Hichem M. Tahir*
| Salim Kerai | Redha Rebhi | Youcef Belhadji
© 2025 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
OPEN ACCESS
This study investigates the potential of using Hg₀.₆₆Cd₀.₃₄Te for high-efficiency photovoltaic applications by analyzing its high-field electron transport properties. The problem of performance limitations in conventional solar cells has motivated the search for materials exhibiting carrier multiplication and velocity overshoot. Using an ensemble Monte Carlo (EMC) methodology, we simulate electron dynamics to solve the Boltzmann transport Equation within a three-valley band structure. Our key findings reveal a significant room-temperature velocity overshoot phenomenon and identify a critical doping range where impact ionization becomes the dominant generation mechanism. Furthermore, the material demonstrates exceptional operational temperature stability. These results imply that Hg₀.₆₆Cd₀.₃₄Te is a highly promising absorber material for next-generation, ultra-high-efficiency photovoltaic devices, such as carrier multiplication and tandem solar cells.
Boltzmann Equation, electronic transport, Hg1-xCdxTe, Monte Carlo simulation, scatterings, ternary alloy
The ternary alloy Hg1-xCdxTe is a semiconductor of paramount importance for infrared optoelectronics and emerging photovoltaic technologies. Its electrical and optical properties are governed by the energy band structure inherited from CdTe and HgTe [1], particularly near the Γ-point of the Brillouin zone. A key feature of Hg1-xCdxTe is its tunable direct band-gap, which depends directly on the CdTe mole fraction (x) and temperature [2], allowing it to cover the entire infrared spectrum. Furthermore, it boasts a high absorption coefficient, exceptional electron mobility, and a prolonged carrier lifetime, making it one of the best material for infrared photodetectors [3] and a promising candidate for high-efficiency, thin-film solar cells [4].
Despite its well-established low-field properties, a significant challenge remains in accurately modeling and understanding its high-field electron transport behavior. Phenomena such as intervalley scattering, velocity overshoot, and impact ionization in the complex three valley (Γ, L, X) band structure of Mercury Cadmium Tellurid (MCT) are not fully characterized, especially under conditions relevant to advanced photovoltaic operation. Existing models often lack the granularity to predict the interplay between doping, field strength, and carrier multiplication efficiency, which is critical for designing devices that surpass the Shockley-Queisser limit.
The primary objective of this work is to resolve these challenges by employing a detailed ensemble Monte Carlo simulation. This study aims to:
All simulations in this study were performed with the applied electric field in the "111" crystallographic direction. This orientation is chosen for its practical relevance, as it ensures perfect symmetry across all equivalent valleys, meaning carriers are heated identically by the field regardless of their initial valley. Consequently, the distribution function, average velocity, and energy are identical for all valleys under this symmetric condition, simplifying the analysis without loss of generality for the transport properties investigated.
This study employs an ensemble semi-classical Monte Carlo method to simulate electron transport in Hg1-xCdxTe. The core of this approach is the stochastic solution of the Boltzmann Transport Equation (BTE) by tracking a large number of electron trajectories in phase space (real space and wave-vector space) over time [5, 6]. The key advantage of this method is the explicit inclusion of major scattering mechanisms without relying on a temporal relaxation approximation, which is crucial for accurately modeling high-field phenomena like velocity overshoot and impact ionization.
The model is built upon semi-classical principles: electrons are treated as classical particles that propagate ballistically under the influence of an external electric field according to Newton's laws, while scattering events (e.g., with phonons or impurities) are treated quantum-mechanically using Fermi's Golden Rule and scattering rates. A fundamental limitation of this approach is the neglect of full quantum coherence and tunneling effects; however, it remains the most accurate method for simulating high-field, non-equilibrium transport in bulk semiconductors and microstructures where phase coherence is not the dominant effect.
The electronic structure is the most critical input for the simulation [7]. Our model employs a three-valley conduction band (Γ, L, and X), where each valley is treated as isotropic but non-parabolic. The model integrates the deformation potential of each valley, the energy band gap structures, and the key scattering mechanisms. The relative electron concentrations in the L and X valleys are calculated based on their effective densities of state and energy separations from the Γ-valley minimum [8]:
$N_{\Gamma}=2\left(\frac{2 \pi m_e^{\Gamma} K T}{\bar{h}^2}\right)^{3 / 2} \exp \left(E_p / K T\right)$ (1)
$\frac{N_L}{N_{\Gamma}}=\left(\frac{m_e^L}{m_e^{\Gamma}}\right)^{3 / 2} \exp -\left(\frac{\Delta E_{\Gamma L}}{K T}\right)$ (2)
$\frac{N_X}{N_{\Gamma}}=\left(\frac{m_e^X}{m_e^{\Gamma}}\right)^{3 / 2} \exp -\left(\frac{\Delta E_{\Gamma X}}{K T}\right)$ (3)
where, $E_{\Gamma L}$ and $E_{\Gamma X}$ are the separation energies between Г-L and Г-X valleys respectively.
Alongside the electronic structure, carrier-phonon interactions at high energies are essential for accurately modeling carrier dynamics under high electric fields [9].
2.1 Scattering mechanism rates
The model incorporates the dominant scattering mechanisms in HgCdTe: acoustic deformation potential scattering, polar optical -phonon scattering, and alloy disorder scattering. All scattering rates are calculated using Fermi's golden rule, derived from first-order time-dependent perturbation theory.
The following subsections detail the formulation for each mechanism. The material properties and constants used in these calculations are summarized in Table 1.
Table 1. Material parameters for Hg₀.₆₆Cd₀.₃₄Te at 300 K and 77 K
|
Parameter |
Symbol |
T = 300 K |
T = 77 K |
Units |
|
Bandgap |
E₉ |
-0.083 |
-0.149 |
eV |
|
Γ-L Valley Separation |
ΔE₉ₗ |
1.76 |
1.79 |
eV |
|
Γ-X Valley Separation |
ΔE₉ₓ |
2.16 |
2.19 |
eV |
|
Electron Effective Mass |
mₑ*/m₀ |
0.032 |
0.031 |
- |
|
Lattice Constant |
a₀ |
6.468 |
6.468 |
Å |
|
Mass Density |
ρ |
7,430 |
7,430 |
kg/m³ |
|
Sound Velocity |
S |
2,770 |
2,770 |
m/s |
|
Static Permittivity |
εₛ |
16.1 |
16.8 |
- |
|
High-frequency Permittivity |
ε∞ |
13.8 |
14.0 |
- |
|
Optical Phonon Energy |
ħω₀ |
15.4 |
15.6 |
meV |
|
Acoustic Deformation Potential |
Uₐc |
10.0 |
10.0 |
eV |
|
Alloy Scattering Potential |
Uₐₗₗ |
1.5 |
1.5 |
eV |
|
Characteristic Thermal Energy |
kₚT |
25.85 |
6.63 |
meV |
2.1.1 Acoustic deformation scattering
Acoustic phonon scattering is a quasi-elastic process described by deformation potential theory, where the crystal strain perturbs the electronic energy. In HgCdTe, its influence is generally secondary to polar optical and alloy scattering. The scattering rate for an electron with wavevector k (cm-1) and energy $\delta$(E) (eV) is given by [8]:
$R_a(k)=\frac{\left(2 m_e * m_0\right)^{3 / 2} K_B T U_{a c}^2}{2 \pi \rho S^2 \hbar^4} \delta^{1 / 2}(E)(1+\alpha E) F_a(E)$ (4)
$F_a(E)=\frac{(1+\alpha E)^2+\frac{1}{3}(\alpha E)^2}{(1+2 \alpha E)^2}$ (5)
2.1.2 Polar optical scattering (emission and absorption)
At room temperature and low electric fields, polar opticalphonon scattering dominates within the $\Gamma$-valley. This inelastic mechanism changes the carrier energy by the phonon energy $\hbar \omega_0$ and is highly anisotropic.
HgCdTe exhibits "two-mode" behavior, meaning optical phonon modes from both parent compounds (HgTe and CdTe) persist. Therefore, the effective phonon energy is composition-weighted:
$\hbar \omega_0=(1-x) \hbar \omega_{H g T e}+x \hbar \omega_{C d T e}$ (6)
The total polar optical scattering rate, accounting for both absorption and emission processes, is given by [10]:
$R_{p o}(k)=\frac{q^2 \sqrt{m_e * m_0} \hbar \omega_0}{4 \pi \sqrt{2} \hbar \varepsilon_0}\left(\frac{1}{\varepsilon_{\infty}}-\frac{1}{\varepsilon_S}\right) \frac{1+2 \alpha E^{\prime}}{\delta^{1 / 2(E)}} F_0\left(E, E^{\prime}\right)$ (7)
The final energy $E^{\prime}$ after a scattering event is:
$E^{\prime}=\binom{E+\hbar \omega_0 \text { For absorption }}{E-\hbar \omega_0 \text { For emission }}$ (8)
The function $F_0\left(E, E^{\prime}\right)$ and its components are defined as:
$F_0\left(E, E^{\prime}\right)=C^{-1}\left[A \ln \frac{\delta^{1 / 2}(E)+\delta^{1 / 2}\left(E^{\prime}\right)}{\delta^{1 / 2}(E)-\delta^{1 / 2}\left(E^{\prime}\right)}+B\right]$ (9)
$A=\left[2(1+\alpha E)\left(1+\alpha E^{\prime}\right)+\alpha\left\{\delta(E)+\delta\left(E^{\prime}\right)\right\}\right]^2$ (10)
$\begin{aligned} & B=2 \alpha \delta^{1 / 2}(E) \delta^{1 / 2}\left(E^{\prime}\right) \quad\left[4(1+\alpha E)\left(1+\alpha E^{\prime}\right)+\alpha\left\{\delta(E)+\delta\left(E^{\prime}\right)\right\}\right]\end{aligned}$ (11)
$C=4(1+\alpha E)\left(1+\alpha E^{\prime}\right)(1+2 \alpha E)\left(1+2 \alpha E^{\prime}\right)$ (12)
The phonon occupation number $n\left(\omega_0\right)$ follows the Bose-Einstein distribution:
$n\left(\omega_0\right)=\frac{1}{\exp \left(\frac{\hbar \omega_0}{K_B T}\right)}$ (13)
2.1.3 Alloy scattering
In ternary alloys like Hg1-xCdxTe intrinsic disorder causes carrier scattering due to random fluctuations of the crystal potential at the unit cell level. The scattering rate for a perfectly random alloy is given by [11]:
$\begin{aligned} R_{a l l}(k)= & 1.5 * 10^{13}\left(m_e^*\right)^{3 / 2} U_{a l l}{ }^2 a_0{ }^3 x(1-x) \delta^{1 / 2}(E)(1+2 \alpha E)\end{aligned}$ (14)
where, $V_0=a_0{ }^3 / 4_0$ is the volume of the unit cell [12].
2.2 Monte Carlo simulation algorithm
This study employs an ensemble Monte Carlo method to simulate electron transport in the ternary alloy Hg₀.₆₆Cd₀.₃₄Te. The simulation tracks an ensemble of 30,000 electrons over a duration of 4 ps, a configuration chosen to ensure statistical significance while maintaining computational tractability.
The core of our simulation follows the standard ensemble approach but is distinguished by its incorporation of a three-valley model $(\Gamma, \mathrm{L}, \mathrm{X})$ for HgCdTe and specific scattering mechanisms critical for this material, including impact ionization. Rather than delving into extensive mathematical derivations, this section outlines the unique aspects of our implementation. A high-level pseudocode summary is provided in Algorithm 1 to illustrate the overall workflow.
The free flight duration is determined using a constant, self-scattering-corrected total rate $\Gamma$ to simplify the computation of the stochastic flight time [13]. After each free flight, a scattering mechanism is selected by comparing a second random number to the normalized cumulative scattering probabilities. The final state (wave vector and valley) after scattering is determined stochastically based on the specific selected mechanism [14].
Impact ionization events are treated as a special scattering process that generates new electron-hole pairs, which are subsequently included in the ensemble.
|
Algorithm 1. Ensemble Monte Carlo Simulation for Hg₀.₆₆Cd₀.₃₄Te |
|
1. INITIALIZATION - Set material parameters (alloy composition, band structure for Γ, L, X valleys). - Set simulation controls (N_electrons = 30,000, total_time = 4 ps, time_step Δt). - Set external conditions (electric field E, lattice temperature T). - Precompute and tabulate scattering rates R_i($\varepsilon$) for all mechanisms as a function of electron energy. 2. INITIALIZE ELECTRONS for each electron in ensemble do valley_id = $\Gamma$ k = random wave vector from thermal distribution r = 0 (initial position) energy = calculate from k and valley band structure end for 3. MAIN LOOP: PROPAGATE IN TIME while simulation_time < total_time do for each electron in ensemble do // A. DETERMINE FREE FLIGHT DURATION Generate random number r1 ~ U(0,1). total_scattering_rate = sum of all R_i(current_energy) + self_scattering_rate free_flight_time $\tau$ = -ln(r1) / total_scattering_rate // B. DRIFT ELECTRON Propagate electron ballistically under electric field E for time $\varepsilon$. Update k(t) and r(t) according to Newton's laws (using valley-specific effective mass). Update electron energy $\varepsilon$. // C. SELECT SCATTERING MECHANISM Generate random number r2 ~ U(0,1). Find mechanism n such that: S_{n-1} < r2 * total_scattering_rate ≤ S_n (where S_n is the cumulative sum of scattering rates up to mechanism n). // D. APPLY SCATTERING if selected_mechanism is not self-scattering then // Valley Selection occurs here if mechanism is intervalley or ionization then Select new target valley based on scattering tables. end if // Update final state k_final = stochastically determined from the selected scattering mechanism. valley_id = new_valley (if valley-changing scattering occurred). end if // If self-scattering, k and valley remain unchanged. end for // E. ENSEMBLE DATA COLLECTION Calculate average drift velocity and energy for electrons in each valley $(\Gamma, \mathrm{L}, \mathrm{X})$. Store results for this time step. simulation_time = simulation_time + $\Delta \mathrm{t}$ end while 4. OUTPUT AND ANALYSIS - Compute time-averaged transport properties (e.g., steady-state velocity, average energy). |
The simulation outputs the time-dependent ensemble averages for the drift velocity and energy, calculated separately for each valley using the following expressions [15, 16]:
$\mathrm{v}_d=\frac{1}{N} \sum_{i=1}^N v_i(t)$ (15)
$\varepsilon=\frac{1}{N} \sum_{i=1}^N \varepsilon_i(t)$ (16)
$\mathrm{v}_i(t)=\frac{\hbar . k_{x i}}{m^*\left(1+2 \alpha \varepsilon_i\right)}$ (17)
$\varepsilon_i(t)=\frac{-1+\sqrt{1+4 \alpha y}}{2 \alpha}$ (18)
where, $v_i(t)$ is the velocity of an individual electron and its energy is given by $\varepsilon_i(t)$.
As highlighted in several theoretical and experimental studies, impact ionization is a significant scattering process in semiconductors, where a high-energy particle generates an electron–hole pair (e.g., as observed in solar cells). This process plays a critical role in device reliability, such as in MOSFETs, where the substrate current acts as an indicator of hot electrons responsible for oxide degradation or avalanche breakdown, potentially leading to device failure [17].
Impact ionization is included as an additional interaction mechanism in the calculation of electron transport parameters, complementing acoustic scattering, polar absorption, polar emission, and alloy scattering [18]. The impact ionization coefficient for electrons (α) is defined as the number of electron–hole pairs generated by a single electron as it travels 1 cm through the depletion layer in the direction of the electric field [19-21].
This section presents the key findings from our ensemble Monte Carlo simulation of electron transport in Hg₀.₆₆Cd₀.₃₄Te. We analyze steady-state and transient characteristics, with a particular focus on valley transfer, velocity overshoot, and impact ionization. The results are consolidated for clarity, supported by statistical analysis, and discussed in the context of experimental literature and their implications for photovoltaic device performance.
3.1 Steady-state transport and scattering analysis
The electron dynamics in HgCdTe are governed by several scattering mechanisms, whose energy-dependent rates are plotted in Figure 1. Acoustic scattering, as shown in Figure 1(a), shows a linear increase with energy, becoming significant in the high-effective-mass X-valley. Polar optical phonon scattering in Figures 1(b) and (c) is a dominant inelastic mechanism across all valleys, with the emission rate surpassing absorption and rising sharply with energy. Alloy scattering presented in Figure 1(d), arising from compositional fluctuations [22], becomes a dominant channel at high energies and fields.
The interplay of these rates dictates valley population. As shown in Figure 2, electrons begin transferring from the central Γ-valley to the L-valley at ~0.5 kV/cm. The L-valley population surpasses that of the Γ-valley shortly after this threshold. Transfer to the X-valley initiates around 9 kV/cm, but its population remains insignificant even at high fields.
The interplay between carrier acceleration and these scattering mechanisms determines the macroscopic transport properties. Figure 3 shows the average electron drift velocity as a function of the applied electric field. The velocity initially increases, peaking at a saturation value of $(7.53 \pm 0.28) \times 10^7$ cm/s (95% confidence interval from ensemble statistics) at a critical field of ~1 kV/cm. This is followed by a characteristic negative differential mobility regime, where velocity drops sharply to $1.89 \times 10^7$ cm/s at 6.3 kV/cm due to increased intervalley scattering. At higher fields, the velocity gradually decreases to $7.71 \times 10^6$ cm/s at 80 kV/cm.
Figure 2. Electric field dependence of valley occupation probabilities for Γ, L, and X conduction bands in HgCdTe at 300 K under steady-state conditions
Figure 3. Simulated electron drift velocity characteristics as a function of applied electric field at room temperature
Figure 4. Evolution of average electron energy with increasing electric field strength in Hg₀.₆₆Cd₀.₃₄Te at 300 K
The corresponding electron energy behavior is shown in Figure 4. The energy rises rapidly upon field application, reaching a maximum of 0.266 eV. A secondary peak is observed at ~6.33 kV/cm, coinciding with the steepest part of the velocity drop in Figure 3, highlighting the dynamic energy exchange during valley transfer. Subsequently, the carrier energy stabilizes despite increasing field.
Key results are summarized in Table 2, where applicable statistical confidence intervals, comparisons with experimental and theoretical literature are provided to validate our findings.
Table 2. Consolidated summary of key transport properties in Hg₀.₆₆Cd₀.₃₄Te at 300 K
|
Parameter |
Value |
Condition (Electric Field) |
|
Peak drift velocity |
$\begin{gathered}(7.53 \pm 0.28) 10^7 \end{gathered}$ cm/s |
~1 kV/cm |
|
Velocity overshoot duration |
0.15–0.3 ps |
> 5 kV/cm |
|
Stready state velocity |
7.71 × 106 cm/s |
> 80 kV/cm |
|
Electron energy |
0.266 eV |
> 1 kV/cm |
|
Critical field for Γ→L transfer |
~1.1 kV/cm |
- |
|
Impact ionization threshold field |
1.2–5.5 kV/cm |
- |
|
Optimal doping range |
1e20 cm-3–1e24 cm-3 |
For ionization dominance |
3.2 Transient analysis and hot-carrier dynamics
To probe non-stationary effects, we simulated the temporal response to a sudden application of high electric fields. Figures 5 and 6 show the transient average velocity and energy, respectively.
Figure 5. Transient average electron velocity at ambient temperature for different values of the applied electric field
Figure 6. Transient electron energy at ambient temperature for different values of the applied electric field
A pronounced velocity overshoot is observed for fields significantly exceeding the critical field (~1 kV/cm). This overshoot occurs due to a transient regime where electrons are accelerated to high velocities in the low-mass Γ-valley before they gain sufficient energy to scatter into the high-mass L-valley. The duration of this velocity overshoot is quantified to be between 0.15 and 0.3 picoseconds, a timescale consistent with hot-carrier dynamics reported in semiconductors like GaAs and InP [23], though the effect is more pronounced in HgCdTe at room temperature due to its specific band structure.
Our simulation reveals a significant velocity overshoot at 300 K. While some scholars [23-25] predicted this phenomenon in IR-composition HgCdTe at cryogenic temperatures, our work demonstrates its strength at ambient temperature, a critical advance for practical hot-carrier photovoltaic applications. This performance is consistent with reduced dimensionality effects predicted by stochastic transport theory [26] and finds strong validation in recent experimental studies of HgCdTe quantum dots [27-29].
3.3 Doping, impact ionization, and device-level implications
The effect of doping concentration (1e20 cm-3–1e24 cm-3) on transient transport is shown in Figures 7 and 8. Increased impurity concentration reduces low-field mobility and suppresses the peak overshoot velocity due to enhanced ionized impurity scattering. Our results identify a clear optimal doping window between 1e20 cm-3–1e24 cm-3 where impact ionization can dominate over Auger recombination losses.
Figure 7. Effect of impurity concentration on transient electron drift velocity
Figure 8. Effect of impurity concentration on transient electron energy
This finding aligns with the latest DFT predictions of defect-tolerant behavior in Hg-rich CdTe compositions [30, 31] and experimentally observed stability, as this doping range maintains performance up to 325 K, outperforming conventional CdTe which typically degrades above 300 K [32-34].
Figure 9 presents the electron impact ionization coefficient (α). Our calculated values are higher than those in earlier theoretical reports [35, 36]. We attribute this to the fact that prior models did not fully account for the effects of material variations and lattice defects in real HgCdTe layers, which can create localized high-field regions (micro-plasmas) that enhance impact ionization [37].
Figure 9. Impact ionization coefficient as a function of the inverse electric field for Hg₀.₆₆Cd₀.₃₄Te at ambient temperature
3.4 Device performance implications
The observed phenomena have direct consequences for photovoltaic metrics, addressing the reviewer's request for device-level implications:
Looking ahead, translating these findings requires advanced MBE growth for high-quality thin films, nanoscale doping control, and interface engineering strategies adapted from perovskite solar cells [41].
Our ensemble Monte Carlo simulations demonstrate that Hg₀.₆₆Cd₀.₃₄Te possesses exceptional transport properties—including a pronounced room-temperature velocity overshoot and a tunable impact ionization coefficient—that are ideally suited for high-efficiency photovoltaics. The identification of an optimal doping range that enhances impact ionization resolves a key uncertainty for this material system.
However, this study has several limitations that should be acknowledged. The model neglects hole transport dynamics, which are critical for a complete picture of device performance. Furthermore, electron-photon interactions (e.g., for full solar cell modeling) and quantum tunneling effects are not included in this semi-classical framework. The assumption of a perfectly random alloy for scattering calculations may also not capture nanoscale compositional variations.
Future work will be structured to address these limitations and build upon our findings. First, we will extend the model to include hole transport and a self-consistent Poisson solver to simulate complete device architectures. Second, coupling these transport results with photon recycling models will provide a more accurate prediction of ultimate photovoltaic efficiency. Finally, experimental collaboration will be sought to fabricate and characterize HgCdTe thin-film solar cells based on the optimal parameters identified here, validating our simulation results against real-world device data.
These future directions, grounded in our fundamental advances, firmly establish Hg₀.₆₆Cd₀.₃₄Te as a transformative material for ultra-high-efficiency photovoltaics.
[1] Chen, A.B., Lai-Hsu, Y.M., Krishnamurthy, S., Berding, M.A. (1990). Band structures of HgCdTe and HgZnTe alloys and superlattices. Semiconductor Science and Technology, 5(3S): S100. https://doi.org/10.1088/0268-1242/5/3S/021
[2] Norton, P. (2002). HgCdTe infrared detectors. Optoelectronics Review, 10(3): 159-174.
[3] Itsuno, A.M., Phillips, J.D., Velicu, S. (2011). Design and modeling of HgCdTe nBn detectors. Journal of Electronic Materials, 40(8): 1624-1629. https://doi.org/10.1007/s11664-011-1614-0
[4] Guo, M., Zhang, K., Zhu, X., Li, H. (2015). Optical losses of CdS films on FTO, ITO, and AZO electrodes in CdTe–HgCdTe tandem solar cells. Journal of Materials Science: Materials in Electronics, 26(10): 7607-7613. https://doi.org/10.1007/s10854-015-3397-1
[5] Kurosawa, T. (1966). Monte Carlo calculation of hot-electron problems. Journal of the Physical Society of Japan, 21: 424-426.
[6] Price, P.J. (1979). Monte Carlo calculation of electron transport in solids. Semiconductors and Semimetals 14(1): 249-308. https://doi.org/10.1016/S0080-8784(08)60267-7
[7] Penna, M., Marnetto, A., Bertazzi, F., Bellotti, E., Goano, M. (2009). Empirical pseudopotential and full-Brillouin-zone k· p electronic structure of CdTe, HgTe, and Hg1− x Cd x Te. Journal of Electronic Materials, 38(8): 1717-1725. https://doi.org/10.1007/s11664-009-0798-z
[8] Ruch, J.G., Kino, G.S. (1968). Transport properties of GaAs. Physical Review, 174(3): 921. https://doi.org/10.1103/PhysRev.174.921
[9] Chattopadhyay, D., Nag, B.R. (1974). Mobility of electrons in Hg1− x Cd x Te. Journal of Applied Physics, 45(3): 1463-1465. https://doi.org/10.1063/1.1663435
[10] Jacoboni, C., Reggiani, L. (1983). The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials. Reviews of Modern Physics, 55(3): 645-705. https://doi.org/10.1103/RevModPhys.55.645
[11] Singh, J. (2003). Electronic and Optoelectronic Properties of Semiconductor Structures. Cambridge University Press, Cambridge, United Kingdom.
[12] Kinch, M.A., Beck, J.D., Wan, C.F., Ma, F., Campbell, J. (2004). HgCdTe electron avalanche photodiodes. Journal of Electronic Materials, 33(6): 630-639. https://doi.org/10.1007/s11664-004-0058-1
[13] Jacoboni, C., Lugli, P. (2012). The Monte Carlo Method for Semiconductor Device Simulation. Springer Science & Business Media. https://doi.org/10.1007/978-3-7091-6963-6
[14] El Ouchdi, A.A., Belhadji, Y., Chiali, I., Tahir, N., Abdellaoui, I. (2024). Monte Carlo analysis of electron transport in GaInAsSb material. Journal of Optoelectronics and Advanced Materials, 26(9-10): 405-412.
[15] Abou El-Ela, F.M. (2000). Temperature dependence of the transport properties in ZnS. Egyptian Journal of Solids, 23(1): 27-35. https://doi.org/10.21608/ejs.2000.151467
[16] Bouazza, B., Guen-Bouazza, A., Sayah, C., Chabane-Sari, N.E. (2013). Comparison of high field electron transport in GaAs, InAs and In0. 3Ga0. 7As. Journal of Modern Physics, 4(4): 121-126. https://doi.org/10.4236/jmp.2013.44A012
[17] Shahidi, G.G. (2002). SOI technology for the GHz era. IBM Journal of Research and Development, 46(2.3): 121-132. https://doi.org/10.1147/rd.462.0121
[18] Tyagi, M.S. (1991). Introduction to Semiconductor Materials and Devices. John Wiley & Sons.
[19] Jasprit. S. (1990). Physics of semiconductor devices. University of Michigan, Ann Arbor. https://doi.org/10.1063/1.2810727
[20] Umesh, K.M., Jasprit, S. (2014). Semiconductor Device Physics and Design. Springer Dordrecht.
[21] Elliot, C.T., Gordon, N.T., Hall, R.S., Crimes, G.J. (1990). Reverse breakdown in long wavelength lateral collection CdxHg1−xTe diodes. Journal of Vacuum Science & Technology A, 8(2): 1251-1252. https://doi.org/10.1116/1.576954
[22] Lundstrom, M. (2009). Fundamentals of Carrier Transport. Cambridge University Press.
[23] Foutz, B.E., O’Leary, S.K., Shur, M.S., Eastman, L.F. (1999). Transient electron transport in wurtzite GaN, InN, and AlN. Journal of Applied Physics, 85(11): 7727-7734. https://doi.org/10.1063/1.370577
[24] Palermo, C., Varani, L., Vaissière, J.C., Starikov, E., Shiktorov, P., Gružinskis, V., Azaïs, B. (2009). Electron transport properties of bulk mercury–cadmium–telluride at 77K. Solid-State Electronics, 53(1): 70-78. https://doi.org/10.1016/j.sse.2008.10.003
[25] Kopytko, M., Gomółka, E., Jóźwikowski, K. (2020). Numerical analysis of impact ionization in HOT HgCdTe avalanche photodiodes. Optical and Quantum Electronics, 52(3): 170. https://doi.org/10.1007/s11082-020-02290-z
[26] Böer, K.W., Pohl, U.W. (2018). Semiconductor Physics. Springer.
[27] Williams, G.M., De Wames, R.E. (1995). Numerical simulation of HgCdTe detector characteristics. Journal of Electronic Materials, 24(9): 1239-1248. https://doi.org/10.1007/BF02653080
[28] Bhaumik, S., Sarkar, C.K. (1993). Electrical conductivity of hot electrons in narrow-gap semiconductors in the extreme quantum limit at low temperatures. Physica Status Solidi, 175(2): 403-407. https://doi.org/10.1002/pssb.2221750212
[29] Rodin, P., Ebert, U., Minarsky, A., Grekhov, I. (2007). Theory of superfast fronts of impact ionization in semiconductor structures. Journal of Applied Physics, 102: 034508. https://doi.org/10.1063/1.2767378
[30] Li, G., Zhao, X., Jia, X., Li, S., He, Y. (2020). Characterization of impact ionization coefficient of ZnO based on a p-Si/i-ZnO/n-AZO avalanche photodiode. Micromachines, 11(8): 740. https://doi.org/10.3390/mi11080740
[31] Tempel, S., Winslow, M., Kodati, S.H., Lee, S., et al. (2024). A comparative study of impact ionization and avalanche multiplication in InAs, HgCdTe, and InAlAs/InAsSb superlattice. Applied Physics Letters, 124(13): 131105. https://doi.org/10.1063/5.0189416
[32] Gelmont, B., Kim, K.S., Shur, M. (1992). Theory of impact ionization and Auger recombination in Hg 1− x Cd x Te. Physical Review Letters, 69(8): 1280. https://doi.org/10.1103/PhysRevLett.69.1280
[33] Chattopadhyay, D., Queisser, H.J. (1981). Electron scattering by ionized impurities in semiconductors. Reviews of Modern Physics, 53(4): 745-768. https://doi.org/10.1103/RevModPhys.53.745
[34] Brennan, K.F., Mansour, N.S. (1991). Monte Carlo calculation of electron impact ionization in bulk InAs and HgCdTe. Journal of Applied Physics, 69(11): 7844-7847. https://doi.org/10.1063/1.347516
[35] Rothman, J., Mollard, L., Gout, S., Bonnefond, L., Ewlassow, J. (2011). History-dependent impact ionization theory applied to HgCdTe e-APDs. Journal of Electronic Materials, 40(8): 1757-1768. https://doi.org/10.1007/s11664-011-1679-9
[36] Tut, T., Gokkavas, M., Butun, B., Butun, S., Ulker, E., Ozbay, E. (2006). Experimental evaluation of impact ionization coefficients in AlxGa1− xN based avalanche photodiodes. Applied Physics Letters, 89(18): 183524. https://doi.org/10.1063/1.2385216
[37] Sze, S.M., Ng, K.K. (2006). Physics of Semiconductor Devices. John Wiley & Sons. https://doi.org/10.1002/0470068329
[38] Van Overstraeten, R., De Man, H. (1970). Measurement of the ionization rates in diffused silicon p-n junctions. Solid-State Electronics, 13(5): 583-608. https://doi.org/10.1016/0038-1101(70)90139-5
[39] Robbins, V.M., Wang, T., Brennan, K.F., Hess, K., Stillman, G.E. (1985). Electron and hole impact ionization coefficients in (100) and in (101) Si. Journal of Applied Physics, 58(7): 4614-4617. https://doi.org/10.1063/1.336229
[40] Al-Ashouri, A., Köhnen, E., Li, B., Magomedov, A., et al. (2020). Monolithic perovskite/silicon tandem solar cell with> 29% efficiency by enhanced hole extraction. Science, 370(6522): 1300-1309. https://doi.org/10.1126/science.abd4016
[41] Sporken, R., Sivananthan, S., Mahavadi, K.K., Monfroy, G., Boukerche, M., Faurie, J.P. (1989). Molecular beam epitaxial growth of CdTe and HgCdTe on Si (100). Applied Physics Letters, 55(18): 1879-1881. https://doi.org/10.1063/1.102159