.4 in Streetman and aneerjee and make sure yu understand the van der Pauw and Hall Effect methds discussed in Sectin 3 f this manual. efre cming t the lab, slve the fllwing rblems. Shw wrk clearly and legibly.. Assume rm temerature (300K) a. Calculate the cnductivity f an n-tye Si samle with N D = 30 5 cm -3 and =350 cm 2 /(V-sec.) using the equatins fund in this n manual (Table 2.) Cmare yur answer with the cnductivity value derived frm the Irwin curves in Fig. 2. Write a tw-three sentence statement f yur findings. b. An etrinsic -tye Si samle has a measured cnductivity f σ = 0. (Ohm-cm) - and a Hall vltage f.6 mv fr I = 0 ma and =,500 Gauss. The samle thickness is 0.06 cm and the width is cm. Find the ding density, N A, and the hle Hall mbility, μ, by using bth the cnductivity and the Hall measurements. Nte: The magnetic field is in CGS units; cnvert it t MKS units and nte that the cnversin is,000 Gauss = 0. Weber/m 2 = 0. Tesla. 2. Refer t the gemetry f yur samle shwn in Fig. and assume that it is ded n-tye with an alied magnetic field inting ut f the age. If current was flwing frm terminal A t C and yu cnnected the negative lead f the Keithley (vltmeter) t cntact and the sitive lead t cntact D what wuld the vltage larity n the vltmeter be? Assume that there is n asymmetry in the samle. Elain yur answer succinctly and cherently. Lab III: Cnductivity and Hall Effect Page 5

16 5. PROCEDURE Fr this lab, a square ded silicn wafer was munted and ackaged nt a DIP4 Scket (dual in-line in scket with 4 ins). If yu lk clsely, this wafer has fur rectangular cntacts (labeled A,, C and D in Figure 9) at the crners. These cntacts are wire bnded t an adjacent ad, which in turn is sldered t the three clsest ins n the DIP4 scket. If yu fli the bard, yu will see these ins are sldered t wires that lead t the fur cnnectrs. The cnnectr sitin crresnds t cntact sitin n the wafer (See Fig. 9.) The wafer thickness (t) is 600 μm. A A Cnnectrs Si wafer D C D C Figure 9. Cntact t Cnnectr cnfiguratin. 5. CONDUCTIVITY MEASUREMENT USING THE VAN DER PAUW METHOD Yu will use the LabVIEW rgram cnductivity.vi in the VIs>30 flder n yur Deskt t make the van der Pauw measurements. The LabVIEW rgram uses tw Keithley SMUs. We will chse the t Keithley SMU as the vltmeter and the bttm Keithley SMU as the current surce. If eecuted crrectly the rgram will yield three clumns f infrmatin with ten entries in each clumn. Clumn gives the Surce Current, Clumn 2 gives the Surce Vltage, and Clumn 3 gives the Measured Vltage. Yu will use the Surce Current and the Measured Vltage clumns fr yur calculatins. Lab III: Cnductivity and Hall Effect Page 6

17 Stes:. Get 4-rbe bard. Recrd the bard number and whether the number is circumscribed by a square r circle. 2. Turn n the tw Keithley SMUs. 3. Oen Cnductivity.vi: Check yes fr the Save Data tin. Assign T SMU as vltmeter; ttm SMU as Current Surce. Fr Current Surce set: Initial current: ma, Final current: 0 ma, Ste current: ma. 4. Get tw airs banana lug leads. Plug the leads t SMUs in t the arriate rts. 5. Cnnect the banana lug leads t the 4-rbe bard as in Figure 0 and run Cnductivity.vi fr each cnfiguratin belw. Save the dataset with an arriate filename:. I AD, V C (shw this setu t and run vi fr TA; get signature) 2. I DA, V C 3. I C, V AD 4. I C, V DA 5. I A, V DC 6. I A, V CD 7. I DC, V A 8. I CD, V A 6. Fr each item in Ste 5, use a sreadsheet t calculate the resistance (i.e. R AD,C = dv C/dI AD) using the SLOPE() frmula. If yu refer, yu may generate lts and use the ADD TRENDLINE feature. Lab III: Cnductivity and Hall Effect Page 7

18 7. In the sreadsheet calculate the fllwing. Clearly label each calculatin:. 2. R R ( R 2 R AD, C AD, C DA, C ( R 2 R C, AD C, AD C, DA ) ) 3. RC, DA ( RAD, C RC, AD ) R R ( R 2 R A, DC A, DC A, CD ( R 2 R DC, A DC, A CD, A ) ) 6. RA, CD ( RA, DC RDC, A ) 2 7. R A, CD RC, DA t R R C DA A CD 8.,, f (use Fig. 6 t estimate ƒ) ln σ 8. Save Ecel results. KEITHLEY A KEITHLEY (OTTOM) D C (TOP) Figure 0. Wiring cnfiguratin van der Pauw methd. Lab III: Cnductivity and Hall Effect Page 8

19 5.2 HALL EFFECT Yu will use the LabVIEW rgram Hall.vi in the VIs>30 flder n yur Deskt t make the Hall Effect Pauw measurements. The LabVIEW rgram uses tw Keithley SMUs. We will chse the t Keithley SMU as the vltmeter and the bttm Keithley SMU as the current surce. If eecuted crrectly the rgram will yield three clumns f infrmatin with ten entries in each clumn. Clumn gives the Surce Current, Clumn 2 gives the Surce Vltage, and Clumn 3 gives the Measured Vltage. Yu will use the Surce Current and the Measured Vltage clumns fr yur calculatins. Stes:. Setu the SMUs cables t the 4-rbe bard like s: Current Surce Vltmeter Figure. Hall Effect Cnfiguratin. 2. Oen Hall.vi. Set current surce arameters t t 0 ma with increments f ma. 3. Run Hall.vi with n magnets near the Si samle. Save and title the dataset. 4. Get data fr + (Nrth u) set u:. Place magnet,nrth u, n table 2. Place lastics sli n magnet 3. Place wafer at center f magnet 4. Place secnd lastic sli n t f wafer 5. Place magnet, Nrth u, n t f secnd lastic sli 6. Run Hall.vi; save and title dataset. 5. Get data fr - (Suth u) set u:. Place magnet,suth u, n table 2. Place lastics sli n magnet Lab III: Cnductivity and Hall Effect Page 9

20 3. Place wafer at center f magnet 4. Place secnd lastic sli n t f wafer 5. Place magnet, Suth u, n t f secnd lastic sli 6. Run Hall.vi; save and title dataset. 6. Setu the SMUs cables t the 4-rbe bard like s: Current Surce Vltmeter Figure 2. Hall Effect Cnfiguratin Reeat Stes 4, 5, and 6 frm abve. 8. Generate Plts (see Sectin 6); get TA s signature. 6. LA REPORT Tye a lab rert with a cver sheet cntaining yur name, class (including sectin number), date the lab was erfrmed n, and the date the rert is due, lab artner name, and title. Use the fllwing utline as guide when writing yur lab rert. Abstract: Give a brief, cherent summary f what the lab is abut, i.e. the methds used and why. Mentin what results yu determined / calculated / cmared. Make sure yu refer t yur samle number. Try t limit yur abstract t 5-6 sentences the gal is t quickly let a eer f equal cmetence knw what yur rert is abut and what significant calculatins it cntains. Van der Pauw cnductivity measurements: Plt all V vs. I data frm the cnductivity dataset in ne lt. Prerly title and label yur aes with units. D the lts almst cincide with each ther? Create a table resenting the calculated values frm sectin 5. ste 6 and 7; remember units. Catin the table. Shw the elicit calculatin f resistivity f the samle i.e. tye ut the equatin f the frmula, shw values used, final result, etc. Lab III: Cnductivity and Hall Effect Page 20

21 What is the rm temerature cnductivity f yur samle? Shw yur calculatins. What is the ding density as determined frm yur resistivity value and the Irwin curves? riefly elain hw yu determined it. Culd yu determine it withut the Hall Effect rcedure? Hall Effect measurements: Cnclusin: Generate V y vs. I lts that shw yur measured vltage when the magnetic field was in the sitive directin, negative directin and yur baseline n the same grah. Yu shuld have tw grahs with 3 lts each ne grah fr cnfiguratins and ne fr cnfiguratin 2. Make sure the lts are clearly distinguishable and labeled. Calculate the true Hall Vltage fr bth cnfiguratins. Remember that the measured vltages are nt true Hall vltage (V H). In rder t calculate the true Hall vltage (V H), yu have t find the difference between vltages measured with and withut the magnetic field. Ideally, the Hall vltages calculated with the sitive magnetic field and with the negative magnetic field shuld be equal in magnitude but larity is reversed. Shw wrk, values used, etc. Clearly rert the values. What is the dant-tye f yur samle? Calculate the ding density. Shw elicit calculatin using frmula, values used, etc. Assume that the magnetic fle density at the surface f silicn samle is 30 gauss. Estimate resistivity using Irwin curves. Hw des it cmare with the resistivity derived frm the van der Pauw methd? Use ercent-errr frmula t quantify the cmarisn. Are the values clse t each ther? Calculate the majrity carrier mbility. Shw elicit calculatin using frmula, values used, etc. Is it near the eected value? Create ne table cntaining these imrtant results:. The van der Pauw methd: cnductivity, resistivity, and estimated ding density f the samle. 2. The Hall Effect methd: Hall Vltage, ding tye, ding density, estimated resistivity, and carrier mbility f the samle. Attach: Signed instructr verificatin frm. Lab III: Cnductivity and Hall Effect Page 2