Impact of Buffer Layer on Electrical Properties of Bow-Tie Microwave Diodes on the Base of MBE-Grown Modulation-Doped Semiconductor Structure

Abstract

Bow-tie diodes on the base of modulation-doped semiconductor structures are often used to detect radiation in GHz to THz frequency range. The operation of the bow-tie microwave diodes is based on carrier heating phenomena in an epitaxial semiconductor structure with broken geometrical symmetry. However, the electrical properties of bow-tie diodes are highly dependent on the purity of the grown epitaxial layer—specifically, the minimal number of defects—and the quality of the ohmic contacts. The quality of MBE-grown semiconductor structure depends on the presence of a buffer layer between a semiconductor substrate and an epitaxial layer. In this paper, we present an investigation of the electrical and optical properties of planar bow-tie microwave diodes fabricated using modulation-doped semiconductor structures grown via the MBE technique, incorporating either a GaAs buffer layer or a GaAs–AlGaAs super-lattice buffer between the semi-insulating substrate and the active epitaxial layer. These properties include voltage sensitivity, electrical resistance, I–V characteristic asymmetry, nonlinearity coefficient, and photoluminescence. The investigation revealed that the buffer layer, as well as the illumination with visible light, strongly influences the properties of the bow-tie diodes.

1. Introduction

The molecular beam epitaxy (MBE) technique has been instrumental in advancing the growth of crystalline thin-film structures with atomic-level precision. The pioneer of this technology, K.G. Guenther, grew thin layers of InAs and InSb on a glass substrate back in the late 1950s [1]. The first submicrometer-thick semiconductor layers grown using this method were not epitaxial, and only a decade later, with improvements in vacuum technology, J. Davey and T. Pankey announced the growth of an epitaxial GaAs layer on a GaAs substrate [2]. A significant contribution to the development of MBE technology was made by A.Y. Cho and J.R. Arthur, who elucidated the mechanisms of material growth and proposed in-situ monitoring of the growth process [3]. To improve the quality of the epitaxial layers, the so-called buffer layers are grown between the substrate and the functional epitaxial layer. The type of buffer layer depends on both the substrate used and the desired epitaxial layer. For example, Y₂O₃ and Si₃N₄ layers of nanometer thickness were employed as the buffer layers between perovskite mixed solid solutions of BaTiO₃-SrTiO₃ and ITO-coated glass substrate for improving the electrical characteristics of the perovskite material [4]. The buffer layers resulted in minimal sacrifice of dielectric constant, reduced dissipation factor and leakage currents, and a significant increase in the breakdown field of this perovskite material. The influence of GaSb and InAs buffer layers on InSb-like and GaAs-like interface roughness in InAs/GaSb super-lattices grown with MBE was investigated in the work [5]. The proper selection of the buffer layer also influenced the properties of 4H-SiC, as stated by the authors of paper [6]. By varying the ratio of C/Si during the growth of the buffer layers, the authors achieved different impacts on the growth rate, uniformity, and roughness of the epitaxial layer. The selection of the buffer layer is crucial for the development of efficient multi-junction solar cells. Thus, the authors of ref. [7] investigated the effect of a GaP buffer layer between the Si substrate and the GaAs epitaxial layer on the properties of the latter. As far as MBE-grown GaN is concerned, there is no consensus on the influence of the buffer layer on the quality of the epitaxial layers. Thus, some authors [8,9] argued that using a buffer layer during GaN growth significantly improves the structural and electrical properties, while others [10,11] omitted the buffer layer and, as they claimed, achieved high-quality GaN layers. A more detailed investigation of the influence of the buffer layer thickness and temperature of its growth was presented in [12]. The authors revealed that despite the general deterioration of the structural properties of the GaN layer with increasing thickness of the buffer, this dependence was different for GaN and AlN buffer materials. However, they observed worse optical and electrical properties of the GaN layers grown on buffers compared with the reference sample without any buffer. On the other hand, the authors of ref. [13] found that growing a GaN layer on a sapphire substrate with a GaN buffer improves the structural, electrical, and optical properties of the layer by increasing the buffer layer thickness and extending its annealing time. The authors of ref. [14] used a composite buffer consisting of multiple AlN layers and a gradually varying Al-content AlGaN layer to grow GaN films on a sapphire substrate. This approach significantly improved the film quality compared to GaN films which were grown with a GaN buffer layer. The proper choice of an AlN buffer layer between the graphene substrate and MBE-grown GaN material enabled the growth of self-assembled GaN nano-columns of high quality [15].

Due to the nearly perfect match of the GaAs and AlGaAs lattice parameters, MBE technology has enabled the fabrication of semiconductor structures that can confine electron motion to the plane. These structures are called modulation-doped (MDS), and the electrons within them are referred to as a two-dimensional electron gas (2DEG). These electrons exhibit record mobility at low temperatures, and their mean free path is on the order of a fraction of a millimeter [16]. Despite good lattice matching between GaAs and AlGaAs, a buffer layer is also required to obtain high-quality epitaxial layers. The buffer layer performs the following functions [17]: (i) it diminishes interface roughness for the 2D electrons, (ii) a thick GaAs–AlGaAs super-lattice buffer layer inhibits the migration of impurities from the semi-insulating substrate to the active layer, and (iii) a thick or partially doped buffer layer can compensate electric field which arises due to Fermi level pinning in the mid-gap due to abundance of mid-gap traps in the substrate. The influence of the interface roughness between the substrate and a single quantum well structure was studied in ref. [18]. The introduction of a super-lattice between the substrate and the quantum well significantly reduced interface roughness, improving the sample’s transport and photoluminescence properties. The interface roughness scattering in modulation-doped heterostructures was studied both experimentally and theoretically [19]. Conditions were determined under which interface roughness scattering became dominant in modulation-doped structures at low temperatures, depending on background ionized impurity concentration.

In this paper, we present an investigation of the electrical and optical properties of planar bow-tie microwave diodes fabricated using modulation-doped semiconductor structures grown using the MBE technique. The operation of bow-tie diodes is based on the inhomogeneous heating of electrons in a strong electric field, which causes the so-called hot electron thermoelectric electromotive force in this semiconductor structure [20,21,22] and the articles cited therein. The structures incorporate either a GaAs buffer layer or a GaAs–AlGaAs super-lattice buffer positioned between the semi-insulating substrate and the active epitaxial layer. A comparison of voltage sensitivity of the bow-tie diodes based on the modulation-doped structure with and without a super-lattice buffer was made in our previous work [23]. It was demonstrated that the buffer layer structure significantly influenced the detected signal: the polarity of the detected voltage in diodes with a super-lattice buffer was opposite to that in diodes with a GaAs buffer layer. The metal contacts of the investigated bow-tie diodes were wider than the mesa structure of the bow-tie diode, i.e., the metal covered the slopes of the mesa. In this work, the bow-tie diode design was modified so that the metal contact remained within the boundaries of the mesa structure, thereby minimizing its negative impact on the detection properties of the diodes.

2. Samples and Methods

Two types of modulation-doped semiconductor structures with thick spacers were investigated in this research:

• The structure with a thick, unintentionally doped i-GaAs buffer layer between the substrate and the active semiconductor layer, hereafter referred to as the structure with a simple buffer layer (SSB).
• The same modulation-doped structure with the buffer layer, including i-GaAs layer and a 30-period GaAs/AlGaAs super-lattice, hereafter referred to as the structure with a super-lattice buffer layer (SSLB).

The selection of a wide spacer layer in the modulation-doped structure was motivated by the objective of minimizing the influence of the doped AlGaAs barrier on the charge transport properties of the two-dimensional electron gas layer [17]. Cross-section views of the investigated modulation-doped structures with buffer layers and their energy band diagrams with electron density distribution are shown in Figure 1.

The electrical parameters of the grown structures were measured using the Hall method at room and liquid nitrogen temperature and are presented in

Table 1. Electrical parameters of the modulation-doped structures measured using the Hall method at 300 K and 77 K temperature in the dark. Here μ is the electron mobility, R_sh is the sheet resistance, and n_s is the sheet electron density.

Structure	μ, cm2V−1s−1	Rsh, Ω/☐	ns, cm−2	μ, cm2V−1s−1	Rsh, Ω/☐	ns, cm−2
	300 K			77 K
SSB	2180	2160	1.33·1012	25,800	880	2.75·1011
SSLB	2370	1925	1.37·1012	65,800	580	1.63·1011

.

At room temperature, both the electron mobility μ and the electron density n_s in the SSB and SSLB structures are similar, but at liquid nitrogen temperature, the SSLB structure demonstrates a substantial increase in electron mobility and less of a decrease in electron density as compared with the SSB structure. This fact can explain the much higher voltage sensitivity of the bow-tie diodes investigated in the work of ref. [23].

Bow-tie diodes of asymmetric (AD) and symmetric (SD) geometry were fabricated. Their micrographs are presented in Figure 2. Bow-tie diodes with different widths d of the narrowest part of the diode (the “neck”) were fabricated. Respectively, the diodes with the 1, 2, and 3 micrometer-wide neck refer to AD1, AD2, AD3, and SD1, SD2, SD3.

The detailed technological sequence of the fabrication of AD and SD bow-tie diodes is described in ref. [24]. The quality of the ohmic contacts of the diodes was controlled using the classical transfer length model (TLM, also known as the transmission line model), which employs the electrical resistance measurement between differently spaced ohmic contacts of a rectangular semiconductor mesa [25]. This method was used to determine both the specific contact resistance ρ_c and the sheet resistance R_sh of the conductive layer of the modulation-doped structures. The specific contact and sheet resistance of the SSB and SSLB structures in the dark and under white light illumination are presented in

Table 2. The sheet resistance R_sh and the specific contact resistance ρ_c of the ohmic contacts of the conductive layers of the SSB and SSLB structures measured at room temperature. The abbreviations “ill” and “drk” in the subscripts refer to the parameters measured, respectively, under illumination and in the dark.

Structure	Rshill, Ω/☐	Rshdrk, Ω/☐	ρcill, Ω·mm	ρcdrk, Ω·mm
SSB	1780 ± 45	1910 ± 130	0.2 ± 1.6	0.5 ± 1.2
SSLB	1370 ± 50	1480 ± 20	0.21 ± 0.38	0.21 ± 0.28

.

The sheet resistance of the SSB structure is slightly higher than that of the SSLB structure. However, this difference is outside the measurement error range. The sheet resistance values of the structures derived from the Hall measurements are higher than those measured by the TLM method. The specific contact resistance of the ohmic contacts to the modulation-doped structure without a super-lattice buffer layer (structure SSB) is characterized by a higher dispersion of the resistance values.

The investigation of the bow-tie diodes was performed using DC and high-frequency probe stations, both when the diodes were illuminated by visible light and when they were shadowed from the illumination. The use of probe stations allowed the study to achieve higher reliability of the measured electrical parameters by averaging the results of measurements from a large number of diodes without wasting a lot of valuable time. The current–voltage (I–V) characteristics were investigated using the Süss MicroTec probe station EP6 with DC probes (FormFactor, Inc., Livermore, CA, USA) and Agilent E5270B precision measurement equipment (Agilent Technologies, Inc., Santa Clara, CA, USA). The voltage–power characteristics of the diodes were measured at 30 GHz frequency using a Cascade Microtech high-frequency probe station (FormFactor, Inc., Livermore, CA, USA), and ACP40-A-GS-250 probes were used to connect the diodes to the commutation station. A SHF BT45 broadband bias tee was used to separate the detected DC voltage signal from the microwave signal. An EiKO EKE21V150W lamp (EiKO Global, LLC, Olathe, KS, USA) with color temperature 3240 K at the maximum illuminance of 14,000 lx was used to illuminate the diodes. The spectral characteristics of the photo-lamp are presented in the work [24]. Photoluminescence (PL) spectra were measured using a photoluminescence setup with a fully automated focal length monochromator of 1 m in length. An Ar-ion laser was exploited as an excitation source, with photon energy in the range of 2.2–2.7 eV. The output power was set to reach an intensity of 1.36 W/cm². The PL was detected by a thermoelectrically cooled GaAs photomultiplier operating in the photon-counting regime. The temperature was varied using an optical closed-cycle helium cryostat.

The voltage sensitivity S, the low-field electrical resistance R₀, the asymmetry of the I–V characteristic, and the coefficient of nonlinearity of the I–V characteristic β of the diodes were investigated. More detailed information about the electrical parameters of these diodes can be found in ref. [24].

3. Results and Discussion

In this section, we first present the optical properties of the modulation-doped semiconductor structures with i-GaAs and GaAs/AlGaAs super-lattice buffer layers, which were investigated using the photoluminescence technique. Then, we compare the electrical parameters of the bow-tie diodes on the base SSB and SSLB structures: voltage sensitivity, low-field electrical resistance, asymmetry of an I–V characteristic, and coefficient of the nonlinearity of an I–V characteristic of the diodes. Statistics of the investigated parameters of bow-tie diodes are presented in

Table A1. Comparison of voltage sensitivity S of bow-tie diodes on the base of SSB and SSLB structures.

Structure	Diode	Illumination	Number of Measured Diodes	Smean, V/W	Smedian, V/W	StD, V/W	RStD, %
SSLB	SD3	ill.	11	0.39	0.42	0.10	27
		drk.	11	0.30	0.32	0.08	27
	SD2	ill.	10	0.47	0.53	0.17	37
		drk.	10	0.31	0.33	0.12	40
	SD1	ill.	10	0.66	0.66	0.22	34
		drk.	10	0.40	0.38	0.18	46
	AD3	ill.	11	0.71	0.74	0.15	20
		drk.	11	0.52	0.53	0.13	25
	AD2	ill.	11	0.80	0.74	0.26	32
		drk.	11	0.51	0.44	0.32	62
	AD1	ill.	11	1.40	1.40	0.42	30
		drk.	11	0.75	0.57	0.37	49
SSB	SD3	ill.	14	0.36	0.38	0.16	45
		drk.	14	0.24	0.25	0.14	58
	SD2	ill.	14	0.54	0.46	0.33	61
		drk.	14	0.33	0.26	0.23	69
	SD1	ill.	14	0.68	0.80	0.54	79
		drk.	14	0.47	0.51	0.34	73
	AD3	ill.	14	0.43	0.47	0.21	48
		drk.	14	0.23	0.21	0.26	113
	AD2	ill.	14	0.43	0.44	0.33	76
		drk.	14	0.19	0.19	0.28	150
	AD1	ill.	13	0.45	0.53	0.71	158
		drk.	13	0.14	0.17	0.56	388

,

Table A2. Comparison of electrical resistance R(0) of bow-tie diodes on the base of SSB and SSLB structures.

Structure	Diode	Illumination	Number of Measured Diodes	R(0)mean, kΩ	R(0)median, kΩ	StD, kΩ	StD/R(0)mean, %	Calculated R(0) kΩ	(R(0)mean- R(0)calc.)/R(0) calc., %
SSLB	SD3	ill.	10	8.41	8.39	0.16	1.9	8.42	−0
		drk.	10	10.41	10.61	0.45	4.3	9.09	15
	SD2	ill.	9	9.58	9.59	0.14	1.5	9.36	2
		drk.	9	12.00	12.00	0.32	2.7	10.10	19
	SD1	ill.	11	11.80	11.87	0.54	4.6	11.35	4
		drk.	11	14.84	15.25	1.16	7.8	12.24	21
	AD3	ill.	11	3.10	3.11	0.05	1.6	2.32	34
		drk.	11	3.80	3.82	0.1	2.6	2.52	51
	AD2	ill.	11	3.50	3.50	0.1	2.9	2.58	36
		drk.	11	4.30	4.34	0.18	4.2	2.80	54
	AD1	ill.	10	4.42	4.43	0.14	3.2	3.10	43
		drk.	10	5.48	5.49	0.26	4.7	3.34	64
SSB	SD3	ill.	14	9.9	10.30	1.26	12.7	10.92	−9
		drk.	14	15.7	16.55	2.2	14.0	11.80	33
	SD2	ill.	14	11.90	11.80	0.85	7.1	12.12	−2
		drk.	14	19.1	19.65	1.93	10.1	13.15	45
	SD1	ill.	14	13.9	14.40	1.2	8.6	14.67	−5
		drk.	14	22.8	23.70	2.6	11.4	16.03	42
	AD3	ill.	14	3.60	3.61	0.22	6.1	3.08	17
		drk.	14	5.50	5.69	0.4	7.3	3.60	53
	AD2	ill.	14	3.85	3.99	0.39	10.1	3.41	13
		drk.	14	5.72	6.09	0.86	15.0	4.03	42
	AD1	ill.	13	4.96	4.95	0.82	16.5	3.96	25
		drk.	13	7.2	7.45	1.1	15.3	4.54	59

,

Table A3. Comparison of asymmetry of I–V characteristics I–V_asym of bow-tie diodes on the base of SSB and SSLB structures.

Structure	Diode	Illumination	Number of Measured Diodes	I–Vasym-mean, arb. u.	I–Vasym-median, arb. u.	StD, arb.u.	StD/I–Vasym-mean, %
SSLB	SD3	ill.	10	−30	−20	35	117
		drk.	10	−100	−80	55	55
	SD2	ill.	9	15	20	30	200
		drk.	9	−80	−60	35	44
	SD1	ill.	11	40	60	30	75
		drk.	11	−60	−60	20	33
	AD3	ill.	11	50	50	13	26
		drk.	11	2	2	3	150
	AD2	ill.	11	60	60	10	17
		drk.	11	−20	−20	5	25
	AD1	ill.	10	100	100	7	7
		drk.	10	−20	−20	14	70
SSB	SD3	ill.	13	60	60	10	70
		drk.	14	−190	−170	80	17
	SD2	ill.	14	70	70	20	−2
		drk.	14	−230	−200	100	29
	SD1	ill.	14	70	70	40	43
		drk.	14	−350	−310	120	57
	AD3	ill.	14	70	70	5	−4
		drk.	14	30	30	3	7
	AD2	ill.	14	60	60	5	10
		drk.	14	−2	−3	4	8
	AD1	ill.	13	60	60	15	200
		drk.	12	−110	−100	30	25

and

Table A4. Comparison of nonlinearity coefficient of I–V characteristics β of bow-tie diodes on the base of SSB and SSLB structures.

Structure	Diode	Illumination	Number of Measured Diodes	β × 1012, m2/V2	StD × 1012, m2/V2	StD/β, %
SSLB	SD3	ill.	10	10.5	0.31	3
		drk.	10	9.4	0.81	9
	SD2	ill.	9	6.9	0.28	4
		drk.	9	5.72	0.38	7
	SD1	ill.	11	2.3	0.12	5
		drk.	11	3	0.16	5
	AD3	ill.	11	0.83	0.2	24
		drk.	11	0.84	0.03	4
	AD2	ill.	11	0.53	0.1	19
		drk.	11	0.5	0.031	6
	AD1	ill.	10	0.25	0.04	16
		drk.	10	0.21	0.01	5
SSB	SD3	ill.	13	12.7	0.53	4
		drk.	13	10.3	0.47	5
	SD2	ill.	14	7.77	0.28	4
		drk.	14	6.45	0.3	5
	SD1	ill.	14	3.1	0.085	3
		drk.	14	2.32	0.09	4
	AD3	ill.	14	0.68	0.2	29
		drk.	14	0.82	0.07	9
	AD2	ill.	14	0.41	0.008	2
		drk.	14	0.52	0.014	3
	AD1	ill.	13	0.19	0.022	12
		drk.	12	0.18	0.006	3

in Appendix A.

3.1. Photoluminescence of the SSB and SSLB Modulation-Doped Semiconductor Structures

Figure 3 shows the photoluminescence spectra of both structures at 4 K and room temperature. The photoluminescence from GaAs layers and Al_0.25Ga_0.75As layers can be easily distinguished in the spectra. The peak intensities are normalized relative to the intensity of GaAs excitonic peak from the SSLB sample at 4 K. At room temperature, we attribute the peaks to the recombination of electron-hole pairs (e-h) in GaAs and Al_0.25Ga_0.75As layers in both samples. Weak PL intensity from the Al_0.25Ga_0.75As layer of the SSLB sample shows that most of the photo-generated carriers leave this layer and recombine within the GaAs layer part, where the 2DEG is located. Thus, the PL line of the 1.4–1.52 eV energies exhibits much stronger intensity at room temperature. The same tendency and the structure of the PL spectrum were observed at 4 K temperature (red lines in Figure 3b). One can distinguish weak luminescence from quantum wells (QW) of the super-lattice in the buffer region within the energies of 1.53–1.55 eV. In the GaAs layer, we observe the free exciton (X) peak at 1.515 eV and the free electron—residual carbon acceptor (e-C) recombination at 1.494 eV. The photoluminescence from the Al_0.25Ga_0.75As layer can be attributed to excitonic (free or bound, X; [BX]) recombination around 1.85 eV. The shoulder at about 1.81–1.84 eV may be attributed to the transitions of the donor band or free electrons to shallow acceptor levels (marked as D-C or e-C). The lowest shoulder at about 1.76–1.81 eV may be related to the electron transitions to deep acceptor levels or defects (marked as D-A and d, respectively).

In contrast to the SSLB sample, the peak from the Al_0.25Ga_0.75As layer prevails in the PL spectrum of the SSB sample at room temperature. This fact can be explained by the dominant nonradiative recombination of electrons and holes in the 2DEG region through defects and residual impurities. The worse quality of the structure without a buffer is evidenced not only by its weaker photoluminescence at both temperatures but also by the dominance of a broad peak about 1.76–1.81 eV, which may be related to the defects and recombination from GaAs donor band to Si acceptor (D-Si).

3.2. Voltage Sensitivity of the Bow-Tie Diodes

Under the action of the microwave radiation, the polarity of the voltage detected by the bow-tie diodes, both SD and AD, corresponds to the polarity of the thermoelectric electromotive force (emf) of hot carriers with positive electrical potential induced on the left side of the diodes shown in the insets of Figure 4. This finding does not agree with the results obtained in ref. [23], when a negative potential was measured on the left side of the AD based on the SSB structure. It means that the voltage detected by the bow-tie diodes on the base of the SSB structure was not caused by the electron heating in the structure, and the detected voltage was caused by another dominant detection mechanism in the case when the metallic contacts were wider than the semiconductor mesa structure. Figure 4 represents the statistics of the voltage sensitivity $S=U_d/P$ (here $U_d$ marks the detected voltage, and $P$ is the incident microwave power). The designation d refers to the width of the bow-tie diode’s neck. One common feature of all the diodes is worth noting: illumination enhances the voltage sensitivity. According to the theory [24], the sensitivity of a microwave diode operating on the basis of the hot electron phenomena is directly proportional to the sheet resistance of a semiconductor the diode is made of. Thus, the observed illumination caused an increase in sensitivity, which contradicts the theory. The dependence of the voltage sensitivity on the diode’s neck width d qualitatively agrees with the theoretical prediction: the narrower the neck, the higher the sensitivity (Figure 4). However, this applies only to the bow-tie diodes based on SSLB structures. The voltage sensitivity of the illuminated SSB-based AD bow-tie diodes is almost independent of the neck’s width, while their sensitivity even increases with the neck’s width in the dark. A relative comparison of the voltage sensitivity values of the studied bow-tie diodes is presented in Figure 5. The sensitivity of the symmetrical bow-tie diodes is almost the same for the diodes based on SSB and SSLB structures. However, the voltage sensitivity of the asymmetric SSLB-based diodes is several times higher than that of the SSB-based diodes, and this difference is bigger with a narrower neck.

The statistics of the voltage sensitivity need to discuss the dispersion of its values. Let RStD be the ratio of the standard deviation (StD) of the measured values to the mean value expressed in percent. In the case of the bow-tie diodes based on the SSLD structure, the voltage sensitivity is dispersed by 30% under illumination, and the RStD increases by several percent when the diode is in the dark. This is true both for SD and AD bow-tie diodes independently of the width d of the diode’s neck. A completely different situation occurs in the case of bow-tie diodes based on the SSB structure. A lower scattering of the voltage sensitivity values is observed for the SD diodes and for the diodes with a wider neck. However, the percent RStD value is twice as much as that in the case of the SSLB-based structure. Even higher dispersion of the voltage sensitivity values was observed for AD bow-tie diodes based on the SSLB structure, and it was significantly higher in the dark case, 100 and 200 percent, respectively. Furthermore, the voltage sensitivity dispersion in this case increased as the neck of the AD bow-tie diode became narrower. Comparing the RStD percentage for AD diodes with 1 and 3 micrometer-wide necks, this value was 150%/50% and 390%/110%, when the diode was illuminated and in the dark, respectively.

Although the polarity of the detected voltage corresponds to the polarity of the hot electron thermo-emf, as it is foreseen by the theory [24], the review of the voltage sensitivity results allows us to state that the nature of the detected voltage still remains unclear due to two reasons: its unusual dependence on the illumination, and not classic its dependence on the design of the bow-tie diodes (diode’s geometric shape and neck’s width). The impact of the buffer layer on voltage sensitivity is pronounced in bow-tie diodes with an asymmetrical shape, with this effect being more significant for diodes in the dark. As the photoluminescence studies of the SSB and SSLB structures have shown, the main difference between them is that usage of the buffer layer with a super-lattice results in more efficient transfer of the photo-generated electrons across the barrier to the two-dimensional electron GaAs layer. Thus, in the case of the SSB structure, the substantial part of electrons, which take part in the charge transport, remains in the doped AlGaAs region, where the conditions for electron transport differ as compared to the 2DEG channel. The main difference between the electron heating phenomenon in SD and AD bow-tie diodes is the gradient values of the electric field that heats the carriers: this gradient is higher in the asymmetric diodes. It is known that electron heating depends on the electric field gradient, and under certain conditions, the so-called bi-gradient electromotive force arises in a homogeneous semiconductor material [24]. It should be noted that the buffer layer, which has an influence on the quality of the modulation-doped structure, also affects the dispersion of the measured voltage sensitivity values: it is significantly higher in the case of low-quality bow-tie diodes based on the SSB structure.

3.3. Low-Field Electrical Resistance of the Bow-Tie Diodes

The I–V characteristic of semiconductor devices is a primary source of information concerning the basic electrical parameters of the device. When dealing with a bow-tie diode, where, by definition, the nonlinearity of its I–V is caused by the charge carrier heating, the diode contacts must be as ohmic as possible. The statistical values of the low-field electrical resistance, i.e., the resistance in the I–V region of zero electrical voltage and electric field, are presented in Figure 6. The I–V characteristics of asymmetric and symmetric bow-tie diodes AD1 and SD1 based on SSB and SSLB structures under illumination and in the dark when the neck width d = 1 μm are presented in Figure A1 of Appendix B.

The significant impact of the illumination on the resistance of the bow-tie diodes is obvious when looking at the statistical diagrams in Figure 6. As the data in Table 2 show, the sheet resistance of the illuminated structures is only slightly lower than that of the “dark” ones (~1.1 times). Meanwhile, the ratio of dark/illuminated resistance values reaches 1.6 for the SSB-based SD diodes and 1.5 for the AD diodes. Concerning the SSLB-based SD and AD diodes, this ratio is the same and equals 1.25. It should be noted that the ratio of dark/illuminated resistance does not depend, within the error limits, on the width of the bow-tie diode’s neck. The stronger influence of illumination on the electrical resistance of the bow-tie diodes based on SSB structures correlates with the photoluminescence studies: the modulation-doped structure without a buffer super-lattice exhibits weaker PL response and broader PL peak.

The comparison of electrical resistance of the bow-tie diodes on the base of SSB and SSLB structures is summarized in Figure 7 as the ratio of the resistances of SSB and SSLB-based diodes. The resistance of the SSB-based bow-tie diodes is higher in any case, and the ratio is almost independent of the neck’s width d. This ratio is close to unity in the case of illuminated AD bow-tie diodes, while it overcomes the value of 1.5 in the case of SD diodes in the dark. The ratio R(0)_SSB/R(0)_SSLB for the AD diodes in the dark and the SD diodes under illumination is close to the sheet resistance ratio R_shSSB/R_shSSLB, which is independent of the illumination and equals 1.3 (it is depicted in Figure 7 by a solid red line).

The dispersion of the measured R(0) values of the bow-tie diodes is lower than that of the experimental voltage sensitivity values. The percentage RStD value of the resistance does not exceed 20 percent. The widest spreading of the resistance values was observed in the case of the SSLB-based SD diodes, while the lowest, just reaching several percent, was inherent to the SSLB-based AD diodes. The RStD values do not depend on the illumination and neck’s width of the SD bow-tie diodes on the base of both structures, while the illumination lowered the RStD value of the AD diodes, and the resistance of the AD diodes on the base of SSLB structure was more sensitive to illumination. The resistance RStD of the AD diodes on the base of both semiconductor structures decreased with an increase in the width of the neck of the bow-tie diode.

Comparison of voltage sensitivity statistical values with the low-field electrical resistance values of the bow-tie diodes (see Figure 5 and Figure 7) lets us easily see one correlation between AD bow-tie diodes on the base of SSB and SSLB structures. The voltage sensitivity of the AD diodes on the base of the SSLB structure is substantially higher than that of the diodes on the SSB structure, while the difference between the electrical resistance of these diodes is smaller than in the case of SD diodes. The greater difference between the electrical resistance of the diodes on the base of SSB and SSLB structures can be explained by comparing the experimentally measured and calculated electrical resistance values using the following formula [24]:

$$R_0=R_g+R_c={\displaystyle \frac{R_{sh}}{2\mathrm{t}\mathrm{a}\mathrm{n}\alpha }}\mathrm{l}\mathrm{n}{\displaystyle \frac{a}{d}}+{\displaystyle \frac{{\rho }_c}{d}},$$

(1)

where $R_g$ and $R_c$ stand for geometrical and parasitic contact resistance of bow-tie diode, and $\alpha , a$ are the constriction angle of the active part of the diode and the width in the widest part of the diode, respectively. A smaller difference between the experimental and calculated resistance values according to Formula (1) was observed for bow-tie diodes based on SSLB structures. Moreover, in the case of SD diodes, the experimental diode values were slightly lower than the theoretical ones, which is why we observe a higher resistance ratio for SD diodes when they are made on the base of SSB and SSLB structures (see Figure 7).

3.4. Asymmetry of I–V Characteristic of the Bow-Tie Diodes

The I–V characteristic’s asymmetry of microwave diodes whose operation is based on charge carrier heating phenomena in case of perfect ohmic contacts of the diode can be a measure of the voltage sensitivity of the diode [24]. Therefore, let us briefly review the statistical data on the asymmetry of the I–V characteristic of the studied bow-tie diodes, shown in Figure 8.

Histograms in Figure 8 show a weak correlation between the presented I–V asymmetry of the bow-tie diodes and the detected voltage measured over the ends of these diodes (see Figure 4). This is true for both types of investigated diodes on the base of SSB and SSLB structures. Only the polarity of the detected voltage of most of the illuminated bow-tie diodes randomly correlates with the sign of the asymmetry of the I–V characteristics of the diodes. The fact that, in the dark, the sign of this asymmetry of the I–V characteristics is opposite to the polarity of the thermo-emf of the hot electrons may partly explain the lower values of the voltage detected in the dark compared to the voltage detected in the light. Regarding the dispersion of I–V asymmetry values, we did not observe a correlation between the magnitude RStD of the I–V asymmetry and the width d of the bow-tie diode neck. A higher I–V asymmetry RStD was characteristic of AD bow-tie diodes, and for AD diodes based on the SSB structure, the RStD value in the dark was several times higher than the I–V asymmetry value itself.

Large variability in the experimental values of the asymmetry of I–V characteristics of the bow-tie diodes and the weak correlation with the experimental voltage sensitivity values suggest that additional factors may influence the electrical characteristics of the bow-tie diodes. This especially concerns dc electrical parameters, such as diode electrical resistance and diode I–V characteristic asymmetry. In the last section of the article, we will examine the I–V characteristic of bow-tie diodes in strong electric fields when electron heating in the electric field must be significant.

3.5. Nonlinearity Coefficient of the I–V Characteristic of the Bow-Tie Diodes

The previous two sections of the article examined the electrical properties of bow-tie diodes in low electric fields when no significant heating of electrons in the electric field occurs. The thermal emf of hot electrons is manifested in strong electric fields that heat the electrons, so in this section, we will discuss the I–V characteristics of diodes in the region of higher voltages applied to the diode. The electric field strength of several kV/cm is revealed in the 1 micrometer-wide neck of the bow-tie diode, as it was stated in [24], which is sufficient to reveal the effective electron heating in the semiconductor structure. The nonlinearity coefficient of I–V characteristics is used to estimate and evaluate the deviation of the current–voltage characteristic from a linear law due to electron scattering in the material. The nonlinearity coefficient can be expressed in terms of the quantities characterizing electron scattering [26]:

$$\beta ={\displaystyle \frac{2e{\mu }_{0}s}{3kT}},$$

(2)

where $k$ is the Boltzmann constant, $T$ notes the lattice temperature, and e and ${\mu }_0$ mark the elementary charge and low-field electron mobility, respectively. The parameter $s$ is the exponent in the dependence of electron momentum relaxation time on electron energy, and this parameter depends on the electron scattering mechanism in the material. In the case of GaAs, the nonlinearity coefficient of the I–V characteristic at room temperature is of the order of 10⁻¹² m²/V². The current density $j$ flowing through a semiconductor can be approximated using the following formula [24]:

$$j={\sigma }_0\left(1+\beta E^2\right)E.$$

(3)

Here ${\sigma }_0$ stands for the low-field electrical conductivity, and $E$ stands for the electric field strength. By following the procedure described in [24], we estimated $\beta$ for the investigated diodes. The histograms of the nonlinearity coefficient of I–V characteristics of the bow-tie diodes are presented in Figure 9. From the presented histograms, we can see that the parameter that will characterize the semiconductor material depends on the geometry of the sample: the nonlinearity coefficient of the current–voltage characteristic of a diode is higher for diodes of symmetrical configuration, and it increases as the neck of the bow-tie diode narrows. Illumination has a greater effect on bow-tie diodes based on SSB structures: the nonlinearity coefficient of the I–V characteristic of illuminated SD diodes is higher than that of diodes in the dark, while for AD diodes, on the contrary, $\beta$ decreases when they are illuminated. However, the value of the nonlinearity coefficient of the SD diodes on the base of both semiconductor structures is greater than that predicted by Equation (2), and for the AD diodes, its value is lower than theoretical. Thus, only SD1 and AD3 bow-tie diodes on the base of the SSLB structure are characterized by the I–V characteristic that meets the requirements of samples with ohmic contacts of sufficient quality. With less reliability, this can also be applied to the SD1 and AD3 diodes based on the SSB structure and to the AD2 diodes based on the SSLB structure.

Figure 10 presents the ratio of the nonlinearity coefficients $\beta$ for the bow-tie diodes on the base of SSLB and SSB structures.

The biggest difference in the $\beta$ values is seen at the neck’s width d = 1 μm, with the exception of the SD1 and SD3 diodes in the dark. Furthermore, the illuminated SD1 diodes reveal ${\beta }_{SSLB}/{\beta }_{SSB}$ < 1. The bow-tie diodes with d = 3 μm in the dark are characterized by almost the same nonlinearity coefficient of I–V characteristic, and the ratio ${\beta }_{SSLB}/{\beta }_{SSB}$, only slightly deviates from unity when the SD3 and AD3 diodes are illuminated.

The ratio of the nonlinearity coefficient of illuminated and “dark” diodes is presented in Figure 11. It is clearly seen that the ratio ${\beta }_{ill}/{\beta }_{drk}$ is close to unity and remains the same for SD and AD diodes based on SSLB structures. In the case of the bow-tie diodes on the base of the SSB structure, the nonlinearity coefficient of illuminated SD diodes is bigger than that of the diodes in the dark, while the illumination either does not change the I–V characteristic of the AD diodes (AD1 case) or makes this parameter lower (AD2 and AD3 case).

The dependence of the ${\beta }_{SD}/{\beta }_{AD}$ ratio on the width of the diode’s neck d is presented in Figure 12. The ratio ${\beta }_{SD}$/${\beta }_{AD}$ is almost 20 times higher when the bow-tie diodes based on the SSB structure are exposed to illumination and decreases slightly when the diodes are in the dark.

An ambiguous dependence of $\beta$ on the bow-tie diode’s structure and its geometry (diode’s shape and width of the neck), as well as on the illumination, leads to the conclusion that the properties of the diodes under study depend more than just on the phenomenon of electron heating by an electric field. The nonlinearity coefficient values bigger than the theoretical ones allow us to state that the current decrease in strong electric fields is caused not only by the heating-caused decrease in electron mobility but also by the decrease in electron density, which was observed in the bow-tie diodes in the case of different modulation-doped semiconductor structures [24]. This decrease in electron density is associated with electron capture by the trapping centers residing in the bulk of the AlGaAs layer, in the interface between GaAs and AlGaAs layer, or on the surface of the semiconductor mesa structure. Higher values of $\beta$ in SD diodes compared to AD diodes suggest that, in the former, electrons travel a longer path within the diode under a stronger electric field, leading to more efficient capture by trapping centers. In contrast, shorter path in AD diodes is attributed to a steeper electric field gradient. The increase in the nonlinearity coefficient as the neck of the bow-tie diode widens can also be explained by the longer exposure of the electrons in the region of a strong electric field, which makes the process of their capture more active. Stronger dependence of $\beta$ of the SSB-based bow-tie diodes (without a super-lattice) on the shape and geometric dimensions of the diode can be explained by higher density of the trapping centers in these diodes. A higher density of the trapping centers also leads to a stronger $\beta$ dependence on the illumination of the bow-tie diodes based on SSB structures.

4. Conclusions

Comparison of the optical and electrical properties of symmetrical and asymmetrical bow-tie diodes based on the modulation-doped structures having an i-GaAs buffer layer and a buffer layer containing a GaAs/AlGaAs super-lattice leads to the following conclusions:

• Photoluminescence study of the modulation-doped structures shows better quality of the semiconductor structure with a super-lattice.
• The buffer layer of the modulation-doped semiconductor structure has no influence on the voltage sensitivity of symmetrical bow-tie diodes, both in the dark and under white light illumination, and the voltage sensitivity is several times higher when the buffer layer of the asymmetric bow-tie diodes incorporates a super-lattice.
• A smaller difference between the experimental and theoretical resistance values is observed in the case of the bow-tie diodes based on a modulation-doped structure with a super-lattice.
• Large variability in the experimental values of the asymmetry of I–V characteristics and weak correlations with the experimental voltage sensitivity values suggest that additional factors are responsible for the electrical characteristics of the bow-tie diodes.
• The stronger dependence of the I–V characteristic asymmetry in bow-tie diodes, based on semiconductor structures without a super-lattice, on the diode’s shape and geometric dimensions can be attributed to the higher density of trapping centers in these diodes.
• Higher density of trapping centers in the modulation-doped structures without a super-lattice leads to stronger $\beta$ dependence on the illumination of the bow-tie diodes based on these structures.