Investigation of AuGeNi contacts using rectangular and circular transmission line model

Mid-State ElectronicsVol. 35, No. IO, pp. 144-1445, Printed in Great Britain. All rights reserved

INVESTIGATION RECTANGULAR

1992 Copyright

OF AuGeNi CONTACTS USING AND CIRCULAR TRANSMISSION LINE MODEL M. AHMAD’ and B. M.

‘Society for Applied Microwave and 2Tata Institute

0038-I lOI/ $5.00 + 0.00 Q 1992 Pergamon Press Ltd

ARORA~

Electronics and Research, I.I.T. Campus, Powai, Bombay 400076, India of Fundamental Research, Colaba, Bombay 400005, India

(Received 13 December 1991; in revised form 23 March 1992) Abstract-The effect of sheet resistance of the contact metal on the contact resistance measurement has been explored using circular-geometry transmission-line structures. Ohmic contacts of AuGeNi and AuCre/Ni/Pd/Au combination were investigated by using electrical and X-ray diffraction measurements.

NOTATION

u, v PC R R, R, 3Rsrn a aI a2 b 1 W,d

2. THEORY

current in semiconductor, current in metal and total current respectively voltage drop in semiconductor and in metal contact resistivity/specific contact resistance measured resistance contact resistance sheet resistance of semiconductor and metal respectively radius of metal contact outer radius of semiconductor annulus outer radius of the annular contact. Practically, this is the boundary where the current is leaving/ entering the annular metal region tip radius of measuring probe contact spacing width and length of contact

2.1. Contact resistance evaluation assuming zero metal resistance 2.1.1. RectanguIar geometry. Contacts to thin semiconductor layers on non-conducting substrates are evaluated using a transmission line model[5]. For rectangular contacts, shown in Fig. l(a), the total resistance R measured between two contact pads is twice the contact resistance R, plus resistance of the semiconductor layer R =2R,+$,

1. INTRODUCTION

As the ohmic contact

resistance

acceptable

for devices

device integration level more accurate measurement of the resistance of ohmic contacts is required. The transmission line method has been widely used for contact resistance measurement[ 1,2]. Marlow and Das[3] have shown that it is necessary to include the effect of metal sheet resistance in order to obtain an accurate measure of the contact resistance. However, they restrict their work to rectangular geometries only. In this work, we extend the inclusion of this correction to circular transmission line geometry. The metal sheet resistance correction becomes very important for refractory contacts for which the sheet resistance of the contact metal is as high as 15 ohm/n[4]. In the case of AuGeNi ohmic contacts to GaAs, which is treated here, substantial correction is still necessary if thin contact layers are used. Even in the case of thicker layers, degradation in the metal sheet resistance may occur[3], requiring careful analysis of the factors affecting contact reliability. becomes

smaller

with

increase

in the

R, = !$

(1)

where R, and R,, are the semiconductor sheet resistance values below the contact and between the pads respectively, L, is the transfer length, W and I are width of the contact pad and spacing between them respectively. Equation (1) assumes that the probe resistance is measured and subtracted, or is eliminated by using a four-probe technique, two probes for passing current and two to measure voltage. 2.1.2. Circular geometry. In the rectangular geometry it is necessary to form mesa structures, which necessitates two processing steps. In contrast, circular geometry would require only a single step process. Furthermore, in this case, an exact analysis is possible which eliminates errors due to lateral current crowding and gap effects[6]. For circular contacts [Fig. l(b)] of radius a separated by an annular semiconductor spacing of I = (a, - a) from the overall metal contact, the measured resistance between the inner circular contact and the outer metal is R=A[,Lt(i+-!-)+RSln:].

(2)

In the above equations, R and the geometrical factors are measured quantities, R, is also assumed

1441

M. AHMADand B. M. AR~RA

1442

2.2. Contact resistance with non-zero metal sheet resistance 2.2. I. Rectangular geometry. Marlow and Das[2] have already treated the case of non zero metal resistance and obtained the value of the effective transfer length. In this case R is given by

1d

R=%[gg+&

(a)

2&n&

2Ri&

- (R, + R,,)3’2 + R,(R, + R,,)3’2

(b) Fig.

1. (a) Rectangular transmission line geometry. Circular transmission line geometry.

(b)

to be known. Thus, the specific contact resistance pC in either case is determined by using L, which is obtained by curve fitting the data of R vs contact spacing pc= R,L;.

1+g

(4)

where R,, is the known sheet resistance of the contact metal. W and d are the width and length of the contact respectively. 2.2.2. Circular geometry. Since the correction due to metal sheet resistance in the circular geometry is not included in the earlier treatment an outline of analysis including this correction is given below. Following the method used by Marlow and Das, the double transmission line model for circular geometry is shown in Fig. 2. Let the total current iOhave two components i, and i,, i, flowing through the semiconductor and i2 through the metal. The resulting potential drop in the semiconductor and metal are U and V respectively. The following equations relate the voltage, current and parameter pc, R, and R,, gi,(r)=:(U-

V)

$ U(r) = 2

i,(r)

$ V(r) = 2

i*(r)

(7)

i2(r) = i, - i,(r).

(8)

(3)

Here it is assumed that R, = R,, Since this assumption is not correct, generally transfer resistance has to be relied upon, which is defined as R, W (ohm-mm).

Fig. 2. Double transmission line model for circular geometry. The lower bank of resistors relate to the sheet resistance of the semiconductor under the metal [R: = R,dr/(2nr)] and away from the metal [R,‘= (R,,/2n)ln(a,/a)]. The top bank of resistors relate to the sheet resistance of the metal [R,,’ = R,dr/(2nr)]. The connecting resistors p,/(2nr dr) denote the interface resistance between the metal and the semiconductor.

AuGeNi contacts on GaAs Using equations (j)-(8) equation is obtained

the following

1443

hence the total measured resistance the circular contact to a, is

differential

from the centre of

r2$(U-V)+r&J- V) -r’Q+J-V)=O.

(9)

Subject to the boundary conditions i, = 0 and i2 = i0 at r = 0; i, = i0 and i, = 0 at r = a, eqn (9) has the following solution Z,(rk’)

R,i,

U-V=--

micron

JC+Rsm -.

DETAIL

thick epitaxial doping

8 x 10’6cm-1. active

(11) .

5 mm x 5 mm

were

cut and

layer

with maximum Pieces of size degreased

I

PC

From equations (5) and (10) the equation for the current through the semiconductor is obtained R,i,, Z,(rk’) i, = /z r. ak pc Z, (ak ‘)

Now the voltage can be written as

3. EXPERIMENTAL

for rec-

(10)

2za, k’ I, (ak’)

where i. and I1 are zeroeth order Bessel function and first order Bessel function of the first kind with imaginary argument and k,2

We can compare this with the formula tangular geometry, given in eqn (4).

(12)

drop across the circular

etched in orthophosphoric acid:hydrogen peroxide:DI 3:l:SO and in DI Samples were patterned ometry by liftoff using a positive photoresist AZ 1350 H on the 650 pm wide mesa with pad spacings

contact etched in the above etchant short time to the oxide and DI water immediately before loading

R, R,,& -___2nak”p,

R, i.

IO(ok ‘)

Z, (ak ‘)

I, (ak ‘) $- 2Rak’ m

where b is radius of the probe tip. Similarly, the voltage drop across the contact is calculated using equations (j)-(8) boundary conditions: i, = i. and i2 = 0 at r = and iz=io at r =a2. Following expressions are obtained for and i, R,i,,

IJ-V=--

(13)

annular with the a,, i, = 0

metal thickness Metallised

10008, for

for a in

obtain con-

(V - V) radius 280 lrn, and annular ing of 125-285 pm were formed.

K,(rk’)

spac-

Zza,k’K,(a,k’) R,i, i, = a,kf2p,

K, (rk’) ~ K,(a,k’)

(14)

where K. and K, are respectively the zeroeth order Bessel function and first order Bessel function of the second kind. The voltage drop across the annular contact is

R, j. 2a

ln

2 + a,

AuGeNi and AuGeNi/Pd/Au contacts. The contact resistance prober AP 4. A constant passed through two contact pads using Keithley source and voltage was measured

R,&m~oKo(a2k’)- Ko(alk’) 2na, k”p,

K,(a,k’)

f---.

Rsio

&(alk’)

(15)

2na, k’ K, (a, k’)

With the assumption that ak and ka, $ 1 and u2 -+ co, equations (13) and (15) reduce to simpler forms,

4. RESULTS

AND DISCUSSION

Figure 3 shows a typical measurement of R vs I by using the rectangular geometry for sample (i). The intercept on y axis gives the values of R,. In Fig. 4

1444

M. AHMADand B. M. ARORA

60-

0

EXPERIMENTAL

-

CALCULATED

Rsm=20fi/n 50-

100 120

Rs

=44on/n

I

i

0

OOW

I (pm)

I (pm)

Fig. 3. Measured resistance vs contact spacing.

Fig. 5. Measured resistance annular spacing. transfer resistance values of a sample annealed at various temperatures are shown. Typical thermal cycle used in the alloying is shown in the inset of Fig. 4. The well known feature that the transfer resistance goes through a minimum for the alloying temperature 440460°C is seen in Fig. 4. It was also observed that annealing at 445°C gives minimum spread of the contact resistance values. This result is similar to that of Murakami et al. [4]. Therefore we have used this alloy temperature in all the subsequent experiments. The lowest contact resistance obtained was 0.16 ohm-mm (1.4 x 10e6 ohmcm’). In order to explore the effect of metal sheet resistance, we fabricated circular TLM patterns with reduced metal thickness on sample (ii). Typical metal film thickness used for this experiment was 3OOA. The sample was subjected to typical heat treatment cycle. Figure 5 shows the measured values of R vs the annular spacing between the two contacts “al-a”. The probe radius b was kept fixed at a value of 20 ,um. The intercept on the ordinate, i.e. R, was obtained by curve fitting. Using this and equations (2) and (3), the value of contact resistivity is found to be lo-’ ohmcm2. Thin layer of AuGeNi offers high metal sheet resistance so that pc value as obtained is not representative of the actual contact resistance. Figure 6 shows a calculated plot [using eqn. (16)] of the apparent contact resistance value as a function

of metal sheet resistance for a test case in which the contact resistivity was 5 x 10~60hm-cm2. It is observed that depending on the value of metal sheet resistance, the apparent value of contact resistivity can vary by more than two orders of magnitude. The effect is particularly severe for larger geometry as shown in the figure. Therefore the result plotted in Fig. 5 was fitted by using eqn (16) with pc as parameter. We obtain contact resistivity value of 10-j ohm-c rn’. This brings pc value closer to that measured for thicker AuGeNi contact. We will now discuss the electrical and structural changes occurring as a result of aging the contact formed on the sample (ii). Deterioration of contact resistance under long term thermal stress was studied by subjecting AuGeNi/Au and AuGe/Ni/Pd/Au to 370400 “C under flowing nitrogen. Samples with rectangular TLM geometry were used. No significant change in contact resistance was obtained after aging for 14 h. After further annealing at 450 “C for 1 h, considerably changes in the colour adhesion and morphology was observed. In particular, contacts became rough in appearance and adhesion became poor. Simultaneously the measured contact resistivity jumped by about 2 orders of magnitude in case of annealing for 2.5 h for AuGeNi contacts and by one order of magnitude for

ho106

-10.5 0.4

I

0.3

Rs

=

LLO-n/O

60 az280flm

“E u < 7 0 x I w

b

50-

(“C

)

Fig. 4. Transfer resistance vs annealing temperature

50

-

40

“E y <

30

g

20

5

)~ ~~ 30-

x 20-

_:::I

a =

75pm

b=

7pt-r

w 10

lo-

0

1 10

1 30

20 Rsm

TEMPERATURE

,um

LO-

0

ANNEALING

= 20

-

1 40

50

(ii/O)

Fig. 6. Apparent contact resistivity vs metal sheet resistance for the test case of contact resistivity = 5 x 10e6 ohm-cm’.

AuGeNi contacts on GaAs

bl d

( b)

LCr,) 35

44

53 2 0

62

71

80

(DEGREE)

Fig. 7. X-ray diffraction spectra of AuGeNi/Au sample, (a) as alloyed (lower trace) and (b) annealed at 450°C for 1 h (upper trace). The labelling of the peaks a, b, c, d, etc. is arbitrary in the two curves. The lower trace shows the following phases (i) a’-AuGa (a, b, c, d, e, f, g, i, j), Ni, -.As (a, d. i) and (iii) NiAs (h). The upper trace shows phases (i) a’-A&a (c; d; e, f, g, h,j), (ii) B-AuGa (a, c, d, g, j), (iiij Ni,_,As, (a,~, h, j), and (iv) NiAs (a, g, i). Some of the peaks are listed simultaneously under different phases because the resolution of our measurement is less than that required for unique assignment. AuGeNi/Pd/Au contacts. It may however be pointed out that the initial contact resistivity of the latter was higher. Structural changes for alloyed AuGeNi/Au contacts were recorded by XRD soon after alloying (440 “C, 2 min) and after aging AuGeNi/Au for 1 h at 450 “C. The as alloyed film consists mostly of hexagonal a’-AuGa and some peaks identified as belonging to Ni, _=As, phase and some belonging to NiAs h.c.p. phase are present. Annealing at 450 “C for 1 h resulted in the appearance of some /I- AuGa phase (h.c.p. structure) appears in addition to the hexagonal a’-AuGa. In addition, h.c.p. NiAs phase and cubic Ni, _,As were present. Murakami[7] has recently summarised the result of X-ray measurements available in the literature. According to him, NiAs(Ge) is the phase responsible for highly conducting contacts. Growth of P-AuGa after prolonged annealing however causes the interfacial NiAs layer to decrease with a simultaneous increase m contact resistance. As seen from Fig. 7 the growth of fi-AuGa is observed in the high temperature annealing experiment. The worsening of contact resistance in our experiment with the growth of AuGa

1445

seems to be in agreement with the results of Murakami et al. In the as-alloyed sample of AuGeNi/Pd/Au, /?AuGa phase and cr’-AuGa phase were found to be present along with Ge,Pd phase and Au. The nickel arsenide phase was however not apparent. From the above results we see that the presence of a Pd layer acts as a barrier against diffusion of Au towards the GaAs. This may be responsible for the better thermal stability observed in these samples as compared to the samples without the Pd layer. However, although Pd acts as a barrier, it suffers from the following problem. Since Ge reacts with Pd, the amount of Ge available for forming good ohmic contact decreases. This explains the higher initial contact resistance of contact with Pd layer. We thus conclude that the use of Pd as a barrier is not exactly satisfactory. 5.

CONCLUSION

We have provided a relation for the contact resistance in the circular TLM geometry which includes the effect of metal sheet resistance. AuGeNi contacts have been studied with and without a barrier layer of Pd by using electrical measurements and XRD structural measurements. Annealing studies show that a 170 A Pd film does not prevent degradation after 450 “C heat treatment. The degradation of AuGeNi/ Au seems to be due to the growth of /3-AuGa phases, which is in agreement with the results of earlier work. Acknowledgements-The author would like to thank Professor S. Raman for supplying the material for the study and Dr 0. S. Shankar and Dr K. Chelapathi for useful discussions. The authors would also like to thank Dr P. Ayub for XRD measurements. REFERENCES

1. V. Ya Niskov and G. A. Kubetski, Soviet Phys. Semicond. 4, 1553 (1971). 2. R. Williams, Modern GaAs Processing Methods, pp. 21 l-240. Artech House, Boston (1990). 3. G. S. Marlow and M. B. Das, Solid-St. Electron. 2S,91 (1982). 4. M. Murakami, W. H. Price, J. H. Greiner, J. D. Feder and C. C. Parks, .I. appl. Phys. 65, 3547 (1989). 5. H. H. Berger, Solid St. Elecrron. 15, 145 (1972). VLSI Electronics6. S. S. Cohen and G. S. Gildenblat, Microstructure Science (Edited by N. G. Einspruch, Vol. 13, p. 112). Academic Press, New York (1986). 7. M. Murakami, Mater. Sci. Rep. 5, 273 (1990).