AC hot carrier transport in 3C- and 6H-SiC in the terahertz frequency and high lattice temperature regime

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AC Hot Carrier Transport in 3C- and 6H-SiC in the Terahertz Frequency and High Lattice Temperature Regime

E. F. Bezerra, E. W. S. Caetano, V. N. Freire,

Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030,

Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil

J. A. P. da Costa,

Departamento de Física, Universidade Federal do Rio Grande do Norte,

Caixa Postal 1641, 59072-970 Natal, Rio Grande do Norte, Brazil

and E. F. da Silva Jr.

Departamento de Fí sica, Universidade Federal de Pernambuco,

Cidade Universitária, 50670-901 Recife, Pernambuco, Brazil

Received on 23 April, 2001

The complex mobility of electrons in 3C – and 6H–SiC subjected to intense high frequency electric fields is calculated taking into account effects of band nonparabolicity. The electric field, given by a dc component plus an ac component in the frequency range 0.1-100 THz, is applied along the [0001] ([111]) direction in the hexagonal (cubic) polytype. The real electron mobility presents a characteristic maximum peaking around 6–8 THz, while the imaginary electron mobility is structured, with characteristic minimum and maximum around 2–3 THz and 20{30 THz, respectively. These mobilities are seen to smooth down for higher temperatures in both polytypes.

Silicon carbide (SiC) polytypes have attracted attention due to their promising applications in the field of high power, high temperature and high frequency devices. High power SiC-based devices, for instance, rectifiers, power MOSFETs, thyristors, static induction transistors, MESFETs, as well as sensors operating in hostile environment conditions, are being developed and tested with success [1]. The SiC breakdown electric field and thermal conductivity is, respectively, about ten times greater than in Si and GaAs, and its bandgap (near to 3 eV) is almost three times greater than Si [1]. On the other hand, the calculated difference in the total energy per atom among the 3C–, 2H–, 4H–, and 6H–SiC polytypes is a few meV [1,2]. However, further fundamental research work is still necessary for a better understanding of some basic properties of the silicon carbide polytypes, which is particularly true in the case of their ac–transport phenomena.

The electron transport characteristics of the various SiC polytypes were studied in the past years, including the investigation of the steady-state regime [3-12], high-frequency transport properties [13], and the ultrafast transient response [14-16]. Effects of an intense electric field were computed using Monte Carlo simulations and equations based on quantum and classical transport theories. Mickevicius and Zhao [8] studied electron transport in 6H–, 4H–, and 3C–SiC for the steady state (at 300 K and 600 K) and transient regime (only at 300 K), which was shown to be shorter than 0.2 ps. They pointed out the possibility of an overshoot in the electron drift velocity, which was more pronounced in the 3C– polytype. In a recent work, Caetano et al. [14], using balance transport equations in the relaxation time approximation, showed that there is an overshoot in the electron drift velocity for electric fields higher than 150 kV/cm. Weng and Lei [13] have calculated the room temperature terahertz complex mobility under low ac+dc fields ( < 50 kV/cm) for electrons in 6H–SiC, showing the existence of frequency dependent peaks in the complex mobility appearing around 1–5 THz.

The purpose of this work is to study the influence of the lattice temperature on the terahertz hot electron complex mobility in 6H– and 3C–SiC subjected to a high ac+dc electric fields applied along the [0001] and [111] directions, respectively. These polytypes were chosen because of their high saturation velocities. The frequency dependent carrier drift velocity and energy are calculated for lattice temperatures 300, 673, and 1073 K, and shows a high nonlinear behavior. They allow to calculate the complex mobility behavior of the carriers in the 0.1 – 100 THz ac frequency range. For higher lattice temperatures, the 6H– and 3C–SiC mobilities are shown to be very close, which is a surprising result if we take into account the difference between the physical properties of the polytypes.

The electron energy e(w, t) and drift velocity v(w, t) are found solving numerically the following balance transport equations:

where e(w, t)[ = 3k_BT(w, t)/2] is the average electron energy, which depends on the frequency w of the ac field component; T(w, t) is the electron temperature, and k_Bis the Boltzmann constant. The electric field, applied along the [0001] (hexagonal structure) and [111] (cubic structure) directions, is given by E(w,t) = E_dc+E_accos(wt). In the calculations here performed, E_acis keep fixed at 200 kV/cm, and E_dc, the field dc component, varies in the 250 kV/cm - 800 kV/cm range. e_L is the electron thermal energy at the lattice temperature T_L, q is the electron electric charge and m_cits effective mass, which for the 3C– and 6H–SiC polytypes were choosed here as those given in Weng and Cui [9]. We take into account the band nonparabolicity according the relation2k²/2m_c= e(1+ae), where a is 0.323 eV^-1 for 3C-SiC , and a = (1-m_c/m₀)² for 6H-SiC, where m₀ is the free space electron mass._e(e, E) and _p(e, E) are, respectively, the energy and momentum relaxation times, which are calculated through the steady-state relations v_ss×E_dcand e_ss×E_dcobtained by Weng and Cui [9] for 3C- and 6H-SiC at lattice temperatures T_L= 300, 673 and 1073 K.

The Fourier transform of the time-dependent electron mobility calculated in the time period T is the dynamic mobility:

where m_R(w) and m_I(w) are the real and imaginary parts of the complex electron mobility, respectively; T is the time period of the ac component of the electric field, and is the time necessary for both the electron drift velocity and energy to arrive at the steady state.

The behavior of m_R(w) and m_I(w) at terahertz frequencies is shown, for 3C-SiC (6H-SiC) at temperatures of 300, 673 and 1073 K, in Fig. 1 (Fig. 2). At 300 K, m_R(w) presents a peak around w/2p » 6-8 THz for E_dc= 250 kV/cm. The maxima in m_R(w) are strongly smoothed when E_dcis increased, and practically disappear for E_dc= 800 kV/cm. Increasing lattice temperature considerably reduces the peak of the real mobility. The peak is very small when T_L= 673 K and disappears completely when T_L= 1073 K. In this case, m_R(w) decreases continuously for high frequencies and low enough E_dc. The imaginary mobility m_I(w) in 3C-SiC and 6H-SiC at low temperatures (300 K) presents a minimum and a maximum around 2-3 THz and 20-30 THz, respectively. These critical points are more pronounced in 3C-SiC than in 6H-SiC. Both the minima and the maxima are smoothed when the dc-component of the field increases. However, the maxima always exists in the dc-electric field intensity range investigated, while the minima almost disappears for E_dc= 250 kV/cm. When the lattice temperature increases, the minima and maxima are considerably smoothed, the former more remarkably than the latter. For low dc-electric fields, a high lattice temperature can preclude the existence of minima in the imaginary component of the mobility. On the other hand, at high E_dc intensities the minima and maxima always exist at high lattice temperatures.

In conclusion, the complex mobility of hot electrons in 3C-SiC and 6H-SiC subjected to intense high frequency electric fields was studied. The overall effect of an increase in lattice temperature for the SiC polytypes was shown to smooth down the complex mobility features (maxima and minima). The modulus of the complex mobility for 3C-SiC was always larger than in 6H-SiC (except for T_L= 300 K and E_dc= 800 kV/cm), which is a consequence of a lower effective mass in 3C-SiC. However, at high enough temperatures the electron mobility behavior and its modulus are very close in both polytypes (except for E_dc= 800 kV/cm), and consequently the choice between 3C- and 6H-SiC for high temperature devices must be based on the suitability of other physical properties. Finally, one limitation of the present work is the fact that changes on the dielectric permitivity were not considered, even with the so high ac-frequency range investigated. However, the results should stimulate research on how the dielectric constant change (when the high-frequency ac electric field is applied to the semiconductor) to include this effect on the transport equations.

Acknowledgments

E. F. Bezerra and E. W. S. Caetano acknowledge the graduate fellowships they received from the Brazilian National Research Council (CNPq) at the Physics Department of the Universidade Federal do Ceará during the development of this work. V. N. F., J. A. P. C., and E. F. S. Jr. are thankful to the financial support from CNPq and the Ministry of Planning (FINEP) under contract FNDCT/CTPETRO-1190/00 #65.00.02.80.00.

• [1] C. I. Harris and A. O. Konstantinov, Physica Scripta, T79, 27 (1999).
• [2] C. Persson and U. Lindefelt, J. Appl. Phys., 82, 5496 (1997).
• [3] D. H. Ferry, Phys. Rev. B, 12, 2361 (1975).
• [4] H. E. Nilsson and M. Hjelm, J. Appl. Phys., 86, 6230 (1999).
• [5] M. Hjelm, H. E. Nilsson, P. Kackell, C. Persson, U. Sannemo, and C. S. Petersson, Physica Scripta, T79, 42 (1999).
• [6] H. E. Nilsson, M. Hjelm, C. Frojdh, C. Persson, U. Sannemo, and C. S. Petersson, J. Appl. Phys., 86, 965 (1999).
• [7] E. Belotti, H. E. Nilsson, K. F. Brennan, and P. P. Rude, J. Appl. Phys., 85, 3211 (1999).
• [8] R. Mickevicius and J. H. Zao, J. Appl. Phys., 83, 3161 (1998).
• [9] X. M. Weng and H. L. Cui, Phys. Stat. Sol. (b), 201, 161 (1997).
• [10] H. E. Nilsson, U. Sannemo, and C. S. Petersson, J. Appl. Phys., 80, 3365 (1996).
• [11] R. P. Joshi, J. Appl. Phys., 78, 5518 (1995).
• [12] K. Tsukioka, D. Vasileska, and D. K. Ferry, Physica B, 185, 466 (1993).
• [13] X. M. Weng and X. L. Lei, Phys. Stat. Sol. (b), 187, 579 (1995).
• [14] E. W. S. Caetano, E. F. Bezerra, V. N. Freire, J. A. P. da Costa, and E. F. da Silva Jr., Solid State Communications, 113, 539 (2000).
• [15] E. F. Bezerra, E. W. S. Caetano, V. N. Freire, E. F. da Silva Jr, and J. A. P. da Costa, Semicond. Sci. Technol., 14, 1007 (1999).
• [16] E. F. Bezerra, E. W. S. Caetano, V. N. Freire, E. F. da Silva Jr, and J. A. P. da Costa, Braz. J. Phys., 29, 785 (1999).

Publication Dates

• Publication in this collection
  26 Nov 2002
• Date of issue
  June 2002

History

• Received
  23 Apr 2001