Appl Phys ADOI 10.1007/s00339-012-7518-x

Effect of annealing on contact performance and electricalproperties of p-type high purity germanium single crystal

Gang Yang · Dongming Mei · Jayesh Govani ·Guojian Wang · Muhammad Khizar

Received: 25 July 2012 / Accepted: 21 December 2012© Springer-Verlag Berlin Heidelberg 2013

Abstract Van de Pauw Hall measurement is an effectivemethod to characterize the properties of semiconductors,such as bulk concentration, mobility, and resistivity, all ofwhich are used to describe the purity level in the semi-conductors. However, the performance of the ohmic con-tacts has a direct impact on the reliability and accuracy ofthe results obtained from the Van de Pauw Hall measure-ment. In the present work, the influences of different an-nealing techniques on the performance of the InSn ohmiccontacts have been investigated using a High Purity Ger-manium (HPGe) crystal sample. The results show that thepreferred annealing condition is at 400 °C for 1 hour, whichhas provided a significant improvement of the InSn contactquality and microscopic homogenization of the impuritiesin the HPGe crystal. The carrier concentration, charge mo-bility, and resistivity of the sample annealed at 400 °C for1 hour are 5.772 × 1010/cm3, 1.883 × 104× cm2/Vs, and5.795 × 103 × � cm at 77 K, respectively.

1 Introduction

Germanium was regarded as the first important semiconduc-tor material in early 1940s, based on the assumption that itwas easier to purify and control the impurity content due toa lower melting point than silicon and other compound ma-terials. However, since the first silicon transistor was intro-duced into the electronics industry in 1954, silicon replacedgermanium and became the dominant semiconductor mate-rial because it was cheaper and available in large quantities.

G. Yang (�) · D. Mei · J. Govani · G. Wang · M. KhizarDepartment of Physics, The University of South Dakota,Vermillion, SD 57069, USAe-mail: gang.yang@usd.edu

Over the last two decades, germanium has regained a lotof interest as a semiconductor material for optoelectronicand electronic applications [1]. Single crystal germaniumhas been mainly used as window materials for infrared op-tics and substrates for optoelectronic devices [1, 2]. HPGewith an electrically active impurity concentration of only109–1010 cm−3 can be used in the construction of large-volume, thick radiation detectors [1, 3–5]. HPGe singlecrystals are usually grown with the Czochralski method [2].However, many problems concerning the characterization ofgermanium single crystals still need to be solved; one ofwhich is how to prepare the ohmic contact with low resis-tance [6].

The ohmic contact refers to the contact between a metaland a semiconductor allowing carriers to flow in and out ofthe semiconductor, having no direct impact on electrical per-formance of the semiconductor and the relevant devices [7].The ohmic contacts play a very important role in preciseconductivity measurements. As a result, extensive studies onthe ohmic contacts for various semiconductor materials havebeen carried out [8]. The various fabrication methods andtheir performance of the ohmic contacts are being studied.The fabrication of the ohmic contacts frequently includesthe past-annealing process, which can either lead to alloyedcontact between the deposited metals and the semiconductoror reduce the unintentional barrier at the interface. There aremany studies on the influences of the past-annealing treat-ment on the performance of the ohmic contacts for varioussemiconducting materials [9, 10]. As we know, the suitablecontact materials for germanium crystals include In, InGaeutectic, InSn, AuGa, and AuSb alloys. Satisfactory contactscan be formed at room temperature by using a liquid InGaeutectic for p-type crystals and liquid indium-mercury eu-tectic for n-type crystals. Additionally, implanting boron onp-type crystals followed by annealing can form the ohmic

G. Yang et al.

Fig. 1 Schematic diagrams ofVan der Pauw configurationused in determination ofresistivity and Hall voltage

contacts down to 1.2 K. The diffusion of lithium at 300 °Cfor 10–30 min into the surface of n-type crystals can formthe ohmic contacts [3]. It was reported that an ohmic contacthas been prepared on the p-type crystals by annealing InGaeutectic at 300 °C in N2 gas and then putting indium solderat 200 °C; annealing to the lithium at 300 °C in N2 gas incombination of 1 %Sb-doped indium solder can prepare theohmic contact on the n-type crystals [11].

Van der Pauw Hall measurement is an effective methodto determine the electrical properties of semiconducting ma-terials, such as resistivity, carrier concentration, and mobil-ity [11–19]. However, because contact metal and germa-nium crystal are two dissimilar materials with different co-efficients of thermal expansion (CTE), they will inevitablymismatch during cooling down to the liquid nitrogen tem-perature. Thus, the performance and stability of the contactwill degenerate so that measured results by the Hall systemwill be invalid. To the authors’ knowledge, there is no re-search on the improvement of performance of InSn ohmiccontact by the annealing treatment. However, it is very sig-nificant to investigate the influences of the past-annealingon the InSn ohmic contact. In the present work, differentannealing techniques were used in order to find the bestway to make good ohmic contacts and improve the Hallmeasurement data. This work will be significant to makinghigh quality ohmic contacts on the dark matter detector con-structed by HPGe single crystals.

2 Experimental procedure

Several germanium samples grown at the University ofSouth Dakota were tested together with a sample fromLawrence Berkeley National Laboratory. In the presentwork, we have used a four-point Van der Pauw Hall mea-surement technique to measure the electrical propertiesof the sample. It is well-known that the Van der Pauwmethod, originally developed for measuring the resistivityof arbitrary-shape sheet samples, puts forward the followingrequirements for contacts and samples: (1) contacts are onthe edge of the sample, (2) contacts are sufficiently small,(3) the thickness of the sample is uniform, and (4) the sam-ple does not contain any isolated holes [20]. We cut the

samples into a 1.5 cm×1.5 cm square sheet sample withthickness of 1 mm. After cut and squared, the samples werepolished, then ultrasonically washed in a methanol solution,rinsed with deionized water, and finally dried by nitrogengas. After cleaning, the indium (95 wt%) and tin (5 wt%)alloy (InSn) ohmic contacts with very small size comparedto the sample dimensions were soldered onto four corners ofthe sheet sample at the welding temperature of 200 ◦C. Theschematic diagrams of the Van der Pauw configuration usedin determination of resistivity and Hall voltage are shown inFig. 1. Prior to annealing, a Vander Pauw Hall measurementof the sample was conducted in a Hall measurement system(Ecopia HMS-3000with a 0.55 T permanent magnet, Ko-rea) at both room temperature and 77 K. Subsequently, thesample was annealed on a ceramic boat in the tube furnace(Barnstead Thermolyne 21100, USA). The annealing tem-peratures were 200 ◦C, 400 ◦C, and 450 ◦C, respectively,with a heating rate of 3 °C/m and dwelling time of 1 hour.After annealed each time, the Vander Pau Hall measurementwas carried out at both room temperature and 77 K again.During the entire annealing process, nitrogen gas with pu-rity of 99.90 % was flowing through the tube to prevent thesample from becoming oxidized.

3 Results

In the present work, we found that all of I–V curves forthe sample prior to and after annealing treatment have agood linearity at both room temperature and 77 K, indi-cating a good ohmic contact characteristic. For example,Figs. 2(a) and (b) show the linear I–V curves at room tem-perature and 77 K for the sample after annealed at 400 ◦Cfor 1 hour. Additionally, in order to investigate the stabil-ity of and improvement to the In/Sn ohmic contacts due toannealing treatment, we have determined the ohmic behav-ior and specific contact resistivity using transmission linemethod (TLM). Figures 3(a) and (b) show TLM data mea-sured by four-point method at room temperature. There-fore, before annealing, the specific contact resistivity ofthe In/Sn ohmic contact was 4.76 × 10−2 � cm2, whilethe specific contact resistivity became 1.88 × 10−2 � cm2

after annealed at 400 ◦C for 1 hour. The reduction in

Effect of annealing on contact performance and electrical properties of p-type high purity germanium single

Fig. 2 I–V curves at room temperature (a) and 77 K (b) for the sample after annealed at 400 ◦C for 1 hour

Fig. 3 TLM measured data for the sample. (a) No annealing and (b) annealed at 400 ◦C for 1 hour

contact resistance shows that annealing at 400 ◦C for1 hour has a great improvement of In/Sn ohmic con-tact.

The influences of annealing temperature on carrier con-centration, mobility, resistivity and Hall coefficient of thesample are shown in Figs. 4(a), (b), (c), and (d). Afterannealing at 200 ◦C with a dwelling time of 1 hour, thecarrier concentration, mobility, resistivity, and Hall co-efficient measured at both room temperature and 77 Kare almost the same as those without an annealing treat-ment, indicating that the annealing treatment at 200 ◦Cdoes not have any improvement of the electrical perfor-mance of the sample. When the annealing temperatureincreases to 400 ◦C, the carrier concentration at roomtemperature decreases by 37.74 % of −8.45E + 13/cm3

to −5.26E + 13/cm3, while the mobility and resistivity

at room temperature increases by 27.13 % of 1.58E +3/cm2 V−1 s−1 to 2.01E + 3/cm2 V−1 s−1 and by 20.99 %of 46.75 � cm to 59.17 � cm, respectively. However, themeasured results at 77 K show that a very significantchange has occurred in the electrical performances dueto annealing treatment at 400 ◦C. In this case, the car-rier concentration is 5.72E + 10/cm3, about 0.69 % of8.25E + 12/cm3 of the sample without annealing treat-ment. The mobility increases by 36.43 times of 4.90E +2/cm2 V−1 s−1 to 1.883E + 4/cm2 V−1 s−1, while the re-sistivity increases by 2.76 times of 1.54E + 3 � cm to5.795E + 3 � cm, also. When the annealing tempera-ture further increases from 400 ◦C to 450 ◦C, the car-rier concentration at 77 K increases by 1.71 times of5.72E + 10/cm3 to 1.55E + 11/cm3, while mobility and re-sistivity decrease by 31.81 % of 1.883E + 4/cm2 V−1 s−1

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Fig. 4 Measured results of the sample, annealed at different temperatures, at room temperature and 77 K. (a) Carrier concentration, (b) mobility,(c) resistivity, and (d) Hall coefficient

to 1.22E + 4/cm2 V−1 s−1 and by 42.58 % of 5795 � cmto 3326 � cm. The Hall coefficient has the same changetrend as the carrier concentration. Additionally, it is notedthat the sign for carrier concentration and Hall coefficient isnegative at room temperature, indicating an n-type germa-nium crystal, while it changes to positive at 77 K, indicatinga p-type germanium crystal. In terms of scattering mecha-nisms in semiconductors, the scattering sources include ion-ized impurity scattering, acoustic phonon scattering (alsocalled lattice scattering) and other scatterings, such as neu-tral impurity scattering, optical phonon scattering, surfacescattering, and defect scattering. The most important scat-terings are ionized impurity scattering and lattice scatter-ing. The lattice scattering is a dominant mechanism at roomtemperature, while the dominant scattering comes from theionized impurities at 77 K [21]. Additionally, the mobilityis dependent on the drift velocity, which is dependent onthe scattering. For the intrinsic germanium, the differencebetween the electron mobility and the hole mobility is re-

sponsible for the Hall coefficient at room temperature. Be-cause at room temperature the electron mobility of intrinsicgermanium is about 3900 cm2 V−1 s−1, which is 2000 big-ger than 1900 cm2 V−1 s−1 of the hole mobility, the sign forcarrier concentration and Hall coefficient is negative at roomtemperature. However, because the intrinsic conduction wasdominated by HPGe crystal at room temperature, which canalways be reduced by cooling to low temperature, the crys-tal type defined by the measurement at room temperatureis not useful for judging the crystal type. On the contrary,to obtain useful information, the crystal must be cooled tothe extrinsic conduction range where the impurity conduc-tion becomes dominant [3]. Thus, the investigated sampleshould be the p-type HPGe crystal due to its positive Hallcoefficient at 77 K. Additionally, the comparison among allof electrical properties of the sample with different anneal-ing treatments shows that the preferred annealing to InSnohmic contacts should be 400 ◦C with a dwelling time of1 hour.

Effect of annealing on contact performance and electrical properties of p-type high purity germanium single

4 Discussions

4.1 Resistivity

In the Van der Pauw Hall measurement, the resistivity of asample could be written in the form of Eq. (1) [17]:

ρ = πd

ln 2× RAD,BC + RCD,AB

2× f

(RAD,BC

RCD,AB

)(1)

where d is the sample thickness and RDA,BC is the resis-tance, which is equal to V BC/IAD. V BC is the voltage dropbetween contacts B and C when the current IAD is appliedbetween contacts A and D. Similarly, RCD,AB is defined asvoltage drop V AB between contacts A and B per unit cur-rent through contacts C and D. The correction factor, f , isa function of the ratio (RAD,BC/RCD,AB), which could bewritten as the form of Eq. (2):

RAD,BC

RCD,AB= VBC

IAD× ICD

VAB(2)

The correction factor is dependent upon the geometricshape and contact configuration [18]. For the symmetricalsamples, such as circles and squares, if the four contacts aresymmetrically located on the edge of the sample, f shouldbe equal to 1 due to (RAD,BC = RCD,AB). However, this isa perfect case. Except for the above influential factors, in-homogeneous distribution of the impurities in the sample isalso a significantly influential factor [16].

In our Van der Pauw Hall measurement system, both V AB

and V BC are produced simultaneously when a given currentis applied to a sample. Thus, the values of IAD and ICD areequal while their directions are different. In this case, Eq. (2)could be further simplified into Eq. (3):

RAD,BC

RCD,AB= VBC

IAD× ICD

VAB= VBC

VAB(3)

Thus, the correction factor could be a function of the ratioof V BC/V AB. Table 1 shows measured voltages in the ab-sence of the magnetic field, and Hall voltages at the appliedcurrent of 1 µA and at 77 K. For the sample without an-nealing or annealed at 200 °C, the ratios V BC/V AB are bothover 2, indicating that the correction factor is less than 1.Because the investigated sample in the present work was aperfect square sample and four point contacts are symmetri-cally located on the four corners of the sample, the correc-tion factor should be 1. This result could be related to theinhomogeneous distribution of the impurities in the sampleand poor contact, which can be further verified by the mea-sured results of the sample after annealing at both 400 °Cand 450 °C. After annealed at 400 °C for 1 hour, V BC/V AB

is about 0.75, but after annealing at 450 °C, it approximatesto 1, hence the correction factor is 1. The improvement ofthe measured results due to annealing treatment could beinterpreted as below. Firstly, the inhomogeneous distribu-tion of the impurities in the sample was greatly improved

in the annealing process due to an assumption that the im-purity atoms redistribute through thermal diffusion. How-ever, because the investigated sample is HPGe crystal, it isvery difficult to determine the distribution of impurities inthe sample. Secondly, the ohmic contact performance wasgreatly improved in the annealing process. Because InSn al-loy and the germanium crystal are two dissimilar materialswith different coefficients of thermal expansion (CTE), theywill inevitably mismatch during cooling down to the liquidnitrogen temperature. Thus, the connection between contactand germanium will degenerate so that a big error may occurin the measured results. In the annealing process, indium andtin can diffuse into germanium crystal, which can in turn fur-ther strengthen the adhesion between the contact and germa-nium. However, the diffusion of indium and tin into germa-nium crystal at much higher temperature may contaminatethe germanium crystal [3], which will result in degenerationof electrical properties of germanium crystal. In order to ver-ify the diffusion of contact materials into the sample, we sentthe sample after annealed at 450 °C to Cerium Laboratories,LLC (Austin, Texas, USA) for High Resolution InductivelyCoupled Plasma Mass Spectroscopic (HR-ICPMS) analysis.The results show that the contents of indium and tin in thesample are 13.620 micrograms and 0.849 micrograms, re-spectively. This is why the electrical properties of the ger-manium crystal, to some degree, degenerate after annealingat 450 °C compared to annealing at 400 °C. Thus, the prefer-able annealing temperature is 400 °C.

4.2 Mobility

The mobility, μH, for the sample can be calculated usingthe data obtained from the Van der Pauw Hall measurement.The mobility is defined by Eq. (4):

μH = |RH|ρ

(4)

where ρ is the resistivity and RH is the absolute value of theHall coefficient, which is given by Eq. (5):

RH = d

B× VH

I(5)

where V H is the average Hall voltage, d sample thickness,B magnetic field, and I applied current. It can be found fromboth Eqs. (4) and (5) that μH is proportional to the absoluteHall voltage, which is equal to the difference between themeasured Hall voltage (for example, V mAC and V -mAC inTable 1) and V AC as shown in Table 1. In fact, V AC is an off-set value, which is the Hall voltage readings in the absenceof a magnetic field, given by Eq. (6):

VAC = VAB − VBC (6)

V AC could result in the error in the measured Hall volt-age. The ideal case is VAC = 0. Table 1 shows that V AC de-creases with increases in the annealing temperature. When

G. Yang et al.

Table 1 Voltages measured at 1 µA and at 77 K for the sample annealed at different temperatures

Annealing temperature ◦C Voltage/mV V BCV AB Hall voltage/mV

AB BC AC Positive magneticfield MAC

Negative magneticfield MAC

No annealing −2.184 −5.094 2.917 2.332 3.297 2.469

2.064 5.069 −2.962 2.456 −3.38 −2.563

200 −1.834 −4.734 2.653 2.581 2.982 2.183

1.82 4.292 −2.666 2.358 −3.02 −2.239

400 −6.176 −4.611 −1.673 0.747 20.238 −29.467

5.946 4.515 1.522 0.759 −20.716 28.996

450 −7.303 −7.497 0.188 1.027 22.949 −21.516

7.106 7.411 −0.312 1.043 −23.402 21.057

Fig. 5 Hall voltage of the sample, annealed at different temperatures, across AC as a function of applied current at room temperature and 77 K.(a) No annealing and annealed at 200 ◦C, and (b) annealed at 400 ◦C and 450 ◦C

the annealing temperature is 450 °C, V AC approximates tozero. In order to correct the error, V AC should be subtractedfrom the Hall voltage readings obtained at magnetic fields.Figures 5(a) and (b) show Hall voltages across AC of thesample annealed at different temperatures as a function ofthe applied current at 77 K, in which V AC has been reducedfrom the measured values. It is found that good linear re-lationships between Hall voltages and the applied currentshave been obtained. The average value of the two slopes forthe different orientations of the magnetic field can be usedto calculate the average Hall coefficient by Eq. (5). Addi-tionally, both Table 1 and Figs. 5(a) and (b) indicate that thesample after annealing at 400 °C and 450 °C has very strongHall-effect, so the mobility, μH, is much higher than thatof the sample without annealing treatment and annealing at200 °C, as shown in Figs. 4(b) and (d). Values of μH ob-tained from the Van der Pauw measurement may be lowerthan true bulk values for several reasons: poor contact, theeffects of surface charge, macroscopic nonuniformity, andmicroscopic inhomogeneities [22]. From our researches, it

can be concluded that the lower Hall coefficient, RH, andlower mobility, μH, at 77 K for the sample without annealingtreatment should be related to the poor contact quality andmicroscopic inhomogeneities in the sample. The annealingtreatment to the sample and contacts has provided a greatimprovement of the contact quality and homogenization ofthe impurities in the sample.

5 Conclusions

The different annealing treatments were used to improve theperformance of the ohmic contacts and microscopic inho-mogeneities in the HPGe crystal. The Van der Pauw Hallmeasurement indicates that for the sample without anneal-ing and annealing at 200 °C for 1 hour, the Hall effect isvery weak at 77 K. On the contrary, the Hall effect at 77 Kis very strong for the sample after annealing at 400 °C and450 °C for 1 hour. These results should be attributed to a fact

Effect of annealing on contact performance and electrical properties of p-type high purity germanium single

that the annealing treatment has greatly improved the adhe-sion between the contact and surface of the sample and themicroscopic homogenization of the impurities in the sample.Both measured and calculated results show that the preferredannealing process is at 400 °C for 1 hour.

Acknowledgements The authors would like to thank Dr. Yuen-DatChan at Lawrence Berkeley National Laboratory for their help inpreparing the materials. We also would like to thank Dr. Qiquan Qiaofrom South Dakota State University for preparing the samples for us.This work was supported by the DOE grant DE-FG02-10ER46709 andthe state of South Dakota.

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