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AN IMPROVED MODEL TO EXPLAIN OHMICCONTACT RESISTANCE OF n-GaAs AND

OTHER SEMICONDUCTORS

WV DINGFEN and WANG DENING

Shanghai Institute of Metallurgy, Academia Sinica, Shanghai, China

and

KLAUS HEIME

Solid State Electronics Department, University of Duisburg, Duisburg, F.R.G.

Received 17 Jun e 1985; in revisedform 1 August 1985)

Abstract A model is proposed which explains the inverse proportionality between specific contactresistance pc and the carrier concentration (N,) of n-GaAs ohmic contact obtained experimentally verywell and can be extended to the ohmic contact of other semiconductors. This model assumes that p, iscomposed of two parts p,., and pc,. The contact resistivity pc, is due to the contact between the alloy andthe underlying heavily doped contact region (N,, for n-type contact, N,, for p-type contact) formed bydoping from the contact alloys during annealing. The contact resistivity p,, is caused by the barrier height( Qz ) of the high-low junction between the heavily doped contact region and the bulk material. There aretwo aspects: (1) If bulk material is degenerated, i.e. N, > NC (N,: effective density of states in conductionband) or N, > N, (N,: effective density of states in valence band), the barrier height Qz vanishes and p,is mainly determined by pc, which depends solely on concentrations N,, and N,,. It is calculatedtheoretically. (2) When the bulk material is lightly doped, i.e. Nn < N, or NA i NV, then Qz appears andincreases with the decreasing of N,,( N*). If NDc or N,, are high enough, the field emission is the mainmechanism to control the carrier transport between the contact alloy and the underlying layer. In this case

pc is predominantly determined by pc, and an inverse proportionality between p, and No or N, can befound.

1. INTRODUCIION

Ohmic contacts with low specific contact resistancepc are very important for both optoelectronic andelectronic semiconductor devices. For the sake ofobtaining a lower p,, the alloys used for ohmiccontact always contain dopants, so that a thin andheavily doped layer can be formed beneath the con-tact alloy after annealing. The carrier concentration

of this heavily doped layer (ND, or NAc) may beseveral orders higher than that in the original bulkmaterial (ND or N,), and, in addition, ND, or NAcdepend soley on technological processes and there isno correlation with ND or N,. Thus, p, should beindependent of ND or N, , but, as a matter of fact, p,was found to have an inverse proportionality to NDby several authors working in the field of n-typeGaAs ohmic contacts[l-51. Consequently, somemodels to explain this phenomenon were put for-ward[6-81. Popovic[7] has derived a pc - Ni equa-tion on the basis of the low-temperature approxima-tion of the V-Z characteristic of the thermionicemission of the Schottky barrier, taking into accountthe quantum-mechanical effect via a generalizedWKB approximation, but the experimental resultscorrespond to it only qualitatively. Braslau[6] andHeiblum et al. [8] point out correctly that this model

is valid only when the ND, region is thin enough incomparison with the carrier mean free path, there-fore Popovics model deviates from most practicalcases.

The fact that AuGeNi forms an inhomogeneousohmic contact on n-type GaAs after alloying had ledto Braslaus[6] assumption that the current flowsthrough the Ge-rich islands, which are connected

together through the overlying metal. Thus for p >10e3 D cm (p-the resistivity of the original bulkmaterial), the contact resistance is dominated by thespreading resistance under the Ge-rich islands. Thespreading resistance is proportional to the p or in-versely proportional to ND since p is - N,qp)- with p as the mobility and q the electronic charge.Heiblum et al. [8] have measured p, of AuGeNiohmic contacts to n-type GaAs MBE epi-layer withdoping concentration in the range of (1016-1019)cmm3 and found that the contact resistance dependson ND in a much weaker degree than pc - l/N,.They have ascribed this evidence to the existence of ahigh resistivity layer under the contact. In this papera model to explain p, - N; dependence, developedby us before [9], has been modified so that it canpredict more details. According to this model there isno contradiction between Heiblum et al.s experi-

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490 W~J DINGF~.N ef ~1.

mental results and p, - Nr) dependence. This model current. Therefore the model in this paper assumesis valid not only for n-type GaAs, but can be ex- that the entire contact area conducts current, but nottended to other semiconductors. necessarily in a uniform manner.

2. IMPROVEI) MODEL TO EXPLAIN THE OHMICCONTACT MECHANISM

2.2 The assumptions of the improved model

2.1 The experimentul hnsis of the model(a) Tseng[lO] has grown l-2 pm thick GaAs MBE

active layers doped in the range of (lOh-lOX) cm .To form the ohmic contacts to these layers a heavilydoped GaAs layer, 500-8000 A thick, n = 8 X 10cm , was subsequently grown. Next a gradual butquick ( < 100 A) transition from these heavily dopedGaAs layers to degenerated or almost metallicsurfaces was obtained. The p, value measured byTseng is dependent on NI, in the active layer, i.e.N,, = 4 X 10 cm , p,=7.8~10~ Q cm andN = 1 x 10 cm , p, = 2.9 X 10 5 D cm. From

t&e experimental results it can be concluded thatthe different p, values are caused only by differentN,,, on which the barrier height of the high-lowjunction (%) depends. This fact considered by usformerly, let us to advance a new explanation[9]. Inthe next paragraph it will be modified and an im-proved model shall be put forward.

The conduction band diagram of a metal-n-GaAsohmic contact is shown in Fig. 1. Jt consists of threeregions: (1) The semiconductor bulk region N,,); (2)the alloyed highly doped semiconductor contact re-gion with average carrier concentration N,, due toinhomogeneous contact: (3) the barrier between themetal and region (2). It is apparent that the motionof electrons from the metal to the semiconductorbulk is influenced by a barrier between the metal andthe highly doped semiconductor region ( Q1 and abarrier between the highly and low-doped semicon-ductor region ( (Ii1 ). Thus p, is the sum of p, , causedby @, and p,, caused by (Ii?.

(A) The calculation of p:, : Depending on the N,,,value, a,, can be determined by either thermionicfield emission (TFE) or field emission (FE) models.Differentiation of the J (current density)- V (volt-age) equations given by Padovani et al. [13] for bothmodels according to the definition of p,,, i.e.

(b) Taking AuGeNi/n-GaAs ohmic contact as anexample-although the contact after alloying is in-homogeneous-our results of a semi-quantitative en-ergy dispersive analysis of both Ge rich islands (phase1) and Au rich overlying layers (phase 2) indicate

that Ge really exists in both phases. The experimen-tal results are summarized in Table 1.

pcothj&jcosh@)=

r(IA*7

(c) In the AuGe system p, increases with thedecreasing of Ge content from 12wt%Ge to 4wt%Ge(12). Certainly, with the decreasing of Ge content thenumber of islands which are relatively rich of Ge will

be reduced. From these two presumptions (b) and (c)it is obvious that not only the Ge rich islands butalso the Au rich phases conduct current; i.e. it can beassumed that both phases have the ability to conduct

X exp (1)

(This equation is va(b) FE model:

C,kE,, sin( nC,kT) Q1P,, = rA*T

exp E. 2)00

Table 1. Semi-quantitative energy dispersive analysis of phases composition?

Alloying Elements %

Alloy system temperature Phases Au Ge Ni Ga As

AuGe 400C Dark 37.62 15.26 21.23 25.68Bright 12.33 x.94 11.93 4.3x

Ni/AuGe/Ni 400C Dark 17.16 11.39 16.91 23.42 24.72Bright 40.57 8.75 6.70 24.66 17.63450c Dark 16.17 18.92 23.13 17.11 16 51

Brieht 67.14 11.47 0.67 16.01 1.69

tSemi-quantitative analysis means that the underlying substrate has a certain influence on theanalytical result, especially Ga and As.

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492 Wu DINGFEN er 11.

p,, < p, I_ p, is approximately equal to p,, and de-pends on the N,, value. It can be calculated accord-ing to eqn (1) or (2). Since N,,- depends solely onthe technological process and has no correlation with

N,, . there is a group of parallel horizontal linesrepresenting the different N,, concentration in theregion N,, > NC on the lg p vs lg Nn plot of Fig. 2.When N,) < NC , QD, appears and increases with de-creasing N,,. If the alloying process is optimum. i.e.N )( is very high, then p,, B p, . In this case pC isdetermined by p,, and according to eqn (8) p =

P - N ] . It is obvious that the horizontal linesshould turn to straight lines representing a differentN,, concentration at N, < NC with the slope about- 1 (see Figs. 2-5).

3. EXPLANATION OF THE EXPERIMENTAL

RESULT OF n GaAs OHMIC CONTACT

The experimental results of p - N; dependencein the AuGeNi/GaAs system published in litera-ture [l-3,5,6,8] are summarized in Fig. 2. Assumingthat the experiments were carried out under opti-mum alloying conditions the average carrier con-centration N,, is very high and tunnelling is thepredominant mechanism for transport of electronsbetween the contact alloys and region (2) (see Fig. 1).Thus the horizontal lines in Fig. 2 are calculatedaccording to eqn (2) and they should turn to straightlines of pc - N j relation, when N, < NC. It can beseen that the theoretical calculations agree very well

with the experimental results. It is reasonable thatNo,- is in the range of (2-5 X 10) cm (6). Thefluctuation of the experimental points can beexplained by more or less inhomogeneous contacts.

Heiblum et al.s experimental points are also shownin Fig. 2. Heiblum ef al. have concluded that p,exhibits a weak dependence on No (much weakerthan N; dependence) and they have ascribed thisphenomenon to an assumed high resistivity layerunder the contact, several hundred nanometers deep.We can see, however, that their results do not onlyagree well with other experimental results but alsowith our calculated lines. The reason is that thedoping levels in their experiments covered the rangeof (lO1h-lO) crnm3. In accordance with our model,this doping range is just located in the transitionregime of the two different mechanisms of ohmiccontact conduction, i.e. pc - pc when No < 4.1 x 10cm-? and P - P > when ND > 4.7 X lOcm- . It isobvious that there is no contradiction betweenHeiblums conclusion and that of other authors. Thisevidence just strongly supports that p - N; depen-dence is valid only when ND < NC..

4. APPLICATION OF THE MODEL TO OTHER

SEMICONDUCTORS

4.1 P-SThe experimental p - Nil dependence of Al/

P-Si ohmic contact published in the litera-ture[l6] expressed with dash-dotted lines up to N4

-3NA cm -

Fig. 3. Specific contact resistance p, vs dopant concentra-tion N for Al contacts on p-Si[l6]. --: eqns (2) and (X)

about 10 cm is shown in Fig. 3. A group ofparallel lines is the result of the theoretical calcula-tions described in this paper. The calculated resultsare in good agreement with the experiments, if N,,-is in the range of 8 x 10-15 x 10 cm . Theinhomogeneity of p in Bergers experiment[16], inaccordance with our model, is due to the inhomo-geneity of NAC after alloying. It is reasonable that Alcan dope p-Si to a hole concentration of about1 x 10 cmm3 with a concentration fluctuation ofabout k 50%. Therefore, this model can well explainthe ohmic contact of P-Si.

4.2 P-GuAs and P-InPRegarding the ohmic contacts of p-type GaAs and

p-type InP, there are no systematic measurements of

PC - NA relations. The experimental results measuredby different authors[17-261 using AuZn as contactalloys (individual points are AgZn and AuMg alloys)are shown in Fig. 4 and Fig. 5. The values of theparameters for the calculation of the horizontal linesare @ap = 0.48 eV, m* = 0.48 m,, and ecr = 13.1 forp-GaAs and (I-,, = 0.6 eV, m* = 0.81 m,, and c,, =12.35 for p-InP. Figure 4 shows that after alloyingthe hole concentration in the p-GaAs layer underthe contact rises to N,c = 3 X 10 cm~ forGopens[17], to 9 X 101ycm~3 for Sanada er al.s[18]and about 2 X 10 for Ishihara et ai.s experimentalresults[l9]. The alloy compositions were 10 nmZn/100 nm Au (GOPEN); 2.5wtSgZn in AuZn(SANADA) and lOwt%Zn in AgZn (ISHIHARA).In addition, Sanada and Ishihara have determinedthe optimum temperature and time for the alloying

process. Therefore, the difference of NAC. consistsin Zn dopant contents in the alloys and the optimi-zation of the alloying process. A similar situationoccurs for p-InP. Kuphals experiments[20] showthat a lower pc value can be obtained, if, instead of a(99/l) Au/Zn composition a (90/10) Au/Zn com-

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Ohmic contact resistance of n-GaAs 493

5. SUMMARY

1. It is assumed that pC is composed of two parts,

10 3p,, and p(,. pC, occurs between the contact alloy andthe underlying heavily doped contact region (N,,for n-type contact, NAC for p-type contact). pC, is

t10 caused by the barrier Qz of the high-low junciion

-E between the heavily doped contact region and thec. 10-5

bulk material. There are two situations: (1) If the

,bulk material is degenerated, i.e. ND B NC or N,, >NV, then @2 vanishes and pC is mainly determined

10+ by P which depends solely on NDC( NAc) values. p, Iis calculated theoretically. (2) When N, < N, orNA < NV, a, appears and increases with the decreas-ing of ND NA). If N,,( NAC) is high enough, i.e. field

1 6 1 7 1 8 ol9 1 2 1021 1022 emission is the main mechanism to control the car-3

Nb / cm -rier transport between the contact alloy and theunderlying layer, then pC is predominantly de-

Fig. 4. Specific contact resistance p, vs dopant concentra- termined by pC,. Only in this case, an inverse propor-

tion N4 for AuZn and AgZn contacts onp-GaAs. 0: tionality between pc and ND( NA) can be found.

Gopen er ul. [17] (AuZn). 0: Sanada et a/. [la] (AuZn). A:Ishihara et 01. [19] (AgZn). -: eqns (2) and (8).

2. On the lg pc - lg N,(lg N,) plot there is a groupof lines representing the above mentioned two mech-anisms of ohmic contact with different NDC(NAC)values, which are determined by the quality of ohmiccontact technology.

1O- 71

Duisburg.

105 1016 10'7 10'8 10'9 10m 1021 1022 REFERENCES

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Acknowledgements-We are much indebted to Mr. D.Majumdar (University of Duisburg) for his skillful semi-quantitative energy dispersive analysis. Part of the work wasperformed while one of the authors (Wu Dingfen) wasan Alexander von Humboldt Fellow at the University of

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