1 Introduction

Numerous applications require that we retrieve information from very weak optical signals, such as those arising from radiation, medical imaging, industrial non-destructive testing (NDT), quantum technologies, astronomy, and various other routine measurements [1,2,3,4,5,6]. To observe such weak signals, it is necessary to investigate certain photodetector designs with low thresholds of sensitivity, thus making it an effective method to solve numerous fundamental science and technology, medical, safety, and space exploration-related problems. In a typical photodetector, the dark currents and the noise level restrict the possibilities of the registration of weak optical signals, since they “mask” the desired signal. Therefore, various technological innovations are used during the processing of these photodetectors to reduce the noise level. From a basic physics standpoint, the amount of the dark current significantly depends on the temperature of the semiconductor structure, since it increases with the increase in the temperature approximately by as much as the reverse current of the p–n junction in any semiconductor device. Therefore, forced cooling is sometimes used to reduce the dark current.

All other things being equal, the amount of the dark current strongly depends on the bandgap width of the semiconductor and decreases with its increase. The representative values of the dark current at room temperature for silicon photodiodes are in the order of nA [7,8,9,10]. The maximum spectral photosensitivity for the silicon photodiode is within the range of 850–1000 nm in the red and near-infrared regions and has a value of up to 0.7 A/W for Hamamatsu [11, 12] long-wavelength photodiodes. For the ultraviolet radiation (~ 200 nm), the photosensitivity decreases by a factor of ~ 6 from the maximum. In addition, the photosensitivity decreases with the increase in the wavelength, and, for wavelengths over ~ 1150 nm, the edge of the optical absorption band of the silicon decreases to zero.

The internal amplification [13, 14] of photodetectors has a relatively slow response due to the final time of the minority carrier escape in the base with the decrease in the illumination. Furthermore, when the voltage in the base changes with the change in the illumination, an additional decrease in the response occurs due to the p–n junction capacitance. In fact, the working frequency range of the phototransistors is restricted from a unity of megahertz up to a few hundred megahertz and further depends on the switching circuit [15, 16]. Thus, highly sensitive photodetectors with low thresholds are highly desired; hence, new designs and technological approaches are required to make such devices.

2 Research objectives

The opportunity to obtain highly sensitive photodetectors with low noise and dark currents has led to the creation of a structure with two oppositely directed barriers (in eV) with heights φ1 and φ2, respectively [16]. The compensation of counter photocurrents takes place within the structure. Figure 1 presents the sectional schematic of the structure with oppositely directed potential barriers and the direction of the photocurrents in an n+–p–n+ structure.

Fig. 1
figure 1

Section of the structure and the direction of the photocurrents in the n+–p–n+ photodetector

Full size image

The prototype production of the photodetector was carried out in the technological laboratories of RD Alfa Microelectronics (Riga, Latvia). The effective thickness of the epitaxial film (base) was 5.8 µm. The impurity density was ~ 1.2·1014 cm−3 in the p-base, ~ 5·1018 cm−3 in the near-surface n+ layer, and 1·1018 cm−3 in the n+-type substrate. Thus, it was possible to cover the base with the depleted regions of the oppositely directed potential barriers. The depleted regions of the barriers in the base had contact points at a distance xm (as shown in Fig. 1). The depth of the near-surface layer was 0.3 µm. The thickness of the plates with the orientation (100) and the resistivity 12.0 Ω·cm was 260 µm. An antireflection coating of ~ 50 nm thick SiO2 transmits ultraviolet (UV) radiation [17, 18]. Current-lead contacts are represented by 1 and 2, as shown in Fig. 1.

To study the spectral characteristics at the input of the monochromator, radiation was supplied from a xenon (Xe) arc lamp (in the wavelength range of 350–750 nm) and a halogen lamp (in the wavelength range of 700–1000 nm), with adjustable brightness. To obtain current–voltage measurements, we used a Keithley 6340 Sub-Femto-amp Remote Source Meter (Cleveland, Ohio, USA) with a step voltage applied to the photodetector with a step of 1 mV. The power of the radiation incident on the photodetector was measured using silicon sensors model 3A-IS with a spectral range of 350–1100 nm and a power range of 1 μW–3 W (5% error wavelength).

3 Results and discussion

In the samples under investigation, the p+ guard ring is annealed at the temperature of 950 °C for 30 min. The samples display high spectral photosensitivity with two spectral maximums (Fig. 2). The open-circuit voltage of the sample (Fig. 3, curve 1, VCV1) is about 5 mV and indicates that the calculated difference in the barrier heights (φ1–φ2 = 0.4 eV, Fig. 1) decreases after annealing.

Fig. 2
figure 2

Spectral distribution of the photosensitivity of the samples upon annealing at 950 °C at different bias voltages

Full size image
Fig. 3
figure 3

Current–voltage characteristic of the samples upon annealing at 950 °C (1) and 1000 °C (2)

Full size image

The other samples are annealed at a temperature of 1000 °C for 30 min. As a result, there is a change in the spectral photocurrent [19] sign along with the difference in the heights of the potential barriers, of about 40–50 meV, which is observed to be comparable to the calculated values. This is indicated by the open-circuit voltage (Vcv) of the sample (Fig. 3, VCV2) which corresponds to the calculated difference in the heights of the potential barriers. The observed photosensitivity, both in the short-wave and the long-wave regions, is low (~ 0.03–0.04 A/W) due to the compensation of photocurrents of the oppositely directed barriers.

In the samples annealed at 950 °C, the current photosensitivity in the short-wave region of the spectrum (Fig. 2, λ = 570 nm, Si = 4.2 A/W) is several times higher than the spectral photosensitivity in the intrinsic region of silicon (Fig. 2, λ = 850 nm, Si = 1.4A/W). The best samples of Hamamatsu photodiodes have photosensitivity of ~ 0.7 A/W in the intrinsic absorption region of silicon. Thus, the samples under this investigation have anomalously high photosensitivity in both regions of the spectrum.

The dark current–voltage characteristics (Fig. 4) show that the annealing at 950 °C preserves the sharpness of the junctions and ensures the low level of the dark currents (at the voltages up to ± 1000 mV, 10 orders of magnitude of pA (curve 1). Upon the annealing at 1000 °C, the sharpness of the junctions decreases, and the dark currents increase and get 10 orders of magnitude of nA (curve 2).

Fig. 4
figure 4

Dark current–voltage characteristics at low-temperature (950 °C, curve 1) and high-temperature (1000 °C, curve 2) annealing

Full size image

In both cases, the dark currents are higher when the reverse-biased rear barrier has a lower height (Fig. 4, curves 1, 2). The dependence of the current photosensitivity on the bias voltage (Fig. 5) shows that the samples with low-temperature annealing have photosensitivity (curve 1) that is significantly higher than the ones with high-temperature annealing (curve 2).

Fig. 5
figure 5

Dependence of the current photosensitivity on the bias voltage during the annealing at 950 °C (curve 1) and 1000 °C (curve 2)

Full size image

Thus, the samples with the guard ring annealed at 9500 C had very low dark currents and high current photosensitivity.

4 On the mechanism of high photosensitivity

It is assumed that the longitudinal absorption of the radiation takes place through the photosensitive surface according to (Fig. 1). The voltage changes at contacts 1 and 2, occur one at the expense of the other, along with changes in the widths of the depleted regions of the p–n junctions and the position of the contact point xm. As a result, the absorption is redistributed among the depleted regions. Furthermore, the n–p–n regions must be homogeneous to avoid any noise created by the inhomogeneous fields.

The difference between the structure under study and the conventional n–p structures is that the spectral distribution of the photocurrent in the former has clearly marked short-wave (560 nm) and long-wave (830 nm) maximums with unusually high photosensitivity (Fig. 2), and the long-wave maximum is in the intrinsic absorption region of silicon.

At negative bias voltages, the surface barrier is forward-biased, and the rear barrier is reverse-biased. The voltage is mainly an incident on the reverse-biased barrier. The waves are absorbed in the region of the depleted layers of both potential barriers in the relevant proportions. The generated photocarriers partially reduce the heights of both barriers and create favorable conditions for the electrons to penetrate (to get injected) from the near-surface layer into the rear layer through the base (where they significantly increase the concentration of minority carriers). Since the base and the near-surface layer are thinner than the diffusion length of the electrons, their transition can be considered to take place almost without recombination. It is, therefore, obvious that the higher the bias voltage, the greater the fraction of the charge carriers passing through the reverse biased rear barrier, and the greater the decrease in the barrier height, the greater the photocurrent (Fig. 2). Due to the relevant ratio of the impurity density in the layers, the calculated surface barrier with the height φ1 is higher than the rear barrier φ2 (Fig. 1), and the decrease in φ1 is especially noticeable when the waves are short, since most of them are absorbed in the region of the surface barrier. This can explain the increase in the spectral photocurrent in the short-wave region. With the increase in the wavelength, the compensating contribution of the photocurrent of the rear barrier increases, and the spectral photocurrent passing through the structure decreases and reaches its minimum. Then, as the waves lengthen, the rear photocurrent becomes dominant, and the long-wave maximum appears (Fig. 2). Figure 2 shows that the photosensitivity is higher with the forward-biased near-surface barrier than with the forward-biased rear barrier. This may be the result of the greater injection through the near-surface layer, where the impurity density and the absorption share radiation are higher. With the reversed polarity of the bias voltage, a similar regularity is observed, just in reverse. The photocurrent sign is determined by the photocurrent of the reverse-biased barrier. Besides, since the exponential absorption of the electromagnetic waves ensures a larger fraction of the absorption at the near-surface barrier, the photosensitivity at negative voltages (when the surface barrier is forward-biased) is higher than at positive voltages (Fig. 2).

With the neglect of the photocurrent conditioned by the background radiation and of the dark photocurrent conditioned by the thermal generation of the electron–hole pairs in the base, it can be stated that the current flowing through the structure is equal to the sum of the dark and light currents.

Under these conditions, the threshold photosensitivity is determined by the signal/noise ratio equal to one: \(\frac{I}{\sqrt{{\overline{I} }^{2}}}\equiv \frac{{S}_{i}\left(\lambda \right){P}_{\mathrm{opt}}}{\sqrt{{\overline{I} }^{2}}}=1.\) The radiation power is determined by the photon energy (\(h\upupsilon\)), the photosensitive surface (\(S)\) and the radiation intensity (\({F}_{0}\)):

$${P}_{\mathrm{opt}}=h\upupsilon *\mathrm{S}*{F}_{0}.$$
(1)

Furthermore, the RMS value of the current fluctuation is a fractional noise, which is given by,

$${{\overline{I} }^{2}}_{\mathrm{dr}}=2q{I}_{\mathrm{tot}}\Delta f.$$
(2)

The shot noise is dominant for most semiconductor devices [13]. Thus

$${P}_{\mathrm{threshold}}=\frac{{\left(2q{I}_{\mathrm{tot}}\Delta f\right)}^{1/2}}{{S}_{i}\left(\lambda \right)},$$
(3)

where \(\Delta f\) is the frequency bandpass, a \({I}_{\mathrm{tot}}={I}_{D}+{I}_{L}\) is the sum of the dark and light currents, thus,

$${S}_{i}\left(\lambda \right)={I}_{\mathrm{Ph}}/{P}_{\mathrm{opt}},$$
(4)

is the current photosensitivity of the structure, and \({P}_{\mathrm{opt}}\) is the power of the absorbed radiation.

With the help of Eq. (2), we can determine the power equivalent to the noise (NEP) of the photodetector, with the given photosensitive surface and the unit of the bandpass, by the following expression,

$${P}_{\mathrm{NEP}}=\frac{S}{{S}_{i}\left(\lambda \right)}\sqrt{\frac{{I}^{2}}{\Delta f}}.$$
(5)

Figure 6 shows the spectral dependence of the power, obtained from the experimental data, equivalent to the noise at different voltages indicated in millivolts. The photosensitive surface of the samples is 0.021 cm2. At the wavelength of 350 nm, where the photosensitivity is low, NEP has a high value.

Fig. 6
figure 6

Spectral dependence of the power equivalent to the noise at different bias voltages

Full size image

With the increase in the wavelength, the photosensitivity increases decreasing NEP. Within the wavelength range of 470–600 nm, at all bias voltages, NEP is below 2.10–12·W Hz−1/2 cm2 and reaches its minimum at the wavelength of 610 nm. This corresponds to the minimum photocurrent passing through the structure (the maximum compensation of the photocurrents of the oppositely directed potential barriers).

Furthermore, with the increase in the wavelength from 620 nm, NEP increases and gets a zigzag form, the maximums, and minimums of which (points 1–5, in Fig. 6) correspond to the minimums and maximums of the spectral photosensitivity (points 1–5, in Figs. 2, 7) within the wavelength range of 620–1000 nm.

Fig. 7
figure 7

Spectral distribution of the photosensitivity of the samples at different bias voltages

Full size image

With the help of the radiation power Popt used in the experiment and the individual monochromatic waves incident on the sample, it is possible to calculate the number of the absorbed quanta with the reflection coefficient equal to unity, by the expression:

$${F}_{0}={P}_{\mathrm{opt}}\lambda /\mathrm{1,24}.$$
(6)

A similar dependence is obtained with the help of the measured values of the photocurrents by the previously obtained expressions [19]:

$${F}_{0}=\frac{I}{qS\left(1-2{e}^{-{\alpha }_{i}{x}_{mj}}+\frac{{e}^{-{\alpha }_{i}d}}{1+{\alpha }_{i}w}\right) },$$
(7)

where \(i=1, 2 3\dots\) changes with the change in the radiation wavelength in the integral flux and \(j=1, 2 3\dots\) changes with the change in the bias voltage, \(F\left({\lambda }_{i}\right)\) is the total flux of the incident photons with the wavelength of \({\lambda }_{i}\), \({\alpha }_{i}\) is the absorption coefficient of the electromagnetic radiation, \(S\) is the photosensitive area, \(w\) is diffusion length of minority charge carriers in the n-region,where

$${F}_{0}={P}_{\mathrm{opt}}(1-R)/\mathrm{Sh\nu },$$
(8)

is the total flux of the incident photons per unit area, \({P}_{\mathrm{opt}}\) is the radiation power, \(R\) is the reflection coefficient, \(h\) is Planck's constant, \(\nu\) is the frequency of the electromagnetic radiation and \(q\) is the electron charge.

The expression for xm (Fig. 1) is determined by the previously obtained expression [19]:

$${x}_{m}=\frac{d-{x}_{0}}{2}-\frac{\varepsilon {\varepsilon }_{0}\left(\Delta \varphi -qV\right)}{{N}_{d}{q}^{2}\left(d-{x}_{0}\right)},$$
(9)

where \({N}_{d}\) is the p-type impurity density in the base, \(\varepsilon\) is the relative permittivity of the substance, \({\varepsilon }_{0}\) is the permittivity of the free space, \(q\) is the electron charge, \(V\) is the bias voltage, \({x}_{0}\) is the thickness of the near-surface layer, \(d\) is the base width, \(\Delta \varphi ={\varphi }_{b1}-{\varphi }_{b2}\) is the difference in the heights of the potential barriers.

In Eq. (9), \({x}_{m}\) changes linearly from \({x}_{0}\) up to d with the change in the bias voltage. It means that the absorbed quanta are uniformly redistributed between the depleted regions within the range of the bias voltage change according to the exponential law.

Figure 8 shows the spectral ratio of the experimental (with amplification) and calculated (without amplification) photocurrents at different bias voltages characterizing the internal amplification of the photocurrent flowing through the structure.

Fig. 8
figure 8

Spectral ratio of the experimental (with amplification) and calculated (without amplification) photocurrents at different bias voltages

Full size image

The figure shows that with the near-surface barrier being forward-biased, the higher the voltage, the higher the short-wave amplification (8·103 times) compared to the long-wave amplification (1.5·103 times) (curve 1). With the increase in the bias voltage, the region of the surface barrier gets narrower, and the region of the rear barrier expands. The redistribution of the number of absorbed quanta leads to the increase, and consequently, to the amplification of the photocurrent of the rear barrier and the decrease of the near-surface barrier (curve 2). At the reverse polarity, the rear barrier is forward-biased, and the opposite pattern is observed (curve 3).

5 Conclusion

The photoelectric properties of silicon n+–p–n+ structures with oppositely directed potential barriers are studied. The joining of the depleted regions in the base is ensured by the choice of the impurity density in the n+, p, and n+ regions. The change in the external bias voltage applied to the sample ensures the change in the widths of the barriers, one at the expense of the other, thus redistributing the fractions of the absorption of the electromagnetic waves between the barriers. Their photocurrents are oppositely directed and compensate each other, thus providing low dark currents (several tens of picoamperes) and photosensitivity thresholds (in the region of the short-wave maximum of the spectral photosensitivity that is lower than 10–12 W Hz−1/2 cm2). Under the conditions of the longitudinal illumination, the spectral distributions of the photosensitivity with short-wave (λ =  ~ 570 nm) and long-wave (λ =  ~ 850 nm) maximums are revealed. The numerical values of the photosensitivity are unusually high (up to 4 A/W). The internal amplification of the photocurrent takes place. This is explained by the injection of the photogenerated carriers through the forward-biased potential barrier, which leads to a decrease in the height of both potential barriers. The internal amplification of the photocurrent up to four orders of magnitude is indicated by the ratio of the actual measured spectral photocurrent to the photocurrent calculated at the quantum yield equal to 1.