Some Aspects of Hot Carrier Photocurrent across GaAs p-n Junction
, Oleksandr Masalskyi 2,*, Ihor Zharchenko 1,2, Algirdas Sužiedėlis 1 and Jonas Gradauskas 1,2Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis work reports some behaviors of hot carrier around a GaAs pn junction. Although it refers to an interesting topic in the field of photovoltaics, this paper lacks some necessary descriptions regarding definition, phenomena and calculation, which makes it hard to read and the conclusions drawn uncertain. My questions are as follows.
1) Regarding Fig. 1b, why only the hot electrons generated at the n-type side of the GaAs p-n junction are considered? Should both sides of p-type and n-type have hot electrons generated?
2) Regarding Fig.2a, what is the generation current? how is it formed?
3) What is the physical meaning of deltaTc as defined in Eq.3? Why can it reflect how strong the carrier heating is as claimed by the authors?
4) What is the significance of the results of this work in improving the performance of solar cell?
Comments on the Quality of English LanguageEnglish writing needs to be improved.
Author Response
Reviewer 1
We thank the Reviewer for the comments and questions which encourage us to improve the manuscript with the aim to more clearly express information that we – along with the Reviewer – reckon as “crucial” for the understanding of the physics of the reported findings. Please find below our answers to the given questions.
- Regarding Fig. 1b, why only the hot electrons generated at the n-type side of the GaAs p-n junction are considered? Should both sides of p-type and n-type have hot electrons generated?
Answ.: Yes, you are right. The process is identical in both sides of a p-n junction: under the illumination, hot electrons are generated on both sides of p-n junction. The HC photocurrent is formed by the hot electron flow from the n- to the p-side because hot electrons generated on the n-side distribute their extra energy to the free electrons, and the whole ‘hot electron ensemble’ tends to diffuse to the other side of the junction. In contrast, hot electrons generated on the p-side are the minority carriers and cannot influence on the HC photocurrent. In Fig.1b, we presented schematic view of formation of generation (blue) and HC (red) photocurrent across the p-n junction. To avoid overloading of the picture with plenty of details, the similar processes considering hot hole effects are omitted in Fig. 1b. Furthermore the heating of holes by light is negligible in GaAs in comparison with electron heating because of difference in their mass (see P.Supancic et al. Transport analysis of the thermalization and energy relaxation of photoexcited hot electrons in Ge-doped GaAs, Phys. Rev. B V.53,N 12, 1996,p.7785-7791; https://doi.org/10.1103/PhysRevB.53.7785).
The caption of the figure refers to hot electrons (2 – free electron heating, 3 – generation of hot electron and hole pair). A clarifying sentence is added there.
- Regarding Fig.2a, what is the generation current? how is it formed?
Answ.: Formation of the generation current is illustrated by blue arrows in Fig. 1b: photon generates electron and hole pair, and the carriers are separated by the built-in electric field of the p-n junction. Since direction of the light-induced generation current is opposite to the direction of forward current across a p-n diode, the net current in this case equals “dark current minus generation current”. That is why the I-Vgen is down-shifted with respect to the I-Vdark.
- What is the physical meaning of deltaTc as defined in Eq.3? Why can it reflect how strong the carrier heating is as claimed by the authors?
Answ.: When there is no excitation, the temperatures of the carriers and the lattice are equal: TC = T. However, these are not equal in case of carrier heating: TC > T. Thus, DTC in Eq.4 (not 3 – it was a misprint) means the difference between the hot carrier temperature TC and lattice temperature T: DTC = TC – T.
How does DTC reflects carrier heating? As Figs. 2a and 3 show, carrier heating causes upward shift of the current-voltage characteristic (process opposite to the generation one described above). The stronger the carrier heating, the stronger the hot carrier current, the higher is the shift. Higher shift is followed by bigger difference in voltage values, and, according to Eq. 4, higher value of DTC. Corresponding explanation is added to the manuscript.
- What is the significance of the results of this work in improving the performance of solar cell?
Answ.: A paragraph is added at the end of the conclusions.
Comments on the Quality of English Language English writing needs to be improved.
The English language of the manuscript was checked by US doctor of technical sciences Romanas Sedlickas, and, accordingly, necessary corrections were made.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript presents an investigation of the hot-carrier photocurrent in a GaAs p-n junction as a continuation of the authors' previous work. The use of the temperature coefficient to estimate the carrier temperature is interesting. The work is significant, well focused and writen, but the results present some flaws.
All the magnitudes need to be clearly defined, for instance TC (equation 3), the bias voltage (line 152) and EF (equation 6).
Also, how curves in Figure 2.a and b are obtained is not clear enough. Authors should specify how they calculate the values determining I-Vhc and I-Vgen characteristics, as well as why generation tends to be negligible for voltages higher than 0.9 V.
The most important parameter for discussion, i.e. the temperature coefficient of the voltage, must be better explained. Why 42.7 mA/cm2 is taken for comparison (Figure 3 and equation 3)? Which is the temperature-coefficient theoretical expression? How is the obtained value of -2.14 mV/K as compared to the literature (I can not see any mention to -2.0 mV/K in ref. 54, as stated in line 158).
Also, the "displacement" and "recombination" characters need a more complete description, and some detailed explanation to support the conclusion in lines 200-202.
Similarly, why is 2.67 mA current taken as a reference in line 204? It has not been mentioned before.
The manuscript does not clarify how curves if Figure 4 have been obtained (how can each curve depend on both T and TC) and the meaning of the green one (TC=990 K).
Bibliography is in general too complete (not necessary to provide 22 references without comments in line 62!), old (many of the cited papers are from 2000 or before) and difficult to reach (many of the cited papers have no doi or belong to conferences).
In summary, conclusions are not well supported by results in the present manuscript nor by the literature.
Author Response
Reviewer 2
We thank the Reviewer for the comments and questions which encourage us to improve the manuscript with the aim to more clearly express information that we – along with the Reviewer – reckon as “crucial” for the understanding of the physics of the reported findings. Please find below our answers to the given questions and suggestions.
All the magnitudes need to be clearly defined, for instance TC (equation 3), the bias voltage (line 152) and EF (equation 6).
Answ.: Corrected.
Also, how curves in Figure 2.a and b are obtained is not clear enough. Authors should specify how they calculate the values determining I-Vhc and I-Vgen characteristics, as well as why generation tends to be negligible for voltages higher than 0.9 V.
Answ.: Since direction of the light-induced generation current is opposite to the direction of forward current across a p-n diode, the net current equals “dark current minus generation current”. That is why the I-Vgen is down-shifted with respect to the I-Vdark. Similar characteristics are typical of photodiodes and solar cells: the higher the light intensity, the larger the shift. Direction of the hot carrier photocurrent is opposite to that of the generation current (see Fig. 1b). Therefore, in the case of carrier heating, the net current equals “dark current plus HC current”. That is why the I-Vhc is up-shifted with respect to the I-Vdark. The values of “generation current” and “HC current” were obtained from the oscilloscope traces by taking absolute peak values of corresponding photocurrent subpulses: slow positive subpulse stands for generation, and fast negative subpulse represents carrier heating (see inset in Fig. 2a).
Fig. 2b displays “pure” hot carrier photocurrent without addition of the dark current value.
Concerning the dependence of the generation current on voltage, it is again typical of photodiodes and solar cells: the higher the forward bias, the lower the potential barrier height of the p-n junction. This leads to narrower depleted region and weaker internal electric field separating the electron-hole pairs, what finally results in weaker generation-caused photocurrent.
The most important parameter for discussion, i.e. the temperature coefficient of the voltage, must be better explained. Why 42.7 mA/cm2 is taken for comparison (Figure 3 and equation 3)?
Answ.: In this search of carrier temperature, two currents having the same magnitude were employed, the HC photocurrent and the dark current. 42.7 mA/cm2 of HC photocurrent density corresponds to the ‘knee’ voltage of 0.7 V. As described below, when this voltage is exceeded, the HC photocurrent gains the recombination nature. The same nature of 42.7 mA/cm2-strong dark current is assumed also.
Furthermore, the dark current is still negligible as compared to the HC photocurrent at 0.7 V (Fig. 3), and the I-Vhc at this voltage point is composed purely of the HC current directly related to the carrier temperature (formation of I-Vs is described above).
Explanation is added in the text above Eq. 4.
Which is the temperature-coefficient theoretical expression?
Answ.: The temperature coefficient is expressed by Eq. 2: it keeps information about how big is the I-V shit on the voltage scale as the temperature of a diode changes.
How is the obtained value of -2.14 mV/K as compared to the literature (I can not see any mention to -2.0 mV/K in ref. 54, as stated in line 158).
Answ.: Corrections are made in the text below Eq. 3; two references are added.
Also, the "displacement" and "recombination" characters need a more complete description, and some detailed explanation to support the conclusion in lines 200-202.
Answ.: Added to the text: “The displacement HC photocurrent is analogous to the AC current across a capacitor; it is present only in case of pulsed carrier heating and resulting recharging of the junction.” (Line 142)
Added to the text: “Therefore, when the ‘knee’ voltage is exceeded, the hot carrier photocurrent changes its nature from a displacement character to a recombination character. Such change indicates that the carriers still do not manage to overcome the barrier, but now the heated electrons and holes meet each other in the depleted region and recombine thus forming the recombination current.” (Line 200)
Similar HC-caused displacement current was also observed across a MOS structure (https://doi.org/10.3390/app11167211).
Similarly, why is 2.67 mA current taken as a reference in line 204? It has not been mentioned before.
Answ.: Misprint coming from the older version of the manuscript. Should be the mentioned 42.7 mA/cm2. Corrected.
The manuscript does not clarify how curves if Figure 4 have been obtained (how can each curve depend on both T and TC) and the meaning of the green one (TC=990 K).
Answ.: The curves in Fig. 4 are calculated using Eq. 6. Here, the first term, i.e., the density of states, depends on the lattice temperature. Therefore, in all three cases (blue, red and green) this term uses T = 300 K. Another term of the equation, the Fermi–Dirac probability function, depends on the carrier temperature TC. Therefore, the second term uses the value of TC equal to 300 K (no excitation, blue area), 454 K (our case, red area), and 990 K (imaginary case, green line). Corresponding corrections are made in the text and in Eq. 6.
Concerning philosophy of calculating TC = 990 K. As statistics shows, at TC = 454 K under our experimental excitation conditions, only 10–4 % of all free electrons have energy higher than the ”knee-bias”-lowered potential barrier of the junction (its height is 1.31 eV – 0.7 eV = 0.61 eV). Then, if no bias is applied, naturally, the potential barrier will be higher. To achieve the same current across the unbiased 1.31 eV-high barrier, we need higher energy electrons, i.e. carriers with higher value of TC, which now should be 990 K.
Bibliography is in general too complete (not necessary to provide 22 references without comments in line 62!), old (many of the cited papers are from 2000 or before) and difficult to reach (many of the cited papers have no doi or belong to conferences).
Answ.: Bibliography is revised, dispensable references removed. Unfortunately, some references are old enough and have no doi or even English version.
In summary, conclusions are not well supported by results in the present manuscript nor by the literature.
Answ.: The conclusions are corrected according to improved discussion of results.
Thank you.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have answered my questions and concerns seriously. I suggest its publication.
