JOURNAL OF APPLIED PHYSICS 106, 063701 共2009兲

Simulation of electron transport in „0001… and „112¯ 0… 4H-SiC inversion layers G. Penningtona兲 and N. Goldsman Department of ECE, University of Maryland, College Park, Maryland 2078, USA

共Received 3 May 2009; accepted 29 July 2009; published online 16 September 2009兲 Monte Carlo simulations are used to investigate electron transport in the inversion layer of a 4H silicon carbide metal-oxide-semiconductor field-effect transistor 共MOSFET兲. The electronic subband structure is solved self-consistently along with the perpendicular field at the semiconductor-oxide interface. Inversion channel scattering rates due to acoustic and polar optical phonons, ionized dopants, trapped charge, and interface roughness are considered. Transport within ¯ 0兲 oriented inversion layers are compared. Simulations of the MOSFET low-field 共0001兲 and 共112 mobility, incorporating previously published experimental results for threshold voltages and charge ¯ 0兲 channel is densities, are found to agree well with experimental results. The mobility of the 共112 2 2 much larger 共90 cm / V s兲 than that of the 共0001兲 channel 共⬍40 cm / V s兲 due to a reduction in interface states. Furthermore, the mobility has a temperature coefficient of approximately ⫺3/2 for ¯ 0兲 layers due to dominant phonon scattering and +1 for 共0001兲 layers, where interface trap 共112 scattering dominates. Since the band structure is very similar, transport variations among the two crystal orientations are found to result largely from the enhanced interface trap density in the 共0001兲-oriented interfaces. © 2009 American Institute of Physics. 关doi:10.1063/1.3212970兴 I. INTRODUCTION

The material properties of silicon carbide 共SiC兲 are well suited for applications in electronic devices operating in the high-temperature, high-power regime. Of particular advantage are the large SiC band gap, thermal conductivity, and breakdown field.1 Furthermore, SiO2 can be thermally grown on SiC allowing for the production of metal-oxidesemiconductor field-effect transistors 共MOSFETs兲 and the use of planar fabrication methods.2 Of all the commercially available SiC polytypes, 4H-SiC has the largest bulk band gap, drift velocity, and mobility.3 Another advantage is its relatively uniform effective mass4 which should lead to isotropic electrical properties. As these properties are desirable in a number of applications including fast switching, highvoltage, and low-loss power electronics, 4H-SiC is promising. Presently SiC-based vertical MOSFETs 共Ref. 5兲 and Schottky diodes6 have reached commercial grade. However, for integrated power circuitry, lateral MOSFETs are desired requiring improvements in the growth of the SiC oxide interface and inversion channel.7 Traditional growth of hexagonal SiC epilayers has focused on the 关0001兴 orientation. Such films are typically formed by step-controlled growth on vicinal substrates that ¯ 0兴 direction.8 are miscut by small angles 共8°兲 toward the 关112 Unfortunately, this process has yet to yield high-quality lateral MOSFET devices. Step-controlled growth leads to a considerable amount of step bunching along with a high probability of inclusions containing additional polytypes.9 Furthermore, growth along the c crystal axis is mired by the presence of micropipes and other screw dislocations, which a兲

Electronic mail: [email protected].

0021-8979/2009/106共6兲/063701/13/$25.00

lead to critical flaws in power devices.10 Although improvements have reduced the level of screw dislocations in 关0001兴 SiC,11 defect levels still impact the development of highquality devices.12 Also of considerable importance is the large density of interface trapping states that have been measured at the 关0001兴-SiC oxide interface.13–19 These defects have been linked to the poor channel mobility20–23 and poor performace7,23,24 of 关0001兴 oriented SiC lateral MOSFETs. The source of these near interface traps 共NITs兲 is still uncertain and may be due to carbon clusters, suboxide bonds, or SiC dangling bonds.25–27 Oxidation processing methods including use of nitrogen,28–31 sodium,32,33 and increases in oxidation temperature34 have been found to increase the mobility of 关0001兴-oriented SiC MOSFETs, presumably by decreasing NIT. The use of alternative gate oxides has also been tried.35 Although much work has been dedicated to the growth of 关0001兴 SiC and its oxide interface, more work is needed. An attractive option is to use nonbasal orientations for SiC MOSFET devices. Advantages include the possibility of homoepitaxial growth,36 the absence of screw dislocations,37 smoother interfaces,11 reduced step bunching and triangular defects,38 enhanced dopant activation,39 and faster oxidation rates. A number of investigations indicate a reduction in NIT ¯ 0兲 SiC oxide interfaces when compared to interfaces at 共112 using the traditional 共0001兲 surface,40 and a commensurate increase in the channel mobility.22,41 Reports indicate enhanced performance for devices fabricated on the ¯ 0兲-oriented material,22 including reduced on-resistance 共112 and smaller leakage currents.38 However, there are drawbacks for using a-plane SiC crystal orientations including reports of significant increases in the density of stacking fault defects42 and an increase in interface states near the

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© 2009 American Institute of Physics

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effective masses parallel to the interface. Here, ms depends on the occupied subband perpendicular to the interface since it depends on the particular subband ladder that the electron occupies.4 The electron energy dispersion, ␧共k兲, parallel to the interface is then determined by ប 2k 2 = 关␧共k兲 − Es兴兵1 + ␣s关␧共k兲 − Es兴其, 2ms

FIG. 1. SiC/oxide interface.

midgap.43 However, such midgap states are not as detrimental to MOSFET operation as the states near the band edges that are prominent in 共0001兲 SiC oxide interfaces. Improve¯ 0兲 growth have been made using “repeated a ments in 共112 face growth” which has reported high quality, almost dislocation free 4H-SiC.44 In addition, postoxidation annealing with hydrogen is found to further increase the mobility on ¯ 0兲 face.45 the 共112 To better understand the influence of crystal orientation on inversion layer channel transport, we employ Monte Carlo simulation46,47 of electron transport along the inversion layer channel of a 4H-SiC/ SiO2 interface. A number of investigations have reported SiC Monte Carlo based transport simulations in the bulk48–50 and inversion channel.51 Here we ¯ 0兲 orientations and comsimulate both the 共0001兲 and 共112 pare the results to experiments. Scattering rates due to acoustic and polar optical phonons, ionized dopants, trapped charge, and surface roughness are included. The band structure and perpendicular field in the inversion layer are solved self-consistently using the methods in Ref. 4 as discussed in Sec. II. In Sec. III the various scattering rates within the inversion layer are developed. Transport results for 共0001兲 ¯ 0兲 4H-SiC are represented in the remaining secand 共112 tions.

共1兲

where the nonparabolicity factor for each subband is given by ␣ = 0.323 for 4H-SiC. To occupy the subband s, the energy ␧共k兲 must be larger than the subband minimum energy Es. Since we deal with conduction band electrons, the zero level for the electron energy is set equal to E0, the energy of the lowest subband at k = 0. Usually the scattering rates are proportional to the density of final electron states 共DOS兲. Here, in two-dimensions, parallel to the interface, we have DOSS共␧兲 =

2␲ms共1 + ␣关␧ − Es兴兲 ␪共␧ − Es兲, ប2

共2兲

where the Heaviside step function ⌰ ensures that DOSs is zero if the electron energy is less than the subband minimum energy Es. Before Monte Carlo simulations of transport along the 4H-SiC inversion layer are undertaken, the subband structure Es, the subband wave functions ␨共z兲, the inversion layer potential ␸共z兲, and average penetration of electrons into the inversion layer Zav, are all determined using the selfconsistent method in Ref. 4 with one exception. Due to the presence of trapped charge at the semiconductor/oxide interface, the surface field in Eq. 共4兲 of Ref. 4 must now include the trapped charge density Nit. The surface field now becomes F0 = e关Ninv + 共NA − ND兲zd + Nit兴 / ⑀, where Ninv is the free mobile inversion charge density, NA − ND is the net dopant density, zd is the depletion depth, and ⑀ is the dielectric constant. Since Nit is quite large in 4H-SiC, the effect on the subband structure will be quite significant, raising the subband energies and increasing the subband energy spacing when compared to the results in Ref. 4.

II. SURFACE ELECTRONIC BAND STRUCTURE

Electron transport in the inversion layer of a 4H-SiC/ SiO2 MOSFET, shown in Fig. 1, will depend on the quasi-two-dimensional 共quasi-2D兲 band structure at the interface. This is composed of two parts: a subband structure perpendicular to the interface along the z direction and a two-dimensional band structure parallel to the interface. The subband structure along z is determined by the methods in Ref. 4. As for the surface parallel to the interface, the electron energy, ␧共k兲, is considered as a continuous function of the two-dimensional electron wavevector k. Since we simulate low-field transport, we consider only energies near the subband minima. To model the electron energy, a spherical band structure is used within the effective mass approximation. The effective mass for an electron in subband s is given by ms = 共m1m2兲1/2, where m1 and m2 are the principle axes

III. SCATTERING

In this section we develop the quasi-2D scattering rate for a free conduction electron at the 4H-SiC/ SiO2 interface. The mechanisms considered are scattering by acoustic phonons, optical phonons, trapped interface charge, ionized impurities, and surface roughness. We assume that scattering effects on the electronic structure is weak, and can be treated using first order perturbation theory.52 The rate is then described by the well known “Fermi’s golden rule.” Using the method of Price,53 the scattering rate for an electron with wavevector k in subband s is expressed as a sum over possible final states in each subband s⬘ with wavevector k⬘. This can be represented as

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2␲ 兺 ប s

⌫s关␧共k兲兴 =

⬘

冕 冕 2␲

d␪⬘

0

k⬘dk⬘兩M ss⬘共Q兲兩2␦关␧共k⬘兲

− ␧共k兲 ⫾ E p共Q兲兴,

共3兲

where M ss⬘共Q兲 are the matrix elements for the electronscatterer interaction energy and E p共Q兲 is the energy lost upon scattering. Here Q = k⬘ − k, is the 2D wavevector involved in the transfer or electron momentum parallel to the interface. The momentum transfer in the perpendicular direction, along z, is defined as qz. Integrations over k⬘ and qz will occur over the limits of 0 to infinity, though this will not be shown explicitly. The quasi-2D interaction, M ss⬘, is found by the integration of the three-dimensional 共3D兲 interaction, Hss⬘, over qz. This is represented by the expression 兩M ss⬘共Q兲兩2 = 共2␲兲2

冕

冕冕

兩Hss⬘共Q,qz兲兩2兩Iss⬘共qz兲兩2dqz ,

兩␵s共z兲兩2兩␵s⬘共z⬘兲兩2exp关iqz共z − z⬘兲兴dzdz⬘ ,

and upon integration over the perpendicular momentum transfer, 兩Iss⬘共qz兲兩2dqz = 2␲

冕

兩␵s共z兲兩2兩␵s⬘共z⬘兲兩2dz ⬅

␲ . bss⬘

ac

=兺

The interaction between a free mobile conduction electron and an acoustic phonon is treated within the deformation potential theory.52 Here long wavelength phonons are considered, and the shift in the electronic energy upon scattering is considered to be analogous to the effect of an equivalent locally homogeneous strain. The scattering rate then depends on the deformation potential parameter Dac, which is the proportionality constant between the band structure energy shift and the strain. For acoustic phonon scattering, the 3D matrix element is then

បbss⬘

冕 ⬘冕 ⬘ 2␲

d␪

k dk⬘␦关␧共k⬘兲

0

共8兲

where the ⫺ 共+兲 sign is for phonon absorption 共emission兲. The phonon energy is E p = បulQ for intrasubband transitions and zero for intersubband transitions when s ⫽ s⬘. In the latter case, the resulting integration of k⬘ is difficult to solve if inelastic scattering is considered. Therefore intersubband acoustic phonon scattering is approximated as being elastic in this work. For intrasubband transitions, however, the inelastic rate is used because the k⬘ integration can be solved analytically. Using the method of Basu,55 the rate becomes

共6兲

A. Acoustic phonon scattering

s⬘

2␲2兩Hss⬘兩2

− ␧共k兲 ⫿ បulQ␦ss⬘兴,

⌫sac关␧共k兲兴 =

Here bss⬘ is a characteristic length scale for the overlap integral, where 1 / bss⬘ identifies how fast 兩Iss⬘共qz兲兩2 falls off with increasing qz. When many different types of scattering mechanisms are present, the total rate is the sum of the individual rates. Here we consider acoustic phonon 共ac兲, optical phonon 共po兲, ionized impurity 共ii兲, trapped inversion charge 共it兲, and surface roughness scattering 共sr兲. As we do not simulate high-field transport, impact ionization54 is not considered in this work. The total scattering rate 共⌫s兲 is then given by the sum ⌫s = ⌫sac + ⌫spo + ⌫sii + ⌫sit + ⌫ssr. In subsections III A–III E each individual rate will be discussed.

共7兲

,

where the limit of small phonon energies, relative to KBT, is assumed and the Bose–Einstein phonon occupation number N is approximated as N共q兲 ⬵ KBT / បqul. Here only longitudinal phonon modes are considered and ul is the longitudinal velocity of sound in the material. For 4H-SiC we use ul = 1 ⫻ 106 cm/ s. Also ␳ here is the 3D mass density. Using results of bulk transport simulations49,50 an acoustic deformation potential of Dac = 17 eV is used for the surface simulations. Now since 兩Hss⬘兩2 is independent of qz and Q, the acoustic rate from Eq. 共3兲 becomes

共4兲

共5兲

冕

2共2␲兲3␳u2l

⌫sac关␧共k兲兴

where Iss⬘共qz兲 is the overlap integral. Using the selfconsistent wave functions in Ref. 4, the square of the overlap integral is 兩Iss⬘共qz兲兩2 =

2 K BT បDac

ac

兩Hss⬘兩2 =

2 K BT Dac

1

兺 bss DOSs⬘共␧兲

8␲␳u2l s⬘

冋

⫻ 1⫾

⬘

册

2 arcsin共ms⬘ul/បk兲␦ss⬘ . ␲

共9兲

During the Monte Carlo simulation, final states after acoustic phonon scattering are determined by the method in Ref. 55. B. Polar optical phonon scattering

Since SiC is a polar material, with the C atoms being smaller and more electronegative than the Si atoms,56 a longitudinal optical phonon will produce a polarization field in the lattice. This field leads to a significant perturbation of the electronic band structure and conduction band electrons are in effect scattered by the phonon. In the case of polar optical scattering, the interaction energy is given by53,57,58 po

兩Hss⬘共Q,qz兲兩2 =

e 3E 0a 0 2 , 兲 4共2␲兲3ប共Q2 + qz2 + qsc

共10兲

where E0 is the polar field and a0 is the Bohr radius. The polar field is taken as E0 = 1.08⫻ 105 V / cm from bulk fullband Monte Carlo transport simulations.49,50 The screening wavevector, qsc, is taken as the inverse of the Debye length qsc = 冑e2Ninv / 苸 ZavKBT for nondegenerate transport, where ⑀ = 9.72⑀0 is the static dielectric constant of 4H-SiC. The term Ninv is the 2D number density of mobile electrons in the inversion layer and Zav is their average distance from the 4H-SiC/oxide interface. This is the screening wavevector expected in 3D for the screening of slowing varying potentials

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in space and time. The 2D interaction for polar optical phonon scattering is given by performing a contour integration po of 兩Hss 共Q , qz兲兩2 in the complex qz plane according to Eq. 共4兲. ⬘ The result is po

兩M ss⬘共Q兲兩2 =

e 3E 0a 0

2 4␲共2␲兲3ប冑Q2 + qsc

冕冕

2 兩␵s共z兲兩2兩␵s⬘共z⬘兲兩2exp共− 冑Q2 + qsc 兩z

ⴱ

共12兲

e 3E 0a 0 兺 关共N兲DOSs⬘共␧ + Epo兲Ps−⬘共k兲 2共2␲兲3ប s ⬘

+

+ 共N + 1兲DOSs⬘共␧ − Epo兲Ps⬘共k兲兴,

共13兲

where the 共⫺兲 sign is for optical phonon absorption and the 共+兲 sign is for optical phonon emission. The phonon occupation probability is N = 关exp共Epo / KBT兲 − 1兴−1 with the phonon energy Epo = 120 meV.49,50 The P terms are integrals over ␪⬘, the angle between the initial and final electron wavevectors. They are equal to 1 = 2␲

冑

冕冑

Fss⬘共Q⫿兲 ⫿ 2

共Q 兲 +

⫿

2 qsc

⫿

共14兲

The term Ks⫿⬘ is the magnitude of the final electron wavevector. It is fixed by the k⬘ integration to the value Ks⫿⬘ = 冑2ms⬘关␧ ⫾ Epo兴共1 + 关␧ ⫾ Epo兴␣s⬘兲 / ប. Here the integrand of Ps⫿⬘ is used to determine the probability of scattering into a final state at an angle of ␪⬘ from the initial wavevector k during the Monte Carlo simulations.50 This is used to determine how often electrons scatter from the polar field as they are transported across the inversion layer by the applied field.

C. Ionized impurity scattering

In the case of a uniform distribution of charge scatterers in the inversion layer, we can continue to find the quasi-2D scattering rates from the 3D interaction potential. Here we will assume a uniform density of dopants NA − ND, where NA is the acceptor density and ND is the donor density. Beginning with the 3D interaction between a free conduction electron and an ionized impurity of charge e, the interaction is e4 2 2. 共2␲兲3苸2ប共Q2 + qz2 + qsc 兲

冕冕

共16兲

共15兲

We include only intrasubband scattering events since intersubband scattering will be weak as long as the subband energy minima are not very close in energy. Proceeding to de-

2 兩␵s共z兲兩2兩␵s⬘共z⬘兲兩2兩z − z⬘兩exp共− 冑Q2 + qsc 兩z

− z⬘兩兲dzdz⬘ ,

共17兲

shown here for the general case when intersubband transitions are included. Since the rate decreases sharply with 2D wavevector Q, scattering can be treated as elastic to a good approximation. In this case the wavevector becomes Q = 2k sin共␪⬘兲. Now the rate is ⌫sii共␧共k兲兲 =

共NA − ND兲e4DOSs共␧兲 P共k兲, 共2␲兲2ប苸2

共18兲

where the integral of ␪⬘ is P共k兲 =

1 2␲

冋

冕

2␲

0

⫻ 1−

d␪⬘ ,

Q⫿ = 共Ks⬘兲2 + k2 − 2Ks⬘k cos共␪⬘兲.

兩Hsii共Q,qz兲兩2 =

2 ⴱ Fss共Q兲兴. + 冑Q2 + qsc

Fss⬘共Q兲 = ␲

This form factor will also appear in the scattering rate for the interface charge. Now for polar optical scattering, the scattering rate from Eq. 共3兲 is

⫿ P s⬘

e4 2 3/2 关Fss共Q兲 共2␲兲3苸2共Q2 + qsc 兲

Here, a second form factor is introduced and is given by

− z⬘兩兲dzdz⬘ .

⌫spo关␧共k兲兴 =

兩M spo共Q兲兩2 =

共11兲

Fss⬘ ,

where the form factor is Fss⬘共Q兲 = ␲

termine the 2D interaction using Eq. 共4兲 and performing a contour integral, we obtain

d␪⬘

2 ⴱ Fss共Q兲 + 冑Q2 + qsc Fss共Q兲 2 3/2 共Q2 + qsc 兲

册

2CiiJ1共QRii兲 . QRii

共19兲

The last term in the above equation takes into account the correlation of the charged impurities. The term J1 is the first order spherical Bessel function. If Cii is set to zero, then these charges are uncorrelated in a random distribution and may even overlap. Here we use, Cii = 1, in which case the charged impurities are no closer than a distance of Rii = 关3Cii / 4␲共NA − ND兲兴1/3. Here again the integrand of P will be used to select the angle ␪⬘ between the initial and final electron wavevectors during the Monte Carlo simulations.

D. Interface trap scattering

Interface traps can reduce the field-effect mobility in the inversion channel by trapping free electrons, reducing the mobile charge density. Mobility if further reduced as the trapped charge interacts with other free mobile conduction electrons via Coulomb scattering. Traps are presently believed to be the cause of the low mobility typically observed in the inversion layers of SiC MOSFETs.20–23 The NITs in SiC MOSFETs are believed to reside close to the semiconductor-oxide interface. Their origin may be dangling bonds, carbon complexes, or suboxide bonding states.25–27 In the case of interface traps, the charge density is not uniform throughout the inversion layer. As a result we cannot develop the rate based on the 3D interaction energy as in the cases of acoustic phonon, polar optical phonon, and ionized impurity scattering. Here we begin with the 2D interaction energy term58–60

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兩M sit共Q兲兩2 =

e4 兺 Nit共zt兲Fss共Q,zt兲 4␲共2␲兲3苸2共Q + qsc兲2 s

冋

⫻ 1−

册

⬘

2CtJ1共QRt兲 . QRt

共20兲

The sum here is over a specified number of layers t along the z direction into the semiconductor. A small distance is chosen for the interlayer distance. Here we use one angstrom. The contribution of each 2D of trapped charge Nit共zt兲 is then added to attain the total rate due to all of the trapped charge. The form factor is the integrand of Fss共Q兲 in Eq. 共12兲, but for the bare potential case without qsc. It takes the form Fss共Q,zt兲 = ␲

冕

兩␵s⬘共z⬘兲兩2exp共− Q兩zt − z⬘兩兲dz⬘ .

共21兲

these surface effects.60,62,63 At the MOS interface, the point of transition from SiO2 to SiC along the z direction is described as a random fluctuation about the average surface position. This average is specified as the z = 0 position in this work. The surface fluctuation, ⌬z共␳兲, depends on ␳, the position vector along the interface, perpendicular to the z direction in Fig. 1. The potential ␸共z兲 in the inversion layer is assumed to vary due to these fluctuations by an amount ⌬␸sr共␳៝ , z兲 = d␸共z兲 / dz⌬z共␳៝ 兲. The potential ␸共z兲 here is the inversion layer potential determined self-consistently by the methods in Ref. 4. Since the effects of surface roughness are not uniform throughout the inversion layer volume, we will again develop the 2D interaction directly. The square of the matrix elements takes the form sr

Since the rate is not developed directly from the 3D rate in the case of interface trap scattering, a screening wavevector appropriate for a quasi-2D system should be used. Many forms for qsc where investigated, such as the result of the random phase approximation in quasi-2D 共Ref. 60兲 and a perturbation solution for the screened coulomb potential in quasi-2D, but the best agreement with experiment was found using the Debye wavevector qsc = 冑e2Ninv / 苸 ZavKBT. The correlation factor for the charges is also included here for each layer, but in this case Rt = 冑Ct / ␲Nit共zt兲. Here Ct is set equal to one for each layer of charge corresponding to a uniform distribution of charges. We will also consider just one layer of interface traps right at the interface at z = 0. The model could easily be extended to include a distribution of charges away from the interface. This was not found to alter the mobility significantly though. The rate for a nonuniform distribution of ionized impurities could also be easily developed with the method of this section. The rate for scattering between a free conduction electron and a layer of trapped charge of density Nit directly at the semiconductor-oxide interface is e NitDOSs共␧兲 P共k兲, 4␲共2␲兲3苸2 4

⌫sit关␧共k兲兴 =

共22兲

where again we assume elastic collisions. In this case the integral P共k兲 is 1 P共k兲 = 2␲

冕

2␲

0

冋

d␪

册

2C0J1共QR0兲 QR0 . 2 共Q + qsc兲

Fss共Q,0兲 1 −

共23兲

E. Surface roughness scattering

Another scattering mechanism that must be included is surface roughness scattering. Surface roughness encompasses the wide range of chemical disorder in the fabrication of surfaces between two dissimilar materials. Simulations of carrier transport in 6H-SiC inversion layers have shown roughness scattering to be very important.51 A method for incorporation of surface step effects61 into the interface roughness scattering rate has been detailed in Ref. 61. Here we will use a simple but commonly used model to describe

兩M ss⬘共Q兲兩2 =

冏冕 冏冕

冏 冏

ជ · ␳៝ 兲 d␳៝ ⌬z共␳៝ 兲exp共− iQ

⫻

ⴱ

dz␨s⬘共z兲

d␸共z兲 ␨s共z兲 dz

2

2

.

共24兲

We use the self-consistent wave functions and inversion layer potential to determine the square of the effective field defined as 2 = e2Eeff

冏冕

ⴱ

dz␨s⬘共z兲

d␸共z兲 ␨s共z兲 dz

冏

2

,

共25兲

where ␸共z兲 is in eV. The best fit to experiments is often obtained by taking ⌬z共␳ជ 兲 to be exponential in form according to62 ⌬z共␳ជ 兲 = 具⌬z典exp共−␳ / ⌳兲, where 具⌬z典 is the average displacement of the surface and ⌳ is the average range of its spatial variation along ␳. The square of the matrix element then becomes sr

兩M ss⬘共Q兲兩2 =

冉

冊

2 ␲e2Eeff 共具⌬z典⌳兲2 . 1 + 共⌳Q兲2/2

共26兲

The terms 具⌬z典 and ⌳ are parameters usually obtained by the fitting of transport simulations to experiment in cases where surface roughness scattering dominates, for example, in cases when the inversion charge is large. In silicon MOSFETs, typical values are found to be 具⌬z典 = 0.2 nm and ⌳ = 2.2 nm. These length scales are related to the size of 2D islands of Si protruding from the surface prior to the deposition of SiO2. As a rough approximation, we will assume that such islands in SiC will have the same number of unit cells as for Si. In this case we will approximate the dimensions of these islands in SiC by simply scaling the corresponding value for Si to account for the unit cell of SiC. To illustrate this scaling we use the case of the 共0001兲 orientation in 4H-SiC. Referring to Ref. 4, the lattice periodicity along z is 1.9 times that of Si, while the lattice periodicity is 冑3 times that of Si along the interface surface. We therefore use values of 具⌬z典 = 0.38 nm and ⌳ = 1.2 nm for the 共0001兲 oriented 4H-SiC. Assuming that surface roughness causes only elastic intrasubband transitions, the rate is

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063701-6

J. Appl. Phys. 106, 063701 共2009兲

G. Pennington and N. Goldsman

FIG. 2. 共Color online兲 4H-SiC MOS Hall bar.

⌫ssr关␧共k兲兴 =

2 共具⌬z典⌳兲2DOSs共␧兲 e2Eeff P共k兲. 2ប

共27兲

The ␪⬘ integral here is P共k兲 =

1 2␲

冕

2␲

d␪⬘

0

Q , 共Q + qsc兲关1 + 共⌳Q兲2/2兴

共28兲

where Q is given by Q = 2k sin共␪⬘兲 for elastic collisions. As in the case of polar optical phonon and interface charge scattering, the screening wavevector qsc is given by the Debye result. IV. RESULTS FOR „0001… 4H-SIC A. Anaylsis of data

In order to simulate electron transport at the MOS interface in 4H-SiC, we use the experimental data of Saks and Agarwal 共SA兲.17 Here the Hall mobility was determined for a MOS Hall bar. Capacitance and gate voltage measurements can typically be used to obtain the total charge density in the MOS channel under inversion conditions but cannot distinguish between the free and trapped charge densities present. The advantage of using Hall measurements is the ability to accurately determine the mobile free charge density Ninv from measurements of the Hall voltage. The density of trapped charge can then be found by subtracting Ninv from the total inversion layer charge. The experiments of SA were performed on polysilicon gated MOS hall bars. A 10 ␮m epitaxial layer of lightly

⌬Ninv =

再

关␹1共T兲共VG/12V兲2 + ␹2共T兲共VG/12V兲 + ␹3共T兲兴 关␹1共T兲 + ␹2共T兲 + ␹3共T兲兴

FIG. 3. 共Color online兲 Change in inversion layer mobile electron concentration Ninv per 1 V change in the gate voltage VG for the Hall experiments of SA 共Ref. 17兲. Temperatures of 200, 297, and 440 K are shown. The solid lines are the analytical fits used in our Monte Carlo calculations. Here ⌬NT is the oxide capacitance Cox / e, the expected result for ⌬Ninv in the absence of trapped charge.

p-doped 共1 ⫻ 1016 cm−3兲 4H-SiC was laid onto a p-doped 共p+兲 4H-SiC substrate. Then heavily doped n-type 共n+兲 regions for the source and drain contacts were produced by ion implantation of nitrogen. The wafers were then annealed at relatively low temperatures to reduce step bunching of 4H-SiC. Following this a 31 nm oxide was deposited and then reoxidized to reduce the interface trap density. A layer of phosphorus-doped polysilicon was laid down onto the oxide for the gate, and nickel contacts were made to the source and drain n+ regions. A diagram representing such a MOS hall bar is shown in Fig. 2. SA were able to determine the VG-dependent free mobile charge density in the inversion layer 共Ninv兲 by measuring the Hall voltage 共VH兲 and the drain current 共Id兲 as a function of the gate voltage 共VG兲. These results were reported in terms of the variation in Ninv per 1 V change in the gate voltage, a quantity we will label as ⌬Ninv共VG兲. These results are reproduced in Fig. 3 for temperatures of 200, 297, and 440K. For a fixed gate voltage, ⌬Ninv is found to increase with temperature. We also show in Fig. 3 our analytical fits used in the Monte Carlo simulations,

1010 cm−2 , VG ⬍ 12 V 1010 cm−2 ,

The values for the coefficients ␹1 – ␹3 are given in Table I. In Fig. 4共a兲 we show the SA experimental results for the drain versus gate voltage. It is clear that there is a dramatic

else.

冎

共29兲

increase in the threshold voltage as the temperature decreases. The threshold voltage appears to vary as approximately T−2. In Si MOS surfaces, where there is significantly

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063701-7

J. Appl. Phys. 106, 063701 共2009兲

G. Pennington and N. Goldsman

TABLE I. Fitting parameters ␹. T = 200 K

T = 297 K

T = 440 K

␹1 = 17 ␹2 = 0 ␹3 = −4.0

␹1 = 17 ␹2 = 0 ␹3 = −0.72

␹1 = 0 ␹2 = 32 ␹3 = 5.5

VG = 8 V

VG = 12 V

共0001兲

␹4 = 6.5 ␹5 = 78 ␹6 = 70

␹7 = 2.63⫻ 10−5 ␹8 = 10 ␹9 = 10.64

¯ 0兲共2.6ⱕ E ⱕ 3 eV兲 共112

¯ 0兲共E ⬍ 2.6 eV兲 共112

␹7 = 0.72 ␹8 = 1 ␹9 = 9.9

␹7 = 1.1 ␹8 = 1 ␹9 = 9

␹4 = 4.4 ␹5 = 7.2 ␹6 = 62 ¯ 0兲共E ⬎ 3 eV兲 共112

␹7 = 4.7 ␹8 = 1 ␹9 = −2

Nit共VG,T兲 =

less trapped charge, the threshold voltage tends to increase much slower as the temperature decreases, with an approximate dependence of 1 / T.64 It is therefore very likely that the behavior of VT in 4H-SiC is due to the large number of charges that are trapped in the inversion layer. The determination of the threshold voltage can be a somewhat arbitrary process, indicating the point when a significant current develops in the MOS channel. The procedure we use to determine VT from the SA experiments is to weight each drain current curve so that the saturation values are the same, then the threshold voltage is determined as the gate voltage when the drain current is about 1/400th of its saturation value. This is shown in Fig. 4共b兲. We find that the extracted gate voltages agree very well with the formula, VT共0001兲共T兲 = 1.5 V +

冉

424 K T

冊

2

V.

is a result of the interface traps only, we can identify the threshold voltage at large temperatures as the threshold voltage for a trap-free surface. For gate voltages in the range of 1.5⬍ VG ⬍ VT共T兲 in this model, there will be a buildup of trapped charge of density dNit共T兲 = Cox共424 K / T兲2 / e, where Cox is the oxide capacitance per unit area. To determine the free and trapped charge concentration in the MOS channel, we use standard theoretical methods for the onset of inversion in MOSFETs.66 Above threshold, the change in the total charge density per 1 V change in gate voltage is taken as ⌬NT = Cox / e = ⌬Ninv + ⌬Nit, where ⌬Nit is the change in trapped charge. In terms of the overdrive voltage, ˜VG = VG − VT, the occupied trap density 共Nit兲 and free charge density 共Ninv兲 are

共30兲

This form, essentially a T−2 dependence with an offset, agrees very well with the experiments of Harada et al.,65 though they observed an offset in the range of 2–3 V instead of 1.5 V. If we assume that the uncharacteristically large increase in the threshold voltage with decreasing temperature

冉

冊

Cox ˜ 兲 + dN 共T兲, − ⌬Ninv ˜VG⌰共V G it e

˜ 兲. Ninv共VG,T兲 = ⌬Ninv˜VG⌰共V G

共31兲

Here, ⌰ is a Heaviside step function indicating that the only charge in the channel is dNit when the overdrive voltage is negative. In Fig. 5 we plot the free charge density and the trapped charge density using the results above. These densities are used in the Monte Carlo simulation of electron transport at the 4H-SiC/oxide interface. The density of surface traps increases with decreasing temperature, while the density of free electrons decreases. This can be explained by the observation of a large density of surface trap states near the conduction band edge.18 As the temperature drops, the occupation of states near the Fermi level increases relative to those further above. For a fixed total charge in the channel, the Fermi energy moves up toward the band edge with decreasing temperature, increasing the trapped charge density and decreasing the free charge density. B. Simulation results

Using our analytical formulas for Ninv and Nit in Eq. 共31兲, we perform a Monte Carlo simulation of electron trans-

FIG. 4. 共Color online兲 In 共a兲 is the experimental drain current vs gate voltage in a 4H-SiC MOS Hall bar at temperatures of 200, 297, and 440 K 共Ref. 17兲. In 共b兲 the currents are scaled for a determination of the threshold voltage VT which is consistent among the three temperatures.

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063701-8

G. Pennington and N. Goldsman

FIG. 5. 共Color online兲 Models for mobile interface charge density and trapped interface charge density vs gate voltage for temperatures of 200, 297, and 440 K.

FIG. 6. 共Color online兲 Results of Monte Carlo simulations of the low-field electron mobility in 共0001兲 4H-SiC for temperatures of 200, 297, and 440 K. Gate voltages correspond to the experiments of SA 共Ref. 17兲.

J. Appl. Phys. 106, 063701 共2009兲

port along the 共0001兲 4H-SiC/ SiO2 interface. Low-field electron mobilities are determined for a low field of 5 kV/cm parallel to this interface 关in the 共0001兲 plane兴, as the gate voltage VG is increased. In Fig. 6, the results for temperatures of 200, 297, and 440 K are shown. The results agree with the average Hall mobility observed by SA, which are roughly ⬇15, 25, and 40 cm2 / V s at temperatures of 200, 297, and 440 K, respectively. In Fig. 6 we see that the mobility actually increases with temperature for all the simulated gate voltages. For a Si/ SiO2 interface with a relatively low density of interface traps, the low-field mobility characteristically decreases with temperature above 300 K. This decrease is due to an increase in acoustic phonon scattering and approximately depends on the inverse square of the lattice temperature 共T−2兲.64 In the case of 共0001兲 oriented SiC, the temperature dependence of the rate indicates that the scattering of electrons from trapped interface charges, not from acoustic phonons, is the dominant scattering mechanism for both high and low temperatures. This can be readily seen from the plots of the scattering rate for electrons in the first subband in Fig. 7. The rates for scattering from interface traps 共⌫it兲, surface roughness 共⌫sr兲, acoustic phonons 共⌫ac兲, and polar optical phonons 共⌫po兲, are all shown in Fig. 7. The rate for ionized impurity scattering is included in ⌫it, but since it is small compared to the scattering from trapped electrons, we still label the combined rate as ⌫it. We see that ⌫it is very large and essentially dominates the other scattering mechanisms within the range of gate voltages and temperatures simulated in Fig. 7. It is larger at lower temperatures where the number of trapped electrons is larger and the number of free electrons is lower. Both trends, seen in Fig. 5, increase the rate. Screening of the electric field from the trapped electrons will weaken as the number of free electrons 共Ninv兲 decreases. This corresponds to a larger scattering rate. Furthermore, as the gate field increases, there is a decrease in ⌫it. This occurs since the increase in the screening charge with increasing VG dominants the increase in the trapped charge Nit. As for the other rates, the phonon scattering rates increase with increasing temperature. We see that ⌫sr, de-

FIG. 7. 共Color online兲 Scattering rate for an electron in the first subband of 共0001兲 4H-SiC. In 共a兲 the rates are for a gate voltage of 8 V and temperatures of 200 and 440 K. In 共b兲 the rates are for a gate voltage of 12 V and temperatures of 200 and 440 K.

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063701-9

J. Appl. Phys. 106, 063701 共2009兲

G. Pennington and N. Goldsman

FIG. 9. 共Color online兲 Experimental and Monte Carlo mobility vs temperature for gate voltages of 8 and 12 V. FIG. 8. 共Color online兲 Fits for the free carrier density 共Ninv兲 and trapped carrier density 共Nit兲 to SA experiments 共Ref. 17兲 as a function of temperature.

creases with increasing temperature due to more effective screening, and increases with increasing gate potential since the effective field increases. At reasonably low temperatures, it is likely that ⌫sr will eventually rise with increasing VG to become the dominant rate. Here a mobility peak should occur, at a particular value of VG. This gate voltage could possibly be used to determine the surface roughness parameters ⌬z and ⌳. It is most likely that this critical point in the mobility could have been identified if the experimental results of SA were extended to higher gate voltages. Such peaks at large gate voltages have been observed in the experiments of Harada et al.65 To simulate the low-field mobility as a function of temperature T, we need to determine Ninv共T兲 and Nit共T兲 at a number of temperatures. By fitting to the SA results at temperatures of 200, 297, and 440 K, we find the following analytical formulas for gate voltages of VG = 8 V and VG = 12 V:

冋

Nit共T,VG兲 = ␹4共VG兲 + and

冋

冉

T − 200 K 200 K

冊册

1012 cm−2

共32兲

V. RESULTS FOR „112¯ 0… 4H-SIC

Ninv共T,VG兲 = ␹5共VG兲 + ␹6共VG兲 ⫻

冉

T − 200 K 200 K

冊册

The Monte Carlo simulations over a wide temperature range are shown in Fig. 9 for gate fields of 8 and 12 V. We find that the mobility increases linearly 共⬀T兲 with temperature. This agrees with the results of SA, also shown in Fig. 9. Experiments by Matsunami et al.67 although have indicated a temperature rise ⬀T2.6. In this work a very large threshold voltage of 7.78 V was measured at 300 K. Since the value extracted from the SA experiments, 3.5 V, was much smaller, the sample of Matsunami et al. likely contained a much larger density of interface traps. This would indicate that the exponent n for the temperature dependence of the mobility 共Tn兲 may very likely increase in samples were there tends to be a larger number of trapped charges at the interface. It is important to note that no adjustable parameters are used in the Monte Carlo simulations. Electron-phonon coupling constants and the polar field are fixed according to the results of bulk transport simulations in Refs. 49 and 50. There are no adjustable parameters within the interface charge scattering rates. The parameters for surface roughness scattering were obtained by scaling the results from Si. Since we find that this is not a dominant scattering mechanism in the case here, where a large number of charges are trapped at the interface, we feel this is justified. As mentioned, it might be possible to determine these roughness parameters from the mobility peaks at high gate voltages.

3/2

1011 cm−2 .

共33兲

The fitting parameters ␹4 – ␹6 are given in Table I. These fits are shown in Fig. 8. The SA experiments do not extend beyond T = 440 K, but we want to simulate higher temperatures. We have therefore extrapolated the fits of Ninv共T兲 and Nit共T兲 to higher temperatures assuming the same trends as found in the SA data range below T = 440 K.

It has been determined experimentally by Yano, Hirao, ¯ 0兲 instead Kimoto, and Matsunami 共YHKM兲 that if the 共112 of the 共0001兲 surface of 4H-SiC is used for the interface with SiO2, the interface trap density is significantly reduced.18 This can be seen in Fig. 10, were we plot the experimental results of YHKM. Now to compare the simulated low-field Monte Carlo mobility along the 共0001兲 surface of 4H-SiC ¯ 0兲 surface, we need to determine with that along the 共112 how the density of free and trapped states changes. We accomplish this by scaling the SA results for the 共0001兲 surface

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063701-10

J. Appl. Phys. 106, 063701 共2009兲

G. Pennington and N. Goldsman

FIG. 11. 共Color online兲 Monte Carlo simulation of electron mobility for ¯ 0兲 oriented 4H-SiC inversion layers vs temperature. 共0001兲 and 共112 FIG. 10. Experimental interface trap density of states 共Ref. 18兲.

as in the last section to account for changes in the surface orientation. The density of interface states is scaled according to

冏冉 冊冏

We also adjust the SA results for the mobile electron density Ninv. This occurs through the adjustment of the threshold voltage in Eq. 共30兲. Since the number of trapped ¯ 0兲 charges decreases on going from the 共0001兲 to the 共112 surface, VT should approximately change according to

¯

¯ 0兲 N共112 兩SA = it

0兲 N共112 it

N共0001兲 it

N共0001兲 兩SA . it

共34兲

YHKM

¯ VT共1120兲共T兲

= 1.5 V +

冏冉 冊 冉 冊冏 2

424 K T

¯

0兲 N共112 it

N共0001兲 it

V. YHKM

¯

0兲 This can be used to obtain N共112 兩SA for comparison with the it experiments of SA. This method enables us to estimate this density in a way which is as independent of sample processing differences as possible. Processing differences between the two orientations in the work of YHKM is assumed to be at a minimum. To determine the trapped interface charge densities from the YHKM experiments, we use the experimental density of traps 兩DOSit共E兲兩YHKM in Fig. 10. The result ¯ 0兲, is for each surface, where 共X兲 is 共0001兲 or 共112

N共X兲 it 兩YHKM = 兩

冕

Es+Eg

f共E兲DOSXit 共E,EF兲兩YHKMdE.

共35兲

0

Here the energy integrals run from the valence band edge at E = 0, to the relative energy of the first subband. With a bulk gap energy of Eg = 3.2 eV for 4H-SiC, the energy of the first subband, relative to the valence band edge, is Es + Eg. The term f共E兲 is the Fermi Dirac equilibrium distribution function f共E兲 = 兵1 + 0.5 exp关共E − EF − Eg兲 / KBT兴其−1 where EF is the Fermi energy. As in Ref. 4, EF is defined relative to the bulk conduction band edge at Eg. To evaluate Eq. 共35兲, we use the following analytical fits to 兩DOSit共E兲兩YHKM in Fig. 10: log10共DOSit兲兩YHKM = ␹7共E兲E␹8 + ␹9 ,

共36兲

where E and DOSit are in units of eV and cm−2, respectively. The results for the fitting constants ␹, which depend on the surface orientation and energy, are given in Table I. ¯

0兲 To calculate N共112 兩SA in Eq. 共34兲, the value of EF for it the calculation of the YHKM trapped charged densities must be determined. Using Eq. 共35兲, EF is determined by requiring N共0001兲 兩YHKM = N共0001兲 兩SA. This gives the Fermi level for the it it YHKM results in Eq. 共34兲.

共37兲 The Fermi energy used here in the calculation of the ratio of trapped charge densities is the value that can be used along with DOSit 兩YHKM to obtain the buildup of trapped interface charge before inversion in the SA experiments. This requires N共0001兲 兩YHKM = 共424 K / T兲2Cox / e. We therefore obtain for the it ¯ 0兲 4H-SiC as V共112¯ 0兲共T兲 = 1.5 V threshold voltage in 共112 ¯

¯

¯

T V. 440 K

T

0兲 0兲 / Cox兲 兩YHKM V with N共112 兩YHKM evaluated at the + 共eN共112 it it aforementioned Fermi energy. We find that the threshold ¯ 0兲 orientation are significantly less and voltages for the 共112 can be accurately model as

VT共1120兲共T兲 = 3.5 V +

共38兲

The mobile charge density in Eq. 共31兲 for the 共0001兲 orientation is then adjusted according to ¯ 0兲 共112 共T,VG兲 Ninv

=

共0001兲 Ninv 共T,VG兲

冋

¯

VG − VT共1120兲共T兲 VG − VT共0001兲共T兲

册

,

共39兲

共0001兲 and VT共0001兲 are given by Eqs. 共31兲 and 共30兲, where Ninv respectively. In Fig. 11 we show the result of our Monte Carlo simulations of low-field electron mobility for a large temperature ¯ 0兲 orientation, range. We find that the mobility for the 共112 using the adjusted charge densities, is much larger than that of the 共0001兲 orientation. Mobilities as large as 90 cm2 / V s at room temperature are found. This agrees very well with the experimental results for this orientation where a value of 95.9 cm2 / V s for current along the 具0001典 crystalline direction and 81.7 cm2 / V s along the 具1100典 direction where ob-

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063701-11

G. Pennington and N. Goldsman

¯ 0兲 oriented FIG. 12. Low-lying subband structure for 共0001兲 and 共112 4H-SiC surfaces. Here E0 and E⬘0 are the lowest subbands of ladders 1 and 2, respectively.

¯ 0兲 oriented surfaces.67 In our simulations we tained for 共112 assumed a spherical conduction band since no current direction was specified in the SA experiments. This approximation is still reasonable for comparison with the 共1120兲 experiments since the effective masses along 具0001典 and 具1100典 are very similar. Our results are close to the average of the two experimental results. We find that the temperature falls of as T−3/2. However the experiments of Matsunami et al. found a fall off proportional to T−2.2.67 To determine the effect of band structure variation with 4H-SiC orientation, we also determine the mobility for electron transport in the 共0001兲 plane, but fix Nit and Ninv equal ¯ 0兲 surface. As to those used in the simulations of the 共112 seen in Fig. 11, the results are very similar to the simulations ¯ 0兲 orientation. This occurs since the surface band for the 共112 structure of the two orientations is very similar even though ¯ 0兲 orientation has two subband ladders while the the 共112 共0001兲 orientation has but one. There are two main reasons for this similarity. The first is a result of the principle-axes effective masses, m1, m2, and m3 in the notation of Ref. 4, which vary little between the two orientations. The second reason is the very small spacing between the two subband ¯ 0兲 orientation. We see this in Fig. 12, ladders in the 共112 where the low-lying subband electronic structure of the two orientations is very similar. Here, in Fig. 12 there is no density of trapped charge at the interface, but if we did included trapped charge, the subband structure would still be similar for the two orientations. In Fig. 13 we also see that the rela¯ 0兲 ladder falls very closely to tive occupancy of each 共112 their degeneracy contributions 2/3 and 1/3 even when inversion is weak. This occurs since the energy spacing between the ladders is very small. One material property, directly related to the subband structure, is the average distance, Zav, that the inversion layer mobile electrons penetrate into the

J. Appl. Phys. 106, 063701 共2009兲

¯ 0兲 oriented 4H-SiC FIG. 13. Occupancy of electrons in 共0001兲 and 共112 surfaces. Here E0 and E⬘0 are the lowest subbands of ladders 1 and 2, respectively.

semiconductor. The larger this distance the larger the mobility since scattering from both the occupied traps and the surface roughness will be weakened. Since the fraction of occupied higher energy subbands is very similar in each orientation, we see in Fig. 14 that Zav is also very similar for the two orientations of 4H-SiC. So based on a comparison of the self-consistent electronic structure calculation at the interface, it is clear to see why the mobility for both 共0001兲 and ¯ 0兲 4H-SiC would be similar if the same density of 共112 trapped charge where present at the surface. VI. NITROGEN REOXIDIZED „0001… AND „112¯ 0… INTERFACES

Many studies have indicated an improvement in the interface state density and inversion layer electron mobility

FIG. 14. Average distance of electrons from the surface in 共0001兲 and ¯ 0兲 oriented 4H-SiC. 共112

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063701-12

J. Appl. Phys. 106, 063701 共2009兲

G. Pennington and N. Goldsman

FIG. 15. 共Color online兲 Charge densities for NO annealed 4H-SiC Hall bars with data from Ref. 68.

when the SiC/oxide interface is reoxidized in the presence of NO. The physical mechanisms at work are still uncertain as nitrogen may act to break up carbon clusters, passivate suboxide bonds or fill dangling bonds at the interface.25–27 As this process reduces Nit, it is of interest to compare transport ¯ 0兲 4H-SiC/oxide interfaces which have at 共0001兲 and 共112 undergone nitrogen annealing. For this we consider the Hall Effect measurements of Naik et al.68 which where preformed on p-doped Hall bars. Devices in this work employed a 100 nm deposited gate oxide that was annealed in NO at 1175 ° C for 2 h. Doping densities where 4 ⫻ 1016 cm−3 for samples with a 共0001兲 4H-SiC oxide interface and 2.4 ¯ 0兲 interface. From ⫻ 1016 cm−3 for devices utilizing the 共112 measurements of the temperature dependence of the threshold voltage, dNit in Eq. 共31兲 is found as dNit共T兲 = 共30 mV/ K兲 · T · Cox / e and dNit共T兲 = 共23.4 mV/ K兲 · T · Cox / e for ¯ 0兲 interfaces, respectively. Using Eq. the 共0001兲 and the 共112 共31兲, Nit is then found from the Hall measured Ninv versus gate voltage curves in Ref. 68. The experimental data for Ninv along with our fitted curves for the charge densities are shown in Fig. 15. Since experiments were taken at a temperature of 225 K, simulations in this section will be taken at this temperature. As seen in the figure, the mobile charge density is slightly larger for the 共0001兲 orientation. Nit is found to be relatively independent of the gate voltage taking on values of 共 ⬃ 3 – 4兲 ⫻ 1012 cm−2 in both orientations. While the trapped charge density is at least eight times that of Ninv in the samples without NO annealing in Fig. 5, it is typically twice of Ninv or less in the NO annealed samples. Simulations of the low-field mobility are shown in Fig. 16. The mobility is very similar in both orientations as the interface charge densities are now comparable after NO annealing. The mobility rises initially with increasing gate voltage due to screening effects, reaches a maximum, and then decreases as surface roughness scattering becomes impor¯ 0兲 tant. In the region of large voltage, the mobility of the 共112 oriented sample is larger as a result of reduced roughness parameters. The Hall mobility measured in Ref. 68 compares ¯ 0兲 samples. However, simuwell with our results for the 共112 lations for the 共0001兲 orientation are up to twice as large as

FIG. 16. 共Color online兲 Simulated low-field mobility for NO annealed samples at a temperature of 225 K.

the experimental results. This discrepancy may indicate the presence of interface step bunching in the experimental 共0001兲 samples, an effect that would not be as significant in ¯ 0兲 oriented samples. the 共112 VII. CONCLUSION

Using the results of experimental data17 for free and trapped charge densities in the 共0001兲 orientation, the lowfield mobility was simulated. The simulation results were found to agree qualitatively very well with experiments. The mobility was found to rise linearly with increasing temperature, in agreement with experiments.17 We also simulated ¯ 0兲 oriented transport along the inversion layer of a 共112 4H-SiC/ SiO2 interface incorporating experimental interface trap densities.18 We found that the reduction in electron traps near the interface lead to a dramatic improvement in the low-field mobility. The mobility increased from ⬇0 – 40 cm2 / V s in the 共0001兲 orientation to ⬇90 cm2 / V s ¯ 0兲 orientation. We also found that the mobility in the 共112 decreased with increasing temperature. These results agreed ¯ 0兲 oriented 4H-SiC.67 We also well with experiments on 共112 found that a commensurate reduction in the density of interface traps for the 共0001兲 orientation lead to mobilities that ¯ 0兲 oriwere essentially equivalent to those simulated for 共112 entation. An analysis of the electronic subband structure revealed a strong similarity among the two orientations. This similarity means that if the density of interface traps could be reduced in the 共0001兲 orientation, the transport properties ¯ 0兲 orientation. To should be very similar to those of the 共112 68 investigate, experiments whereby the SiC oxide interface was reoxidized in the presence of NO are examined. Samples ¯ 0兲 orientations were found to exhibit with 共0001兲 and 共112 similar trapped charge density profiles and as expected, similar simulated low-field mobility. R. W. Erickson, Fundamentals of Power Electronics 共Chapman and Hall, New York, 1997兲. J. W. Palmour, R. F. Davis, H. S. Kong, S. F. Corcoran, and D. F. Griffis, J. Electrochem. Soc. 136, 502 共1989兲. 3 I. A. Khan and J. A. Cooper, IEEE Trans. Electron Devices 47, 269 共2000兲. 1

2

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