<p>This study presents a comprehensive investigation of the composition (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Cd\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Cd</mi> </mrow> </math></EquationSource> </InlineEquation> mole fraction m, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( 0 \, &lt; \, m \, &lt; \, 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mspace width="0.166667em" /> <mo>&lt;</mo> <mspace width="0.166667em" /> <mi>m</mi> <mspace width="0.166667em" /> <mo>&lt;</mo> <mspace width="0.166667em" /> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>) and temperature-dependent (20–400&#xa0;K) optoelectronic and electrophysical properties of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p{\text{Si}}/n{\text{Cd}}_{m} {\text{Z}}_{1 - m} {\text{S}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mtext>Si</mtext> <mo stretchy="false">/</mo> <mi>n</mi> <msub> <mtext>Cd</mtext> <mi>m</mi> </msub> <msub> <mtext>Z</mtext> <mrow> <mn>1</mn> <mo>-</mo> <mi>m</mi> </mrow> </msub> <mtext>S</mtext> </mrow> </math></EquationSource> </InlineEquation> heterojunctions. A hybrid approach combining analytical modeling, numerical simulations, and experimental validation was employed to capture the effects of incomplete dopant ionization, dielectric bowing, and temperature on key device parameters. Standard doping concentrations of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(p \, = \, 1 \times 10^{16} {\text{cm}}^{ - 3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mspace width="0.166667em" /> <mo>=</mo> <mspace width="0.166667em" /> <mn>1</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>16</mn> </msup> <msup> <mrow> <mtext>cm</mtext> </mrow> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation><InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(p - {\text{Si}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>-</mo> <mtext>Si</mtext> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(n \, = \, 4 \times 10^{16} {\text{cm}}^{ - 3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mspace width="0.166667em" /> <mo>=</mo> <mspace width="0.166667em" /> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>16</mn> </msup> <msup> <mrow> <mtext>cm</mtext> </mrow> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation><InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(n{\text{Cd}}_{m} {\text{Z}}_{1 - m} {\text{S}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <msub> <mtext>Cd</mtext> <mi>m</mi> </msub> <msub> <mtext>Z</mtext> <mrow> <mn>1</mn> <mo>-</mo> <mi>m</mi> </mrow> </msub> <mtext>S</mtext> </mrow> </math></EquationSource> </InlineEquation> were used. The study quantifies temperature- and composition-dependent bandgap energy <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(Eg\left( {T,m} \right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mi>g</mi> <mfenced close=")" open="("> <mrow> <mi>T</mi> <mo>,</mo> <mi>m</mi> </mrow> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, Debye temperature <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\Theta \left( m \right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Θ</mi> <mfenced close=")" open="("> <mi>m</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, built-in electric field <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(E\left( {T,m,x} \right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mfenced close=")" open="("> <mrow> <mi>T</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>x</mi> </mrow> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, and junction capacitance. As <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\({\text{Cd}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Cd</mtext> </math></EquationSource> </InlineEquation> content increases, the bandgap of <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(n{\text{Cd}}_{m} {\text{Z}}_{1 - m} {\text{S}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <msub> <mtext>Cd</mtext> <mi>m</mi> </msub> <msub> <mtext>Z</mtext> <mrow> <mn>1</mn> <mo>-</mo> <mi>m</mi> </mrow> </msub> <mtext>S</mtext> </mrow> </math></EquationSource> </InlineEquation> decreases from ~3.6&#xa0;eV (<InlineEquation ID="IEq13"> <EquationSource Format="TEX">\({\text{ZnS}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>ZnS</mtext> </math></EquationSource> </InlineEquation>-rich) to ~2.42&#xa0;eV (<InlineEquation ID="IEq14"> <EquationSource Format="TEX">\({\text{CdS}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>CdS</mtext> </math></EquationSource> </InlineEquation>-rich), while Si maintains a thermally stable bandgap (~ 1.1–1.17&#xa0;eV), resulting in a favorable type-II band alignment (<InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(\Delta Eg \, &gt; \, 1.25\,eV\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mi>g</mi> <mspace width="0.166667em" /> <mo>&gt;</mo> <mspace width="0.166667em" /> <mn>1.25</mn> <mspace width="0.166667em" /> <mi>e</mi> <mi>V</mi> </mrow> </math></EquationSource> </InlineEquation>). The decrease in <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(\Theta \left( m \right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Θ</mi> <mfenced close=")" open="("> <mi>m</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation> enhances phonon scattering and modifies recombination behavior. The derived analytical expression for <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(E\left( {T,x} \right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mfenced close=")" open="("> <mrow> <mi>T</mi> <mo>,</mo> <mi>x</mi> </mrow> </mfenced> </mrow> </math></EquationSource> </InlineEquation> explicitly incorporates incomplete ionization, enabling prediction of space charge and electric field distribution at cryogenic temperatures. The model shows excellent agreement with experimental data, emphasizing the critical role of temperature and composition in charge transport. These results highlight the potential of <InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(p{\text{Si}}/n{\text{Cd}}_{m} {\text{Z}}_{1 - m} {\text{S}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mtext>Si</mtext> <mo stretchy="false">/</mo> <mi>n</mi> <msub> <mtext>Cd</mtext> <mi>m</mi> </msub> <msub> <mtext>Z</mtext> <mrow> <mn>1</mn> <mo>-</mo> <mi>m</mi> </mrow> </msub> <mtext>S</mtext> </mrow> </math></EquationSource> </InlineEquation> heterostructures for high-performance optoelectronic devices operating under variable thermal and vibrational conditions.</p>

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Composition-Driven Band Engineering and Temperature Effects in pSi/nCdmZn1−mS Heterojunctions

  • Jo‘shqin Shakirovich Abdullayev,
  • Jonibek Shakirovich Abdullayev,
  • Ibrokhim Bayramdurdiyevich Sapaev,
  • Jamoliddin Inotullaevich Razzokov,
  • Davron Aslonqulovich Juraev,
  • Ebrahim E. Elsayed

摘要

This study presents a comprehensive investigation of the composition ( \(Cd\) Cd mole fraction m, \( 0 \, < \, m \, < \, 1\) 0 < m < 1 ) and temperature-dependent (20–400 K) optoelectronic and electrophysical properties of \(p{\text{Si}}/n{\text{Cd}}_{m} {\text{Z}}_{1 - m} {\text{S}}\) p Si / n Cd m Z 1 - m S heterojunctions. A hybrid approach combining analytical modeling, numerical simulations, and experimental validation was employed to capture the effects of incomplete dopant ionization, dielectric bowing, and temperature on key device parameters. Standard doping concentrations of \(p \, = \, 1 \times 10^{16} {\text{cm}}^{ - 3}\) p = 1 × 10 16 cm - 3 \(p - {\text{Si}}\) p - Si and \(n \, = \, 4 \times 10^{16} {\text{cm}}^{ - 3}\) n = 4 × 10 16 cm - 3 \(n{\text{Cd}}_{m} {\text{Z}}_{1 - m} {\text{S}}\) n Cd m Z 1 - m S were used. The study quantifies temperature- and composition-dependent bandgap energy \(Eg\left( {T,m} \right)\) E g T , m , Debye temperature \(\Theta \left( m \right)\) Θ m , built-in electric field \(E\left( {T,m,x} \right)\) E T , m , x , and junction capacitance. As \({\text{Cd}}\) Cd content increases, the bandgap of \(n{\text{Cd}}_{m} {\text{Z}}_{1 - m} {\text{S}}\) n Cd m Z 1 - m S decreases from ~3.6 eV ( \({\text{ZnS}}\) ZnS -rich) to ~2.42 eV ( \({\text{CdS}}\) CdS -rich), while Si maintains a thermally stable bandgap (~ 1.1–1.17 eV), resulting in a favorable type-II band alignment ( \(\Delta Eg \, > \, 1.25\,eV\) Δ E g > 1.25 e V ). The decrease in \(\Theta \left( m \right)\) Θ m enhances phonon scattering and modifies recombination behavior. The derived analytical expression for \(E\left( {T,x} \right)\) E T , x explicitly incorporates incomplete ionization, enabling prediction of space charge and electric field distribution at cryogenic temperatures. The model shows excellent agreement with experimental data, emphasizing the critical role of temperature and composition in charge transport. These results highlight the potential of \(p{\text{Si}}/n{\text{Cd}}_{m} {\text{Z}}_{1 - m} {\text{S}}\) p Si / n Cd m Z 1 - m S heterostructures for high-performance optoelectronic devices operating under variable thermal and vibrational conditions.