Article Applied Physics
July 2011 Vol.56 No.21: 2206–2209 doi: 10.1007/s11434-011-4557-1
SPECIAL TOPICS:
Ballistic transport in nanoscale self-switching devices CHEN ZiMin1, ZHENG ZhiYuan1, XU KunYuan2 & WANG Gang1* 1 2
State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China; School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510631, China
Received March 7, 2011; accepted April 18, 2011
Using the Monte Carlo method, a type of semiconductor nano-device called self-switching device (SSD), which has diode-like I-V characteristics, was simulated. After analyzing the microscopic transport behavior of the carriers, we show that the ballistic effects exist in the SSDs when the channel length of the device is extremely short (~120 nm). Furthermore, we show that the ballistic effect doubles the average drift velocity of the carriers (to ~6.0×107 cm/s) in short-channel SSDs, which decreases the transit time. This implies that when the dimensions are decreased to nanoscale length, the SSD can operate much faster because the ballistic effect increases the operation speed of the device. Moreover, because of the ballistic transport, the energy efficiency may also be improved. self-switching device, ballistic transport, nano-device, Monte Carlo simulation Citation:
Chen Z M, Zheng Z Y, Xu K Y, et al. Ballistic transport in nanoscale self-switching devices. Chinese Sci Bull, 2011, 56: 2206−2209, doi: 10.1007/s11434-011-4557-1
During the last two decades, the dimensions of compound semiconductor devices have become smaller. Electronic devices at micrometer and nanometer scale have attracted increasing attention [1–3]. In 2003, using an asymmetric structure, Song et al. designed a novel device with diodelike I-V characteristics, which was called a self-switching device (SSD) [4]. The fabrication of SSD is remarkably simple, and only requires one etching step to produce the two required insulating trenches. This simplicity makes it possible to downscale the geometrical dimensions of the device to nanoscale, which increases its cut-off frequency. It has been reported that a SSD can operate at a frequency over 110 GHz at room temperature [5] and at 2.5 THz at 150 K [6]. SSDs are fabricated using modulation-doped quantum well structures such as InGaAs/InP and InGaAs/InAlAs, in which the carriers transported in the active layer form two dimensional electron gas (2DEG). After the growth of each layer, only two insulating L-shaped trenches (with a width *Corresponding author (email:
[email protected])
© The Author(s) 2011. This article is published with open access at Springerlink.com
of d and a length of L) along the direction perpendicular to the surface needed to be etched. This etching can be done using high-resolution lithography (as shown in Figure 1). Between these two trenches, there is a channel with a width of W in which the electrons are transported. When in operation, the left side is grounded and a bias voltage is applied to the right side. The diode-like I-V characteristics were simulated using the Monte Carlo method in this paper. It has been shown [4,7,8] that the electrical properties of a SSD are partially determined by its geometrical structure. Increasing either the width of the channel, W, or the trenches, d, will decrease the threshold voltage of the SSD (but not decrease it below zero). These parameters also influence the drain current when the reverse bias voltage is applied. This means that, as a switching device, the threshold voltage of a SSD is adjustable. If the geometrical parameters W, d or L are chosen properly, the threshold voltage can be set to zero. It has been suggested that SSDs have a diode-like I-V characteristics because of the field effects resulting from the charging regions near the channel [9]. When a reverse bias csb.scichina.com
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voltage is applied, these regions are negatively charged, which depletes the channel. The channel can be narrowed to zero width. Therefore, the electrons may not be able to traverse the channel. The channel can be narrowed or widened by adjusting the bias voltage. Previously, most research (experiment and simulation) on SSDs has focused on microscale devices. However, at this scale, an electron being transported through the SSD experiences a large number of collisional scatterings. Such phenomena exist in various conventional devices and results in the loss of energy through Ohmic heating. This slows the drift velocity of the electrons, which limits the working frequency of the device and generates more heat that is harmful to devices. In this work, we show that an unconventional type of transport occurs when the physical dimensions of the SSD are on the nanoscale using a Monte Carlo simulation. The simulation is based on an In0.53Ga0.47As/In0.53Al0.47As structure. This process is ballistic transport or quasi-ballistic transport, where the electron transport involves only a few scatterings. During the ballistic transport, the collision time becomes so small. Therefore, the energy of electric field primarily accelerates the electron and is not lost in the form of heat.
1 Monte Carlo simulation for SSD To demonstrate the ballistic transport in device in electric field, tracing the microscopic parameters of the electrons such as energy, drift velocity or collision frequency, is the most direct way. This is what a Monte Carlo simulation does. Because of the limitations of the computational resources, and the fact that the transported carriers form a 2DEG, we use a 2D simulator [4,6–8]. In the In0.53Ga0.47As/In0.53Al0.47As structure, the simulated layer is the active layer of 2DEG, and its geometrical structure is shown in Figure 1. Most previous studies investigated SSDs at the microscale [4–7,9,10]. At this scale, the maximum average drift velocity of the electrons is about (2–3)×107cm/s [10]. However, as discussed above, the miniaturization of SSDs may change their transport properties. In this work, the length of the entire device is scaled down to 180 nm with a 120 nm-long channel. We show that, in such design, ballistic transport occurs and the drift velocity of the electrons is doubled. In the device shown in Figure 1, the geometric parameters are L=120 nm, W=40 nm and d=10 nm, and the sample is In0.53Ga0.47As/In0.53Al0.47As with a 2DEG in InGaAs layer. The Monte Carlo simulator for the InGaAs material uses a three-valley model, and the gap between the Г-valley (lowest valley) and L-valley (second lowest valley) is 0.61 eV [10]. If the length of the device is sufficiently short, the carri-
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Figure 1 Top view of a SSD with an extremely short channel length. Black areas are etched and insulating, and white areas are conductive. When in operation, the left side is grounded, and the right side has an applied voltage.
ers may traverse the device without scattering or scatter a few times with little energy loss [11]. This is called ballistic transport or quasi-ballistic transport. Once the electron experiences ballistic transport, the transport properties may differ greatly from common transport mechanism. The other transport extreme is when the electrons are fully scattered into the upper energy-valley, which results in the transferred electron effect (Gunn effect) [12]. For ballistic transport, the device is designed short enough to avoid collisions that would slow down the electron. This means that the drift velocity can reach a value higher than that in a long-channel device.
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Results and discussion
In Figure 2, the simulation results of the SSD which has its design shown in Figure 1, are shown. The device has diodelike I-V characteristics, but a drain current presents when the system is reserve biased. Notice that the threshold voltage here is not zero, but is actually near +0.1 V. This will not affect our analysis. If the parameters L, W and d, are properly adjusted, we achieve a zero threshold voltage and eliminate the drain current. In Figure 3, the velocity distribution for the electrons in this device is shown for different applied voltage. The distributions are measured from the electrons in the middle of the channel. There are no essential differences among these distributions, which means that the transport types for these bias voltages are the same. It was found that the velocity increase from the start of the channel to the end. This is typical of ballistic transport
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For a bias of +0.65 V in Figure 3, the electrons reach their highest instantaneous velocity at the end of the channel. The value is slightly more than 9×107 cm/s. However, this value does not represent the mean velocity of the electrons in the device. In Figure 4, we show the calculated mean velocity of the electrons across the entire device for different bias voltages. It can be seen that when the voltage is +0.65 V, the mean velocity reaches its maximum value: vmax = 598888 m/s ≈ 6.0×107 cm/s.
Figure 2
I-V characteristics of the SSD.
[13,14]. In the effect of electric field, the velocity of the electrons increases with the displacement of the channel. As mentioned above, ballistic transport requires that the carriers experience as few scatterings as possible, and these should be low-energy-loss scatterings. To achieve this requirement, the energy of the field cannot be used to compensate for the energy loss during scatterings. It must be used to accelerate the electrons. Therefore, the velocity of electrons increases with displacement as shown in Figure 3. By contrast, if the channel is too long for ballistic transport to occur, the velocity will not increase with displacement. The energy from an external field will only compensate for the energy loss during scatterings even if a strong field is applied. In this common transport type, the velocity does not increase with displacement. This means that for ballistic transport to increase the electron velocity, a short channel is necessary.
Figure 3 voltages.
Velocity distribution of the electrons in SSD for various bias
This value is larger than that which has been observed in bulk InGaAs. In [10], using the same Monte Carlo simulator as ours, the maximum mean velocity of the electrons in a long-channel (3.2 μm) SSD was found to be about (2–3)×107 cm/s. This comparison shows that, by reducing size of the device to the nanoscale, ballistic transport became dominant. The mean velocity of the electrons increased and the transit time decreased. However, outside the channel, the geometrical configuration of the conductive layer changes. This results in an increased scattering probability. From Figure 3, it can be seen that the velocity of the electrons decreases, and the ballistic transport does not dominate in this region. The behavior of electrons in this region has a negative effect on the mean velocity of the device. However, it can be still considered that the transport type in such a SSD is primarily ballistic.
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Conclusion
Using a 2D Monte Carlo simulation, we investigated carrier transport in a novel nano-device called self-switching device in detail. We show that ballistic transport dominates in a SSD when the device is properly designed. In this work, the requirements are fulfilled by reducing the dimensions of the SSD to 180 nm with a 120 nm-long channel. The ballis-
Figure 4 voltages.
Average velocity of the electrons in the SSD for various bias
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tic transport results in limited scattering, which increases the mean velocity of the electrons in the SSD. The results of our simulation show that in this extremely small device, the mean velocity of the electrons is about twice that of bulk material. In comparison with other microscale SSDs (3.2 μm), the velocity increases from (2–3)×107 cm/s to 6.0×107 cm/s. As the physical dimensions of modern semiconductor devices decrease, ballistic effects cannot be neglected. This is important because ballistic transport affects SSDs and other nanoscale semiconductor devices such as field effect transistor [13,14]. Because of the reduction of scattering, the electrons can reach speeds that cannot be achieved through conventional transport. This improves the highfrequency performance of the devices. Furthermore, the low scattering frequency can decrease the energy loss and consequently, increase the working efficiency of the devices.
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10 This work was supported by the FOK YING TONG Education Foundation (122004) and the Natural Science Foundation of Guangdong Province, China (9451063101002244, 10151063101000025).
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