2.3 Carrier injection and transport
2.5.6 Vacuum tube triodes
The electrodes in vacuum-tube triodes are surrounded by vacuum as shown in Fig. 2.20. The cathode is the electron emitter which is heated to high temperature for sufficient electron emission. The operation of a vacuum tube is based on the thermionic emission of electrons from metal to vacuum. [95]
)
2exp(
kT AT q
J = − φ . (2.74) In a vacuum tube, the medium have very low conductivity, hence the current can be described by the Child-Langmuir law
2
where L is the spacing between the cathode and the plate.
For a triode have three electrodes, the grid electrode placed between the cathode and the plate is utilized to modulate the current. The plate current can be described by
( )
321 G P
P C V V
I = μ + (2.75) where μ is called the amplification factor and VG is the grid voltage.[95] If the electron in a retarding field, is can not reach the plate. If the grid voltage is made more positive, current will flow only in the region midway between the grid wires. Since the grid is much closer to the cathode than the plate, a given change in potential of the grid has a much greater effect on the field intensity at the cathode than does the same change in potential of the anode. The exact dependence of the amplification factor is not known.
Figure 2.20 Structure of a vacuum-tube triode. From Ref. [95].
The quantity
grid plate
V I
∂
∂ (2.76)
gives the ratio of an increment of plate current to the corresponding increment in grid potential for constant plate potential. This quantity is known as the plate-grid transconductance. This is also referred to the mutual conductance and is designated by the symbol gm.[96]
53
Polymer hot-carrier transistor
3.1 Introduction
3.1.1 Background
Polymer-based organic transistors provide a promising future for large-area and low-cost applications in display technology, sensors, and radio frequency identification cards from the perspectives of their easy solution process as well as the potential integration with organic optoelectronics.[15,17,18,97] Polymer field-effect transistors (FETs) are mostly horizontal devices in which source and drain electrodes lie in the same plane of the substrate. The highest polymer hole mobility of about 0.1 cm2 /V s is reported for poly(3-hexylthiophene) (P3HT) FET [15,16] a few years ago.
Beyond this value little progress has been made. Due to the limited mobility, such horizontal devices are not candidates for high current and high frequency application unless the channel length is made submicron. Consequently, how to shrink the channel length in polymer FET has been a demanding issue. Though the well developed technology of submicron lithography can be directly applied to reduce the polymer FET channel length, this strategy is in opposition to the advantages of low-cost and large-area solution process unique to conjugated polymers.
Aside from FET, the bipolar junction transistor (BJT) is a successful vertical device with high current and high frequency for inorganic semiconductors. BJT consists of two back-to-back pn junctions formed by heavily doped base (B), emitter (E) and collector (C). In principle this device structure can be applied to conjugated polymer using multiply spin coating. The thickness and therefore the effective channel length can be reduced down to 10 nm. However, the major problem is that the base layer needs to have low resistance in order to maintain a uniform voltage throughout the active area and reduce the emitter-to-collector transient time. Even for heavily doped conducting polymer, the resistivity is too large to serve as the base material. Despite of its vertical nature, polymer BJT is quite unlikely to succeed.
Polymer FET with vertical channel has been proposed to achieve submicron channel length. For vertical polymer FET the channel length is defined by the thickness of the layer. However, in order to realize a vertical FET channel one usually needs to employ an unreliable mechanical method like embossing.[59] There are another type of polymer transistor, namely the vertical metal-based transistor.[64,68-73,95,99,106,107] Due to its potential to overcome the limit of FET recently metal-base organic transistors, including the space-charge-limited transistor [72,73] and hot-carrier transistor [70,71], gain more and more attention for both polymer and small molecules.[64,68,106-110] In this chapter we present a vertical polymer hot-carrier transistor with metal base, which combines the advantage of short effective channel length, low base resistivity, and easy large-area solution process.
Similar to BJT, in hot-carrier transistor the carriers are injected from the emitter into the base. Because of the large energy barrier at the emitter-base junction, they become hot carriers in the metal. Assuming the metal is thinner than the mean free path of the carrier, most of the injected carriers will be collected by the collector. The loss of the carrier to the base contributes to the base current. The ratio is called the transport
In this chapter, the vertical polymer hot-carrier transistors with metal base are demonstrated. For the emitter material with high band gap, electrical properties and fabrication procedures are described in Section 3.2, while Section 3.3 discusses the hot-carrier transistors with low band gap emitter. The properties of the hot-carrier transistor with a blend polymer as emitter are described in Section 3.4. Optical response of a polymer light-emitting diode connected to the hot-carrier transistor are also shown in Section 3.4
3.2 Polymer hot-carrier transistor with high bandgap emitter
3.2.1 Motivation
For silicon BJT, the replacement of semiconductor base by metal was proposed in the early 1960s.[98] However, since silicon is a nearly perfect crystal, the backscattering of carrier at the base-collector junction is severe as the interface varies abruptly. The current gain β is therefore usually poor. A similar idea of using C60 as the emitter but still utilizing silicon as the collector is recently reported.[62,99] But such device turns out to be a permeable base transistor instead of the hot-carrier one.
Because of the disorder of polymer and that the interface does not vary so abruptly, we expect the backscattering in our polymer hot-carrier transistor will not be as severe as in silicon hot-carrier transistor and higher β is expected. Indeed we found that high
current gain with low operation voltage can be realized in polymer hot-carrier transistor. Interestingly, in addition to the base for hot-carrier transistor, metal sandwiched between organic semiconductors has been shown to exhibit current memory effect [100], and transistor-like device can be made based on such an effect.[101]
3.2.2 Device structure and fabrication
The multilayer structure of the polymer metal-base transistor is indium tin oxide (ITO) glass/P3HT/Al/LiF/PVK/Au. P3HT is used as the collector because of the small Schottky barrier with Al and high mobility. PVK is poly(9-vinylcarbazole), which is used as emitter because of the large Schottky barrier with Al. Fig. 3.1 shows the structure and energy band profile of hot-carrier transistor in the active mode, i.e., the base-emitter (BE) junction is forward biased while the base-collector (BC) junction reverse biased. The hot carrier in our device is hole. In order to illustrate the picture of hole, the negative of all the energy levels is shown. The work function of Au and Al are 5.1 and 4.3 eV, respectively. The lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) for PVK are 2.3 and 6.1 eV below the vacuum level, and those for P3HT are 3 and 5.1 eV, respectively. Note that LUMOs of the polymers are irrelevant to the device operation and not shown. The resultant energy barrier between base and emitter is as large as 1.8 eV, which enables the holes to be far above the Fermi level (i.e., hot carrier) when passing through the thin metal base. The hot holes are expected to have such a high kinetic energy that they are easily injected into the collector since the collector-base barrier is less than that of emitter-base by 1 eV. In addition to the energy level requirements, the base layer thickness must be less than the mean free path for the hot hole in the base in order to reduce the probability of hole capture by the base through inelastic
Figure 3.1 (a) The structures of polymer hot-carrier transistor with high bandgap emitter. (b) The energy band profile of metal-base hot-carrier transistor with high bandgap emitter. (c) The energy band profile of metal-base hot-carrier transistor in the active mode. The negatives of the actual energy are shown in order to illustrate the picture of holes better. The energies are indicated in eV.
scattering.[95] The mean free path of Al is about 100 Å.[102] The unwanted electron current is negligible because the electron injection barrier from Al to PVK is 2 eV, and 1.7 eV from ITO to P3HT. Under active mode bias, holes are injected into the
(b)
(c)
HOMO of PVK from the Au electrode, followed by tunneling through the LiF layer and passing ballistically across the base high above the Fermi level. Because P3HT is not crystalline, the quantum mechanical reflection at the base-collector interface which has plagued the inorganic hot-carrier transistor will not happen here. The LiF layer between emitter and base is intended to provide two advantages. First, the voltage drop across LiF lowers the Al Fermi level relative to HOMO of PVK and further increases the energy difference between PVK and P3HT. Hence the holes have higher kinetic energy in base with LiF. Second, the LiF layer serves as a protection layer which prevents the P3HT from possible dissolution when spin coating PVK.
Indeed, the insertion of LiF layer enhances the device stability and reproducibility.
The I-V curve of EB and BC junctions shown in Fig. 3.2 demonstrate good diode characteristic with rectification ratio of about 103 and 105, respectively.
The device is fabricated on patterned ITO glass substrate cleaned by de-ionized water, acetone and 2-propanol consecutively in ultrasonic bath. Fourteen hundred angstroms of P3HT is spun cast from chloroform solution (1.2 wt %) onto the substrate, followed by a thin aluminum film of 90 Å evaporated as the base at 0.2 Å/ s through a shadow mask. To wire out the base, a 1000 Å Al strip is deposited with another shadow mask. LiF layer of 28 Å is deposited on the thin Al film, followed by 3300 Å of PVK spun cast from toluene solution (7 wt %) to form the emitter. Gold is deposited as the emitter contact. The devices are packaged in a glove box and all electrical measurements are performed in ambient condition. The polymers are purchased from Aldrich. All metal layers are deposited in a chamber having a base pressure of 1.0×10−6 mbar. The device active area, defined by crossover between the Au and ITO electrode, is 4 mm2. The thickness of each polymer layer is measured by Kosaka ET4000 surface profiler. Current-voltage curves are measured by semiconductor parameter analyzer.
C
current I does increase with the base current C IB. The common-emitter current gain β is 25 when V is −5 V. β is the average of five current gains at different C IB. Each current gain is given by
[
IC−IC(
IB =0) ]
/IB. However, for fixed IB, IC increases with VC without saturation. This is probably due to the image-forcebarrier lowering at the BC junction and β increases with VC .[103,104] In Fig. 3.4, the voltage drop across the EB and BC junctions are plotted as functions of V at C fixed IB = − 0.2 μA. The BC voltage drop VBC =VB −VC increases with VC while the EB voltage drop VEB =VE −VB is nearly a constant after VC exceeds 2 V.
This behavior implies that further increase of VC mostly falls on the reverse biased BC junction as expected. Common-base measurement shows consistent results. When
VC is −5 V and the base electrode is open, the IC leakage current is 1.9 μA as shown in Fig. 3.3. Since the reverse current for BC junction is of the order nA as shown in Fig. 3.2, the leakage current is believed to result from some unexpected path caused by residual mutual dissolution of PVK and P3HT outside the active area. IC leakage can be in principle reduced to a few nA if process control is improved. Au migration into PVK layer during the evaporation may reduce the effective resistance of PVK layer, and consequently the device has a small turn-on voltage despite the large hole injection barrier at Au/PVK junction. Finally, from the atomic force microscope image of the base metal, the Al roughness is less than two nanometers and
Figure 3.2 The I-V curves of emitter-base and base-collector diodes.
Figure 3.3 The characteristics of the polymer hot-carrier metal-base transistor in common-emitter configuration. (a) Unit: Ampere (b) Unit: milliampere per centimeter square
0 1 2 3 4 5 Voltage distribu -1
-VC (V)
VEB VBC
Figure 3.4 The characteristics of the polymer hot-carrier metal-base transistor in common-emitter configuration.
no pinholes can be seen. It shows that our metal-base hot-carrier transistor is not in fact a permeable base one.[99,105] The device reported in this letter is therefore the first organic hot-carrier transistor.
3.2.4 Summary of section 3.2
In summary, a solution-processed vertical polymer hot-carrier transistor is demonstrated to have current gain of 25. This device has high current output and low operation voltage. The active area can be made arbitrarily large and no lithography is needed. The use of LiF tunneling barrier not only improves the hot carrier kinetic energy and current gain but also serves as a protecting layer to prevent mutual dissolution between the polymers.
3.3 Polymer hot-carrier transistor with low bandgap emitter
3.3.1 Motivation
Previously a high bandgap organic semiconductor poly(9-vinylcarbazole) (PVK)
is selected for the emitter in order to maximize the energy barrier at the emitter-base junction, thus enhancing the hot carrier kinetic energy and reducing the base current.[70] Even though reasonable common emitter current gain β is achieved the high bandgap emitter comes at a great cost. The high bandgap implies a large barrier for the holes to be injected from the metal contact to the emitter valance band.[111]
Au is used for the emitter electrode. Depending on the surface contamination level the work function of Au varies from 4.7 eV to 5.1 eV.[112] The ionization potential of PVK is 5.8 eV, implying a large hole injection barrier of 0.7 eV to 1.1 eV. The resulting collector density is therefore as low as 0.56 mA/cm2 as shown in Fig. 3.3 (b).
Similar low current density also occurs in hot-carrier transistor based on evaporated small molecules.[108-110]
In this section, we replace the high bandgap emitter by a low bandgap polymer poly(3-hexylthiophene) (P3HT) with ionization potential (IP) at 5.1 eV, which is much closer to the Au work function than PVK. In fact P3HT is also the material used for the collector. There is therefore no energy offset between emitter and collector valence band which is usually required for the hot carrier collection. Similar to the case of PVK emitter a thin layer of LiF is used as the tunneling barrier to enhance the relative energy. Unlike the PVK device where LiF is only auxiliary to create the hot carrier energy offset above the collector bandedge, for P3HT emitter the energy offset depends entirely on the LiF layer. The prerequisite of hot-carrier transistor using low bandgap emitter is therefore that the tunneling barrier alone must be able to maintain a good common emitter current gain. It turns out that the common emitter current gain is not compromised even without the high bandgap emitter, indicating that the tunneling barrier is more crucial than the semiconductor band positions for the operation of the transistor. As for the collector current density, it increases dramatically from 0.56 mA/cm2 for PVK emitter to several tens mA/cm2 for P3HT
The device structure of the hot-carrier transistor in this work is ITO/PEDOT:PSS/P3HT(C)/Al(B)/Al2O3/LiF/P3HT(E)/Au. P3HT is used as both the emitter (E) and collector (C). PEDOT:PSS is poly(3,4-ethylenedioxythiophene) doped with polystyrene sulfonated acid, which is used to flatten the ITO surface and serve as the collector contact. The middle Al layer is the base (B), and the top Au layer is the emitter contact. Fig. 3.5 shows the structure as well as the energy band profile of hot-carrier transistor in the active mode. The hot carrier in the transistor is hole. The work function of Au and Al are 4.7 eV and 4.3 eV, respectively. As described above the holes injected from the emitter into the base are hot carriers because the large energy difference between the emitter valence band and the base Fermi level. α is the probability for the hot carrier to enter the collector valence band while 1−α is the probability for the carriers to relax to the base by energy loss. The β is defined as ratio between the collector current and base current J /C JB which is equal to α
(
1−α)
. Apparently the larger the emitter IP, the higher the hot carriers are above the base Fermi level, and the higher the gain β is. Emitter with high IP value is therefore chosen in the previous study.[70] The thin LiF/Al2O3 layer is the tunneling barrier which further separates the emitter valance band and the base Fermi level by a voltage drop across it. The device is fabricated on cleaned ITO substrate, and a 300 Å PEDOT:PSS layer is spin coated. P3HT is then spin coated to form the 1200 Å collector layer. A thin Al film around 80 Å is evaporated (10 Å /s) as the base through a shadow mask, followed by a LiF layer of various thicknesses. The optimal Al2O3layer is formed by air exposure for 3 minutes after Al deposition. The oxidation time
Figure 3.5 (a) The structures of polymer hot-carrier transistor with low bandgap emitter. (b) The energy band profile of metal-base hot-carrier transistor with low bandgap emitter. (c) The energy band profile of metal-base hot-carrier transistor in the active mode.
The negatives of the actual energy are shown in order to illustrate the picture of holes better. The energies are indicated in eV.
for the Al is limited to be 3 minutes since a 15 Å Al can be completely oxidized in 5 minutes.[113]Another P3HT layer is spin coated from xylene (2 wt %) to form 320 Å emitter layer. Au is evaporated as the emitter contact. The active area is 2 mm2. The devices are encapsulated by glass cap with UV glue in a glove box, and measured in
(a)
(b)
(c)
the topmost layer without any surface treatment, the work function of Au should remain close to its lower level of 4.7 eV. To confirm this we measure the diode with structure ITO/PEDOT/P3HT/Au. The I-V relation is highly asymmetric, implying that PEDOT is able to inject more holes than Au into P3HT. Since PEDOT work function is 5.1 eV the work function of Au is lower than 5.1 eV, consistent with the previous reports.[114] Even though there is still a moderate injection barrier from Au to P3HT, it is much smaller than the barrier between Au and PVK which is more than 0.7 eV.
3.3.3 The effect of the insulating layer thickness
Figure 3.6 shows the β of hot-carrier transistor with different LiF layer thickness with or without Al2O3 layer in the common-emitter configuration. The emitter voltage VE is 0 V, collector voltage V is − 5 V, and base current density C JB is 2 mA/cm2. For transistor without Al2O3, β initially increases with increasing LiF thickness, and reaches a maximum β = 0.6 when LiF thickness is 10 Å. For LiF thickness higher than 10 Å, β decreases due to the insulating nature of LiF. For the transistor with Al2O3, β also has a maximum value of 1.6 when LiF thickness is 7 Å. The inset in Fig. 3.7 shows the atomic force microscopy (AFM) image of Al base on P3HT. No pinhole can be observed. In addition, the roughness of 2.6 nm is much smaller than the mean
Figure 3.6 shows the β of hot-carrier transistor with different LiF layer thickness with or without Al2O3 layer in the common-emitter configuration. The emitter voltage VE is 0 V, collector voltage V is − 5 V, and base current density C JB is 2 mA/cm2. For transistor without Al2O3, β initially increases with increasing LiF thickness, and reaches a maximum β = 0.6 when LiF thickness is 10 Å. For LiF thickness higher than 10 Å, β decreases due to the insulating nature of LiF. For the transistor with Al2O3, β also has a maximum value of 1.6 when LiF thickness is 7 Å. The inset in Fig. 3.7 shows the atomic force microscopy (AFM) image of Al base on P3HT. No pinhole can be observed. In addition, the roughness of 2.6 nm is much smaller than the mean