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Device Physics: Behavior at Elevated Temperatures HIGH-TEMPERATURE EFFECTS: FUNDAMENTAL, MATERIALS RELATED PROPERTIES Although technological considerations such as gate and ohmic contact metallization, as well as dopant profiles are an inextricable component of device behavior at elevated temperatures, it is useful to specifically focus on the device physics expected at elevated temperatures, aside from the technologically relevant, but perhaps addressable issues, such as increased diffusion of dopants. The fundamental device physics, dependent on the materials properties, include parameters such as carrier concentrations, scattering, and leakage current, and are described below. ~ Carrier Mobilities2 The mobilities of the charged carriers will determine the speed of operation of the devices, and those mobilities are expected to change with increased temperature of operation. There are a variety of carrier scattering mechanisms in the semiconductor material that will limit carrier mobilities: principal among these are acoustic phonon scattering (also referred to as lattice scattering and ionized impurity scattering), which refers to the Coulom- bic interactions between the charged carriers (electrons or holes) with the ionized dopants that give rise to the free carriers. To a first approximation, for a given material, the mobility limitation from ionized impurity scattering ' For a more detailed consideration of some of We properties described In this chapter, it is suggested that a basic semiconductor text be consulted, such as S.M. Sze's Physics of SemiconductorDevices (1981). 2 Furler discussion on this topic can be found in Ridley (1993). 31 scales with temperature as T3/2 (that is, the mobility decreases at lower temperatures), while that from acoustic phonon scattering scales as T-3/2 (mobility decreases at higher temperatures). However, the mobility also depends on factors such as the density of ionized impurities, which also varies with temperature. In addition, for polar semiconductors, such as GaAs, optical phonon scattering becomes important. Moreover, the critical, current-carry- ing area of some devices comprises a thin sheet of charge near a hetero-interface. This characterizes the inversion- layer charge at the interface of silicon and silicon dioxide in metal-oxide semiconductor field effect transistors (MOSFETs). In this case, other factors will affect the charge scattering and hence the mobility. Some of these factors include the presence of charged defects in the oxide, or at the interface, as well as morphological roughness of the interface. The total mobility at a given temperature is then determined by summing up all the significant contributions to carrier scattering. Figure 3.1 shows the calculated dependence of mobility on temperature for undoped 6H-SiC and 3C-SiC (Shur et al., 1993~. The mobility of the 6H-SiC decreases from 420 cm2/V s at 25 C to around 120 cm2/V s at 200 C. The room-temperature mobility for SiC doped in the 10~7 cm~3 range is expected to be lower ~ ~ 250 cm2/V s), since the impurity scattering has been in- creased. Figure 3.2 shows the calculated electron mobility as a function temperature for e-type GaN, doped 10~7 cm~3. Intrinsic Carrier Concentrations: Dependence on Bandgap Energy and Temperature Thermal energy, kT, can be sufficient to promote electrons from the valence band to the conduction band, giving rise to a thermally generated current, which is not

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1 200 1 000 2 800 cat ,` 600 ._ n o 400 200 n \ 3C-SiC \ \ \ \ \ \ ~ burl \ ~ L I 200 300 400 500 600 700 Temperature (K) FIGURE 3-1 Calculated electron mobility as a function of temperature for undoped 6H-SiC and 3C-SiC. SOURCE: Shur et al. (1993). controlled by explicit device operation. In fact, at suffi- ciently high temperatures, the thermally generated intrin- sic carrier concentration can exceed the density of explic- itly introduced dopants: thus the ability is lost to control the concentration of the charge carriers in the device. The intrinsic carrier density for a given material is given by ni = (2n h-2) Ohm/ e~p(-~;), (3.1) where k and h are Boltzmann's and Planck's constants; T is the absolute temperature; Mae and math are the electron and hole effective masses, expressed in multiples of the 1 200 1 000 - cn 2 800 cut - ~ 600 o o c' UJ 400 200 Materials for High-Temperature Semiconductor Devices free electron mass; and Eg is the bandgap energy. In an intrinsic semiconductor, ni = n = p, where n is the electron density and p is the hole density. The simple effect of increased temperature on Equation (3.1) is to increase ni, hence leakage current. This is a critical concern for technologies that depend on an insulating or semi-insulating substrate, which is the case for GaAs metal semiconductor field effect transistors (MESFETs). A semi-insulating GaAs substrate will show approximately six orders-of-magnitude decrease in bulk resistivity from 25-300 C, resulting in a substrate leakage current that cannot be controlled by the device gate (Look, 1989; Lee 8 et al., 19951. For a given temperature, the intrinsic carrier density is less for a larger bandgap material. These data are plotted in Figure 3.3 for silicon, GaAs, and SiC (the temperature dependence of Eg is neglected here). As the temperature is increased, ni increases rapidly. Moreover, most semiconductors have bandgaps whose magnitudes decrease as the temperature is increased. This is shown in Figure 3.4 for silicon, doped with either e-type or p-type at different concentrations. For example, the bandgap energy in intrinsic silicon decreases by 0.083 eV from room temperature to 300 C. This represents an increase in intrinsic carrier density at 300 C of 2.5 times over the room-temperature intrinsic carrier density. 1 E + 20 1 ~ ~GaN co 'A 1E+ 18 c 1E+ 16 ~ 1E+ 14 .c' 1E + 12 .m .~ ' 1E + 10 _ _ O - 1 1 1 1 1 1 200 300 400 500 600 700 800 1E + Temperature (K) FIGURE 3-2 Calculated electron mobility as a function of temperature for GaN doped e-type, 10~7 emu. SOURCE: Shur et al. (1993). T 8 1 0 200 1 1 400 600 800 1 000 Temperature (C) FIGURE 3-3 Intrinsic carrier density for silicon, GaAs, and SiC. 32

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Device Physics: Behavior at Elevated Temperatures S 0.6 a) - 0.4 a) c 8 0.2 ~ 0.0 o Al -0.2 ._ Cal A, 0.4 - (5 -0.6 llJ z _ E N = ~cm~ Intrinsic Level ~ 0 200 400 600 Temperature (K) FIGURE 3-4 Decrease In silicon bandgap win increasing temperature. SOURCE: Sze (1981). PREDICTING HIGH-TEMPERATI)RE DEVICE PERFORMANCE: MATERIALS-RELATED [IGlJRES OF MERIT The high-temperature effects described above have been reported to have first-order effects on device operat- ing characteristics (Khan et al., 1993b), which are de- scribed in greater detail below. Figures of merit, based on the materials parameters affecting devices, provide a useful basis of comparison for the possible technologies. In the figures of merit discussed below, the highest values possible are desirable. Johnson's Figure of Merit (JFM; Johnson, 1965) relates to the frequency and power product of a semiconductor transistor, and is given by JFM = (Emvs) (3.2) where Em is the avalanche breakdown electric field and VS is the carrier saturated velocity. JFM can also be viewed as the square of the quotient of the breakdown voltage of a semiconductor layer and the intrinsic transit time for carriers moving through the layer. JFM accounts for the fact that in an intrinsic device (i.e., one without parasitic resistance or reactance) there is a tradeoff between the time a carrier spends gaining energy in an electric field as it drifts through a device and the response time of the device. JFM is related to electronic properties and does not account for thermal effects. The Keyes' Figure of Merit (KFM; Keyes, 1972) takes into account the thermal properties of a material and IS given by KFM = ~ ( CVs ) 1/2 (3 3) where ~ is the material thermal conductivity, c is the velocity of light in vacuum, and ~ is the material dielectric constant. Keyes assumes that smaller devices are inherent- ly faster in response at fixed electronic-input impedance level. However, devices cannot be made smaller without increasing the thermal resistances, thereby limiting the power output and introducing thermal conductivity as a factor. The breakdown field is not significant in this figure of merit since KFM addresses a thermal rather than an electronic limit. Baliga (1982) noted the role of the saturation velocity, vs. in both the JFM and KFM, which is important for high-speed electronics but not necessarily the major parameter for devices to be used in power applications. Instead, he emphasized the role of high carrier mobility and large electric field at breakdown (Em). For lower- frequency power devices, where conduction loss in the on-state is the dominant power loss, the figure of merit is BFM = e,uEm3 . (3.4) At higher frequencies, switching losses due to charging and discharging of the device capacitance assumes greater importance. In that case, BHFM = epEm2 . (3.5) Recently, Chow and Tyagi (1994) have carried out a comparison of figures of merit of various semiconductors for high-power and high-frequency unipolar devices. A portion of their results are shown in Table 3-1. The calculations are made at room temperature, rather than at some elevated temperature of operation, as has been the norm for these calculations. It is generally a safe assump- tion that the materials advantages leading to higher figures of merit at room temperature will persist at higher temperatures. Breakdown voltages, mobilities, and saturation velocities will be degraded in all cases, but should fall off with temperature less precipitously for the wide bandgap materials than for silicon or GaAs. For JFM, the high breakdown field dominates, making all of the wide bandgap materials attractive compared to silicon, germanium, and GaAs. Since the figures of merit weight various properties, they do not appear to provide a clear 33

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Materials for High-Temperature Semiconductor Devices TABLE 3-1 Companson of Normalized Figures of Ment of Vanous Semiconductors for High-Power and High-Frequency Unipolar Devices Material JFM KFM BFM BHFM Silicon 1.00 1.00 1.00 1.00 Germanium 0.13 0.28 Diamond (a) 5,330 31 14,860 1,080 Diamond (p) 6,220 32 11,700 850 A1N (p = 14) 5,120 2.6 390 14 AlN (p = 1,090) 5,120 2.6 31,670 1,100 AlAs 630 7.3 2.0 GaAs 11 0.45 28 16 GaN 790 1.8 910 100 6H-SiC 260 5.1 90 13 3C-SiC 110 5.8 40 12 4H-SiC 410 5.1 290 34 SOURCE: Chow and Tyagi (1994). choice among the different wide bandgap materials. The high thermal conductivities of the wide bandgap materials increase the values of KFM. Also, their lower dielectric constants reduce the capacitance per unit area, thereby further increasing KFM. The figures of merit suggest that devices whose limitations are principally due to their electronic limita- tions, such as saturated velocity or breakdown electric field, can achieve higher power density in the wide bandgap materials. Field effect transistors are among this class of devices. For devices whose operation is limited by thermal considerations, such as the material thermal resistance, higher power density should also be achievable in the wide bandgap materials. Among these devices are bipolar transistors. These predictions must be moderated by the fact that figures of merit generally provide a rough estimate of performance, since only the "intrinsic" device is considered. The figures of merit do not fully account for parasitic resistance and other detailed effects that limit device performance and that require more careful exami- nation for a particular device technology. 34 Device Physics at High Temperatures More-detailed discussions of the effects of high temperature on device performance are given in Appendi- ces A and B for silicon- and GaAs-based technologies operating at high temperatures. Appendix C presents detailed considerations of the influence and issues that surround insertion of the wide bandgap semiconductors into microwave devices. Specific issues of consequence for high-temperature device operation are (1) the effect on device conductivity in the on-state, and (2) the effect of leakage currents in the off-state. The examples below provide an introduction to the issues that are of concern for device technologies, building upon the high-tempera- ture changes in carrier density and mobility. Junction Leakage: pen Junctions and Diodes Shenai et al. (1989) have approximated junction reverse leakage currents to have the following depen- dence, at elevated temperatures:

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Device Physics: Behavior at Elevated Temperatures 1 10-1 10-2 a: ~ 10-3 in a) ~5 a) a) a) 10-4 10-5 10-6 10-7 \~ \~` _ '\ ~ >~` GaAS \ \\` si \ _ ~ t it\ , , , ~ , ~ - \ GaP \ N~ 6H - SiC \ creased temperature can cause increased base and collec- tor resistances. This in turn can bring about an increased collector-emitter saturation voltage, V`e OCR for page 31
Materials for High-Temperature Semiconductor Devices 1.0 _ A 0.5 _ - a) ~_ 0.0 _ o en a) _ -0.5 _ -1 .0 ~__ ._e-Channel -__ ~ ~ / , ~1 1 , 1, 1 , 1 ~1 1 1 1 0 50 100 150 200 250 300 Temperature (oC) FIGURE 3-6 Variation In threshold voltage versus temperature for n- and p-channel MOSFET devices. SOURCE: D.M. Brown et al. (1994). Leakage currents represent the ultimate degradation factor with respect to high-temperature operation of silicon MOSFETs and metal-oxide semiconductor (MOS) integrated circuits. At high enough temperatures, the drain to body leakage currents can increase by orders of magnitude and become comparable to the drain channel currents; the transistor can no longer be turned off by the gate. Such leakage lowers noise margins, making the design of static digital devices difficult, and making dynamic circuits and memories impossible to produce. In addition, mobility degradation in MOSFETs at elevated temperatures causes the transistor transconductance to decrease. Choice of High-Temperature Device Technologies The impetus for high-temperature, high-power operation is sufficiently compelling, and there have already been demonstrations of such operation in silicon and GaAs devices. In addition, temperature-dependent extrapolations of device performance and materials- dependent figures of merit allow us to make some assess- ment of device performance at elevated temperatures for the newer wide bandgap materials such as SiC and GaN. These factors are the basis for the predictions of Figure 3- 7, suggesting the materials technologies that will be appropriate for the various temperatures of operation. 36 In general, the limitations of leakage currents at elevated temperatures places a greater constraint on small- signal devices, compared to digital logic. Reduced mobility and leakage sets a more stringent limitation yet on the performance of microwave devices. Dynamic random access memories (DRAMs) may be further limited by leakage of charge stored in capacitors. We note that the temperature range of -55 C to 125 C are the current military specifications that many device technolo- gies must satisfy. For silicon technology, transistor operation has been demonstrated up to 450 C (Migitaka and Kurachi, 1994~; since leakage currents are already large at this tempera- ture, it is unlikely that silicon devices will be operated at significantly higher temperatures. Since analog-device operation is more strongly affected by the changes in leakage current, gain, and threshold voltages that occur with temperature, it is estimated by the committee that high-temperature operation of these devices will hold good to only 350 C. Microwave devices, operating at high power densities, would be subject to more severe temper- ature limitations than small-signal analog devices; hence the committee extrapolates a maximum operating tempera- ture of 200 C. Power devices have been demonstrated, operating at temperatures as high as 250 C. Since conventional DRAMs are strongly affected by the leakage currents associated with higher temperature, the commit- tee estimates the maximum temperature of operation to be 150 C. Devices that were specifically designed for high- temperature operation, with larger charge storage capaci- tors or based on other memory-cell architectures, perhaps with larger areas, would be capable of a somewhat higher-temperature operation. Finally, reasonable reliabili- ty has been demonstrated at 250 C for bipolar logic (Migitaka and Kurachi, 1994) and at 200 C for comple- mentary metal-oxide semiconductor (CMOS) logic (Foyt, 1994~. The higher bandgap of GaAs is expected to lead to a somewhat higher-temperature operation than silicon. Transistor operation has indeed been demonstrated at 500 C (Shenoy et al., 19941. The alloy system AlGaAs, with still larger bandgaps, should allow still higher temperature operation. Small-signal analog devices have been shown to operate at 300 C (Bottner et al., 19911; the extrapolation to operation at 400 C is based on the observation that analog applications are more strongly affected than digital

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Device Physics: Behavior at Elevated Temperatures -55 0 100 200 Silicon Microwave Silicon Digital Logic Silicon Small Signal Silicon Power Silicon DRAM GaAs Power GaAs Digital Logic GaAs Small Signal GaAs Power N/A GaAs DRAM N/A GaAs Static RAM SiC Power SiC Digital Logic SiC Small Signal SiC Power N-C MODSFET SiC DRAM Nitrides (e-type) Nitrides Microwave Temperature (C) 300 400 500 600 700 800 Amp Current operating temperature - - FIGURE 3-7 Operating temperatures for different devices per material. by the changes in leakage currents, gain, and threshold voltages caused by high temperature. Microwave devices have been operated at 300 C (Wurfl et al., 1994), and the extrapolation to 350 C operation reflects again the more constraining effects of temperature on these devices, compared to small-signal analog devices. DRAMs, in the conventional sense, are not made using GaAs. As for power devices, conventional metal- insulator semiconductor field effect transistors (MISFETs), popular power devices in silicon, are not possible in GaAs, due to the high interface recombination velocity. Other power devices, including the thyristor- based devices, have not yet been attempted, even with the excellent development of other device types and integrated circuits in this materials system. Although the wide bandgap materials still represent nascent technologies, there have already been demonstra- tions of devices that have exhibited DC transistor opera- tion at considerably higher temperatures than available through silicon or GaAs devices. SiC transistors have shown operation at temperatures as high as 650 C 37 chug . Projected operating temperature (Palmour et al., 1991), and they are projected to operate at still higher temperatures. Based on material fundamen- tals, operation to over 1000 C should be possible. There is as yet little information on SiC digital logic. Xie et al. (1994) demonstrated some SiC enhancement-mode n- channel metal-oxide semiconductor (NMOS) circuits to 300 C, which included simple gates, latches, and flip- flops. Based on the demonstrated transistor characteristics, and on material fundamentals, operation to at least 650 C should be possible. D.M. Brown et al. (1994) have demonstrated operational amplifier operation to 350 C. The extension to 550 C is based on estimates similar to those for silicon and GaAs. Similarly, the same estimates apply to the expected performance of power devices at elevated temperatures. The high-frequency results for SiC are currently not available. Thus the committee was unable to make an accurate appraisal of its microwave potential. The lack of a SiC CMOS for analog could restrict potential device applications, however. Device work in the nitrides is in the very early stages; however, the results are already very exciting. The

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Materials for High-Temperature Semiconductor Devices current devices are made in epitaxial layers with very high defect densities. Nevertheless, reasonable transistor action has already been achieved to 350 C (Binari et al., 19941. Based on fundamentals, operation to over 1000 C should be possible. Although it is too early to give an accurate estimate of high-temperature operation of most applica- tions (e.g., digital logic small-signal analog, power, and DRAM), if the estimates based on operation of transistor action are reasonably accurate, operation to very high temperatures should be possible. The projected operating temperatures in Figure 3.7 are based on estimates similar to those for silicon, GaAs, and SiC. As for transistor 38 operation, the results for microwave devices at this early stage of materials development are very encouraging. Maximum frequencies of oscillation as high as 35 GHz have already been reported (Khan et al., forthcoming). Figure 3.7 should serve only as an approximate basis of comparison, as is true for the figures of merit, repre- senting informed extrapolations. To uncover the true limitations or capabilities will require further experimenta- tion. The intention is to more clearly focus on desired operating temperatures and the concomitant most promis- ing device technologies in those temperature regimes.