Thesis organization

The first part is the introduction which briefly introduces the topic. Chapter 2 begins with the introduction of the two-dimension device simulator, MEDICI, which is used throughout this thesis. It is followed by the important bulk parameter set for 4H-SiC devices.

Chapter3 the SiC power device is then proposed and analyzed. We also make the general analysis of 4H-SiC as compared to Si power MOSFET. The fourth part is “result and discussion” which represents the advantages of silicon carbide applied in power devices.

Finally a conclusion of this thesis is given some recommendation of future work are suggested.

Chapter 2

Models and Parameters for Device Simulation.

Numerical device modeling and simulation are essential for analyzing and developing semiconductor devices. They help a design engineering not only gain an increased understanding of the device operation, but also provide the ability to predict electrical characteristics, behavior, and parameter-effects influence of the device. With this knowledge and abilities the designer a better structure, estimate device performance, perform the analysis of worst case, and optimize device parameters to yield an optimize device performance.

2.1. Introduction

Medici is a powerful device simulation program that can be used to simulate the behavior of MOS and bipolar transistors, and other semiconductor devices [2]. It models the two-dimensional distributions of potential and carrier concentrations in a device. The program can be used to predicted electrical characteristics for arbitrary bias conditions. As in any device simulator, any quantitative, or even qualitative, simulation of device relies heavily on applicable device models and their parameter values. A number of physical models are incorporated in MEDICI for accurate simulations. Furthermore MEDICI also supports a variety of semiconductor materials including SiC [13].

2-2 MEDICI Description

The primary function of Medici is to solve the following three partial differential equations [2].

The Poisson equation

(

^{p n N N}

)

^ρ

q ψ

ε∇² =− − + _D⁺ − _A⁺ − (1)

Continuity equation for electron and hole.

n

Throughout Medici, ψ is always defined as the intrinsic Fermi potential. That is,

ψ

=

ψ

^intrinsic

. N

D+ and NA+

are the ionized impurity concentrations and ρ

_sis a surface charge density that may be present due to fixed charge in insulating materials or charged interface states .

The numerical algorithms used in MEDICI to solve the fundamental equations are based on the finite element method, which discretized these equations on a simulation grid. This discretization process yields a set of coupled nonlinear algebratic equations which represent a number of grid points, for the unknown potentials and free-carrier concentrations. This set of coupled nonlinear equations in return must be solved a nonlinear iteration method. Two iteration methods, Gummel’s and Newton’s method are available in MEDICI. Regardless which iteration method used, the solutions are carried out over the entire grid until a self-consistent potential and free-carrier concentrations are obtained. Once the potentials and free-carrier concentrations have been calculated at a given bias, it is possible to determine the quasi-Fermi levels and the hole and electron currents ( Jn and Jp ).

2-3 Simulation Physical Models

2-3-1 The Parameter Set for 4H-SiC

In order to achieve realistic results, it is imperative to use proper models for the 4H-SiC properties. The most important physical models employed in the simulations are for intrinsic concentration, carrier mobility in bulk, transverse and parallel field within the channel region, SRH recombination, Auger recombination and impact ionization.

(1) Intrinsic concentration:

Accurate models for the carrier concentration in semiconductor devices are a necessity if qualitatively and quantitatively correct simulation results are to be obtained. The intrinsic carrier concentration ni is determined by the fundamental energy gap Eg and the effective density of states NC

and N

_V in the conduction and valence bands. Where, neglecting band gap narrowing, the intrinsic carrier concentration is [2]

2kT)

where Eg is the bandgap energy of the semiconductor, that is, E

the parameters NC300 and NV300 are user specified and can be modified from their values on the Material statement to fit the 4H-SiC in unipolar devices.

At high doping levels, the carrier-carrier interaction and overlap of the electron wave functions are not negligible. Since no study of bandgap narrowing effects has been performed, these BGN (bandgap narrowing effects) known from Si are taken into account by an effective carrier concentration [13].

2kT)

The V.BGN, N.BGN, and CON.BGN are constant parameters that can be adjusted from their default values.

2-3-2 Carrier mobility in bulk

By definition, mobility is a measure of average velocity of free carriers in the presence of an impressed electric field. In the presence of an electric field in a semiconductor, the free electrons and holes are accelerated in opposite directions [23]. As the free carriers are transported along the direction of the electric field, their velocity increases until they undergo scattering. In the bulk, the scattering can occur by either interaction with lattice or at ionized

donor and acceptor atoms. In analyzing the influence of the preceding parameters on the mobility, one assumes the electric field strength to be small. The mobility is then defined as the proportionality constant relating the average carrier velocity to the electric field. At high electric field such as those commonly encountered in power devices the velocity is no longer found to increase in proportion to the electric field and in fact attains a saturation value [11].

Since the free-carrier mobility depend strongly on the magnitude of the mobility model on MEDICI consists of low field and high field mobility components. These effects have important implications to current flow in power devices. So the accurate I-V model is strongly based on physical and accurate mobility and velocity saturation models [26].

Low Field Mobility

At low electric fields the electron velocity increases almost linearly with field and the mobility has the constant value

µ

₀. The low-field mobility is a function of the doping concentration and the temperature. A widely used empirical expression given by Caughey-Thomas equation for modeling the doping dependence of the low-field mobility has been proposed [25]. parameters. The parameterμmax in (12) represents the mobility of undoped or unintentionally doped samples, where lattice scattering is the main scattering mechanism, whileμmin is the mobility in highly doped material, where impurity scattering is dominant [18]. And Nref is the doping concentration at which the mobility is halfway between μmin and μmax , and α is a measure of how quickly the mobility changes from μmin to μmax .For modeling the

low-field mobility of 4H-SiC at room temperature. Equation (12) has been used. Several sources of experimental data were available for good fitting. Fig. 2.1 shows the experimental low-field mobility fit for 4H-SiC, which the following parameters were determined shown in Table 2.1

High Field Mobility

When strong electric fields are applied, the electron velocity is no longer proportional to the field, and can thus no longer be described by a field independent mobility. An expression frequently used for modeling the field dependence of the mobility in Si is [25]

β is a constant specifying how abruptly the velocity goes into saturation. To obtain the velocity-field characteristics, both sides of (13) have to be multiplied by the electric field.

Only little is known about the high-field mobility of SiC. For 4H-SiC the only experimental data on this comes from Khan and Cooper [26], where the drift velocity in epitaxial 4H-SiC (n-doped to about 10¹⁷cm^-3 ) was measured as a function of the applied electric field. A fit of equation (13) through the experimental high field data by Khan and Cooper is shown in Fig.

2.2, and the

µ

₀,

ν

_sat, and

β

parameter values at 300K are 450 cm²/Vs, 2.2x10⁷cm/s, and 1.2 respectively.

2-3-3 Channel mobility model

SiC is a viable semiconductor for high-power device applications due to its superior material properties. Although several MOS-based high-voltage devices have been demonstrated, most of them suffer from large on-state resistance due to poor inversion-layer mobility, attributed to a large interface state density at the interface [19]. The use of accumulation-mode MOSFETs was suggested to circumvent the poor inversion-layer mobility problem because a larger accumulation-layer mobility is expected compared to inversion-layer mobility as seen in Si MOS technology [22]. Extracted parametric mobilities and threshold voltage are shown for inversion and accumulation mode MOSFETS on both 4H-SiC and 6H-SiC in Fig. 2.3

Medici also incorporates an empirical model that combines mobility expressions for semiconductor-insulator interfaces and for bulk silicon. The basic equation is given by Mathiessen’s rule [27]:

µ is total electron or hole mobility accounting for surface effects. s

µ is the carrier mobility limited by lattice scattering (surface acoustic phonons). ac

µ is mobility in bulk silicon. b

µ is mobility degraded by surface roughness scattering. _sr

Where µ is the carrier mobility in bulk of the semiconductor, _b µ is the carrier _ac mobility limited by lattice scattering (surface acoustic phonons), and µ is the carrier _sr mobility limited by surface roughness scattering. In this model, the contributions of various scattering mechanisms are separated, thus offering advantages in terms of initial estimation of

the model parameters, needed for any curve fitting, as well as convenience for including more scattering mechanisms without altering the model structure itself. At low normal electric fields, the carrier mobility in a semiconductor is a function of the total doping concentration and the temperature. The bulk or low field mobility, µ , was modeled using the empirical _b model proposed by Caughey-Thomas as mention above (12). The acoustic-phonon term, used in MEDICI simulator, has the following form [2]:

3

There are two fitting parameters, B and C, allowing adjustment of the strengths of the effects due to parallel electric field and temperature, respectively.

Surface roughness is known to cause severe degradation of the surface mobility at high electric fields. The electron mobility term due to the surface-roughness scattering is frequently expressed in the following way:

⎟⎟ ⎠

Where D is the fitting parameter.

The surface-mobility parameters have not been studied for 4H SiC because of the erratic behavior of the inversion layer mobility in the case of MOSFETs with ordinary dry or wet oxides. However, recently made MOSFETs with nitrided gate oxides exhibit not only significantly increased mobility, but also mobility behavior that is similar to the case of Si MOSFETs. This indicates that it is possible to use the existing mobility models by setting the parameter values. MEDICI two-dimensional device simulation program was used to

determine the surface-mobility parameters. Two-dimensional impurity profile was generated using the same parameters as the experimental test MOSFET and material parameters for 4H SiC. Lombardi surface mobility model, available in MEDICI, was used as the combination of low field and transverse field effects. The complete list of parameter value, providing the good fit shown in Fig. 2.4, is listed in Table 2.2.

2-4 Impact ionization

Impact ionization, punch through mechanism, and oxide breakdown due to high electric stress are the major factors for determining the maximum voltage that a device can stand.

Impact ionization results in the generation of electron-hole pairs during the transport of the mobile carriers through the depletion layer. To characterize this process, it is useful to define the ionization coefficients [20]. The probability that electrons or holes create electron-hole pairs is given by the product of a proportionality factor α（called impact ionization rate）and the electron/hole concentration. The maximum EB and the blocking capability

V

_B is determined by the impact-ionization rate for electron-hole pairs. In the forward blocking mode, the gate electrode of the power MOSFET is externally short-circuited to the source.

Under these conditions, no channel forms under the gate at the surface of the P-base region.

Thus impact ionization coefficient rates are the key parameters that have to estimate accurately to get reliable prediction of the device blocking performance. In ordered to obtain the critical electric field as function of doping, we had to solve the integral equation (17)

( )

¹

numerically. For the avalanche generation rates α the same model used for Si was taken [9]:

⎟⎟

αn, are the electron and hole ionization rates that are defined as the generated electron-hole pairs per unit length of travel by per electron and hole. It is not importance whether the ionization integral for the holes or the electrons is calculated since both reach unity at V=V^B. Therefore, the kind of dopants (N or P) in the space charge region is not important. It was determined that the coefficient a in 4H-SiC has a value of _p

(

3.25±0.3

)

×10⁶

1

cm

at room temperature and b has a value _p

(

1.79±0.04

)

×10⁷

V cm

at room temperature from Fig. 2.5 .

2-5 Summary

MEDICI simulations are able to obtain the breakdown voltage using the obtained ionization coefficients. However, in real devices, tunneling may take place before avalanche breakdown at high doping levels. Normally breakdown occurs at edges of the space charge region or at the surface prior than in the bulk. And in this chapter, the important material parameter set for 4H-SiC device simulation in MEDICI 2D-simulation program has been complied from literature data.

Chapter 3

SiC Power MOSFET

The physics of the operation of power MOSFETs is simpler than that for other power devices because of the absence of minority carrier injection. However, it is necessary to understand the interaction between the cell geometry and the devices characteristics before taking an accurate device design. In the following, the on-state characteristics are first treated followed by analysis of the blocking characteristics.

3-1 On-resistance

The on-resistance is an important device parameter because it determines the maximum current rating. The on-resistance of a power MOSFET is the total resistance between the source and drain terminals in the on-state. The specific on-resistance of silicon carbide power MOSFET’s have been projected to be far superior to their silicon counterparts due to the high breakdown field strength of SiC. The power dissipation in the power MOSFET during current conduction is given by [7]:

Ron,sp is the specific on-resistance, defined as the on-resisitance per unit area. These expressions are based upon the assumption that the power MOSFET is operated in its linear region at a relatively small drain bias during current conduction. The maximum power dissipation per unit area is determined by maximum allowable junction temperature and the thermal impedence. The specific on-reisitance of the power MOSFET is determined by the resistance component for the DMOS structure. Fig. 3.1 shows a cross section of a power DMOS MOSFETs structure.

S the accumulation layer resistance, RJ is the resistance from the drift region between the p-base region due to JFET pinch-off action, RD is the drift region resistance and RS is the substrate resistance. In a power MOSFET, blocking voltage is supported across the drift layer and thus, drift-region resistance is considered to be minimum possible theoretical limit for the on-resistance of a MOSFET. This assumption is not accurate at lower breakdown voltages where the drift-region resistance RD is compariable to other resistive components and these resistances should also be included in calculating Ron,sp

. However, at higher breakdown

voltage, RD is significantly higher than other resistances and Ron,sp

. could be approximately by R

_D. The specific on-resistance of the power MOSFET will then be determined by the drift region alone. Thus:

3-2 The analysis of blocking voltage

The drift region analysis can be performed to express the relation between the specific on-resistance (Ron) and the blocking voltage capability (VB) of a MOSFET. By approximating the depletion layer in the drift region as an abrupt one-dimension junction, and it is uniform doped ; the doping level NB

(cm

^-3

) required to supported a given breakdown voltage V

_B and depletion width W (cm) at breakdown can be calculated as follows [7]:

B

where VB is the breakdown voltage. The ideal specific on resistance is the resistance per unit area of this layer of material required to support the voltage. Using the above doping and thickness, this given by

Thus, the ideal specific on-resistance decreases inversely proportional to the mobility and as

the cube of the breakdown electric field strength. The denominator (

ε ⋅ µ ⋅ E

_B³) in Eq. (7) has been referred to as Baliga’s figure of merit (BFOM) for unipolar power devices. In 1983, Baliga drived a figure of merit

BFOM= ε ⋅ µ ⋅ E

_B³

(8) which defines material parameters to minimize the conduction losses in power MOSFET’s.

Here μ is the mobility and EB is the critical electric field of the semiconductor. The BFOM is based upon the assumption that the power losses are solely due to the power dissipation in

the on-state by current flow through the on-resistance of the power MOSFETs.

3-3 Material advantages of 4H-SiC for power devices

By using the known material properties of semiconductors, it is possible to select those that will exhibit a lower ideal specific on-resistance when compared with silicon by using this expression It has been found that most promising semiconductor are gallium arsenide, whose Baliga’s figure of merit is 12.7 times larger than silicon, and silicon carbide whose Baliga’s figure of merit is 200 times larger than silicon. Although some research has been performed on the fabrication of vertical power MOSFET’s from gallium arsenide, this material has been found to be difficult to work with due to dissociation of the compound during processing. In contrast, silicon carbide offers a such larger improvement in ideal specific on-resistance and is stable even at extremely temperatures.

In the case of Si, the extract dependency of the electron mobility and the breakdown field on the doping concentration is known [23]

91 MOSFET’s, a closed form analysis which requires the solution of ionization integral, using an abrupt junction diode, is used for calculating expressions for

N

_B and

W

for a Si power MOSFET are obtain as [17]

4

the dependency of the breakdown field strength of 4H-SiC and 6H-SiC on

N

_B was determined from the calculated values from [17,9]. The empirical relationship between

E

Band

V

_B on

N

_B was obtained as voltage for Si and SiC power MOSFET’s. This analysis suggests that 4H-SiC MOSFET would have lower

R than 6H-SiC. For a given breakdown voltage,

_on

R for the SiC

_on MOSFET is at least two orders of magnitude smaller than for Si MOSFET, and the ratio of

R of the Si MOSFET to that of SiC MOSFET increases with increasing breakdown voltage.

on

Due to the excellent characteristics of SiC, it would be desirable to utilize power MOSFET for high voltage power applications. Unfortunately, the specific on-resistance of the drift region increases very rapidly with increasing breakdown voltage because of the need to reduce its doping concentration and increase its thickness [4]. Thus, in spite of the ability to obtain nearly ideal specific on-resistance with silicon power MOSFET structures, they are not

satisfactory for applications that require breakdown voltages above 300V due to their high on-state power dissipation. So, many reasons make SiC an attractive candidate for fabricating power devices.

3-4 Summary

The superiority of 4H-SiC illustrated in this chapter is just one of the potential projections in using this wide semiconductor material for high power devices. These advantages in terms of calculated figure of merits provide a motivation for the design and development of power devices on SiC. Despite the unique problems in device fabrication, which many are not yet totally resolved, promising progress in the device development has taken place in the area of power MOSFETs.

Chapter 4

The electrical performance of SiC MOSFET

Silicon-based switching devices have reached the theoretical limitations for high power and for high power and high temperature applications whereas silicon carbide (SiC) has emerged as an alternate material system to overcome the limitations and can be used in extreme environment.

4-1 Introduction

Since SiC is a attractive semiconductor materials for high-power electric devices because they have excellent physical properties such as a wide bandgap, high breakdown voltage, and high saturation electron drift velocity. However, due to higher layer mobility as compared to inversion layer mobility, ACCUFETs emerge as the preferred solution for power MOSFETs

Since SiC is a attractive semiconductor materials for high-power electric devices because they have excellent physical properties such as a wide bandgap, high breakdown voltage, and high saturation electron drift velocity. However, due to higher layer mobility as compared to inversion layer mobility, ACCUFETs emerge as the preferred solution for power MOSFETs

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