Single crystal diamond for electronic applications

Diamond and Related Materials 13 (2004) 320–324

Single crystal diamond for electronic applications J. Isberga,*, J. Hammersberga, D.J. Twitchenb, A.J. Whiteheadb a

Division for Electricity Research, Uppsala University, Box 534, S-751 21 Uppsala, Sweden b Element Six Ltd, King’s Ride Park, Ascot, Berkshire, SL5 8BP, UK

Abstract There is significant academic and industrial interest in developing electronic devices for high-frequency, high-power and hightemperature applications. This interest has generated considerable research efforts in wide-bandgap semiconductors. Of these materials diamond has by far the most interesting and extreme properties, i.e. mechanical, optical, thermal as well as electronic. Diamond exhibits the highest breakdown field and thermal conductivity of any material and has the highest carrier mobilities of any wide-bandgap semiconductor, thereby enabling the development of electronic devices with superior performance with regards to power efficiency, power density, high-frequency properties, power loss and cooling. Nevertheless, the breakthrough of diamondbased electronics has not yet happened, largely due to the difficulty of synthesising high-quality single crystal diamond. Recent advances in growing intrinsic and boron-doped single crystal diamond intended for electronic applications have resulted in films with exceptionally low defect densities. In the intrinsic material we have reported measured room temperature drift mobilities of 4500 cm2 yV s for electrons and 3800 cm2 yV s for holes (Science 297 (2002) 1670). These mobility values were determined by using the time-of-flight technique on thick intrinsic diamond plates. For comparison, this experiment was also performed on polycrystalline and natural diamond and on silicon. Here, we describe the details of these low-field drift mobility measurements and the modeling used to describe the space-charge-limited transient current. 䊚 2004 Elsevier B.V. All rights reserved. Keywords: Space-charge-limited current; Drift mobility; Diamond

1. Introduction Diamond has many extreme properties making it ideal as a semiconductor material for many high-power, highfrequency or high-temperature applications, see for example Refs. w1,2x. These properties include: a very high electric breakdown field strength, high mobility of both electrons and holes and the highest room temperature thermal conductivity of any material. However, due to the inconsistent crystal quality of both natural and synthetic diamonds the development of electronic devices in diamond has been severely limited up to now. Using diamond as a semiconductor material for electronic applications is not a new idea. As early as the 1920s, diamond was considered for use in photo detectors. However, the lack of control of electronic properties, high defect density, size limitations and of course the high cost prohibits the wider use of natural diamonds in semiconductor applications. In the 1950s the first synthetic diamonds were produced in a high-pressure, *Corresponding author. Tel.: q46-18-471-5821; fax: q46-18-4715810. E-mail address: [email protected] (J. Isberg).

high-temperature (HPHT) process. Today HPHT diamonds are in widespread use in many industrial mechanical applications, such as drilling or cutting, but are generally unsuitable for electronic applications. The only way to meet the most demanding applications of highpower and high-frequency electronics that have been long predicted for diamond is to achieve large area doped and un-doped single-crystal chemically vapor deposited (SCCVD) diamond. Recently reported advances in the quality and size of SCCVD diamond w3x and advances in n-doping of diamond w4,5x indicate that diamond electronics are becoming a real possibility. Drift mobility measurements of un-doped SCCVD diamond have shown very high mobilities (4500 and 3800 cm2 yV s) for electrons and holes, respectively w3x. In this article we describe in more detail these drift mobility measurements. 2. Time-of-flight measurements 2.1. Experimental setup

0925-9635/04/$ - see front matter 䊚 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2003.10.017

The response of a semiconductor to a transient optical

J. Isberg et al. / Diamond and Related Materials 13 (2004) 320–324

excitation can be employed to study the transport and recombination of charge carriers. The measured photocurrent following a short pulse of exciting radiation is dependent both on the recombination of carriers within the sample and on the extraction of carriers by an electric field. Information about lifetime and mobility can be extracted from the current decay curve. An example of such an experiment to measure minority carrier lifetime and mobility of extrinsic material is the well-known Haynes–Shockley experiment w6x. For intrinsic material similar techniques are available, although the interpretation is generally more complicated w7x and comparison with simulations may be necessary to extract the desired parameters. For the drift mobility measurements we use a 5= frequency multiplied Q-switched Nd–YAG laser to illuminate the samples. This laser delivers 5-ns pulses with a wavelength of 213 nm at a repetition rate of 10 Hz. The pulse energy has a maximum of 18 mJ, but it can be reduced using an attenuator to the desired level. UV photons with wavelength 213 nm have energy larger than the bandgap of diamond of 5.47 eV (corresponding to 225 nm) and indirect (phonon-assisted) electron– hole pair generation across the bandgap will occur with this illumination. The absorption of photons in this process is very strong; therefore, carriers are generated only in the first few micrometers closest to the illuminated surface of the sample. For the measurements on silicon the laser was 2= frequency multiplied to obtain 512-nm wavelength. This wavelength has a similar penetration depth in silicon as 213-nm light has in diamond. The SCCVD samples in this report were synthesized using a microwave plasma-assisted CVD technique w3x and were characterized using several methods including Raman, SIMS, EPR, photo-luminescence, cathodo-luminescence, X-ray rocking curves, TEM and traditional absorption techniques. The material was found to be of exceptional purity with respect to intrinsic and extrinsic defects, showing a characteristically strong CL freeexciton signal and a measured total nitrogen concentration below 1=1015 ycm3. In addition, the growth conditions and careful substrate preparation resulted in a very low dislocation density (-106 ycm2). All samples to be measured were patterned with metal contacts, the top one of which was semi-transparent to enable illumination. For this purpose, titaniumyaluminiumygold mesh contacts were formed on the {1 0 0} surfaces using physical vapor deposition combined with standard lithography and wet chemical etching (Fig. 1). The contacts are annealed in an argon atmosphere at 600 8C. The sample thickness, L, of the processed CVD diamond plates studied ranged between 390 and 690 mm. After application of metal contacts the samples are mounted in sample holders and placed inside a purpose-

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Fig. 1. Optical micrograph of a single-crystal CVD sample with a TiyAlyAu mesh contact. This sample is 690 mm thick and the illuminated zone is 3 mm in diameter. Inset shows an enlargement of the contact, which has a mesh spacing of 40 mm. The dark appearance of the sample, which is in fact transparent, is due to the lighting conditions in this micrograph.

built current probe. This probe was carefully designed to give the necessary bandwidth to be able to measure transit times of a few nanoseconds. The sample is biased via a 50 V, 30 m long coaxial cable charged to a maximum of 2 kV by a pulsed power supply. To achieve lower impedance up to four, identical cables can be connected in parallel. The current is measured over a resistive load, either a 50-V termination of the outgoing cable or over an auxiliary resistance inside the probe. The digital oscilloscope used was a Tektronix TDS684C with a 1 GHz bandwidth and 5 Gsys sampling rate. The oscilloscope was triggered by the laser Q-switch signal. The bias is applied in 100-ms pulses, synchronized with the laser to minimize undesirable polarization effects, although for the work here a DC bias seems to work equally well. A schematic of the current probe is shown in Fig. 2. The sample is illuminated from above, the incoming bias cables are connected to the top connectors (2) while the oscilloscope is connected to the bottom connector (4). Using this setup, the transient current was measured for several SCCVD samples, polycrystalline and natural diamond. For comparison, measurements on samples of high-resistivity silicon were also performed. 2.2. Transient space-charge-limited current simulations When a sample is illuminated by above-bandgap radiation an electron–hole plasma is formed near the illuminated surface. From this plasma, carriers (electrons or holes depending on the bias polarity) are drawn towards the back electrode. The idea behind the timeof-flight (TOF) technique is to measure this transit time

J. Isberg et al. / Diamond and Related Materials 13 (2004) 320–324

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Fig. 3. Transient currents following optical excitation measured in three different samples (SCCVD, polycrystalline CVD and natural IIa diamond) biased to y50 V. The SCL transient can only be detected in the SCCVD sample. Fig. 2. Schematic of the current probe. (1) Sample holder; (2) bias connectors; (3) outgoing connection; (4) auxiliary ballast resistors.

for a given bias from which the mobility can then be calculated. In the very simplest case, with no trapping and assuming that the electric field is constant across the sample during the transit, the transit time tTOF is given by tTOFs

L2 me,hU

the sample must be homogeneous, and the carrier lifetimes in the plasma must at least be of the order of tTOF. In samples with a very long carrier lifetimes a third peak is observed, which is due to ambipolar diffusion of the plasma across the sample. The basic theory of the SCL transient was first given by Many and Rakavy w11x, who derived analytical expressions for the transient SCL current. In the absence of trapping they derived a modification of Eq. (1):

(1)

where L is the sample thickness, U the bias voltage and me,h the drift mobility for electrons or holes. For the assumption that the electric field is constant to hold true, it is necessary that Q, the charge of the carrier in the electron–hole plasma created by the light pulse, is substantially smaller than the charge on the electrodes of the sample, i.e. Q
tTOFs

bL2 me,hU

(2)

with bs2(1y(1y6e))f0.787, i.e. the transient is faster than in the small signal case due to the space-charge effects. In the presence of traps the transient is generally slower and the current maximum less pronounced. This theory was further developed by Juska et al., who included a realistic absorption profile of the incident light w12x.

Fig. 4. Transient currents in a SCCVD sample following optical excitation clearly showing the variation in TOF with bias voltage.

J. Isberg et al. / Diamond and Related Materials 13 (2004) 320–324

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accounts for the optical generation of electron–hole pairs. The mobilities are assumed constant for the low carrier concentrations and fields in our experiments. In solving this system of equations it is convenient to rescale to dimensionless quantities, e.g. x9sxyL, t9styŽL2ymnU. E9sEy(UyL) n9snyŽ´UyqL2. , p9spyŽ´UyqL2. r9SRHsrSRHyŽ´mnU2yqL4. g9sgyŽ´mnU2yqL4. j9sjyŽ´mnU2yL3.

Fig. 5. Plots of electron (n) and hole (p) concentrations in the sample during the SCL transit. In this example g9s1000 exp(yx9y 0.015)d(t9), t9n,p41.

To get a more detailed understanding of the SCL current data and to be able to extract mobility values, the experiment was modeled by numerically solving the coupled drift-diffusion and Poisson equations, which in the presence of traps read jnsqnmnEqqDn

≠n ≠x

jpsqpmpEyqDp

≠E q sy B nypq8ntiy8ptjE F ≠x ´C D G i j ≠p 1 ≠jp sgyrSRHq ≠t q ≠x

≠p ≠x

≠n 1 ≠jn sgyrSRHq ≠t q ≠x

≠nti scni ŽnŽNtiynti.yuni nti. ≠t

(4)

In the absence of trapping (cinscjps0) simulations show that there is a weak dependence of t9TOF'tTOF y (L 2 ymnU) on other parameters assuming that the penetration depth of the radiation is much smaller than the thickness of the sample and that the recombination lifetime is large compared to the timescale of interest. Thus t9TOF, or equivalently b in Eq. (2), can be determined from the simulations with good accuracy for a given experimental situation. The time evolution of a typical SCL transient is illustrated in Fig. 5, where the carrier concentrations are plotted as a function of the distance x9 from the illuminated electrode for three different times (t9s0, 0.15 and 0.65). The illuminated electrode is negatively biased in this example so that electron conduction is responsible for the SCL current. In Fig. 6 the resulting current is plotted against time. The current maximum occurs at t9s0.65 in this example. We use this model to calculate the b factor under given experimental conditions. By measuring tTOF for a given bias voltage the mobility can then be calculated from Eq. (2). Due to the immature understanding, at present, of trapping phenomena in CVD diamond the inclusion of trapping adds many unknown parameters to the simulations. In general, however, with trapping present, the

≠pjt np scjpŽpŽPjtypjt.yujppjt. rSRHs ≠t tnpqtpn jsjnqjpq´

≠E ≠t

(3)

where x (0(x(L) is the distance from the illuminated contact, nit(pjt) is the density of trapped electrons (holes) in trap i( j), Nit(Pjt) is the trap concentration, cni (cjp) is the probability of capture of an electron (hole) by the trap, uin(ujn) is a constant describing thermal release from the trap and gsg(t, x) is a generation term that

Fig. 6. Simulation of the transient SCL current (same parameters as in Fig. 5). The current maximum occurs at t9TOFs0.65 here.

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J. Isberg et al. / Diamond and Related Materials 13 (2004) 320–324

Fig. 7. TOF data from 500-mm-thick high-resistivity silicon samples at two different temperatures.

transient is retarded and the corresponding current maximum occurs later (or disappears altogether). Thus, mobilities calculated using values of b from the trapfree model are underestimated if there is substantial trapping, and mobility values obtained in this way are lower bounds of the actual mobility. In addition, with shallow trapping a tTOF;(L 2 yU)a behaviour, with a) 1, is expected w13x. For the SCCVD samples we have studied a is very close to 1, from which we conclude that shallow trapping has an insignificant influence on the SCL current in the SCCVD samples. 2.3. Experimental results The method, described above, to combine the measurements of the TOF with a numerical calculation of the correction factor b in order to find the carrier drift mobilities was tested by verifying the carrier mobility in high-purity silicon. The setup for this experiment was identical to the one used for diamond, except that 512nm wavelength was used. To get mobilities comparable to diamond at room temperature the silicon samples were held at constant temperatures in the interval 150– 200 K. Fig. 7 shows the measured tTOF in silicon for holes at two different temperatures. From these data we find drift mobilities mh (152 K)s3100"200 cm2 yV s, mh (174 K)s2200"200 cm2 yV s in agreement with values reported in Refs. w14,15x. In four samples of SCCVD diamond we have, using this method, measured mobilities as high as 4500 and

3800 cm2 yV s for the electrons and holes, respectively w3x. In polycrystalline and natural diamond, on the other hand, it has not been possible to detect any current peak with the correct bias dependence. We attribute the absence of a detectable SCL transient current in these samples to a short lifetime of the carrier plasma, and in the case of the polycrystalline material possibly also to its lack of homogeneity. These experimental data on the electron and hole mobility, respectively, indicate a vast improvement in the growth of electronic grade CVD diamond material, which is a major step toward diamond electronics. In devices that utilize carrier transport across intrinsic layers, e.g. p–i–n or p–i–metal diodes, the advantage of high mobility in these layers can be fully exploited. The measured hole mobility in diamond even exceed the electron mobility in SiC and GaN, two other widebandgap semiconductors currently explored for highfrequency and power electronic devices. Many questions concerning diamond device processing remain to be solved but these results indicate that the full potential of single-crystal CVD diamond is substantial and eventually diamond will push the boundaries of wide-bandgap semiconductor electronics forward. References w1x E. Kohn, M. Adamschlik, P. Schmid, A. Denisenko, A. Aleksov, W. Ebert, J. Phys. D 34 (2001) R77. w2x C.E. Weitzel, Inst. Phys. Conf. 142 (1996) 765. w3x J. Isberg, J. Hammersberg, E. Johansson, et al., Science 297 (5587) (2002) 1670. w4x S. Koizumi, H. Ozaki, M. Kamo, Y. Sato, T. Inuzuka, Appl. Phys. Lett. 71 (1997) 1065. w5x Z. Teukam, et al., Nature Mater. 2 (2003) 482. w6x J.R. Haynes, W. Shockley, Phys. Rev. 81 (1951) 835. w7x E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic Press, San Diego, 1998. w8x S.F. Kozlov, R. Stuck, M. Hage-Ali, P. Siffert, IEEE Trans. Nucl. Sci. NS-22 (1975) 160. w9x F. Nava, et al., IEEE Trans. Nucl. Sci. NS-26 (1) (1979) 308. w10x L. Reggiani, S. Bosi, C. Canali, F. Nava, S.F. Kozlov, Phys. Rev. B 23 (1981) 3050. w11x A. Many, G. Rakavy, Phys. Rev. 126 (1980) 1962. w12x G. Juska, M. Viliunas, O. Klima, E. Sipek, J. Kocka, Philos. Mag. B 69 (1994) 277. w13x J. Mort, D.M. Pai (Eds.), Photoconductivity and Related Phenomena, Elsevier, 1976. w14x G. Ottoaviani, L. Reggiani, C. Canali, F. Nava, A. AlberigiQuaranta, Phys. Rev. B 12 (1975) 3318. w15x C. Canali, C. Jacoboni, F. Nava, G. Ottaviani, A. AlberigiQuaranta, Phys. Rev. B 12 (1975) 2265.