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The Minimum AC Signal Model of Bipolar Transistor in Amplification Region for Weak Signal Detection

Lidong huang.

1 Ocean College, Zhejiang University, Hangzhou 310058, China; nc.ude.ujz@gnauhgnodil

Qiuyan Miao

2 College of Biomedical Engineering and Instrument Science, Zhejiang University, Hangzhou 310058, China; nc.ude.ujz@04051711 (Q.M.); nc.ude.ujz@us_ourix (X.S.)

Kaichen Song

3 School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310058, China; nc.ude.ujz@gnosck

Associated Data

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This paper presents a minimum signal model via the AC small-signal model and the uncertainty principle, which reveals the minimum AC signal that can be amplified by a bipolar transistor. The Ebers—Moll model (EM3) can describe the small signal amplification process, but it is difficult to define the minimum amplifiable signal of the bipolar transistor. In this study, the correspondence relationship between the non-equilibrium carrier and the electric injection is proved, and the relationship between the life of the non-equilibrium carrier and the measurable signal is proposed by the uncertainty principle. Next, the limit of perceived minimum voltage is also derived in this paper. Then, combining with EM3 model, the minimum AC signal model of bipolar transistor is presented to calculate the minimum voltage signal of bipolar transistor that can be amplified. Finally, a number of the simulation and experiment results show that when the minimum signal in the model is used as input, the carrier concentration of the bipolar transistor does not change and the base electrode cannot perceive the signal, which verifies the validity of the minimum AC signal model.

1. Introduction

Nowadays, bipolar transistor amplifiers are widely used in weak signal detection, especially for small AC signals [ 1 ]. To achieve weak signal detection, the bipolar transistor amplifier requires lower self noise and better performance. The semiconductor material is the most important factor that determines the performance of the amplifier circuit [ 2 ]. On the one hand, a large number of experts and researchers use silicon and germanium with different doping concentrations to improve the amplifying circuit’s ability of perceiving weak signals, while some people use semiconductor materials with different elements to reduce self-noise [ 3 , 4 ]. On the other hand, a lot of theoretical models of bipolar transistor have also been proposed and applied to the internal self-generating capacitance and self-generating conductance of semiconductors, including Ebers–Moll model (EM1), EM2, EM3 and Gummel–Poon model (GP) [ 5 ]. These studies have greatly promoted the development of transistor amplifier circuit and improved the weak signal detection ability.

Although these small-signal models can be used to describe the operation of bipolar transistor well, it seems that any small signal can be amplified by bipolar transistor [ 6 ]. An important question here is what is the minimum signal limit that a triode amplifier can amplify. If this problem is not solved, it is impossible to know what the small signal limit of bipolar transistor amplifier is, which is a big theoretical obstacle for weak signal detection. So far, weak signal detection has been widely used in underwater acoustic detection, target recognition, geophysical exploration and other important scientific fields [ 7 , 8 , 9 ]. Weak signal detection is based on bipolar transistor amplifier circuit, so the ability of bipolar transistor to detect weak signal is very important [ 10 ]. In other words, the most critical problem is how to determine the minimum perceived voltage signal limit of bipolar transistor amplifier circuit. At present, many scientists have done a lot of work and put forward corresponding models to solve this problem, but the problem has not been solved yet [ 11 , 12 ].

So far, there have been related works to promote the performance of the transistor amplifier circuit, mainly including two parts of the transistor manufacturing process and the theoretical calculation model of the transistor [ 13 , 14 , 15 ]. In terms of semiconductor manufacturing process, T. Maloney et al. [ 16 ] have studied the relationship on different materials and the self-noise of semiconductor devices. C. Su et al. [ 17 , 18 ] have developed the gate all-purpose junction less transistor with heavily doped polycrystalline silicon nanowire channel via using a new process, and have studied the current-voltage characteristics associated with the device. Su et al. [ 19 ] have designed a silicon-based arch gate omnipotence (GAA) tunnel field effect transistor (TET) and analyzed its current characteristics. With the development of microelectronics, Li et al. [ 20 ] find that graphene material has a high carrier mobility, which has a significant advantage in improving semiconductor sensing ability. For the theoretical calculation model of transistor, Ebors and Moll propose a semiconductor equivalent circuit model (EM1) for nonlinear DC analysis [ 21 ]. On the basis of the first generation model, considering the effect of nonlinear charge storage and series resistance, the second generation small signal model (EM2) is proposed, which has higher simulation accuracy and faster calculation speed [ 22 ]. With the continuous improvement of the calculation model, considering the secondary effects of bipolar transistor amplifier circuit (base region width modulation effect, base region broadening effect, and temperature effect), the third generation of small signal model is put forward to calculate the AC small signal, which has higher accuracy [ 23 ]. From the micro-perspective to explore the characteristics of transistor amplifier signal, Gummel-Poon model (G-P) is proposed to establish the connection between the device performance material, structure, and the process parameters [ 24 ]. G-P model has three advantages: first, it can directly relate the electrical characteristics of the device to the multi-subcharge in the base region. Second, the small signal problem can be effectively dealt with by its mathematical model [ 25 ]. Third, many physical effects can be taken into account by the relationship between the charge of the majority carrier and the bias voltage in the base region [ 26 ]. For the detection of weak signal, the main concern is how to amplify the AC small signal. The G-P model is proposed to calculate process of amplifying a small AC signal [ 27 ]. These research results greatly promote the development of weak signal detection [ 28 , 29 ]. However, the research on the small signal limit of transistor amplifier is still an unsolved problem, and few scholars and experts have done research and work in this field.

In order to explore the limits of transistor amplifier size signals, several main objectives need to be accomplished in this study. First, we need to prove the equivalent correspondence between the AC small signal and the non-equilibrium carrier. Then, on this basis, the relationship between the life of non-equilibrium carrier and semiconductor material is given in this paper. Next, the minimum limit model is established by combining the Heisenberg uncertainty principle with the EM3 model. At last, the validity of the model is verified by simulating the effective indexes of the triode model, including the changes of internal carriers and base current. The research of this paper solves the problem of the minimum signal limit of the bipolar transistor in the amplification region, which is of great significance for weak signal detection.

The rest of this paper is organized as follows. Section 2 presents the minimum AC signal model of bipolar transistors, which includes the proof of the relationship between the non-equilibrium carrier concentration and the injection voltage, the limit sensing voltage signal model of transistor amplifier, and the improved EM3 model. Section 3 carries out a lot of simulation and completes the analysis in the discussion, which verifies the effectiveness of the minimum AC signal model proposed in this paper. The conclusion and future researches are presented in Section 4 .

2. The Minimum AC Signal Model

In this section, the paper proposes a minimum AC signal model to calculate the bipolar transistors limit of small signal, which is divided into three parts. The theory of the relationship between non-equilibrium carriers and applied voltage is proposed in first part. The second part presents the limit sensing voltage signal theory of transistor amplifier. The last part improves the EM3 model for bipolar transistor calculation of limit small signal.

2.1. The Non-Equilibrium Carrier Theory

In weak signal measurement, bipolar transistors are mainly used to amplify small AC signals [ 30 , 31 , 32 ]. For the triode amplifier circuit, DC bigoted voltage plus AC small signal is equivalent to the periodic micro-variation of DC voltage. Δ V denotes the voltage change applied to the semiconductor, Δ r denotes the change in the resistance inside the semiconductor, and Δ σ represents the change in the conductivity of semiconductor. When a bipolar transistor detects a weak signal, the base conductivity of the bipolar transistor changes slightly. At this point, the conductivity of the semiconductor is as follows:

where σ denotes the conductivity after the change and σ 0 denotes the conductivity of the semiconductor at equilibrium.

As the conductivity changes, the resistivity of the semiconductor also changes accordingly, as follows:

Similarly, the semiconductor resistance changes as follows:

where l and s denote the cross-sectional area and length of the semiconductor, respectively.

From (1)–(3), the applied weak voltage change Δ V is proportional to the semiconductor resistivity Δ r . The following relationship can be obtained as follows:

Combining the theory of non-equilibrium carrier diffusion inside the semiconductor [ 33 ], the relationship between electronics, holes and conductivity is as follows:

where Δ n , Δ p , μ n and μ p denote the electron concentration change, the hole concentration change, the electron mobility and the hole mobility, respectively. q denotes the electron charge quantity constant.

By combining (4) and (5), the relation between the weak voltage variation of semiconductor and the carrier can be obtained as follows:

In general, the voltage change across the semiconductor is equivalent to the carrier change inside the semiconductor. This relationship provides a theoretical foundation for the establishment of the limiting weak voltage signal model in the next part.

2.2. The Limit Small Voltage Signal Theory

From the above conclusion, we know the relationship between the change value of voltage and the change of non-equilibrium carrier concentration. In [ 34 , 35 ], we know that the lifetime of the non-equilibrium carrier can be calculated by the experiment of measuring the change of the concentration of the non-equilibrium carrier. According to the Heisenberg uncertainty principle [ 36 ], when the product of its lifetime and energy needs to be greater than the Heisenberg constant, a non-equilibrium carrier to have an effect in a semiconductor, as follows:

where τ denotes the lifetime of the non-equilibrium semiconductor carrier and h denotes Planck constant.

Through (7), the following relation can be obtained as follows:

From (8), we can draw the corresponding conclusion that when the applied voltage small change is greater than Δ V , the small change can be detected by the semiconductor.

2.3. The Minimum Signal Model

In the bipolar transistor amplifier circuit, the base induced AC voltage amplitude should satisfy the following relationship:

where w denotes frequency of AC voltage and t denotes time.

When the bipolar transistor amplifying circuit is in the amplifying region, the total voltage on the base is the DC bias voltage plus the AC small signal, as follows:

where V 0 denotes the DC bias voltage.

According to the carrier diffusion theory in the semiconductor [ 37 ], the relationship between the change of the hole diffusion concentration P n and the total voltage V t o t a l is as follows:

where V b i denotes the barrier voltage inside the bipolar transistor, P n 0 denotes the intrinsic hole concentration of a semiconductor, K denotes Boltzmann constant and T denotes the temperature. The thermal voltage of a semiconductor is defined as v T = K T / q and the hole concentration constant at equilibrium is defined as P d c = P n 0 e x p − q V b i / K T e x p q V 0 / K T .

According to the semiconductor carrier diffusion theory [ 38 ], the hole diffusion equation in the semiconductor under equilibrium state is

where D p is the rate of hole formation, δ P n is the change in hole concentration and τ p is the lifetime of the hole.

In the case of applied voltage, the solution of the diffusion Equation ( 12 ) should be as follows:

where δ P 0 is the change of hole under DC voltage and P 1 ( x ) e j w t is the change of hole under small AC voltage.

Combining (12) and (13), the semiconductor hole diffusion equation under the applied electric field can be obtained as follows:

According to the diffusion properties of semiconductor carriers [ 39 ], the semiconductor diffusion equation needs to satisfy three boundary conditions as follows:

Through (14)–(17), the AC solution of the hole diffusion equation can be obtained as follows:

Therefore, the hole current density and its current at a small AC voltage are as follows:

where A is the cross-sectional area of the base of a bipolar transistor.

Similarly, from the carrier diffusion theory in semiconductor, the relation between the change of electron diffusion concentration n P and the total voltage V t o t a l can be obtained as follows:

According to the semiconductor carrier diffusion theory [ 40 ], the electron diffusion equation under the semiconductor equilibrium state is as follows:

where D n is the rate of electron formation, δ n P is the change in electron concentration, and τ n is the lifetime of the electron.

Similarly, under applied voltage, the solution of the diffusion Equation (22) should be as follows:

where δ n 0 is the change of electron under DC voltage and n 1 ( x ) e j w t is the change of hole under small AC voltage.

Combining (22) and (23), the semiconductor electron diffusion equation under the applied electric field can be obtained as follows:

In the same way, according to the diffusion properties of semiconductor carriers, the semiconductor diffusion equation needs to satisfy three boundary conditions as follows:

Through (24)–(27), the AC solution of the electron diffusion equation can be obtained as follows:

Therefore, the electron current density and its current at a small AC voltage are as follows:

Therefore, the minimum current caused by the minimum AC voltage is as follows:

In total, the limit changes of resistance, conductivity, carrier concentration, and current, which are caused by the small signal of the applied AC voltage, are shown below.

The minimum sensing signal model of the bipolar transistor is described in three parts, which explain the whole process of carrier change and current diffusion caused by the minimum limit voltage.

3. Simulation and Experiment

3.1. the simulation of model.

In this section, a number of simulations are designed to verify the minimum AC signal model proposed in this paper. We design an NPN bipolar transistor with a parameter of 1.25 μ m × 1.5 μ m × 1 μ m, as shown in Figure 1 a. The initial potential distribution of the intrinsic semiconductor under the equilibrium state is shown in Figure 1 b. In this simulation, bipolar transistors of different semiconductor materials are used to calculate the corresponding base carrier distribution and its base current characteristics. First, the minimum perceived voltage of semiconductor is calculated according to the carrier life of different semiconductor materials. Then, when the minimum voltage is used as the base drive, the change in the carrier distribution concentration of the base is calculated. Finally, the corresponding base current response is calculated by the minimum AC voltage signal model.

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g001.jpg

( a ) The three-dimensional model of NPN bipolar transistor. ( b ) The initial potential distribution of the intrinsic semiconductor. (Two-dimensional section: x axis represents the length of the model, y axis represents the height of the model. There is no external electric field.)

This section uses different semiconductor materials to simulate, including silicon, germanium, gallium arsenide and different doping concentrations of germanium. When T = 300 K and other environmental factors are in ideal state, the corresponding carrier lifetime and their minimum perceived voltage of different semiconductor materials are shown in the Table 1 .

The carrier lifetime and their minimum perceived voltage of different semiconductor materials.

According to the minimum signal model, we get the theoretical minimum voltage of different semiconductor materials and use it as the input of transistor base. This paper focuses on the detection of weak signals by bipolar transistors, so the transistors are in the amplification region (The base is applied with DC bias voltage). We can get the potential distribution, carrier concentration variation and the corresponding voltage-current characteristics of the bipolar transistor by inputting a sinusoidal voltage signal with the amplitude of V m i n and the frequency of 73 Hz at the base. The effectiveness of the minimum signal model proposed by this paper can be verified by analyzing these results. The potential distribution, carrier concentration variation and the corresponding voltage-current characteristics of the different bipolar transistor are shown in Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 .

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g002.jpg

The corresponding sinusoidal voltage signal is applied to the bipolar transistor in the amplification region, which is made of silicon (Si) with doping concentration of 1.5 × 10 10 cm − 3 and carrier lifetime of 10 − 3 s. ( a ) The potential distribution of the intrinsic semiconductor under sinusoidal small voltage signal. (2-D front view) ( b ) The variation of base carrier concentration with time. ( c ) The input weak sinusoidal voltage signal and corresponding base current response.

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g003.jpg

The corresponding sinusoidal voltage signal is applied to the bipolar transistor in the amplification region, which is made of germanium (Ge) with doping concentration of 2.4 × 10 13 cm − 3 and carrier lifetime of 10 − 2 s. ( a ) The potential distribution of the intrinsic semiconductor under sinusoidal small voltage signal. (2-D front view) ( b ) The variation of base carrier concentration with time. ( c ) The input weak sinusoidal voltage signal and corresponding base current response.

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g004.jpg

The corresponding sinusoidal voltage signal is applied to the bipolar transistor in the amplification region, which is made of gallium arsenide (GaAs) with doping concentration of 1.8 × 10 6 cm − 3 and carrier lifetime of 10 − 8 s. ( a ) The potential distribution of the intrinsic semiconductor under sinusoidal small voltage signal. (2-D front view) ( b ) The variation of base carrier concentration with time. ( c ) The input weak sinusoidal voltage signal and corresponding base current response.

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g005.jpg

The corresponding sinusoidal voltage signal is applied to the bipolar transistor in the amplification region, which is made of impurity germanium (Ge-1) with doping concentration of 1.2 × 10 13 cm − 3 and carrier lifetime of 2 × 10 − 4 s. ( a ) The potential distribution of the intrinsic semiconductor under sinusoidal small voltage signal. (2-D front view) ( b ) The variation of base carrier concentration with time. ( c ) The input weak sinusoidal voltage signal and corresponding base current response.

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g006.jpg

The corresponding sinusoidal voltage signal is applied to the bipolar transistor in the amplification region, which is made of impurity germanium(Ge-2) with doping concentration of 4.8 × 10 13 cm − 3 and carrier lifetime of 5 × 10 − 5 s. ( a ) The potential distribution of the intrinsic semiconductor under sinusoidal small voltage signal. (2-D front view) ( b ) The variation of base carrier concentration with time. ( c ) The input weak sinusoidal voltage signal and corresponding base current response.

Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 show the potential distribution, carrier concentration changing with time, and current response of base of bipolar transistor with different carrier life. First, Figure 2 a, Figure 3 a, Figure 4 a, Figure 5 a and Figure 6 a show the potential diagram of semiconductor with silicon (Si) doping concentration of 1.5 × 10 10 cm − 3 , germanium (Ge) doping concentration of 2.4 × 10 13 cm − 3 , gallium arsenide (GaAs) doping concentration of 1.8 × 10 6 cm − 3 , impurity germanium (Ge-1) doping concentration of 1.2 × 10 13 cm − 3 and impurity germanium (Ge-2) doping concentration of 4.8 × 10 13 cm − 3 , respectively. It is observed that the potential of the base does not fluctuate significantly.

Next, Figure 2 b, Figure 3 b, Figure 4 b, Figure 5 b and Figure 6 b show the base carrier concentration change of the different bipolar transistors in one second. At respective minimum sensing voltage of different material ( 0.6 × 10 − 12 V, 0.6 × 10 − 13 V, 0.6 × 10 − 7 V, 0.3 × 10 − 11 V, and 0.1 × 10 − 10 V), these corresponding carrier concentration remain around 1.5 × 10 10 cm − 3 , 2.4 × 10 13 cm − 3 , 1.8 × 10 6 cm − 3 , 1.2 × 10 13 cm − 3 , and 4.8 × 10 13 cm − 3 , respectively. We can know from the minimum signal model that the change of applied voltage is proportional to the change of carrier concentration. However, the carrier concentration of the base of these different transistors does not change periodically with the applied sinusoidal voltage signal, which indicates that the minimum voltage signal is not perceived by the base of bipolar transistors.

Then, Figure 2 c, Figure 3 c, Figure 4 c, Figure 5 c and Figure 6 c show the corresponding minimum sinusoidal voltage signal and base current response of different bipolar transistors in one second. From these figures, these small signals applied to the base satisfy the minimum limit voltage of different semiconductor materials and maintain the frequency characteristics, but their respective base current do not produce corresponding frequency response and periodic changes. From Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 c, the base response voltage is almost zero and there is no change in the carrier concentration, which are 1.5 × 10 10 , 2.4 × 10 13 , 1.8 × 10 6 , 1.2 × 10 13 and 4.8 × 10 13 . In others words, it shows that the bases of these transistors does not sense the applied sine voltage signal applied by them.

From the potential distribution, carrier concentration changing with time, and voltage response of bases of different bipolar transistor, we can draw a conclusion that when the minimum limit voltage signal is applied to the bipolar transistor, its potential, carrier concentration and response voltage will not change as the sinusoidal voltage signal, which verifies the effectiveness of the minimum signal model. Generally speaking, if the weak voltage signal is less than the minimum limit voltage of the semiconductor, the bipolar transistor amplifier circuit can not detect the signal.

3.2. The Experiment of Model

In this part, a number of experiments are designed to verify the minimum limit signal model of bipolar transistor. First, We choose bipolar transistors of materials Si, Ge, GaAs, Impurity-1 Ge and Impurity-2 Ge, respectively, and they are as front-end amplifiers of the signal acquisition circuit. ART-PXI8812-PXI with the sampling accuracy of 24-bits is used as the data acquisition module and its the measurement range and sampling rate are selected as ± 1 V and 500 Hz in the experiment, respectively. Similarly, we use AWG5200 as signal generator to generate a sine wave of frequency 73 Hz. Then, we use the signal attenuator of XMA to achieve the amplitude of the input signal at 0.6 × 10 − 7 V, 0.3 × 10 − 11 V and 0.1 × 10 − 10 V respectively. Finally, the experiment is carried out in an ultra-static shielded room. In order to suppress background noise, different acquisition lengths are needed to satisfy the time gain.

In this experiment, the time gain characteristic of Fourier transform is used to judge whether the signal appears on the spectrum. Due to the difference in the amplitude of the input signal, each signal acquisition experiment requires different time gain. The input signal of 0.6 × 10 − 7 V, 0.3 × 10 − 11 V, and 0.1 × 10 − 10 V need the time length of 24 h, 168 h and 96 h, respectively.

Figure 7 a shows the input voltage signal and its frequency spectrum. After 24 h of data collection, we can get the signal and its frequency spectrum in Figure 7 b. With time gain of 24 h, background noise is suppressed to 0.4 × 10 − 7 V. We can observe that there is no signal with amplitude of 0.6 × 10 − 7 V and frequency of 73 Hz on the frequency spectrum. That explains that when the amplitude of input voltage signal is 0.6 × 10 − 7 V, the bipolar transistor of material GaAs does not sense the input signal.

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g007.jpg

( a ) The input-voltage signal with amplitude of 0.6 × 10 − 7 V and its frequency spectrum. ( b ) The acquisition voltage signal in time-domain and its frequency spectrum after time gain of 24 h.

Figure 8 a gives the input voltage signal and its frequency spectrum. With 168 h of data collection, we obtain the signal and its frequency spectrum in Figure 8 b. With time gain of 168 h, background noise is suppressed to 0.3 × 10 − 11 V. We can observe that there is no signal with amplitude of 0.3 × 10 − 11 V and frequency of 73 Hz on the frequency spectrum. That explains that when the amplitude of input voltage signal is 0.3 × 10 − 11 V, the bipolar transistor of material GaAs does not sense the input signal.

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g008.jpg

( a ) The input-voltage signal with amplitude of 0.3 × 10 − 11 V and its frequency spectrum. ( b ) The acquisition voltage signal in time-domain and its frequency spectrum after time gain of 168 h.

Figure 9 a provides the input voltage signal and its frequency spectrum. After 168 h of data collection, we get the signal and its frequency spectrum in Figure 9 b. With time gain of 96 h, background noise is suppressed to 0.1 × 10 − 10 V. We can observe that there is no signal with amplitude of 0.1 × 10 − 10 V and frequency of 73 Hz on the frequency spectrum. That explains that when the amplitude of input voltage signal is 0.1 × 10 − 10 V, the bipolar transistor of material GaAs does not sense the input signal.

An external file that holds a picture, illustration, etc.
Object name is sensors-21-07102-g009.jpg

( a ) The input-voltage signal with amplitude of 0.1 × 10 − 10 V and its frequency spectrum. ( b ) The acquisition voltage signal in time-domain and its frequency spectrum after time gain of 96 h.

In total, from Figure 7 , Figure 8 and Figure 9 , we can draw a conclusion that when the minimum limit voltage signal is applied to the bipolar transistor, its response voltage signal will not change as the sinusoidal voltage signal, which verifies the effectiveness of the minimum signal model. Generally speaking, if the weak voltage signal is less than the minimum limit voltage of the semiconductor, the bipolar transistor amplifier circuit cannot detect the signal.

4. Conclusions

In this paper, a minimum AC voltage signal model is proposed to illustrate the minimum perceptible signal limit of bipolar transistor. This model not only proves the positive proportional relationship between the weak voltage signal and the carrier from the microscopic point of view, but also puts forward a clear minimum limit voltage signal theory of triodes via combining Hessian uncertainty principle and improved EM3 model. Finally, from three aspects of the semiconductor potential distribution—the change of carrier concentration with time, the base voltage response and output response voltage signal, the simulation and experiment of bipolar transistors with different materials is carried out to verify the effectiveness of the model, which is of great significance for weak signal detection.

Author Contributions

Conceptualization, L.H. and Q.M.; methodology, L.H.; software, X.S.; validation, B.W. and K.S.; formal analysis, L.H.; writing—original draft preparation, L.H.; writing—review and editing, B.W. All authors have read and agreed to the published version of the manuscript.

This research received no external funding.

Data Availability Statement

Conflicts of interest.

The authors declare no conflict of interest.

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  • Published: 22 June 2022

Organic bipolar transistors

  • Shu-Jen Wang 1   na1 ,
  • Michael Sawatzki 1   na1 ,
  • Ghader Darbandy   ORCID: orcid.org/0000-0003-0537-3984 2 ,
  • Felix Talnack   ORCID: orcid.org/0000-0002-7472-906X 3 ,
  • Jörn Vahland 1 ,
  • Marc Malfois   ORCID: orcid.org/0000-0001-5231-1896 4 ,
  • Alexander Kloes   ORCID: orcid.org/0000-0002-6485-1512 2 ,
  • Stefan Mannsfeld   ORCID: orcid.org/0000-0003-0268-519X 3 ,
  • Hans Kleemann   ORCID: orcid.org/0000-0002-9773-6676 1 &
  • Karl Leo   ORCID: orcid.org/0000-0003-3313-1843 1 , 3  

Nature volume  606 ,  pages 700–705 ( 2022 ) Cite this article

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  • Electrical and electronic engineering
  • Electronic and spintronic devices
  • Electronic devices

Devices made using thin-film semiconductors have attracted much interest recently owing to new application possibilities. Among materials systems suitable for thin-film electronics, organic semiconductors are of particular interest; their low cost, biocompatible carbon-based materials and deposition by simple techniques such as evaporation or printing enable organic semiconductor devices to be used for ubiquitous electronics, such as those used on or in the human body or on clothing and packages 1 , 2 , 3 . The potential of organic electronics can be leveraged only if the performance of organic transistors is improved markedly. Here we present organic bipolar transistors with outstanding device performance: a previously undescribed vertical architecture and highly crystalline organic rubrene thin films yield devices with high differential amplification (more than 100) and superior high-frequency performance over conventional devices. These bipolar transistors also give insight into the minority carrier diffusion length—a key parameter in organic semiconductors. Our results open the door to new device concepts of high-performance organic electronics with ever faster switching speeds.

Organic field-effect transistors (FET) were first reported in 1986 and have shown impressive improvements in the past two decades 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 . Nevertheless, they are still restricted to the low-to-medium megahertz range, which does not allow broad application 12 , 13 , 14 . The substantially lower charge carrier mobility in organic semiconductors (OSCs) compared with their inorganic counterparts is a limitation to the performance of organic transistors. Reducing the length of transistor channels is an effective strategy for improving the operational speed of the device, as shown both in FET 13 , 14 and other device concepts such as organic permeable-base transistors 11 , 15 . However, other factors, such as contact resistance and overlap capacitances, often limit further improvement of operational frequencies 16 , 17 .

A device that offers both low capacitance and contact resistance is the bipolar junction transistor. Although they have disadvantages with regard to miniaturization and process integration, bipolar transistors possess substantially higher operational speeds than comparable field-effect devices 18 . However, organic bipolar junction transistors (OBJTs) have not yet been realized, mainly because they rely on minority carrier diffusion through a thin and precisely doped base layer. Most studies have addressed exciton diffusion, which dominates owing to the weak dielectric screening in organic compounds 19 , 20 . Majority carrier diffusion length in fullerenes has been estimated to be on the centimetre scale, raising interesting questions about carrier diffusion physics in OSCs 21 , 22 . Charge carrier minority diffusion lengths have remained unexplored in OSC materials until now. In comparison to exciton diffusion, they can be expected to be in the nanometre range, at least for typical disordered organic films 23 , 24 , 25 .

Here, we realize an OBJT based on crystalline films of n- and p-type doped rubrene. In contrast to common furnace-grown single crystals, these films are made directly on the surface of a substrate and are thus compatible with mass production. We have demonstrated previously the excellent device potential of such highly ordered films by showing record-high vertical charge carrier mobilities that enabled ultrafast diode devices to operate in the gigahertz range 26 . Here we demonstrate that OBJTs based on crystalline rubrene thin films provide a promising route towards gigahertz organic electronics. Numerical simulations clarify the principles of transistor operation and present routes towards further optimization. A careful analysis of the device operation enables the direct measurement of minority carrier diffusion length in any OSC.

A key challenge in realizing an organic bipolar transistor is to find a suitable material and a device configuration that (1) allow both n- and p-type doping; (2) have sufficiently high (more than 1 cm 2  V −1  s −1 ) mobility allowing for balanced hole and electron transport, giving hope that the, so far unknown, minority carrier diffusion lengths are high enough to allow the carriers to travel through the base layers; and (3) allow a sufficiently thin base held at a defined potential to allow emitter–collector current control. We made use of the highly crystalline rubrene thin-film crystals with n- and p-type doping for the construction of this OBJT and analyse its operation experimentally and theoretically (for details of materials development and characterization, see Methods ).

Development of OBJTs

Using these highly crystalline doped films, we produced an OBJT. The device geometry is shown in Fig. 1a–c , featuring a vertical stacking of a rectangular emitter electrode at the bottom, a finger-like structured base electrode in the middle and a rectangular collector (top) electrode. The distancing between adjacent fingers of the base electrode and the width of each base finger itself are crucial, as discussed below. The final device is of pnp type, with an n-doped base, as we expect the p-type minority diffusion length to be higher owing to higher mobility. As is common for organic diode-like devices 26 , intrinsic films are added in between p- and n-doped films to improve reverse leakage behaviour, ending up with a pinip structure. Emitter and collector electrodes are made from gold to facilitate efficient hole injection, whereas the base electrode consists of aluminium for better electron injection. A thin film of n-doped C 60 is added on the emitter side of the base electrode to further facilitate electron injection. Additional layers of intrinsic and weakly doped material can be added on top of the base electrode to minimize base–collector leakage.

figure 1

a , Vertical stack configuration of the OBJT. b , Definition of active and parasitic currents and lateral geometric parameters in the OBJT. c , The OBJT device under a polarized microscope. Scale bar, 100 μm. d , Transfer characteristics of the OBJT device with blocking layers deposited on top of the base electrode for different V CE : solid lines give the absolute collector current I C , dashed lines give added current ∆ I C  =  I C  −  I C0 . e , The corresponding differential amplification for the device in d . f , Definition of the biasing and measurement setup for all OBJT curves and representation of the equivalent circuit of the OBJT containing active and parasitic components analogous to the currents defined in b : D B1 , direct base–collector diode with I BC leakage current; D B2 , direct base–emitter diode with I BE leakage current; R CE , direct emitter–collector overlap with I C0 output off-current. g , Transfer characteristics of the OBJT device without blocking layers deposited on top of the base electrode at different V CE : solid thick lines, absolute collector current I C ; dashed lines, added current ∆ I C  =  I C  −  I C0 ; solid thin lines, absolute direct current amplification. h , Absolute and area-normalized capacitance of an individual rubrene-based pin (input) diode at different biasing conditions and varying measurement frequencies. The active area is 100 × 100 μm 2 . i , Transition frequency estimation from transconductance.

It might seem self-evident to use the triclinic crystal phase of rubrene for bipolar junction transistors owing to their higher vertical charge carrier mobility, facilitating a more efficient vertical diffusion through the base layer. However, in addition to vertical transport, the n-doped rubrene layer of the base should be an area of equipotential with the metallic base electrode, which requires a high lateral conductivity. The distance between adjacent metallic base electrodes is the defining geometric parameter for this device concept and is in the range of micrometres. Therefore, orthorhombic crystals are used here successfully for OBJT because of their isotropic charge transport properties—transistor operation using triclinic crystals was not observed.

We first look at a device based on orthorhombic spherulite crystals with more blocking layers deposited on top of the base electrode (Fig. 1d,e ). The base–emitter diode, the base–collector diode and the emitter–collector pinip structure are first investigated separately to check functionality at component level (Extended Data Fig. 1a ). The input and output components function individually as diodes, with distinguishable forward and reverse behaviour. The base–collector diode possesses a substantially lower forward current than the base–emitter input diode owing to the extra blocking layers on top of the base electrode. However, the reverse current and forward leakage on both sides of the base are almost identical. This is a sign that the leakage current is governed by lateral leakage paths rather than the current going through the pin diodes. As expected, the direct current from emitter to collector is fully symmetric (see impedance measurements in Extended Data Fig. 2 ). However, this current is substantially higher than the current through the diodes themselves. The high emitter–collector current can be explained partly by the simple electrode design, which creates a large area of parasitic overlap between emitter and collector. It is possible to reduce the emitter–collector current by structuring the electrode. A discussion about the optimal geometric configuration based on simulations is given in the next section. Our main focus here is on the base region to enable the operation of the OBJT.

Figure 1d shows the transfer curve of the full OBJT (the electrode gap in base electrode is 12 µm), that is, the emitter (output) current over the base (input) current at different emitter–collector voltages. It is obvious that the absolute value of the emitter current is large and barely changes throughout the measurement. Only at high base currents is a slight increase noticeable. This is caused by the emitter–collector leakage current discussed above. This leakage current can be seen as a constant shunt R CE in parallel with the output of the device (an equivalent circuit is presented in Fig. 1f ). Thus, the real output of the transistor reflects the change in collector current (also shown in Fig. 1d ) controlled by the base current. A steady increase in output current over input current is visible, with a steep increase at low and high base currents and a substantially shallower slope in the medium current regime. The general behaviour is similar for all applied emitter–collector voltages, albeit shifted by an absolute current. Focussing on the largest V CE of −8 V, the added collector current surpasses the input base current only until a base current of 15 μA.

Figure 1e shows the differential signal amplification ∂ I C /∂ I B . It is as large as 100 at a low base current, clearly proving transistor action, and then decreases steadily with increasing base current. The loss of differential amplification occurs at I B  = 2 μA. This decrease in differential amplification can be understood from the geometry of the device: an illustration of the current paths is given in Fig. 1b . In addition to the already mentioned current path through R CE , leading to a large I C0 , the top and bottom diodes of the transistor can be split into two parts. First, a large part of each diode is defined by the area of direct overlap of the base and the collector or emitter electrode. This region contributes only to the leakage current and does not contribute to transistor operation. The leakage current through the base–collector diode D B1 is denoted as I BC and the leakage current through the base–emitter diode D B2 as I BE . Second, a smaller part is defined by the area around the base electrode fingers in which the base potential is present. This distance is given by the base reach L R . The corresponding area is marked in Fig. 1b . Only the second part (current I B,S ) can contribute to the modulation of the collector current in the form of I C,S . The equivalent circuit of this configuration is shown in Fig. 1f . The amplification of the transistor component starts to saturate at higher base currents owing to the exponential increase in input current through the parasitic parts of the input diode such that differential amplification cannot be maintained at higher base current. The measured differential amplification is therefore not an intrinsic property of the transistor but a property of the device functioning as a circuit.

The blocking layers deposited on top of the base electrode aimed at suppressing leakage current from the parasitic diode D B1 can, however, also block part of the channel next to the base electrode fingers that would contribute to the transistor operation due to the geometry of thermal evaporation through shadow masks. A balance must be found between the configuration of blocking films and electrode geometry. We also investigated a device based on orthorhombic platelet crystals without the use of blocking layers on top of the base electrode, the current–voltage ( IV ) characteristics of the device are shown in Fig. 1g . The transistor operation of the device at low currents is reduced, because the changed biasing of the base and the resulting change in parasitic current of the diode D B1 overcompensate for any diffusion-based amplification. However, at high base currents, the output collector current is increased substantially, and the transistor clearly shows large-signal amplification, although only moderate values. We would like to note that the unstable behaviour at high base current is probably caused by the high current density in the device, which is close to the onset of self-heating effect. Therefore, both differential and absolute current amplification can be observed in our OBJT devices based on doped rubrene crystals.

TCAD simulations of OBJTs

Technology computer-aided design (TCAD) simulations are performed to obtain a better understanding of the charge transport in the OBJT device and design rules for optimization of the device geometry. The simulations are based on the device stack that showed large-signal amplification as shown in Fig. 1g . The fabricated devices and experimental data are taken as a reference to calibrate the TCAD simulator. The IV characteristics of the individual components (base–emitter diode and emitter–collector structure) show good agreement between the calibrated simulation results and measured data as shown in Fig. 2a , thus confirming the viability of the device operation. On the basis of the calibrated TCAD, electrostatic potential, electric field, carrier density and the current, distributions can be simulated and extracted for different bias conditions and geometries. As an example, Fig. 2b shows the current density distribution in the OBJT. The lateral electric field distribution between two adjacent base fingers is shown in Fig. 2c .

figure 2

a , Congruence of simulation and measurement on the basis of the experimental data from Fig. 1g . The simulation is tuned to reproduce IV characteristics of the emitter–collector and emitter–base (inset) individually. b , The geometry and current density distribution for an exemplary configuration of the OBJT as given by TCAD simulations. c , Field strength of the internal electric field in a lateral direction for different distances between adjacent base electrodes at V BE  =  V CE  = −3 V. The inset shows a close-up view of the panel for clarity. d , Simulated maximum differential amplification with different widths of the base electrode L B . e , Simulated maximum differential amplification with hypothetical lateral offset between the end of the base electrode and the start of the emitter electrode L BE . f , Simulated maximum differential amplification with different distances between adjacent base electrodes L BB (all other parameters were kept constant in each set of simulations). The insets show the geometry of L B , L BE and L BB in the OBJT device. The parameters used are summarized in Supplementary Table 1 .

The simulation provides an insight into a key parameter of the transistor: the finger design of the base electrode. The length required for the field to drop from its maximum value to almost zero can be interpreted as the base reach L R . For an electrode distance of more than 25 μm, the lateral field is close to zero for an important part of the device, causing a large initial off-current that is not controllable by the base current. On the basis of the simulation, a base-to-base distance of 5 μm to 10 μm seems to be optimal.

Figure 2d shows the impact of the size and arrangement of the base electrodes on amplification. When the width of the base electrode is reduced from 25 μm to, theoretically, 0 μm (this is equivalent to no direct overlap between base, emitter and collector), the maximum amplification increases substantially, as the part of the base current that does not contribute to amplification decreases, whereas the controllable collector current remains the same. However, a base overlap of 0 μm is impossible to achieve for technological reasons. By contrast, a negative overlap in the sense of a spacer/gap between the end of the base and the beginning of the emitter can be achieved. Figure 2e shows the resulting amplification for such configuration. The amplification is reduced as expected as the important edge area near the base electrode is now substantially less involved in the transport. However, the reduction is comparably modest for a gap length of 1 μm. This degree of alignment precision would be achievable with advanced stencil lithography techniques.

Finally, the distance between adjacent base electrodes is varied, as shown in Fig. 2f . Surprisingly, the amplification increases slightly for increased distances between adjacent base electrodes, although a saturation is seen above 50 μm. This is because, although the lateral field is close to zero far from the base (Fig. 2c ), a small amount is still contributing to the output current. However, the off-current is also increased when the distance between bases is increased because the emitter–collector overlap increases simultaneously (Fig. 2f ). Therefore, there is a trade-off between the current amplification and the off-current when designing the base electrode.

Overall, the simulations confirm the operation of the OBJTs with differential as well as large-signal amplification. Furthermore, they give clear design guidelines how to further improve the devices.

Operation speed of OBJTs

With a total device thickness of approximately 1 µm and a high vertical mobility of approximately 3 cm 2  V –1  s –1 , OBJTs seem well suited for high-frequency operation. The most important dynamic performance parameter for any kind of transistor is the unity-gain cut-off frequency. A direct measurement of this quantity requires sufficient large-signal amplification and stability of operation. Unfortunately, in our OBJTs, we obtain large-signal amplification only at the highest applied bias, which results in unstable behaviour (Fig. 1g ). Still, we reasonably estimate the maximum speed of operation by evaluating the resistor–capacitor time of the system. Similar to the calculations done for FET, it is possible to estimate the maximum speed of operation in the form of the transition frequency from static properties using:

where g m and C denote the transconductance of the transistor and the capacitance, respectively. The transconductance describes the change in output current with input voltage. In case of the OBJT, it can be written as:

Because the output current ( I C ) is linked to the input current ( I B ) through the amplification ( β ), the transconductance is defined by the differential conductance of the input diode. Similarly, the defining capacitance is given by the input diode, assuming diffusion through the base is sufficiently fast, the transition frequency is seemingly limited only by the properties of the input diode. On the basis of the results obtained from the simulations, one goal is to reduce the direct base current as much as possible, which would reduce conductance of the input diode. However, the amplification of the device would increase accordingly, leaving the g m constant. A direct transition frequency measurement is challenging for OBJTs owing to the parasitic diodes that influence the phase of small signal measurements. Nevertheless, the high degree of agreement between the direct transition frequency measurements and the transconductance/capacitance estimations in the literature allow us to estimate the frequency response of our OBJTs 13 , 14 , 27 . For the device shown in Fig. 1g , the resulting transconductance is as high as 0.1 S (Fig. 1i ), in the range in which devices show amplification, whereas the capacitance is around 10 pF (Fig. 1h ). This results in a transition frequency of 1.6 GHz, which is similar to the speed of operation found for the single, rubrene-based diodes 26 and hence provides a significant step (10–40×) above the current state of the art of organic transistors 12 , 14 . Two reasons for the superiority of the OBJT are (1) highly crystalline films that feature improved mobilities compared with most OSCs and (2) the ultralow capacitance of devices associated with the vertical bipolar junction transistor design. In addition, limitations to contact resistance are less prominent here, because all the metal–OSC interfaces are doped by default and do not limit injection, proven by the space-charge-limited current analysis-like behaviour in rubrene pip devices.

Minority carrier diffusion length

The working principle of the OBJT is based on the diffusion of minority carriers (holes) through the base (n-doped film). In an ideal device, the diffusion length could be calculated directly from the doping concentrations, the width of the base layer and the resulting amplification. However, as discussed, the amplification measured here does not represent the intrinsic amplification of the transistor itself but of the device as a circuit. Nevertheless, the observation of amplification proves the diffusion of minority carriers through the base, with a minority diffusion length of at least 20 nm for devices with 1 wt% of base doping. In addition, we conducted experiments for which we varied the properties of the doping and structure of the base. Consistent with the inorganic bipolar junction transistor theory, both an increase in base doping from 1 wt% to 5 wt% and an increase in base layer thickness substantially reduce current amplification. The strong dependency of OBJTs on the base thickness and doping concentration is associated with the minority carrier diffusion operation, which is in stark contrast to organic permeable-base transistor operation based on most carrier transport. It is possible to estimate the diffusion length from devices with different base thickness when all remaining parameters remain identical. Figure 3 shows the OBJT operation based on a new set of devices with improved electrode geometry, reducing the area of electrode overlap that does not contribute to the transistor operation. The reduction in the parasitic electrode overlap area improves transistor performance, which is in line with the TCAD simulations (Fig. 3d ). On the basis of these measurements, the diffusion length for holes through the n-doped rubrene is estimated, by fitting the classical bipolar transition relation \(\beta \propto {\rm{\coth }}\left(\frac{W}{{L}_{{\rm{D}}}}\right)\) together with the calibrated TCAD simulation, to be roughly 50  nm, showing excellent agreement with experimental results and minority-carrier-dominated device operation by using an input diffusion length of 50 nm (Fig. 3d–f and Extended Data Figs. 1 and 3 ). Exciton diffusion lengths in the micrometre range found in photoexcitation experiments on single crystals of rubrene 28 indicate fundamentally different mechanisms governing the transport and relaxation of minority holes. Considering the high structural order of rubrene crystals after doping, the recombination processes are probably caused by the slight widening of the density states. Our OBJT device provides a tool to obtain direct access to the physical properties of minority carrier diffusion in similarly high mobility OSC systems, opening the possibility to investigate fundamental questions about mechanisms of minority recombination in OSCs.

figure 3

a , b , Differential amplification of OBJTs with different base layer thicknesses ( a ) and tetrakis(hexa-hydropyrimidinopyrimidine)ditungsten(II) (W 2 (hpp) 4 ) doping concentrations ( b ). c , d , Optical microscope images of different OBJT electrode designs ( c ) and corresponding device differential amplification curves ( d ). The solid lines denote experimental results and the hollow symbols denote TCAD simulation results. Scale bars, 100 μm. The device has a base thickness of 20 nm with 1 wt% W 2 (hpp) 4 doping concentration. e , Normalized differential amplification as a function of effective base width and doping. The effective base width is the base thickness minus the space charge length (2LSCL is approximately 10 nm determined from TCAD simulation and electrical characterization). The differential amplification was taken at a base current of 10 −5 mA, for which there is a good agreement between the TCAD and experiment results. The error bars denote the standard error of the mean by averaging over five devices prepared in a single run. The red curve is a coth fit with minority diffusion length of 50 nm. f , TCAD-simulated hole current density as a minority carrier (top) and electron current density (bottom) in the n-doped base layer.

In summary, we demonstrate a functional OBJT, delivering a missing piece of the puzzle on the organic transistor roadmap. Our OBJTs, based on highly crystalline rubrene thin-film crystals, not only provide a promising route towards ultrahigh-frequency organic transistors, but also allow the study of important fundamental physical parameters such as the minority carrier diffusion length, estimated to be around 50 nm for a doping concentration of 5 wt% for rubrene crystals. We believe that our results pave the way for next-generation high-performance organic electronic devices and provide a tool for understanding carrier diffusion physics in high mobility OSCs.

Details of rubrene thin-film crystal development

Growth procedures.

The general process for growing thin-film crystals of rubrene was described in refs. 29 , 30 . In Extended Data Fig. 4a,b , we show the fabrication process for rubrene thin-film crystals and types of rubrene thin-film crystal phase upon doping, respectively. A thin layer of amorphous rubrene is deposited on a substrate by vacuum deposition and then annealed in a nitrogen atmosphere to initiate crystal growth. Different crystal phases are possible depending on surface properties and heating temperature. The three most common types of crystal are triclinic spherulites, orthorhombic spherulites and orthorhombic platelets (Extended Data Fig. 4b ). Triclinic crystals start to form from approximately 120 °C and are the most robust and reproducible of the common crystal phases. Previously, we have shown the improved properties of triclinic films in gigahertz diodes 26 . Although the vertical mobility in these triclinic films is high, lateral transport is inefficient because of the strongly branched nature of these films. Orthorhombic crystals are the main focus in most publications owing to the isotropic charge transport properties originating from its herringbone molecular packing with ideal wavefunction overlap 31 , 32 , 33 . The spherulitic configuration of the orthorhombic packing grows at higher temperatures above 170 °C without strong branching, and can be identified easily under a polarized microscope by straight rays fanning out from the individual centre of each crystallite. Orthorhombic platelets are the most difficult phase to be created consistently. Heating at 150 °C to 170 °C commonly results in a few single crystals or clusters of crystals distributed over the surface. A previous study showed that a uniform and surface-covered distribution of platelet crystals can be achieved by the introduction of a sublayer with appropriate glass transition temperature 34 . Here we use 5 nm of 4,4′-cyclohexylidenebis[ N , N -bis(4-methylphenyl)benzenamine] (TAPC), resulting in successful crystal growth on glass and silicon substrates as well as structured metal and indium-tin-oxide electrodes 35 .

Epitaxy and doping

To make an OBJT, we need to control the total thickness of the crystal and the sequence of doped films precisely to realize complex device stacks. We introduced doping using coevaporation into initial seed and epitaxially grown layers. The maximum concentration of dopant that allows reproducible crystallization of the seed is below 2 wt% for both the p-type and n-type dopants studied here. Films added using epitaxy can be doped at substantially higher concentrations without any great changes in morphology visible by polarized microscopy. However, a change in surface properties can be seen in atomic force microscopy (AFM) measurements. The plateaus intermixed with line and screw dislocations that are described in ref. 36 are visible for the undoped crystals but gradually change into a more granular surface with fewer distinct features when doping is introduced (Extended Data Figs. 5 and 6 ).

Structural analysis

GIWAXS measurements of thin films of seed and bulk material show a change in the molecular packing of the rubrene crystals upon doping. Two-dimensional (2D) plots of the scattering image (Extended Data Fig. 7a ) prove the high degree of crystallinity, especially of the orthorhombic platelet form. The widths of the corresponding scattering peaks indicate the degree of disorder along the corresponding axis. Here the in-plane signal ( xy ) corresponds to the a - and b -crystal axis of the rubrene unit cell, which is important for lateral transport. The out-of-plane axis is defined by the c axis, relevant for the vertical transport. Extended Data Fig. 7b shows the change in peak width in both directions depending on the doping concentration and type. Peaks are substantially broader in the out-of-plane direction, which can, however, be attributed partly to the way the data are analysed (see the ‘ GIWAXS analysis’ section and Extended Data Fig. 8 ). The relative change is, however, more important than the absolute values. The in-plane data behave as expected in that a higher doping concentration results in a broadening of peaks, indicating a reduction in molecular order. Introduction of the n-dopant tetrakis(hexahydropyrimidinopyrimidine)ditungsten(II) (W 2 (hpp) 4 ) has a stronger impact than the p-dopant 1,3,4,5,7,8-hexafluorotetracyanonaphthoquinodimethane (F 6 -TCNNQ) when both films are doped to the same weight concentration. The introduction of dopant to the bulk part of the film generally increases the disorder in the film for both platelet and spherulitic samples (Extended Data Fig. 7b ). The out-of-plane axis behaves differently. Here doping of the seed shows a strong change in peak width, suggesting that integration of the dopant into the structure during seed crystallization is influencing mainly the c direction. Integration of dopant into the bulk films gradually increases the peak width, similar to the in-plane behaviour. However, the relatively stronger impact of the n-dopant compared with that of the p-dopant is even more pronounced. It can be concluded that the introduction of dopant molecules changes the molecular structure of the rubrene films, but only to a limited degree. Higher doping concentrations create stronger disturbance, whereas W 2 (hpp) 4 shows a stronger impact than F6-TCNNQ, presumably because of the size and steric properties of the three molecules.

Charge transport

Lateral electrical transport has been studied extensively in undoped films of all three crystal phases 26 , 29 , 34 , 35 , 37 , 38 . Lateral mobilities are in the range of 10 −2  cm 2  V −1  s −1 for triclinic films 25 and 1–4 cm 2  V −1  s −1 for orthorhombic films 34 , 35 , 37 , 38 . Lateral charge carrier mobility in platelets is usually slightly better than in spherulitic crystals, depending on the orientation of the crystal towards the electrode. However, in vertical organic devices, including the bipolar junction transistors investigated here, lateral and vertical transport occur simultaneously. Previously, we presented data on the vertical and lateral transport of undoped and doped films of the triclinic crystal phase 25 . Despite their superior transport properties in the vertical direction, these films are not suitable for OBJT devices owing to their mediocre lateral transport properties. Therefore, we will focus mainly on the vertical charge transport properties in orthorhombic crystals that are relevant to our OBJT devices.

Extended Data Fig. 4c shows IV curves of crystalline thin films of all three crystal phases for 400 nm undoped material sandwiched between gold electrodes. In contrast to the lateral measurements, vertical conduction is largest for triclinic films, whereas both orthorhombic crystal types behave similarly. This finding is expected because the stacks perpendicular to the surface are denser in the triclinic polymorph and identical for both orthorhombic crystal types. The differences between platelet and spherulitic films can be explained by the impact of injection owing to the low mobility and deep ionization potential of the TAPC sublayer used for the platelets 39 .

To further analyse the transport, we performed a space-charge-limited current analysis (SCLC) for the spherulite crystals based on sets of films with 400 nm and 600 nm of intrinsic crystal ( L ) sandwiched between 40 nm of injection layers doped with 5 wt% of the p-dopant F6-TCNNQ and gold electrodes (Extended Data Fig. 4e ). At high voltages (more than 1 V), a clear quadratic dependence is visible, indicating the SCLC behaviour of holes. The estimated vertical mobility for spherulite crystals is around 3 cm 2  V −1  s −1 (see Extended Data Fig. 9a for detailed SCLC analysis), which is lower than that of the triclinic crystal phase (approximately 10 cm 2  V −1  s −1 ) 26 . The difference between vertical and lateral mobility in orthorhombic crystals is close to isotropic, which is beneficial for applications in which charge transport occurs in both the lateral and vertical directions. As an illustration, Extended Data Fig. 4d (spherulites) and Extended Data Fig. 9b (platelets) show the impact of doping with F6-TCNNQ on the vertical current conduction. Even small amounts of doping increase the vertical conduction by orders of magnitude. The increased conduction at small voltages (less than 0.1 V) indicates that a significant part of this increase in conduction could be attributed to the reduction in injection resistance. A further increase in doping concentration causes a matching increase in current; however, the efficiency of the doping process decreases with higher doping concentration as expected from highly crystalline systems 40 . Electron doping of rubrene with the n-dopant W 2 (hpp) 4 works analogously, albeit with a lower doping efficiency and lower charge carrier mobility 26 , 41 .

Sample preparation

Devices are fabricated on glass wafers with a size of 25 × 25 mm 2 . Substrates are cleaned in acetone, ethanol, isopropanol and deionized water. Each substrate is treated in piranha solution for 15 min to generate a clean and hydrophilic surface before being rinsed in deionized water and dried with nitrogen. Rubrene is provided by TCI, and F 6 -TCNNQ and W 2 (hpp) 4 are provided by Novaled. Layers are deposited using thermal evaporation under vacuum with a base pressure of 1 × 10 −8  mbar. The evaporation rate of the seed has no influence on the remainder of the process. After deposition of the bottom metal electrode (30–40 nm), the sublayer of TAPC (5 nm) and the first amorphous layer of rubrene (30–40 nm), samples are transferred to a nitrogen glovebox, without exposure to air. Heat treatment takes place on a preheated hotplate at 160–180 °C, for 1–3 min. If needed, more layers are added using coevaporation of rubrene and dopant with the same vacuum deposition at rates between 0.5 Å s −1 and 3 Å s −1 , depending on the doping concentration. Electrodes and semiconductor are structured using shadow masks. Active areas for conductivity and SCLC measurements range from 50 × 50 μm 2 to 150 × 150 μm 2 . Devices used for conductivity measurements have a total thickness of 400 nm. The initial seed is undoped. No further doping other than the given bulk doping is introduced at the electrodes. SCLC was analysed using two sets of devices with 400 nm and 600 nm total thickness L each and active areas between 50 × 50 μm 2 and 150 × 150 μm 2 . The stack consists of 20 nm of undoped seed and the corresponding thickness of undoped bulk layer sandwiched between 40 nm of doped film (5 wt% for injection) and 30 nm of gold. The mobility value is extracted using the 1/ L 3 dependence of the fits gained from the fits of the V 2 -dependent SCLC current. For OBJT devices, silicon-based stencil masks are used to structure the metal electrodes, the emitter and collector electrodes consist of simple overlapping rectangles, whereas the base electrodes consist of a comb-like structure with rectangular fingers. The widths of the emitter and collector electrodes are 100 μm and 60 μm, respectively. The width of the base fingers is 12 μm, with spacing between them kept to 12 μm. The number of fingers in each of the comb-like structures of the base electrode is adjusted to the width and spacing of the fingers to approximately cover the overlap area between the emitter and collector electrodes. The devices used for the tests shown in Fig. 3 have a finger-like electrode that is around 15 μm each for both the emitter and base. The collector electrode is either a standard rectangular stripe or finger-like electrode (details provided in Extended Data Fig. 10 ).

Measurements

We performed electrical direct current measurements using Keithley 236, Keithley 2400 and Keithley 2600 source measure units, in which capacitance measurements were done with an HP 4284A in a nitrogen atmosphere. The electrical measurements were taken using the measurement software SweepMe! (sweep-me.net). Micrographs were taken with a Nikon Eclipse LC100 PL/DS polarization microscope. We performed AFM measurements with an AIST-NT Combiscope1000 and GIWAXS measurements at the Bl11 NCD-Sweet beamline at the ALBA synchrotron in Barcelona, Spain. The thin films were illuminated under a grazing angle of 0.12 with a beam energy of 12.95 keV and a beam size of 70 × 150 m 2 (vertical × horizontal). The diffraction pattern was recorded with an LX255-HS area detector from Rayonix, which was placed approximately 14 cm behind the samples. Chromium oxide (Cr 2 O 3 ) was used to calibrate the sample–detector distance and the beam position on the detector. The data were analysed with the WxDiff software (S.M.).

TCAD simulation

Synopsys TCAD was used with advanced physical models and the device simulation tools (structure editor, sdevice, svisual and inspect) to simulate the electrical characteristics of OBJT and to analyse simulation results. Measured OBJT data were used for adjusting and calibrating the TCAD simulator from Synopsys’ Sentaurus. Gaussian density of states were considered to approximate the carrier’s effective density of state in OSCs. The electric-field-dependent mobility Poole–Frenkel mobility model was used to enable the hopping transport of the carriers. We used the constant carrier generation model to compute a constant carrier generation and recombination process.

GIWAXS analysis

Evaluation of crystal quality in the in-plane and out-of-plane directions.

To evaluate the crystal quality of the differently doped rubrene films for both crystal structures (that is, spherulites and platelets), the (121) reflection ( Q xy  = 1.23 Å −1 and Q z  = 0.23 Å −1 ) was analysed in the 2D scattering images obtained by GIWAXS measurements ( Q is the scattering vector, Q xy is the in-plane scattering vector and  Q z is the out-of-plane scattering vector). Both the in- and out-of-plane directions were analysed to gain information about the crystal quality in the substrate plane and normal to it. We rotated each sample 360° in the substrate plane during the measurements and took individual images every 1.23°.

Analysis of the in-plane direction

To analyse the in-plane crystal quality, we took single images at specific angles, to minimize the appearance of multiple peaks originating from the same reflection (caused by different scattering positions on the sample). First, cake segments were extracted from the scattering image ranging from Q  = 1.15 Å −1 to Q  = 1.35 Å −1 and from χ  = 6° to χ  = 15° (where χ  is the azimuthal angle). The cake segment was then converted into a χ versus Q plot. From this plot, the columns were summed up in an area ranging from Q  = 1.15 Å −1 to Q  = 1.35 Å −1 and from χ  = 6.1° to χ  = 14.9°. Five per cent of the data on each side, horizontally, was used to remove a linear background by fitting.

Analysis of the out-of-plane direction

To analyse the out-of-plane crystal quality, we averaged the images taken at individual angles. This was possible because the multiple peaks caused by scattering from different positions on the samples result in peaks with their centre aligning on a line from the beam centre. First cake segments were extracted from the scattering image ranging from Q  = 1.15 Å −1 to Q  = 1.35 Å −1 and from χ  = 6° to χ  = 15°. The cake segment was then converted into χ versus Q plot. From this plot, the rows were summed up in an area ranging from Q  = 1.15 Å −1 to Q  = 1.35 Å −1 and from χ  = 6.1°to χ  = 14.9°. Five per cent of the data on each side, vertically, was used to remove a linear background by fitting.

Peak analysis in the in-plane direction

The resulting spectra were fitted using Gaussian curves and a constant offset. The number of Gaussians used was determined by the goodness of the fit and an estimation of the number of peaks that are distinguishable in the 2D scattering images. The resulting spectra were fitted using a single Gaussian curve with a constant offset.

Data availability

The data that support the findings of this study are available from https://opara.zih.tu-dresden.de/xmlui/handle/123456789/2048 .

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Acknowledgements

We thank A. Hiess and F. Winkler for fabrication of the stencil masks. The GIWAXS experiments were performed at the Bl11 NCD-SWEET beamline at ALBA Synchrotron with the collaboration of ALBA staff. F.T. and S.M. acknowledge financial support from the German Research Foundation (DFG, MA 3342/6-1) and acknowledge support by the German Excellence Initiative through the Cluster of Excellence EXC 1056 Centre for Advancing Electronics Dresden (cfaed). K.L. acknowledges funding by DFG project Le747/52.

Author information

These authors contributed equally: Shu-Jen Wang, Michael Sawatzki

Authors and Affiliations

Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP), Technische Universität Dresden, Dresden, Germany

Shu-Jen Wang, Michael Sawatzki, Jörn Vahland, Hans Kleemann & Karl Leo

NanoP, Technische Hochschule Mittelhessen, University of Applied Science, Gießen, Germany

Ghader Darbandy & Alexander Kloes

Center for Advancing Electronics Dresden (cfaed), Technische Universität Dresden, Dresden, Germany

Felix Talnack, Stefan Mannsfeld & Karl Leo

ALBA Synchrotron, Barcelona, Spain

Marc Malfois

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Contributions

S.-J.W., M.S., H.K. and K.L. designed and planned the experiments. S.-J.W. and M.S. performed the device fabrication and electrical characterization with input from J.V. G.D. and A.K. performed the TCAD simulations. F.T., M.M. and S.M. performed the GIWAXS analysis. H.K. and K.L. supervised the work. All authors discussed the results and contributed to manuscript preparation.

Corresponding author

Correspondence to Karl Leo .

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Extended data figures and tables

Extended data fig. 1 doped rubrene thin film crystals and their electrical characteristics..

( a ) Schematic illustration of the crystallization method. ( b ) Polarized microscope images of orthorhombic platelets and spherulites at different doping concentrations (wt.%). ( c ) IV characteristics of undoped rubrene films in three different crystal phases: Stack consists of 30 nm of undoped seed and 370 nm of undoped bulk film between Au-electrodes (active area of 100 μm×100 μm). ( d ) IV characteristic of orthorhombic spherulite in vertical direction with different concentrations of the p-dopant F6-TCNNQ:Stack consists of 30 nm of undoped seed and 370 nm of doped bulk film between Au-electrodes. ( e ) IV -curve for different orthorhombic spherulite rubrene crystal thicknesses and SCLC fitting. The V ²-regime expected from an SCLC is fitted with orange lines and used to calculate a vertical mobility of 3.3 ± 2.5 cm 2 V −1 s −1 (details given in SI) .

Extended Data Fig. 2 Morphology of rubrene thin-film seed crystals.

Surface properties measured via AFM of undoped orthorhombic rubrene platelets under different magnifications and growth conditions. ( a ) crystal grown without the sublayer (30 nm seed only). ( b-d ) crystal grown with 5 nm of TAPC as sublayer (30 nm seed, 80 nm bulk). ( e, f ) crystal grown with 5 nm of TAPC as sublayer and 40 nm of Al between seed and bulk (30 nm seed, 80 nm bulk).

Extended Data Fig. 3 Morphology of rubrene thin-film crystals with doping.

Surface properties measured via AFM of orthorhombic rubrene platelets doped with F6-TCNNQ under different magnifications. ( a ) crystal grown with 5 nm of TAPC as sublayer and 5 wt.% of F6-TCNNQ (30 nm seed, 80 nm bulk). ( b ) crystal grown with 5 nm of TAPC as sublayer and 20 wt.% of F6-TCNNQ (30 nm seed, 80 nm bulk).

Extended Data Fig. 4 X-ray characterization of the doped rubrene thin-film crystals.

( a ) Overview of an entire GIWAXS measurement for an orthorhombic platelet film. Structural characterization of thin films. Width of 221-peak from GIWAXS measurements extracted from fit of Gaussian distributions of orthorhombic spherulite ( b ) and orthorhombic platelet ( c ) crystals. Inset shows example peak and corresponding fitting. Details regarding the extraction of the peak width are given in the experimental section. The number in round bracket after seed (doping in the seed layer) or bulk (subsequent doping in the bulk film) denotes the doping concentration in wt. % and p/n in square bracket denotes p-type or n-type doping.

Extended Data Fig. 5 GIWAXS analysis.

( a ) Peak shape of 121 signal for a spherulite crystal film extracted from GIWAXS measurement. ( b ) Peak shape of 121 signal for a platelet crystal film extracted from GIWAXS measurement. ( c ) Example fit for the in-plane fitting procedure.

Extended Data Fig. 6 Vertical charge transport analysis.

( a ) SCLC analysis of charge carrier mobility of orthorhombic spherulite films in vertical direction (p-type doped layers at bottom and top electrode for injection). The SCLC regime was extracted from devices with 400nm and 600nm thickness with eight devices per thickness of varying active area. The error bars denote the standard deviation calculated from multiple devices and different device active areas (the thinner devices show a larger spread). The resulting mobility is calculated from the 1/ L ³-dependence of the Mott Gurney law. The uncertainty of the value is based upon the variation measured from the individual devices. The inset shows the SCLC fittings as shown in the Fig. 1e . ( b ) IV characteristic of orthorhombic platelets crystals in vertical direction with different concentrations of the p-dopant F6-TCNNQ: Stack (inset) consists of 30 nm of undoped seed and 370 nm of doped bulk film between Au-electrodes. Crystals are grown on 5nm TAPC as sublayer.

Extended Data Fig. 7 Capacitance measurements.

Area normalized capacitance of an individual rubrene-based pinip device at different biasing conditions and varying measurement frequencies. The active area is 150 μm × 75 μm. The device is fully symmetric and consist of two times 200 nm p-doped, two times 200 nm intrinsic, and 40 nm n-doped rubrene.

Extended Data Fig. 8 Additional OBJT characterization.

( a ) IV measurements of the individual components of the OBJT shown in Fig. 2c . The third, unused electrode is left floating in each of the individual measurements. ( b ) Added current at the output, collector with increased base current for a device with the same stack design as the one shown in Fig. 2d but with a thicker base (50 nm) doped at a higher doping concentration (5 wt.%) for different emitter-collector voltages of −12 and −20V. ( c ) Resulting amplification for a device with the same stack design as the one shown in Fig. 2d but with a thicker base (50 nm) doped at a higher doping concentration (5 wt.%) for different emitter-collector voltages of −12 and −20V.

Extended Data Fig. 9 Further thickness and temperature dependent OBJT measurements.

( a ) Resulting amplification of devices with the same stack design as the one shown in Fig. 2d but with a higher doping concentration (5 wt.%) and base width of 10 nm and 50 nm, respectively. As expected, higher doping of the base and thicker base layer reduce amplification. From the change in amplification with base thickness W , an estimation for the diffusion length can be extracted via β ∝ coth( W / L D ). As an average from these calculations, a value of 50 nm can be extracted. ( b ) Temperature dependent differential amplification of devices with the same stack design as the one shown in Fig. 2d . The temperature dependent differential amplification of the device implies an increase in charge diffusion length with temperature which is consistent with a diffusion driven device. The temperature values in the legend are in K.

Extended Data Fig. 10 OBJT device layout.

Schematic cross-section of the fabricated OBJT with 10-Fingers ( a ) design 1, ( b ) design 2, and the relevant dimensions of one single finger ( c ) design 1, ( d ) design 2.

Supplementary information

Supplementary information.

Supplementary Figs. 1–4 and Table 1.

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Wang, SJ., Sawatzki, M., Darbandy, G. et al. Organic bipolar transistors. Nature 606 , 700–705 (2022). https://doi.org/10.1038/s41586-022-04837-4

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Experiment 2 Experiment No: 2: Construction of Bipolar Transistor Logic Gate

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In this experiment we examine how to build logic gates from bipolar transistors using the RTL, DTL and TTL design.

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research paper on bipolar transistor

Mohammad Jawaid Siddiqui

In this paper, Threshold logic gates (TLG) are implemented using Resonant Tunneling Diodes (RTD). TLG is conceptually similar to the early McCulloch-Pitts model of the neuron and is normally used to implement linearly separable binary functions. RTD has demonstrably promising electronic features due to its high speed switching capability and functional versatility. Great circuit functionality can be achieved through integrating field-effect transistors (FET) in conjunction with Resonant Tunneling Diodes to modulate effective negative differential resistance (NDR) of the RTD. RTDs are intrinsically suitable for implementing threshold logic rather than Boolean logic, which has dominated CMOS technology in the past. The basic functional unit in the proposed implementation is the monostable-bistable transition logic element (MOBILE). Commonly used logic functions like the OR, AND, and MAJORITY function have been implemented and tested through SPICE simulation. Keywords-threshold logic, ...

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The basic building blocks for Resonant Tunnelling Diode (RTD) logic circuits are Threshold Gates (TGs) instead of the conventional Boolean gates (AND, OR, NAND, NOR) due to the fact that, when designing with RTDs, threshold gates can be implemented as efficiently as conventional ones, but realize more complex functions. Recently, RTD structures implementing Multi-Threshold Threshold Gates (MTTGs) have been proposed which further increase the functionality of the original TGs while maintaining their operating principle and allowing also the implementation of nanopipelining at the gate level. This paper describes the design of n-bit adders using these MTTGs. A comparison with a design based on TGs is carried out showing advantages in terms of latency, device counts and power consumption.

Procedia Computer Science

IJERA Journal

Logic gates are the fundamental components of any digital system and can be considered the "building blocks". A logic gate is a simple electric circuit consisting of two inputs and a single output. The most frequent names for logic gates are AND, OR, NOT, XOR (Exclusive or), NAND (NOT AND), and NOR. An OR logic gate begins with the provision of two electrical inputs. If one of the inputs has the value one or indicates that it is "on," then the output will also be one. In electronics, there is a type of logic gate known as an inverter or NOT gate. The report is broken up into five distinct parts or sections. The first section of this report covers the experiment's results on logic gates. They are used in the process of performing logical operations on one or more binary inputs to produce a single binary output. This article will examine the functions of the NOT, OR, and AND gates found in a logic circuit. The findings of the experiment are presented in the fourth section. The discussion, recommendations, and conclusions drawn from the results are in the last part. In a NOT gate, the input determines whether the output is true or false, and vice versa. ALTERNATIVELY, gates output a value of HIGH if either of the two inputs is. HIGH and LOW if both inputs are LOW; this type of gate is also known as an inverter. A truth table was used to validate the information of each NOT, AND, and OR integrated circuit. Knowing how to use these seven fundamental logic gates makes it much simpler to comprehend Boolean algebra and simplifies the process of conducting circuit analysis. These gates are most commonly used in the manufacture of automatic machines. Learning how to design logical circuits was made possible by utilizing gates such as NOT, AND, and OR.

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INTERNATIONAL JOURNAL OF ADVANCE RESEARCH, IDEAS AND INNOVATIONS IN TECHNOLOGY

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In this paper, we have developed a circuit which gives the output for 4-Logic gates of "AND, NAND, OR, NOR" simultaneously by taking only two inputs "A" and "B". I used bipolar junction transistors (BJT) to design this circuit. Previously we have each circuit for each logic gate but now in our new circuit, we developed four logic gates in a single circuit. Thus we can decrease the size of the special circuits. Instead of using four IC's for four logic gates if we use this single IC for all the four logic gates then the space used for the remaining three IC's can be used for other purposes. This circuit is very easy to design because it has only six bipolar junction transistors (BJT's).

International Journal of Electronics and Telecommunications

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In the paper we consider fast transformation of a multilevel and multioutput circuit with AND, OR and NOT gates into a functionally equivalent circuit with NAND and NOR gates. The task can be solved by replacing AND and OR gates by NAND or NOR gates, which in some cases requires introducing the additional inverters or splitting the gates. In the paper the quick approximation algorithms of the circuit transformation are proposed, minimizing number of the inverters. The presented algorithms allow transformation of any multilevel circuit into a circuit being a combination of NOR gates, NAND gates or both types of universal gates.

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