This parameter, B-1, of a dimension of mobility, decrease 1/with increasing gate-to-source voltage for the transistor T(expect for a very small increase at lowest Ugs ) and shows a mimimum for the transistor T5. The curves shown in Fig. 6 coincide for Ugs < -0.3, which for both transistors Figure 4. The resistance of a group A transistor, normalized at zero magnetic fild, for Ugs = 0, 0.2 and 0.3 V (from top to bottom).
The unset shows normalized Lorenzian magnetoconductivity, (B), curves characterized by decreasing µ for increasing Ugs.
Fig. 4 shows an example of a normalized drain-to-source resistance of a group A transistor vs. the magnetic field for a few values of the gate-to-source voltage. A background of these curves was fitted up to 4 T with a very high accuracy by a parabolic dependence, 1 + µ3B2, with the mobility µ as a single fit parameter. We obtained µ equal to 0.60, 0.38 and 0.17 m2/Vs for Ugs equal to 0, –0.2 and –0.3 V, respectively. This decrease of µ corresponds to a broadening of Lorentzian curves shown in the inset in Fig. 4, which present magnetoconductivity, (B), normalised to Figure 5. An influence of the magnetic field on conductivity its value at B = 0 T. The halfwidth of each Lorentzian, for the transistor T3 (upper line) and T5 (lower line) —both B1/2, is given, of course, by an appropriate value of µ-1.
transistors are from group B. The inset shows a square root of A simple inspection of the Shubnikov–de Haas oscillations magnetoresistance R = R(B) - R(0) of the transistors T3 and in Fig. 4 shows that the number and position of maxima do T5, normalised to its value at 1 T. The curves correspond to gatenot change with the applied gate-to-source voltage which to-source voltage equal (in Volts) to 0, –0.1, –0.2, –0.3, –0.4 for means that in this transistor they are mainly due to the T5 and 0, –0.1, –0.2, –0.3 for T3.
ungated part of the source-drain channel. The carrier density obtained from these oscillations (equal to 1.9 · 1012 cm-2) is expected to correlate with the carrier density in the transistor channel at the zero gate voltage. (It might be somewhat different depending on the values of the surface potential and of the gate contact built-in voltage.) Let us concentrate now on measurements carried out on two transistors (T3 and T5 from group B). The transistors differed by the length of the gate, and the lateral dimension, which were equal to 2.5 and 55 µm for T3 and 1.5 and 25 µm for T5, respectively.
Fig. 5 shows the normalized magnetoconductivity for the transistors T3 and T5 for zero gate-to-source voltage.
Lorentz-like curves show a strong decrease of the drain-tosource conductivity,, with an increase of the magnetic field. Curves of a similar shape were obtained for all gate-to-source voltages; they differ only in their halfwidth.
The shape of magnetoconductivity curves is not strictly Figure 6. An inverse of the halfwidth of magnetoconductivity Lorentzian, in contrast to the curves shown in the inset curves, B-1, for the transistors T5 (L = 1.5 µm, down triangels) 1/in Fig. 4. This is illustrated by the inset of Fig. 5 and T3 (L = 2.5 µm, solid circles), as a function of gate-to-source which shows the square root of a transistor magnetoresis- voltage, Ugs.
Физика твердого тела, 2004, том 46, вып. 142 J. Lusakowski, W. Knap, N. Dyakonova, E. Kaminska, A. Piotrowska, K. Golaszewska, M.S. Shur, D. Smirnov...
correspond to a drain current of about 20% of its value at the zero gate-to-source voltage.
Fig. 7 compares the conductivity of the transistors T3 and T5 (measured at Ugs = 0V) as function of the magnetic field — up to 7 T. After Lorentz-like behaviour at low fields, the oscillation of conductivity were observed. Taking into account the positions of minima of the magnetoconductance data, one can evaluate a concentration of the 2DEG, which appears to be 3.0 · 1011 and 3.2 · 1011 cm-2 for the transistors T3 and T5, respectively. One can note that the oscillations on the magnetoconductance curves are different from usual traces observed in the quantum Hall experiments. This is related to a difference in the samples geometry, which is Corbino-like for the case of Figure 9. The electron mobility (squares) and concentration the transistors. Gated Hall bar structures placed close to the (down triangles) determined from measurements of the Hall transistors were used to perform a precise analysis of the effect on a gated Hall-bar of GaInAs/GaAlAs heterostructure from influence of a gate-to-source voltage on the electron mobility group C.
and concentration in heterostructures used for transistor fabrication. In Fig. 8 we show examples of results obtained on one of the Hall-bars placed together with the group (C — GaAs/GaInAs heterostructure). Fig. 8 shown the resistance values measured berween the Hall-bar probes as a function of the magnetic field. The curves were normalized to their value at B = 0 T and a monotonic background magnetoresistance was subtracted for a better visualization. The typical Shubnikov–de Haas oscillations were observed. The period (in B-1) of the oscillations changes with decreasing the gate-to-source voltage swing, which corresponds to a decrease of the electron concentration. It is important to note, however, that not only the carrier density but also the mobility changes with inscreasing gate voltage — the amplitude of oscillation decreases and close to the threshold Figure 7. Magnetoconductance of the transistor T3 (upper curve) they are practically smeared out.
and T5 (lower curve).
Fig. 9 summarizes the mobility and carrier density measurement results. As expected, the carrier density decreases linearly with application of a negative gate voltage. The linear extrapolation of the density versus gate voltage dependence to zero sheet density yields the threshold voltage equal to Uth = -1.6 V. The threshold voltage obtained this way is different from the transistor ” threshold“ voltage — this point will be discussed later. The mobility first encreases slightly and then rapidly decreases with the gate voltage swing. Typically, we observed the mobility decrease by a factor of 2 to 3 at the gate voltage equal to half of the threshold voltage.
2. Discussion The following discussion is divided into two parts.
First, we consider a possibility of evaluating the electron Figure 8. Shubnikov–de Haas oscillations of magnetoresistance concentration and mobility in the transistor channel basing of a Hall-bar processed out of GaInAs/GaAlAs heterostructure on magnetoconductivity measurements. In view of this, (group C of devices), as a function of the magnetic field, for gate we discuss the influence of geometry of investigated potential equal to 0, 0.4, 0.6 and 1 V (from bottom to top). The structures in the result of such a procedure. Also, the curves are normalized at B = 0 T and shifted vertically for a better influence of the gate potential on the carrier density and visualization.
Физика твердого тела, 2004, том 46, вып. Magnetotransport characterization of THz detectors based on plasma oscillations in submicron field... mobility in transistors and Hall-bars is discussed. Second, conducting channel geometry approaches the limiting case the electron mobility and concentration determined from of the Corbino geometry. This condition is fulfilled for a magnetotransport measurements are used for interpretation very wide channel“ — with the source-to-drain separation ” of recently observed resonant detection and determination length, Ic, being much smaller than the channel width, of the parameters of new field effect transistors processed D. In this case, the magnetoresistance is parabolic (or for resonant detection of THz radiation. the magnetoconductance is Lorentzian). Such a parabolic The magnetoresistance measured between the source (R 1 + µ2B2) behaviour was observed for group A tranand the drain of the transistor is an integral phenomenon sistors (gate of 0.15 µm) that have a very short (Lc 1 µm) because of two effects i) comprises contributions from both and wide (d 50 µm) channel.
the gated and the ungated part of a transistor channel and For transistors T3 and T5 D/Lc ratio is 5.5 and 2.5, ii) channel geometry is often intermediate between Corbino respectively, and the geometry is neither Corbino nor a and Hall-bar like. Hall-bar type. We speculate that the observed exponent The gated part of the channel (gate length) was 0.15 µm of 1.3 is related to the fact that the geometry of the for the group A devices and 0.8–2.5 µm for others. The current flow is far from the ideal cases presented above. In total channel length was around 1 µm for group A devices particular, an essential part of the current may flow outside and 10 µm for B and C groups. A clear evidence of of the transistor due to violation of the condition jy = 0.
the importance of the ungated part of the channel can be Nevertheless, and in spite of difficulties in interpretation seen in Fig. 4 which shows Shubnikov–de Haas oscillations mentioned above, one can consider the parameter B-1 as 1/of the group A transistor. One can see that positions an estimate of the electron mobility. This interpretation of maxima/minima do not depend on the gate-to-source is consistent with the behaviour of two curves shown in voltage but the resistance of the transistor quickly grows Fig. 6, which coincide for higher gate-to-source voltage, with Ugs. This is because the oscillations come mainly from close to the threshold value (Ugs < -0.3V), when the the 2D electron gas confined in the ungated part of the transistor resistance is determined by the gated section. The transistor. The background changes however — because fact that we find the same exponent (equal to 1.3) for the total resistance increases due to the modulation of the both transistors confirms that although determination of the transistor channel by the gate voltage. electron mobility as B-1 is an approximation, it can be used 1/The mobility µ, determined as a coefficient of the to compare the electron mobility in different transistors.
parabolic dependence of resistance, corresponds to an It is important to note that both mobility obtained on average“ mobility in the entire region between the source gated Hall-bars (shown in Fig. 9) and the mobility extracted ” and the drain. For the zero gate voltage the carrier using B-1 values for ghe transistors (shown in Fig. 6) 1/densities in the gated and ungated regions of the channel decrease with decreasing the gate-to-source voltage swing.
are nearly the same. However, as it is clearly evidenced This might be is linked to the screening effects that diminish by measurements on the gated Hall-bars (where the whole at smaller electron sheet densities. This decrease reduces conducting region is gated), a gate potential decreases both the effectiveness of screening of ionised centres and results the mobility and the concentration of electrons (Fig. 9). We in a decrease of the mobility. The application of the gate also expect that the mobilities in the gated and ungated voltage also changes the shape of the quantum well at the sections of the device are close at zero gate bias, even heterointerface. The quantum well is wider at smaller sheet though the scattering in the device channel might be affected densities. Hence, the peak of the 2D electron wavefunction by the effects related to the metal gate . Once the is further away from the heterointerface, which decreases gate voltage applied, the mobility under the gate is different scattering by the interface roughness. This effect can lead from measured averaged mobility, since the mobility is a to a mobility increase. It is possible that the non-monotonic strong function of electron sheet density. With decreasing behaviour of B-1 observed for both transistors (close to 1/gate voltage swing, the resistance of the gated region starts zero gate — source voltage for T5 and at about –0.2 V for to dominate the total transistor’s resistance. In this case T3) and for the Hall-bar at around –0.4 V can be attributed the measured (average) mobility approaches the value of to the interplay of these two mechanisms.
mobility under the gate. Therefore, the measurements of Measurments of the carrier density and mobility made on magnetoresistance of the channel allow a relatively accurate the gated Hall-bars also show that the threshold voltage for determination of the mobility in the gated region for small the carrier density and for the channel conductivity can be gate voltage swings. In the intermediate region, one fairly different. From the linear approximation of the carrier obtains the approximate average“ mobility. Comparison of density versus gate dependence shown in Fig. 9 we obtained ” Fig. 6 with Fig. 9 shows, however, that overall functional the threshold voltage (voltage for which the carrier density is dependence of the mobility versus gate voltage in the zero) equal to Uth = -1.6 V. If we use the same procedure transistor channel and in the gated Hall-bar are similar. The for conductivity, the threshold voltage of Uth = -1.4V is mobility decreases by a factor of 2–3 at the half of the obtained. This is because both the carrier density and threshold voltage. mobility enter into conductivity and both decrease with an Another point to be discussed is the conducting channel increase of the gate voltage. It is important to note that the geometry. As mentioned in the introduction, the interpre- threshold that in estimations of the plasma wave frequency tation of the transistor magnetoresistance is simple if the is the carrier density threshold.
Физика твердого тела, 2004, том 46, вып. 144 J. Lusakowski, W. Knap, N. Dyakonova, E. Kaminska, A. Piotrowska, K. Golaszewska, M.S. Shur, D. Smirnov...
In principle, the simplest way to increase the maximum frequency (and the quality factor) is to decrease the gate length (L) —see Eq. 1. The shortest gate length (Lmin) for a given type of devices can bi defined by an approximate relation Lmin 5d where d is the gate to channel distance (in order to preserve the gate control). Looking at the dimensions of the three groups of devices one can see that the devices of group A (d 0.025 µm, L 0.15 µm) and B (d 0.16 µm, L 0.8 µm) are close to the limit. Only the heterostructures used for group C devices (d 0.04 µm, L 0.8 µm) can be used for fabricating shorter gate length transistors. The minimum gate length for these transistors is approximately 0.2 µm. One can expect then to reach the maximum detection frequency of about 2.4 THz with a maximal quality factor of about 6.
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