IEEE ELECTRON DEVICE LETTERS, VOL. EDL3, NO, 5, MAY 1982 [ 8 ] H. Morkoc, “Current transport in modulationdoped (A1,Ga) As/GaAs heterostructures: applications to field effect transistors,” Elect. Device Lett., EDL2, pp. 260261, 1981. [9] T. Mimura, S. Hiyamizu, T. Fujii, and K. Nanbu, “A new field effect transistor with selectively doped GaAs/nAl,Gal ,As heterojunctions,”Japan. J. A p p l . Phys., vol. 19, pp. L225227, 1980. [ l o ] M. Laviron, D. D. Delagebeaudeuf, P. Delescluse, and N. T. Linh, “Low noise twodimensional GaAs FET,” Electron. Lett., vol. 17, pp. 536437,1981. [ 111 H. Morko?, T. J. Drummond, R. Fischer, and A. Y . Cho, “Moderate mobility enhancement in single period A1,Gal ,As/GaAs heterojunctions with GaAs on top,” J. A p p l . Phys., in print March 1982. and 1%’. Kopp, [12] H. Morkog, T. Y. Drummond, R . E. Thorne, “Mobility enhancement in inverted A1,Gal .,As/GaAs modulationdoped structures and its dependence on donorelectron sepa
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ration,”Japan. J. Appl . Phys., vol. 20, pp. L913916, 1981. [13] Y. M . Shannon, “A majorlty carrier camel diode,’’ Appl. Phys. Lett., vol. 35, pp. 6365, 1979. [14] T. J. Drummond,H. Mork.o$, and A . Y. Cho, “MBE growth of (AI, Ga)As/GaAs heterostrxtures,” J. Crystal Growth, vol. 56, pp. 449454, 1982. . Shaw, “Single step optical [15] M. Hatzakis, B. J. Canavelh, and Y. M liftoffprocess,” IBM J. des. Develop., vol. 24,pp.452460, 1980. [16] P. Piennata, I. kindau, W. E. Spicer, and C. M . Garner, “The surface electronic structure a’nd surface chemistry of GaAs (110),” Proc. 7th Int. Vac. Congr. m d 3rd Int. Con$ Solidstate Surfaces, Vienna, p. 615, 1971. [I71 T . J. Drummond, W. Kc.pp, R. E. Thorne, R . Fischer, and H. Morkop, “Influence of Al,Gal ,As buffer layers on the performance of modulationtloped field effect transistors,” Appl. Phys. Lett., in print.
Obtaining the S Transmission Line
G.K. REEVES AND H.B. HARRISON
AbstractIn characterizing ohmic contacts using the transmission line model, it is necessary t o make a measurement referred to as .the contact end resistance, as a result of modification t o the sheetresistance In this articleweshow that this contact end reunderthecontact. sistance and the consequent specific contact resistance can be deduced from simple resistance measurements carried out between contacts on a standard, transmission line model test pattern, T
lr
t
INTRODUCTION NE OF THE MORE common methods for quantitatively assessing the performance of ohmic contacts to semiconductors is to measure the value of the specific contact resistance pc (ohm  cm’). The transmission line model (tlm) originally proposedbyShockley [ l ] offeredaconvenientmethodfor determining p c for planar ohmic contacts. Shockley also proposed an experiment in which the total resistance RTbetween any two contacts (of lengthd and width separated by a distance Q could be measured and plotted asa function of (2.The resulting equation between RT and R provided an estimate of pc through the so called “transfer length” LT, measured from the intersection of the R curve for R T = 0 as shown in Fig. 1. Here Q = 2 LT for RSK = RSH,RSH being the sheet resistance of thesemiconductorlayeroutsidethecontact region and RSK the sheet resistance of the layer directly under the contact. The assumption of an electrically long contact d >> L T enabled the relationship pc = RSH * L $ t o be invoked. However,there havebeen instancesreported [2,3] where the experimental data measured would not fit the tlm unless
0
w>
Fig. 1. Plot of total contact to contact resistance as a function of Q to obtain transfer length and contact resistance values.
a modification was made to the sheet resistance beneath the ohmic contact  a modification brought about by the alloying/ sintering process occurring at the metalsemiconductor interface, that is R S K# R S H .Extra experimental data to obtain the magnitude of this modjfication can be obtained by the SO called “endresistance”measurement.” A knowledgeofthe sheet resistance beneath the contact provides valuable insight into the effectof the alloyirlg/sintering process [4]. In this article we explain and verify the additional end resistance measurement, which is needed to obtain an accurate
*Note:Oddlyenough, in his original paper, Shockley [ I ] proposed this technique of measurement to obtain LT for electrically short contacts (d < L T ) making no reference to the alloying/sintering effect to R SH.
Manuscript received November 30, 198l;revised February 26,1982. G. K. Reeves is with Telecom Australia Research Laboratories, Clayton, Victoria, Australia. H. B. Harrison is with the Royal Melbourne Institute of Technology, Melbourne, Australia.
01938576/82/05000111$00.750 1982 IEEE
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IEEE ELECTRON DEVICE LETTERS, VOL. EDL3, NO. 5 , MAY 1982
I I I
I
I
I
I
I
I
I I
R1
V//A
Ii1
I
R2
I{qdd&I,A
Fig. 2. Experimental measurements for obtaining total resistance and end contact resistance values.
value of pc for alloyed contacts to gallium arsenide and sintered contacts to silicon. We also propose a simple, practical technique to determine end resistance; this technique is justified experimentallyforalloyedcontactsto gallium arsenide and for sintered aluminum contacts to silicon.
then LT may be found and thusp c determined from ( 5 ) . With the aid it ofthat Fig. show 3, we is.possible deter to mine RE by an extension of the simple resistance measurements used to obtain the plot of Fig. 1. In Fig. 3 the contact resistance with the current entering the left hand port is R h (I2 = 0) and that of the right h a n d p o r t is R c ( I l =0)and the values of R y x, and RZ become R~=R;:RE,R~=RE~~~R~=( R 7) ~RE By making R x # R z , the relationships of (7) apply for the general case of electrically asymmetrical contacts, such as circular contacts, where the contact resistance depends upon the direction from which the current enters the contact [6] . With reference to Fig. 4 we see that the addition of an extra resistance measurement on the tlm patterns provides a value of R E ,viz.
USINGTHE TLM T O OBTAIN SPECIFIC CONTACT RESISTANCE VALUES To determine the ohmic contact parameters with the tlm, resistance measurements R 1 and R 2 are madebetweenadjacent contacts as depicted in Fig. 2. The total resistance ( R T ) between any two contacts is given by:
R T = ~ c +  RSH     i! W
Howevercontact Rc, the equal t o [ 5 ] resistance, can
*
R~ + = RR bc o + R A Rz=Rc+R~tRc2
(8)
(9)
R ~ = R ~ ~ + R A + R ~ + R c ~ R E + R B(10) +Rc~
(1) thus and
be shown t o be
1 RE =(Rl t R 2 R3) 2
(1 1)
R c =R S K
W
L T coth ( ~ / L T )
(2)
where R A and R B represent the resistance of the epilayer between the contacts and RCOand Rc2 are contact resistances.
where R S K is the modified sheet resistance under the contact. The relationship of (4) is plotted in Fig. 1 and shows that, if the sheet resistance under the contact is significantly modified, then LX # LT. In this case, the correct value of pc can be found by performing an additional measurement  the contactend resistance ( R E ) measurement where the standard technique is t o pass a constant current between two contacts (Fig. 2 broken lines) and to measure thepotentialbetween one ofthese contactsand an oppositeoutsidecontactpad. The value ofRE is then V/I. In terms of the tlm contact parameters, RE can be shown to be 151
RE=
11


12
Fig. 3. Equivalent electrical circuit under the contact.
J” w
SK
PC
.
1 sinh (d/LT)

PC 1 LT W sinh (d/L,)
.
1
RC2
on eliminating R S Kusing (3). From ( 2 ) , (3), and ( 5 ) , since
Fig. 4. Extra resistance measurement ( R , ) used to derive contact end resistance.
REEVES AND HARRISON: OBTAINING THE SPECIFIC
CONTACT RESISTANCE FROM TRANSMISlSION LINE
113
TA:3LE 1 Hence, by taking a third resistance measurement R3, RE can be found. The model of Fig. 4 is in agreement with the experimental observation of Berger [7] who noted that for the tlm MATERIAL CONTACT ACTIVE R S H R S K test pattern with identical contacts, the difference between a PC PROCEDURE :;AYER (a/o)(a/o) (fi2.cm2) loaded R , measurement and an “unloaded” measurement of ~EPTH R 1 (made using separate voltage andcurrentmeasurements) was equal to the contact end resistance RE. Also, with reference (PI to Figs. 2 and 3, itis easily seen that the standard technique of 22 7 x lo’ 430 3 .O currentinjectionand voltage measurementprovidesthe re GaAs Alloyed quired RE value (V/I). 2100 430 4.9 x 0.03 Si Sintered RESULTS AND DISCUSSION Measurements were carried out on test patterns of alloyed AuGeNi contacts (d = 50 pm) formed on an ntype epitaxial the CaAs contacts, is summ,srized in Table I, and confirms the layer (No = 1.5 x 10‘ ~ m  of ~ )galliumarsenide onasemiimportance ofincluding th,: modifiedsheetresistance even insulating substrate, From tlm measured data and assuming the for sintered contacts. layer under the contact to be unmodified, values of p c typicalCONCLUSION ly 5 X !2.cm2and RSH= 430 S 2 / 0were obtained.HowIt has been shown that, to obtain the correct value of ever, a contact end resistance measurement using the current voltage technique of Fig. 2 yieldedRE values of around 1 .O S2. specific contactresistancefortlmtestpatterns,thecontact Using (3) and (5) this gives a p c value of 7 x lo’ S2.cm2 and end resistance mustbefou.nd.Also,wherethecontactrea value for R S Kof 22 S2jU. These changes are similar to those sistance forms a significant part of the intercontact resistance and particularly for electrically short contacts, by making one observed by Kellner [2] and are evidence of significant alloyadditional resistance measurement the contact end resistance ing modification to the epitaxial layer under the ohmic condetermined with the same instrument tact. We also derived values of RE using (1 1). These showed a can be conveniently greater spread of values (0.6 f2 to 2.1 S2) due in part to the used to measure R 1 and R 2 . relatively large values of R 1 and R , and al.so due to the fact ACKNOWLEDGMENT that the contacts here are electrically “long” resulting in small The permission of the Research Director, Telecom Australia, RE values ( 5 ) . Reducing the length of the contactcauses RE + t o publish this paper is hereby acknowledged. H. B. Harrison Rc and using test patterns on thesame substrate with contacts acknowledges the financial mistance of the Australian Radio half as long caused the average value of RE to increase by apResearch Board. proximately 4 times, reducing the spread in RE. The values of REFERENCES RE thus obtained confirmed the p c values measured previously. W. Shockley, “Research and investigation of inverse epitaxial UHF A second series of tlm patterns were deposited usingsinpower transistors,” Report No. A1TOR64207,Air Force Atomic tered A1 metallization on a shallow (< 3008) Sb ionimplanted Laboratory, WrightPatterson Air Force Base, Ohio, September layer on a ptype (1 0  20 f2cm < 100 >) silicon wafer. Values 1964. W. Kellner, “Planar ohmic contacts to ntype GaAs: determination for p c showedatrend similar to the alloyed GaAs contacts of contact parameters using the transmission line model,” Siemens where, on assuming amodifiedsheetresistancebeneaththe Forsch.u. EntwicklBer., vol. 4, p. 137,1975. contact, p c 4.9 x S2.cm2 and R S K 430 S 2 / 0 were I. F. Chang, “Contact resistance in diffused resistors,” J. Electrochem. Soc., vol. 117, p. 3681, 1970. 1.2 X obtained. These valuescanbe compared to pc E. Yamaguchi et al., “Ohmic contacts to Siimplanted InP,” Solidf2.cm2and RSH 2100 S 2 / 0 whicharecalculatedby asState Electron., vol. 24, p. 263, 1981. suming no modification to the sheet resistance. For the pata . B. Harrison, “Characterizing metal semiconductor ohmic contacts,” Proc. IREE Aust., vol. 41, p. 95, 1980. terns on the silicon wafer, the contact resistances were a sigG. K. Reeves, “Specific contact resistm’ce using a circular transnificant part of the measured intercontact resistance (on the mission line model,” Solid!!?ate Electron., vol. 23, p. 487,1980. order of lo%), and values of RE derived using (1 1) were in H. H. Berger, “Contact resistance ondiffused resistors,” IEEE ISSCCProc., vol. 160,19659. close agreement with RE values found using separate current and voltage measurements. This data, together with that for


