Temperature Effect On Mobility In Gaas Mesfet With a Short Gate Length.docx

=== Temperature effect on mobility in GaAs Mesfet with a Short Gate Length. ===

Temperature Effect on Mobility in GaAs MESFET with a Short Gate Length.

AZIZI Mounir1

Larbi Ben M’Hidi university, Oum El Bouaghi, Algéria.

1Faculty of exact sciences and natural and life sciences, Active Devices and Materials Laboratory

1e-mail : [anonimizat]

Abstract:

Performance and reliability of active field-effect devices like GaAs MESFET’s are strongly related to thermal conditions. Temperature is a very important parameter that affects the carrier mobility and the drift velocity of the devices. It must be taken into account in the design of digital and analog circuits based on GaAs MESFET’s. In this paper the degradation of mobility from different scattering mechanisms depending on the temperature is studied. Also we present a comparison of four main analytical expressions of mobility-field dependence in the GaAs MESFET’s devices. Hence, a numerical simulation of mobility and velocity versus electric-field was performed. Then, we propose a simple mathematical relation for the mobility-field dependence in GaAs. This proposed approach can be used in the case of logic or analog circuits based on submicron GaAs MESFET’s.

Keywords : Carrier Mobility, Drift Velocity, Scattering effects, MESFET’s GaAs, Temperature.

Introduction

The active devices such as transistors constitute the largest share of modern microelectronics activity. In this context a special attention is given to unipolar devices and more particularly to gallium arsenide field effect transistors with Schottky gate. This is due to their many interesting properties such as high electron viability, low effective mass, thermal conductivity and high saturation velocity [01].

For low electric field the carrier mobility remains constant and varies from one material to another. It is usually a strong function of material impurities and temperature. However, when the applied electric field becomes important, the interaction of carriers with lattice vibrations causes a decrease in the carrier mobility. This decrease results in a non-linear variation of the drift velocity of the carriers. Therefore, a few mathematical expressions have been proposed but no one was taken as the reference law. Thus, each analytical model for static properties Ids-Vds was proposed with a special mobility expression that fits better its theoretical results.

We performed a simulation of the different carrier mobility and drift velocity expressions as a function of the electric field at different temperatures.

Scattering Effects and Mobility Expressions

Usually, the electron drift velocity in a material is directly proportional to the electric field, which means that the electron mobility is a constant (independent of electric field). The drift velocity is defined by the equation:

(01)

Where E(in units V/m) is the electric field, µn the electron mobility(in units (m2)/V.s). 

Scattering time has a great effect on the carrier mobility and drift velocity. It has two main origins, carrier interactions with the lattice and impurities [2]. These two types of interactions are themselves the result of several mechanisms.

The most important sources of scattering in typical semiconductor materials, discussed below, are ionized impurity scattering and acoustic phonon scattering (also called lattice scattering). In some cases other sources of scattering may be important, such as neutral impurity scattering, optical phonon scattering, surface scattering, and defect scattering [20].

When the temperature is greater than 0K, the carriers can then collide with the crystal lattice [3]. Electron scattering by lattice vibrations depends on the nature of these vibrations. The concept of phonons (elementary quantum of vibrational energy), which are quantized modes of vibration propagation is then introduced.

Acoustic phonon is obtained when two atoms of the neighboring lattice vibrate in phase [3,4]. However, optical phonon which can be easily excited by light waves is produced when the atoms vibrate in opposition phase.

The mobility drops at high temperature. However, in purely covalent crystals such as GaAs, the free carriers interact mainly with longitudinal acoustic vibration modes [5]. The dependence of mobility with temperature according to this mode of vibration is given by:

(02)

m* is the effective mass, T the temperature and α ~ 3/2 for acoustic longitudinal vibration methods.

When we take into account the longitudinal modes of the optical vibration, as in the III-V ionic materials (GaAs, InP, GaN), the mobility temperature dependence is given by

(03)

With α ~ 2 for optical longitudinal modes

The diffusion process of the collision with the ionized impurities is predominant. In this case, the mobility temperature dependence is given by the relation [5]:

(04)

The phonons and the lattice scattering cover the deformation mechanisms of piezoelectric and acoustic scattering, where the lattice scattering is a process at low temperature. In this case the mobility is related to temperature by the relation [5,6]

(05)

The impurities scattering occurs when an electron approaches a neutral atom. This is the result of non-ionized donors or neutral defects. This diffusion plays an important role in the mobility degradation [7]. Mobility due to the neutral scattering is given by:

(06)

NNI is the concentration of neutral impurities.

The total mobility according to the Matthiessen rule [8, 9]is given by:

(07)

The classic law of the carrier mobility versus temperature at low electric fields in the case of gallium arsenide [10,11] is given by the following relation.

(08)

for GaAs MESFET’s.

The saturation velocity varies with temperature as [12]:

(09)

The dependence of threshold voltage may be approximately given bythe relation [12]:

(10)

The value of αvT is in the range of 1.2mV/°C

However, when the electric field becomes important, there is no a standard analytical expression that really reflects mobility-field dependence and this could only be defined and fixed by a complex Monte Carlo method. From that, several analytical expressions have been proposed for this purpose (relations 12-15).

For low fields, where E <E0 which corresponds to the critical field, we have:

(11)

And for high fields where E ≥ E0, we have tested the following equations:

First expression [13]:

(12)

Second expression [14,15,16]:

(13)

Third expression [17]:

(14)

Fourth expression [18,19]:

(15)

with

(16)

and

(17)

(18)

(19)

(20)

is the relaxation time, m* the effective mass of the electron and vs is the saturation velocity of GaAs.

Ec : the critical field at which the velocity in the linear regime is equal to the saturation value.

Es : the threshold field, corresponding to the maximum value of the electrons velocity, which can be calculated from the following relationship:

(21)

III. Results and Observations.

In this paper, we have proposed a very simple law of mobility which is based on the first analytical expression presented in the expression (12).
The proposed expression is given by:

(22)

The coefficient n that occurs in this relationship may be taken equal to 1 or 2 in order to be as close as possible to the two segments approach. This law of mobility differs significantly from the original expression and gives more accurate results.

Figures (01) and (02) show the obtained results of numerical simulations of the carrier mobility models μ1, μ2 μ3 and μ4under room temperature conditions (300K). The results were carried out using MATLAB software.

As we can see on figure (01), the profiles of mobilities calculated from the previous expressions are very similar and all begin with a decrease with the increase of the electric field. Except for μ2 in which a slight increase of electron mobility as the electric field is increased up to the maximum value of 0.380 m2/V.s at E=2×105 V/m. Then the mobility decreases with the electric field until the minimum value of 0.140m2/V.s. at E=8×105V/m.

The results of numerical simulations of models 3 and 4 of the mobility for GaAs MESFET’s shown clearly the similarity of the carrier mobility shapes versus electric field, figure (01).The values ​​of the mobility decreases when electric field increased.

The maximum values ​​approximated using the different models are very close to each other (μ3max=0.369m2/V.s, μ4max=0.377m2/V.s). While minimum values ​​are slightly different (μ3min=0.123m2/V.s, μ4min=0.104m2/V.s at E=8×105V/m).

On figure (02) we have gathered the four carrier mobility expressions by zooming on the area where it exist a large shift between the results. The shift begins from E=2×105V/m to E=4.5×105V/m Using the same rough estimate for the figure (01), we clearly see that there is a high concordance between the models except in the enlarged area.

Drift velocities versus electric field for the different models are shown on Figure (03). We note that the four expressions give the same shape with a significant difference for the values of the velocities for the same electric field.

Figure (04) describes the carrier mobility versus electric field at different temperature using the expression (08). Temperatures begin from 0K up to 500K. We observe a strong decrease in mobility from 8 m2/V.s at 50 K to achieve0.9m2/V.s at 200K. Then begins a slight decrease until reaching 0.14 m2/V.s at 477° K.

Figures (05) to (08) are the results of our simulations of the different carrier mobility expressions versus electric field at different temperatures. We begin the simulation for the cryogenic temperature (96K) up to 373K.
It is observed that low temperature gives greater values to the mobility.

The profiles of V3 and V4 are closely the same and both begin with a linear increasing until reaching a saturation values around 9×105m/s.

On figures (13) and (14) respectively, we demonstrate together the four expressions previously studied with the proposed one to describe mobility and velocity versus electric field.

Discussion.

By closely examining the mathematical relations of carrier mobility we notice that they are rational functions with E as a variable, except for the fourth model where the variation of μ has a tangential form. It is very important to note that the form of the mobility and velocity curves versus electric-field in GaAs are closely related to the value of the low-field mobilityµ0.

We already know that the carrier mobility is limited by several different scattering mechanisms depending on temperature. It depends on the timing of different collisions they may undergo during the carrier displacement which may be due to impurities, phonons, other carriers and any other defects in the lattice. However, the lattice vibration increases with the amplification of the applied electric field. These vibrations increase the probability of collisions, so it may explain the decrease in mobility versus electric field. The main mechanism limiting the mobility by both the scattering mechanisms due to acoustic impurities is piezoelectric scattering and deformation potential.

A good fitting of mobility has substantially enhanced the non-linear modelling of the static characteristics of the GaAs MESFET’s.

With the proposed model we were able to define the drift velocity behaviour which is adjustable by a simple parameter to be as close as possible to the two segments approach. The first segment is where the drift velocity increases linearly with a tangent of μ0, and the second is when the velocity reaches a limit value.

Conclusion

In this paper we give a broad review of different types of scattering mechanisms in GaAs materials and their influence on the change in total mobility. We have also shown the decrease of mobility with temperature. We then make a synthesis of some mobility-field expressions for GaAs MESFET’s.

Generally, at a low temperature (<100K), the mobility is seriously affected by ionized impurity scattering. As the temperature increases, the other scattering mechanisms including lattice scattering become significant. Therefore, the general shape of the measured µ/T curve shows an increase in mobility at low temperatures. We can conclude that for the room temperature and those which vary between 223K and 373K, the expressions of the mobility in GaAs MESFET’s mentioned in our article gives a very close results. The difference occurs at low temperatures. The degradation of mobility is mainly due to acoustic phonon scattering and neutral impurity scattering mechanisms.

We propose a new expression for the mobility-field dependence in GaAs. This expression can explain very well the carrier behavior at a wide range of temperature and electric field. It can also be implemented easily into computer models describing GaAs devices; in particular, GaAs ion implanted FET’s with non-uniform mobility profiles. They also may be used in analytical calculations of the device performance (for example, when an analytical expression for the differential mobility as a function of the field is needed).

VI. Figures

 Figure 1: Carrier mobility versus electric field calculated using the four expressions at 300° K.

 
Figure 2: zooming on Carrier mobility versus electric field calculated using the four expressions at 300° K.

Figure 3: Drift velocity versus electric field calculated using the four expressions at 300° K.

Figure 4: low field-mobility at different temperatures.

  Figure 5: Carrier mobility versus electric field calculated using the first expression at different temperatures.

Figure 6: Carrier mobility versus electric field calculated using the second expression at different temperatures.
 
Figure 7: Carrier mobility versus electric field calculated using the third expression at different temperatures.

  Figure 8: Carrier mobility versus electric field calculated using the forth expression at different temperatures.
 

Figure 9: velocity-field dependence calculated using the first expression at different temperatures.

 

Figure 10: velocity-field dependence calculated using the second expression at different temperatures.

  Figure 11: velocity-field dependence calculated using the third expression at different temperatures. 

Figure 12: velocity-field dependence calculated using the forth expression at different temperatures.

  Figure 13: Carrier mobility versus electric field calculated using all the expressions and the proposed one at different temperature.

 Figure 14: velocity-field dependence calculated using all the expressions and the proposed formula at different temperatures. 

Figure 15: Carrier mobility versus electric field calculated using the new expression at different temperatures.
 
Figure 16: velocity-field dependence calculated using the new expression at different temperatures.

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Thanks:

The authors would like to thank all those who have contribute in this work.

Mounir Azizi was born in Constantine, Algeria on 1977. He received the DEUS (Superior University Study Diploma) from the University of Mentouri, Constantine, Algeria in 2001.And the Magister Degree from the same university on 2005. He is actually preparing a Doctorate thesis at the University of Larbi Ben Mhidi, Oum El Bouaghi, Algeria.

His interests include GaAs MESFET’s, small-signal modeling of active devices, and microwave and millimeter-wave circuit design.