Theoretical Study on Electrical Properties of n-AlGaAs Schottky Barrier Diodes in a Diverse Temperature Range ()
1. Introduction
Electron manipulation and storage are used in semiconductor electronics devices. Semiconductor devices operate on the basis of the basic principle that the conducting and optical properties of semiconductors can be altered easily and rapidly [1] [2]. One way this can be done is through the use of junctions between dissimilar materials. Junctions can form between N-type and P-type materials, between materials with different bandgaps, and between metals and semiconductors. The P-N junction is one of the most important junctions in solid-state electronics. The junction is used as a device in applications such as rectifiers, waveform shapers, variable capacitors, lasers, detectors, etc. These junctions also have special properties that are useful for devices. Metals by themselves are necessary to connect the semiconductors to the “outside world” of voltage sources and circuits [3]-[8]. They are also able to produce rectifying junctions. Insulators are also an integral part of electronics. These materials provide isolation between two regions of a device, can be used for band structure tailoring, can be used as capacitors, etc. In this research, we will examine some important properties of a variety of junctions.
Schottky diodes are unipolar devices, which means that only one type of carrier is available for current transport [9]-[12]. If they are designed for large blocking voltages, the resistance of the base will increase strongly due to the lack of charge carrier modulation, as will be shown in the following. Schottky power diodes have been used for a long time, but in the last few years, they have gained increased importance in the medium power range [13]-[15]. Schottky diodes are made from semiconductor materials with a wide bandgap. With these materials, much higher blocking voltages are possible due to the higher critical fields. However, since the increased bandgap leads to a comparatively high junction voltage in a bipolar device, a Schottky junction with a much smaller junction voltage has become an attractive alternative [16] [17].
In this work, we will study the electrical behavior and Schottky barrier height inhomogeneities of Schottky structures, by using classical model of TE current. First, the structure is studied for different metal work function ranged from 4.33 eV to 5.93 eV, at room temperature. Then, electrical parameters such as saturation current
, ideality factor (n), barrier height (
) are extracted from the current-voltage characteristics as a function of temperature. Electrical parameters are extracted for each temperature.
2. Simulation Setting
MATLAB, a computer software program, was used to simulate and discuss the contact AlGaAs structures and Schottky diode with n-doping. The modeled structure has a three-dimensional design. Once the structure has been defined, takes into account all the electrical and the optical properties. Among these attributes we mention mobility of electron μn, mobility of hole μp, dielectric constant, electronic affinity, the energy band gap, the effective state density in the conduction band and valence band, and so forth. The negligible density of donor and acceptor states eliminates the impact of the interface states [18]. Furthermore, the impact of both temperature and work function on the electrical characteristics of the metal/n-AlGaAs Schottky structure was examined. The physical mechanisms of concentration-dependent mobility (CONMOB) [19] [20], Auger recombination rate (Auger) [21], and Shockley-Read-Hall (SRH) recombination [22] are modeled. In addition, the classical method is employed for the numerical solution operations.
3. Simulation and Results Outcomes
3.1. Aspects of the Physics of the Metal-Semiconductor Junction at Room Temperature
Metals form an important part of semiconductor technology. As shown in Figure 1, they are used as interconnects (i.e. low resistance conductors), they form Schottky barriers and Ohmic contacts, and they form gates in field effect transistors. The high density of mobile electrons, the resistivity of metals is very low.
Figure 1. Metal used in semiconductor technology for three important applications.
In Table 1 we show the resistivities of some important metals used in electronics [18] [23]. In semiconductor circuits, interconnects provide pathways through which charge travels from one point to another. While these interconnects are obviously passive elements of the circuit, they are extremely important and play a role in circuit performance. The metal strips making up the interconnect must be able to carry adequate current and make good contact with the devices. Interconnects are deposited on insulators and touch the active devices only through windows that are opened at select points [24] [25].
Table 1. Some metals used in semiconductor devices and their resistivity’s [18].
Materials |
Resistivity (µΩ∙cm) |
Aluminum (Al) |
|
Bulk |
2.7 |
Thin Film |
0.2 - 0.3 |
Titanium (Ti) |
40 |
Tungsten (W) |
5.6 |
Ti-W |
15 - 50 |
Gold (Au) |
2.44 |
Silver (Ag) |
1.59 |
Copper (Cu) |
1.77 |
Platinum (Pt) |
10 |
Silicide’s |
|
PtSi |
28 - 35 |
NiS2 |
50 |
The metal-semiconductor junction can result in a junction that has non-linear diode characteristics similar to those of the P-N diode except that for many applications it has a much faster response since carrier transport is unipolar. Such a junction is called a Schottky barrier diode [26]-[28].
To understand the charge carrier transport across this junction we need to define some quantities relating the electron energies in the metal and semiconductor to the energy of a free electron, the so-called vacuum level:
: work function for the metal
This is the energy, that must be added to an electron to allow it to escape from the metal, and this is equivalent to the difference between Fermi level, EF, which is located in the conduction band of a metal and the vacuum level. In the semiconductor:
: work function for the semiconductor
The work function for a semiconductor is also defined as the distance between the Fermi level and the vacuum level. However, the Fermi level of a non-degenerate semiconductor is positioned between the valence band and the conduction band and no electron is allowed to have this energy. Therefore, additionally we need to define:
: electron affinity for the semiconductor
This is the energy needed to remove an electron located at the bottom of the conduction band, EC, where most of the conduction electrons reside, to the vacuum level outside the semiconductor.
The working of the Schottky diode depends upon how the metal-semiconductor junction behaves in response to external bias [29]. Let us pursue the approximation used for the P-N junction and examine the band profile of a metal and a semiconductor.
We will assume an ideal surface for the semiconductor in the first calculation. Later we will examine the effect of surface defects. If we assume that
so that the Fermi level in the metal is at a lower position than in the semiconductor. This condition leads to an N-type Schottky barrier. When the junction between the two systems is formed, the Fermi levels should line up at the junction and remain flat in the absence of any current. At the junction, the vacuum energy levels of the metal side and semiconductor side must be the same [30] [31].
To ensure the continuity of the vacuum level and align the Fermi levels. Electrons move out from the semiconductor side to the metal side. Note that since the metal side has an enormous electron density, the metal Fermi level or the band profile does not change when a small fraction of electrons are added or taken out. As electrons move to the metal side, they leave behind positively charged fixed dopants, and a dipole region is produced in the same way as for the P-N diode.
In the ideal Schottky barrier with no bandgap defect levels, the height of the barrier at the semiconductor-metal junction, is defined as the difference between the semiconductor conduction band at the junction and the metal Fermi level. This barrier is given by:
(1)
The electrons coming from the semiconductor into the metal face a barrier denoted by
. The potential
is called the built-in potential of the junction and is given by:
(2)
It is possible to have a barrier for hole transport if
. In this case of a metal-P-type semiconductor junction where we choose a metal so that
. Therefore, at equilibrium the electrons are injected from the metal to the semiconductor, causing a negative charge on the semiconductor side. The bands are bent once again and a barrier is created for hole transport. The height of the barrier seen by the holes in the semiconductor is:
(3)
The values of work function of some metals are given in Table 2 [2] [29] [32]. These values are approximate as they are very sensitive to surface impurities.
Table 2. Work function of some metals used.
The first section examines the impact of the metal work function on the electrical behavior at ambient temperature (300 K). The semi-log and linear current-voltage I-V characteristics of the metal/n-AlGaAs Schottky structure for some metal work functions are shown in Figure 2.
Figure 2. I-V characteristics of metal/n-AlGaAs for some metal work function at room temperature.
It is evident from the semi-log characteristics and reverse bias voltage that, for low metal work function, we get a significant reverse current that decreases as
increases from 3.00 eV to 5.00 eV (Figure 2).
The Schottky characteristic behavior is observed under forward bias voltage for all values of
. At low bias voltages V < 0.75 V, the current increases linearly with bias voltage and subsequently drops as
increases.
Furthermore, it is evident that for
, the plot has two separate linear regions with differing slopes, which correspond to Region II (at a bias region 0.35 < V ≤ 0.75 V) and Region I (low-bias region V ≤ 0.35 V). This double barrier phenomenon can be explained as the emergence of an aberrant current under low forward bias. The current increases linearly with bias voltage and gradually falls with rising
for linear characteristics and forward bias voltage. Furthermore, it is noted that as
grows, the threshold voltage V rises as well.
3.2. Thermionic Emission Theory
The thermionic emission is a phenomenon related to field emission. The thermionic emission is that the thermal energy given to charge carriers overcomes the binding potential, also known as work function of metals, such that electrons escape out from the surface of solid. The charge carrier can be electrons or ions. The basic theoretical model of thermionic emission is also based on Sommerfeld model of metal, the triangular vacuum potential barrier and the equilibrium electron emission [18]. The key point of the thermionic emission is that electrons in conduction band are driven to high excited states by heat such that the kinetic energy of electrons overcomes the vacuum potential barrier.
Besides, the diffusion and thermionic emission mechanisms, electrons can also be transported across the barrier by quantum mechanical tunneling.
The two ways in which tunneling can occur in a Schottky barrier junction are for both forward bias and reverse bias. The semiconductor is assumed to be doped to degeneracy such that the Fermi level lies above the bottom of the conduction band. Because of heavy doping, the depletion region is very thin, and at low temperatures, electrons with energy close to the Fermi level can tunnel from the semiconductor into the metal. This process is known as “field emission” (FE). At higher temperatures, a significant number of electrons are able to rise high above the Fermi level, where they see a thinner and lower barrier. These electrons can thus tunnel into the metal before reaching the top of the barrier. This tunneling of thermally excited electrons is known as “thermionic field emission” (TFE). Since the number of electrons decreases rapidly with energy above the Fermi level, and the barrier thickness and height also decrease, there exists an energy Em at which the contribution of TFE reaches its maximum. If the temperature is gradually raised still further, a limit is reached at which practically all the electrons are able to reach the top of the barrier, and thermionic emission predominates.
The rectifying characteristics of the Schottky junction can be described by an equation for the I-V characteristics, in analogy to related equation for the I-V characteristics of the PN-junction.
The current-voltage conduction classical model can be considered, by assuming that the TE theory is true in the current range for each temperature. For real Schottky contacts, the classical model of I-V characteristics is represented by this form [23] [33] [34]:
(4)
where,
So,
(5)
where
and
are the ideality factor and series resistance, respectively.
is the electron charge,
is the Boltzmann constant,
is the applied forward-bias voltage,
is the absolute temperature in kelvin. And
is the saturation current. Which can be defined as the following equation:
(6)
where
and
denote the contact diode area and the effective Richardson constant, respectively.
represents the effective barrier height.
By taking into consideration that at the low bias voltage
, the current
is low, therefore the term
is low compared to
, Equation (5) becomes:
(7)
By taking the logarithm of both sides
(8)
Then, when we emplace
we obtained:
(9)
This last equation is in the form of a line equation
with
. To determine each parameter, we draw the graph
as a function of
from the equation of the line.
By taking the derivation of Equation (9) as a function of the voltage
, we can extract the ideality factor by:
(10)
Since:
(11)
We can extract
:
(12)
where
is the Boltzmann constant,
is the temperature, and
is the electron charge. Here
is the slope of region 2.
The ideality factor (𝑛) depends on the slope (a) of Equation (9) in the form of a straight line where:
. From this equation we obtain:
(13)
which gives
(14)
From the saturation current equation (Equation (6)), we can extract the barrier height. By taking the logarithm of both sides:
(15)
(16)
where,
(17)
By employing
values, the zero bias barrier height
values are obtained from the following relation:
(18)
For a fixed work function, I-V Characteristics of the Schottky contact on the linear scale and a semi-logarithmic scale simulated at different temperatures ranging from 50 K to 500 K are shown in Figure 3 and Figure 4, respectively.
Figure 3. Linear forward bias I-V characteristics of metal/n-AlGaAs Schottky diode at different temperatures (100 K-500 K).
In low bias voltage (V < 0.75 V), the current rises rapidly with increasing bias voltage and varies linearly vs bias voltage. On the other hand, in high bias V > 0.75 V the current shows down enormously and varies also linearly with bias voltage and decreases gradually with decreasing temperature.
The value of the current at 50 K is very small due to the freezing phenomenon, where the mobility carriers are very low. Therefore, at 500 K the current increases with increasing temperature. We see a significant leakage current which causes the influence of both temperature and barrier height on the saturation current. The reverse current increases with increasing reverse bias and no saturation are observed. This is a well-known defects-related phenomenon, for example surface state and or bulk defects [18] [34] [35].
The forward and reverse (I-V) characteristics of the Schottky diode on a semi-logarithmic scale measured at different temperatures ranging from 50 K to 500 K are shown in Figure 4. The diode has good rectifying behavior, as can be shown. Additionally, it is noted that when temperature rises, the linear region moves towards lower voltage values.
Figure 4. Semilogarithmic forward bias I-V characteristics of Metal/n-AlGaAs Schottky diode at different temperatures (100 K - 500 K).
The values of n,
, and
are obtained from Equations (6), (12), and (18). The linear region in the logarithmic (I-V) characteristics was used to derive these parameters. Figure 5 shows the temperature dependence of the ideality factor n of structure. Figure 6 shows the temperature dependence of the barrier height
of structure. From Figure 5, the ideality factor n is decreased with increasing temperature. From Figure 6, the barrier height
is increased with increasing temperature. For our structure, the values of n range from 3.16 at 50 K to 1.38 at 500 K. While the values of
are ranged from 0.162 eV at 50 K to 1.073 at 500 K. These results are summarized in Table 3.
The conventional theory of TE theory that in an ideal situation, n should equal unity [35] [36]. However, a high value of n is found, indicating a departure from the hypothesis of TE. The breadth of the depletion region (Wd) and levels created by the interface states, which rely on the density of the doping atoms, may be the cause of these greater values of n at low temperatures [36]-[39]. This variation of the ideality factor n may be due to many factors. Such as generation–recombination effects, formation of barrier inhomogeneities… [40]-[43]
Moreover, Figure 6 illustrates that while
increases virtually exponentially. On the other hand, the value of n decreases with increasing temperature (Figure 5), following a double Gaussian distribution. The discrepancy seen in ideality factors and barrier height values implies that n-AlGaAs is not a perfect diode, and its charge transport mechanism is not limited to TE [18] [44]-[46].
Figure 5. The temperature dependence of n of n-AlGaAs Schottky diode at a range of temperatures (50 K - 500 K).
Figure 6. The temperature dependance of
of n-AlGaAs Schottky diode at a range of temperatures (50 K - 500 K).
Table 3. The electrical parameters, in a range of 50 K to 500 K temperatures, calculated using Thermionic emission theory.
T (K) |
Thermionic emission theory |
N |
(eV) |
(A) |
50 |
3.16 |
0.162 |
2.26 × 10−14 |
100 |
2.98 |
0.316 |
2.256 × 10−13 |
150 |
2.5 |
0.434 |
1.15 × 10−11 |
200 |
2.32 |
0.531 |
3.25 × 10−10 |
250 |
2.27 |
0.628 |
2.55 × 10−9 |
300 |
2.15 |
0.738 |
6.84 × 10−9 |
350 |
1.95 |
0.835 |
2.25 × 10−9 |
400 |
1.7 |
0.918 |
6.95 × 10−8 |
450 |
1.48 |
1.018 |
1.55 × 10−7 |
500 |
1.38 |
1.073 |
2.76 × 10−7 |
4. Conclusion
A study of the current voltage (I-V) characteristics of Metal/n-AlGaAs Schottky diodes is investigated in wide temperature range 50 K to 500 K, using MATLAB programming language simulator. From the (I-V) characteristics, the electrical parameters are extracted using the thermionic emission theory. The ideality factor n is increased and the barrier height
is decreased with decreasing temperature for our structure. The barrier height
is exponentially distribution. On the other hand, the value of n decreases with increasing temperature, following a double Gaussian distribution.
Conflicts of Interest
The authors declare no conflicts of interest.