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    4

    4

    4

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characteristics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.

    4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4

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    both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4electrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.4

    4

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4t

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    he4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4potential.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,420114

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure

    4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4highe

    r-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characteristics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4t

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    he4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4electrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potent

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    ial4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4the4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4potential.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,420114

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium

    4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

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    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characteristics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4

    both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4A

    lso,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4electrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:4

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    4

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4t

    he4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4potential.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,420114

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential

    4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

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    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characteristics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4t

    he4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so

    -called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4el

    ectrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

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    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4electrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium44

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,42011

    4

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characterist

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    ics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4r

    efers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4electrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers

    .4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

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    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4the4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4pote

    ntial.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,420114

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4a

    s4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

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    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characteristics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4n

    o4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4ele

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    ctrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4the4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4potential.4

    44(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,420114

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

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    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characterist

    ics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.

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    4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4electrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4the4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4potential.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,42011

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    4

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characteristics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.4

    4

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram44

    4Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

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    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4ele

    ctrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

    4.2.3.4The4built-in4potential4

    4Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4the4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4pote

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    ntial.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,420114

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characteristics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

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    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.

    4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4electrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4beh

    ind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

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    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4the4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4potential.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,42011

    4

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4as4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characterist

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    ics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4r

    efers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4no4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4electrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers

    .4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

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    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4the4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4pote

    ntial.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also410164444

    Title4Page4-4Table4of4Contents4-4Help44B.4Van4Zeghbroeck,420114

    Chapter44:4p-n4Junctions4Previous4chapterPrevious4sectionBack4to4textNext4sectionNext4chapter4

    4.2.4Structure4and4principle4of4operation4.2.1.4Structure4.2.2.4Thermal4equilibrium4.2.3.4The4built-in4potential4.2.4.4Forward4and4reverse4bias

    A4p-n4junction4consists4of4two4semiconductor4regions4with4opposite4doping4type4a

    s4shown4in4Figure44.2.1.4The4region4on4the4left4is4p-type4with4an4acceptor4density4Na,4while4the4region4on4the4right4is4n-type4with4a4donor4density4Nd.4The4dopants4are4assumed4to4be4shallow,4so4that4the4electron4(hole)4density4in4the4n-type4(p-type)4region4is4approximately4equal4to4the4donor4(acceptor)4density.44

    4

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    Figure44.2.14:4Cross-section4of4a4p-n4junction4

    We4will4assume,4unless4stated4otherwise,4that4the4doped4regions4are4uniformly4doped4and4that4the4transition4between4the4two4regions4is4abrupt.4We4will4refer4to4this4structure4as4an4abrupt4p-n4junction.44

    Frequently4we4will4deal4with4p-n4junctions4in4which4one4side4is4distinctly4higher-doped4than4the4other.4We4will4find4that4in4such4a4case4only4the4low-doped4region4needs4to4be4considered,4since4it4primarily4determines4the4device4characteristics.4We4will4refer4to4such4a4structure4as4a4one-sided4abrupt4p-n4junction.44

    The4junction4is4biased4with4a4voltage4Va4as4shown4in4Figure44.2.1.4We4will4call4the4junction4forward-biased4if4a4positive4voltage4is4applied4to4the4p-doped4region4and4reversed-biased4if4a4negative4voltage4is4applied4to4the4p-doped4region.4The4contact4to4the4p-type4region4is4also4called4the4anode,4while4the4contact4to4the4n-type4region4is4called4the4cathode,4in4reference4to4the4anions4or4positive4carriers4and4cations4or4negative4carriers4in4each4of4these4regions.4

    4.2.1.4Flatband4diagram444Next4Subsection4

    The4principle4of4operation4will4be4explained4using4a4gedanken4experiment,4an4experiment,4which4is4in4principle4possible4but4not4necessarily4executable4in4practice.4We4imagine4that4one4can4bring4both4semiconductor4regions4together,4aligning4both4the4conduction4and4valence4band4energies4of4each4region.4This4yields4the4so-called4flatband4diagram4shown4in4Figure44.2.2.44

    4

    Figure44.2.24:4Energy4band4diagram4of4a4p-n4junction4(a)4before4and4(b)4after4merging4the4n-type4and4p-type4regions4

    Note4that4this4does4not4automatically4align4the4Fermi4energies,4EF,n4and4EF,p.4Also,4note4that4this4flatband4diagram4is4not4an4equilibrium4diagram4since4both4electrons4and4holes4can4lower4their4energy4by4crossing4the4junction.4A4motion4of4electrons4and4holes4is4therefore4expected4before4thermal4equilibrium4is4obtained.4The4diagram4shown4in4Figure44.2.24(b)4is4called4a4flatband4diagram.4This4name4refers4to4the4horizontal4band4edges.4It4also4implies4that4there4is4no4field4and4n

    o4net4charge4in4the4semiconductor.4

    4.2.2.4Thermal4equilibrium44Next4Subsection4

    To4reach4thermal4equilibrium,4electrons/holes4close4to4the4metallurgical4junction4diffuse4across4the4junction4into4the4p-type/n-type4region4where4hardly4any4ele

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    ctrons/holes4are4present.4This4process4leaves4the4ionized4donors4(acceptors)4behind,4creating4a4region4around4the4junction,4which4is4depleted4of4mobile4carriers.4We4call4this4region4the4depletion4region,4extending4from4x4=4-xp4to4x4=4xn.4The4charge4due4to4the4ionized4donors4and4acceptors4causes4an4electric4field,4which4in4turn4causes4a4drift4of4carriers4in4the4opposite4direction.4The4diffusion4of4carriers4continues4until4the4drift4current4balances4the4diffusion4current,4thereby4reaching4thermal4equilibrium4as4indicated4by4a4constant4Fermi4energy.4This4situation4is4shown4in4Figure44.2.3:44

    4

    Figure44.2.34:4Energy4band4diagram4of4a4p-n4junction4in4thermal4equilibrium4

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.44

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4the4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4potential.4

    44(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also41016444

    While4in4thermal4equilibrium4no4external4voltage4is4applied4between4the4n-type4and4p-type4material,4there4is4an4internal4potential,4fi,4which4is4caused4by4the4workfunction4difference4between4the4n-type4and4p-type4semiconductors.4This4potential4equals4the4built-in4potential,4which4will4be4further4discussed4in4the4next4section.4

    4

    4.2.3.4The4built-in4potential44Next4Subsection4

    The4built-in4potential4in4a4semiconductor4equals4the4potential4across4the4depletion4region4in4thermal4equilibrium.4Since4thermal4equilibrium4implies4that4the4Fermi4energy4is4constant4throughout4the4p-n4diode,4the4built-in4potential4equals4t

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    he4difference4between4the4Fermi4energies,4EFn4and4EFp,4divided4by4the4electronic4charge.4It4also4equals4the4sum4of4the4bulk4potentials4of4each4region,4fn4and4fp,4since4the4bulk4potential4quantifies4the4distance4between4the4Fermi4energy4and4the4intrinsic4energy.4This4yields4the4following4expression4for4the4built-in4potential.44

    4(4.2.1)4

    Example44.14An4abrupt4silicon4p-n4junction4consists4of4a4p-type4region4containing424x410164cm-34acceptors4and4an4n-type4region4containing4also41016444


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