Specific contact resistance measurements of

Specific contact resistance measurements to semiconducting diamond

of ohmic contacts

C. A. Hewett and M. J. Taylor Naval Command Control and Ocean Surveillance Center; RDT&JZ Division, Code 555, 49285 Bennett Street RM 111, San Diego, California 92152-5790

J. FL Zeidler Naval Command, Control and Ocean Surveillance Center, RDTXE Division, Code 804, 53570 Silvergate Avenue, San Diego, California 92152-5070

M. W. Geis Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02173

(Received 28 January 1994; accepted for publication 15 August 1994) A simplified version of the specific contact resistance measurement scheme of G. K. Reeves [Solid State Electronics 23, 487 (1980)] has been developed. Its applicability to semiconducting diamond is demonstrated using four sample types: epitaxial films doped to mid 1019 acceptors/cm3 on (100) and (110) type IIa substrates; type IIb diamonds 0.25 mm thick, and type IIb diamonds thinned to 0.035-0.05 mm thick. The ohmic contacts were based on a solid-state annealing process using carbide forming metals. The measured specific contact resistance depends mainly on the doping level in the diamond. Measured values ranged from 8X 10m6 0, cm* for heavily doped films to 1X10-’ a cm2 for lightly doped bulk samples. A simple analysis shows that the contacts to highly doped layers are suitable for device applications. 8 299.5 American Institute of Physics.

INTRODUCTION The unique material and electronic properties of diamond make it a potentially important candidate for use in high power or high frequency applications, as well as in high temperature and corrosive environments. Several authors have recently reviewed the motivation and prospects for semiconducting diamond based electronic devices.rm3 Figures of merit based on these properties have shown diamond to have a significant advantage over other semiconducting materials for high frequency and high power applications, as well as for transistor switching speed. The low neutron crosssection and the large bond energies suggest applications requiring radiation hardening. In particular, however, the wide band gap of diamond has attracted interest in its use for devices operating at high temperature. The performance of any electronic device is determined by a combination of device structure and the materials properties of the structure. The development of ohmic electrical contacts is an integral stage in the implementation of a new material technology. A low contact resistance is the primary requirement for such contacts. They must also be strongly adherent, able to withstand the high temperatures for which diamond devices are intended, and as much as possible, they should be compatible with conventional device processing techniques. The formation of low resistance ohmic contacts to any wide band gap semiconductor is a difficult problem due to the large potential barrier which arises when a metal is deposited on the semiconductor. To further complicate the problem, diamond has a large surface state density, effectively pinning the Fermi level far from the band edges. In spite of these difficulties, techniques have been developed to produce ohmic contacts to naturally occurring p-type semiconducting diamond. Ohmic contacts produced via a solid state annealing process have been studied extensively J. Appl. Phys. 77 (a), 15 January 1995

and are believed to satisfy the four requirements noted above.4 In this process- a thin film of a transition metal carbide forming metal is deposited on the diamond surface. Annealing at high temperature (950 “C) leads to the formation of a carbide layer at the interface. This layer provides an intimate contact to the diamond and promotes good adhesion. Figure 1 shows the resistance measured between two molybdenum-diamond contacts as a function of annealing time at 950 “C in hydrogen. Prior to annealing, the resistances ranged from tens to hundreds of mega-ohms. From the figure it is clear that annealing the contact produced a decrease in total resistance of several orders of magnitude. Auger electron spectroscopy studies indicated that the decrease was associated with the formation of a carbide phase. Similar results have been observed for Ti/Au, V/Au, and Ta/Au contacts. Measurements of the specific contact resistance are required in order to determine the metallizations that provide the lowest electrical impedance for device applications. Ohmic contacts are characterized by measuring the series resistance arising at the contact-semiconductor junction, R,. Normalizing the contact resistance to the contact area gives rise to the specific contact resistance, r, . For the ideal case of uniform current flow perpendicular to the contact, we have rc= R,IA, with A being the contact area. In reality, however, the current flow is rarely perpendicular, and the finite resistance of the semiconductor leads to current crowding.‘-’ Measurement techniques have been developed to allow the current crowding and bulk resistance of the semiconductor to be deconvolved from R, , thereby uniquely determining the specific contact resistance.7’8 Conceptually, the simplest technique is that of Cox and Strack8 in which contacts are made to both the front and back sides of the sample. The primary advantages of this technique are the

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0 1995 American Institute of Physics

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1 2

I 4

I 8 TIME

A

50-pm

spacing

0

30-pm

spacing

*

ZO-pm spacing

0

IO-pm

spacing

A

5-pm

spacing

r,

= 11.71.lmr1’ = 20.4 pm r, = 32.5 pm + r,’ = 52.3 ).un -

1% (mid

FIG. 1. Resistance between two MO/diamond contacts as a function of annealing time at 950 “C in an H2 ambient.

ease in processing the contacts and the simplified analysis due to the geometry. However, due to the semi-insulating nature of bulk diamond, there is a large series resistance contribution to the total resistance from the substrate itself. Thus, in order to determine the specific contact resistance one is forced to take the difference of two (nearly equal) large numbers. In practice, this limits the method of Cox and Strack to contact resistances of 10-t R cma or greater on diamond. A second technique utilizes an array of contact pads of equal size, but varying separation, contacting a thin conducting layer. The contact resistance in these structures is analyzed using the transmission line model.7 The primary drawback to transmission line model measurements is the need to perform a mesa etch in order to reduce the analysis of current flow between contacts to a two dimensional problem. Because diamond is relatively chemically inert, this mesa etch must be performed using ion beam milling, or reactive ion etching. Two techniques for eliminating the mesa etch requirement from the transmission line model measurement have been demonstrated.9V10One approach” is to simply extend the contact pads across the width of the sample, forming an array of contact lines. The second approach is to use a circular test pattern consisting of a central dot and concentric ring contacts. The measurements are interpreted using a circular transmission line model. W e judge the second approach to be superior to the first in analyzing diamond samples for two reasons. First, the use of contact lines requires rectangular (or square) samples and is not adaptable to samples of irregular shape. Second, natural diamonds are frequently non-uniformly doped and the use of circular contacts permits probing over a smaller area. Thus, we chose the circular transmission line model for determining rc , the geometry of which is outlined in Fig. 2. 756

J. Appl. Phys., Vol. 77, No. 2, 15 January 1995

FIG. 2. Circular contact pattern used for this work. The dimensions are r; = 1.74ro,r,=2.78ro,r; = 4.47ro,andr,=5.58ro withro=11.7pm.

Following Reeves,’ the contact resistance of the inner circular “dot” contact may be written as:

&o=

RsdO(~rO) 27raroZ, (are)

’

where R,, is the sheet resistance of the thin-layer of semiconductor under the contact, Zo(aro) and It(aro) are modified Bessel functions of the first kind of orders zero and one, with pc being respectively, and (Y is defined by $=RJp,, the specific contact resistance. For the central ring contact there are two contact resistances, depending on whether the current flow is between the central ring and the inner dot, or between the central ring and the outer ring. In the first case we have

(2) where Ko( crx) and K,( a~> are modified Bessel functions of the second kind of orders zero and one, respectively. In the second case, that of current flow between the central ring and the outer ring, we have R Rcl=---%-. 27rarl

~I(~~;).Ko(~~I)+ZO((Y~~).K~((Y~;)

Zl(arl).K,(ar;)-Zl(cri;).Kl(nrl)’ (3)

The contact resistance for the outer ring is given by R Rc2=---slk-. 2~arJ

zl(ar2).K0(arl)+lo(~rb).Kl(ar2)

Z,(ar,).Kl(~r;)-Zl(crr;).Kl(cura)’ (4)

These expressions for the contact resistance may be greatly simplified by considering the asymptotic expressions (for x>lO) for the modified Bessel functions, given by the following: Hewett et al.


TABLE I. Percent deviation between actual and approximate

a

mo=3.70

aro=11.7

1yro=37.0

RsK=103,~,=10-~

R,=104, ~,=10-~

R,=104,pc=10-5

14.91% -7.40 5.07 -2.92

CO

R'cl

R Cl R c2

e” I&>

R, calculations.

-

1+-

4.37 -2.43 1.55 -0.95

l2 1!.8.x

1.36 -0.77 0.49 -0.30

(1.3)2 + 2!.82.x’ (5)

-

Ko(x)m

(6)

J-i

2

eux

l-&C

aro=370 R,,=105, p,=lO-’

aro=117

RsK=10S,pc=10-5 0.43 -0.24 0.15 -0.096

0.14 -0.08 0.05 -0.03

choice for the r. dimension will allow the simplified equations to be used with minimal error. This could be accomplished by either having one photolithography mask incorporating two or three different r. dimensions, or, as in our experiments, by having a set of masks with differing dimensions. The other contributions to the measured resistance between two contacts are the bulk semiconductor resistances, R, , between the inner dot contact and central ring contact, and R, , between the central ring contact and the outer ring contact. These are given by and

2~f,~!~z

(12)

Thus the total resistance measured between the inner two contacts is (13)

R,=RA+(&o+R~I)

K,(x)%

and the resistance between the outer two contacts is 04)

R,=RB+(R,I+&,).

The contact dimensions in our case are 11.7, 20.4,32.5,52.3, and 65.3 pm for r. through r2, respectively. For R k between lo3 and lo5 JKI, and for pc between 10m4 fi cm’ and low6 R cm’, (Y will range between 3.16X103 cm-’ and 3.16X105 cm-‘. czro then ranges between 3.70 and 370. Clearly, for the higher values one need only consider the first term in each of the asymptotic expansions. Then equation 1 reduces to R

R sk

Equation (2) reduces to

ecr(rl-ri)+edr;-rl) Rsk ea(rl-‘;Lea(r;-r*)

Similarly

The percentage of the total measured resistance due to the contact resistance, i.e.,

i&o+Rf,) andi&l+R,z) RI

has been calculated and is tabulated in Table II. If we now make the assumption that Rsk=Rsh (the sheet resistance under the contact is the same as the sheet resistance between contacts), then ~=Rshlp,. This, along with the previously noted reduced expressions, greatly simplifies the analysis of measured data. One should be aware, how-

‘L4BJ.E II. Percentage of total resistance due to contact resistance.

Eqs. (3) and (4) reduce to

R sk R cl=+ 2%-cv~

and

R RC2- sk 2?rarz ’

For lower values of cure, neglecting all but the first term will lead to errors in lo(x), II(x), Ko(x), and K,(x). The effect of using just the first term in the asymptotic approximations is shown in Table I, where the deviation between (1) and (9), (2) and (lo), etc. has been calculated for several values of crro. It should be noted, however, that for samples where a is expected to be outside the range noted above, an appropriate J. Appl. Phys., Vol. 77, No. 2, 15 January 1995

05)

R2

R,,,=103NO

p,=lO-*

fi

cm2

Rsh=lOsf-L/U

48.1% of

RI

21.5

7.8

27.6% of

R2

10.6

3.6

21.5

7.8

2.6

10.6

3.6

1.2

7.8

2.6

0.84

3.6

1.2

0.37

pC=10V4 n cm’

pc= lo+

R,,,=1041L/U

n cm’

Hewett et al.

757


ios h 10’ n? to6 5 d g $ re”ro‘ Z. d 5 lop Y+ 10’ IO0

FIG. 3. A plot of the function tion of Rlk , R,, , and pC .

[In(r2/r,)~R,-ln(rllro).R,YRE a as a func-

ever, that this is frequently not a valid assumption, and that the range of validity is limited. Following the lead of Reeves,g we plot

as a function of Rsh , R,, and pc (Fig. 3). The regions where the surfaces are less steeply sloped indicate where the assumption may be valid, in particular for low values of Rsk . Also, for heavily doped samples it is likely that Rsk is low, and that Rsk=R,, is a valid approximation. Substituting Eqs. (9)-(12) into Eqs. (13) and (14), and with the assumption that Rsk= Rsh , it is easily shown that

or, in our case, =

1.88x1o-5 R sh

(R, -O.O868R,,,)‘.

1.62X 1O-4

t (R2-0.0664R,yH)2.

Similarly, PC=

RSH

Thus, it is possible to determine pc by measuring RI and R, if Rsh is known. R,, may be determined by direct measurement using a four point probe (on highly doped samples), or by using a van der Pauw resistivity measurement with deposited contacts. EXPERIMENTAL

PROCEDURE

Three different diamond sample types were used in this study. The samples were classified as either heavily doped or lightly doped. Two heavily doped samples were obtained by growing homoepitaxial layers with a large boron concentration on type IIa insulating diamond substrates. The first sample consisted of a diamond film with a high boron concentration and about 4 pm in thickness grown epitaxially on a (100) type IIa insulating diamond substrate with the dimen758


sions of 5X5X0.25 mm3. The second sample consisted of a 6-pm-thick diamond film with a high boron concentration grown epitaxially on a (110) type IIa substrate, also 5X5 X0.25 mm3. These films were grown at MIT Lincoln Labs using a hot filament source consisting of a 2 mm Ta wire heated with 6.5 V and 205 A (giving an approximate temperature of 2300 ‘C).” The pressure during growth was 150 Torr, with a hydrogen l-low of 300 scc/min and an acetone flow rate of 10 scc/min. Boron doping of the diamond layer was accomplished by adding 1 part saturated solution of methanol and boron oxide (B203) to 100 parts of acetone. The graphite substrate holder was maintained at a temperature of 815 “C. The growth time was 30 min for each sample. The lightly doped samples consisted of two irregularly shaped type IIb (naturally boron doped) diamonds thinned to 44 and 50 m thickness, and a 5X5X0.25 mm3 type IIb diamond window. The samples were cleaned using Decontam degreaser, de-ionized water, and methanol, sequentially. The samples were then coated with photoresist and patterned using standard photolithographic techniques. Samples were baked at 120 ‘C for 20 min following photoresist patterning and loaded into an ion pumped ultra-high vacuum system (base pressure 5X10e9 Torr). Electron beam evaporation was used for deposition of the carbide forming metal (either Ti or MO). The thickness of the carbide forming metal was about 100 A, as determined with a quartz crystal deposition monitor. Subsequently, 1500 A of Au was deposited from a resistively heated boat onto the surface of the Ti or MO without breaking vacuum to prevent oxidation prior to annealing. The pressure during evaporation was 2X10m7 Torr. Film thicknesses were determined using a crystal monitor during deposition. After deposition a lift-off process was used to remove undesired metal, leaving contact structures with the geometry shown in Fig. 2. The dimensions (in the notation of Reeves) were r; = 1.74ro, r,=2.78ro, t-6 = 4.47ro, and r2=5.58ro with r,=11.7 pm. Following patterning, the contact structures were probed using a current source and digital multimeter. After probing, the samples were baked at 120 “C for approximately 20 min and then annealed in a purified hydrogen ambient at 950 “C. Anneal times were 2 min for Ti and 6 min for MO. After annealing, the samples were remeasured. The measurements consisted of placing tungsten probes on the inner dot, the central ring, and the outer ring. The total resistance between the central ring and the inner dot, and the central ring and the outer ring were measured. The resistance of the metallization from one side of a ring to the other is easily calculated, and is approximately 0.5 and 1.2 n for the center and outer rings, respectively. In comparison, the resistance of the diamond between contacts is two to four orders greater in magnitude. Thus, any errors induced by the finite resistivity of the metallization will be small. The end resistance was determined by passing a current through the central ring and the inner dot and measuring the voltage between the central ring and the outer contact. This result was checked by switching contact pairs and remeasuring. Using these three results, the specific contact resistance can be calculated using the methods described above and by Reeves.’ Hewett et al.


TABLE III. Specific contact resistance results for various samples. Conducting layer thickness

Sample epi-(lOO) epi-(110) thin type IIb thick type IIb

!w! 4 6 44,50 250

Metal Ti, MO Ti, MO MO MO

NA (cmm3) at 300 K

as deposited

r, (iI cm”) post anneal

5x1019 7x 10’9 10’4 = 10’4 a

3.2X10+ 7.6X lo-’ over-ranged over-ranged

1.8x10+ 2x 10-5 1.2x 10-3 1.4x10-”

rc (Sa.cm’)

aRepresentative value from other type IIb diamond samples.

RESULTS AND DISCUSSION Ohmic contacts between a metal and a semiconductor may be formed by various means. Lowering the barrier height is difficult since diamond has a barrier height essentially independent of the metal work function.” Introducing a large number of efficient recombination centers, thereby allowing recombination in the depletion region to become the dominant conduction mechanism, can also cause a decrease in the contact resistance. A third approach is based on heavily doping the semiconductor at the interface. Heavily doping the semiconductor leads to a decrease in barrier thickness, thereby increasing the tunneling probability of the charge carriers. Increasing the doping in natural semiconducting diamqnd is a difficult task, but has been demonstrated by both ion implantation13 and by RTA solid state diffusion.14 &However, increasing the doping concentration during epitaxial growth of diamond, as in the samples used for this study, is rather easily accomplished. The results of the specific contact resistance measurements are summarized in Table III. As expected, the highly doped epitaxial films (epi-(100) and epi-(110)) show the best results. Both the titanium- and molybdenum-based metallizations showed excellent results as deposited, with little or no improvement upon annealing. Contacts formed by placing tungsten probe tips on the diamond surface showed only a slight deviation from linearity. Contacts formed by the Ti films were highly linear. This may be due to the highly doped nature of these layers. The measured value of specific contact resistances after annealing are more than satisfactory for device fabrication. Lightly doped diamond (represented by the “thin” and “tl&k” samples) are much more difficult to contact. Nonohrhic behavior was observed for the as-deposited contacts in these samples, with ohmic behavior observed after annealing. The accuracy of these measurements is strongly influenced by the thickness of the conducting layer. A fundamental assumption in the transmission line model is that current flow is itrictly two-dimensional, i.e., no vertical current flow in the diamond. This condition is at least approximately true in the epitaxial films, where the separation between contact pads is on the order of 16 pm with film thicknesses of 4-6 ,um. For the 44, 50, and 250 ,um bulk layers, however, there is almost c&tainly a large component of vertical current flow in the sample. The result of the vertical component is the addition of a large spreading resistance term to the overall contact resistance, greatly complicating the analysis of the contact structurer J. Appl. Phys., Vol. 77, No. 2, 15 January

1995

Recent articles in the literature have called into question the effect of hydrogen on the resistivity of diamond. Large increases in the resistivity have been observed after annealing in nitrogen following plasma chemical vapor deposited (CVD) growth of diamond films.15 In addition, exposure of natural type IIb diamonds to a hydrogen plasma has been shown to result in a large decrease in resistivity.16 In a previous paper we noted that annealing in argon had the same effect as annealing in nitrogen, but without the possibility of nitrogen interacting with either the contacts or the diamond itself.17 In order to clarify this picture, we monitored the effect of a “dehydrogenation” step added to the annealing sequence. In this procedure the diamond sample was annealed at 300 “C for 2 h in a high purity argon ambient (dew point less than - 115 “C) after each hydrogen annealing step. This experiment was carried out on both a highly doped film and a lightly doped sample. The results of this test were inconclusive. Figure 4 indicates that hydrogen annealing has little, if any, effect on specific contact resistance measurements to highly doped films. Similar results were observed for lightly doped samples. It is also of interest to note the specific contact resistance of the silicon carbide and tantalum carbide contacts on type IIb natural diamond substrates studied by Fang et aZ.l’ They obtained an average value of about 1X10e3 c1 cm2 for both cases. The conventional linear transmission line was used in their study leading to the necessity of forming a mesa. This was accomplished using a CF4 plasma etch. A thin conducting layer was formed by inducing ion damage in the diamond. Thus the difference in rc between the two studies may be due to a difference in doping level, a difference in con-

*H,ANNEALED

10" 1 ASDEPOSITED

1 2

f No H,

, 4

I 8

ANNEALING TIME (mid

FIG. 4. Effect of a post-anneal dehydrogenation step on the specific contact resistance of a highly doped epitaxial diamond layer. Hewett

et al.

759


bide contacts, indicating that the modified circular transmission line model presented here can be used to quickly and easily determine specific contact resistances of metal contacts to diamond, while avoiding the need for a mesa etch. Furthermore, contacts produced by the method outlined here are suitable for device applications.

c 8 lo” % 5 10-Z a L z IO-3 P 2 IT 10.4

ACKNOWLEDGMENTS

L n IO”

-------OHMIC CONTACT

10” 10’ VERTICAL

102 103 FIELD EFFECT TRANSISTOR

The diamond samples used in this study were provided by Dr. Michael Seal of Sigillum, B.V., and Drukker International, B.V. The authors gratefully acknowledge the support of the SDIO/IST through Max Yoder of the Office of Naval Research.

RESISTANCE

IO’ BREAKDOWN

VOLTAGE

105 (V)

FIG. 5. Theoretical drift region resistance of a vertical field effect transistor as a function of breakdown voltage for several temperatures. The diamond was assumed to have a mobility of -1500 cm$V s with no compensating dopants and a breakdown field of 5 X 10” V/cm.

lightly damaged diamond versus undamaged diamond, or an effect of the plasma etch. A consideration of the contribution of ohmic contact resistance to overall device resistance is also instructive. Figure 5 shows the calculated resistance of the drift region between the gate and collector of a vertical field effect transistor as a function of break down voltage.‘l Also plotted in this figure is a flat line representing the ohmic contact resistance measured on the highly doped epitaxial films. It is clear from the figure. that there exists a wide range over which these contacts are suitable for device applications, with negligible effect on device performance. tatting

CONCLUSIONS The specific contact resistance of Ti and MO refractory carbide contacts to diamond has been measured. The values determined from the contacts to the bulk type IIb diamond samples are in reasonable agreement with those published previouslyl’ for silicon carbide or tantalum carmetal

760


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Hewett et al.
