Введение
Уравнение электротехники
The Shockley diode equation, or the diode law, named after transistor co inventor William Shockley of Bell Labs, models the exponential current–voltage (I–V) relationship of semiconductor diodes in moderate constant current forward bias or reverse bias:
where
is the diode current,
is the reverse bias saturation current (or scale current),
is the voltage across the diode,
is the thermal voltage, and
is the ideality factor, also known as the quality factor or emission coefficient. The equation is called the Shockley ideal diode equation when the ideality factor equals 1, thus is sometimes omitted. The ideality factor typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material. The ideality factor was added to account for imperfect junctions observed in real transistors, mainly due to carrier recombination as charge carriers cross the depletion region. The thermal voltage is approximately 25.852mV at At an arbitrary temperature, it is a known constant:
where
is the Boltzmann constant,
is the absolute temperature of the p–n junction, and
is the elementary charge (the magnitude of an electron's charge). The reverse saturation current is not constant for a given device, but varies with temperature; usually more significantly than , so that typically decreases as increases. Under reverse bias, the diode equation's exponential term is near 0, so the current is near the somewhat constant reverse current value (roughly a picoampere for silicon diodes or a microampere for germanium diodes, although this is obviously a function of size). For moderate forward bias voltages the exponential becomes much larger than 1, since the thermal voltage is very small in comparison. The in the diode equation is then negligible, so the forward diode current will approximate
The use of the diode equation in circuit problems is illustrated in the article on diode modeling.
Уравнение диода Шокли, или закон диода, названный в честь соизобретателя транзистора Уильяма Шокли из Bell Labs, моделирует экспоненциальную зависимость тока от напряжения (I–V) полупроводниковых диодов при умеренном постоянном прямом или обратном смещении:
The Shockley diode equation, or the diode law, named after transistor co inventor William Shockley of Bell Labs, models the exponential current–voltage (I–V) relationship of semiconductor diodes in moderate constant current forward bias or reverse bias:
where
is the diode current,
is the reverse bias saturation current (or scale current),
is the voltage across the diode,
is the thermal voltage, and
is the ideality factor, also known as the quality factor or emission coefficient. The equation is called the Shockley ideal diode equation when the ideality factor equals 1, thus is sometimes omitted. The ideality factor typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material. The ideality factor was added to account for imperfect junctions observed in real transistors, mainly due to carrier recombination as charge carriers cross the depletion region. The thermal voltage is approximately 25.852mV at At an arbitrary temperature, it is a known constant:
where
is the Boltzmann constant,
is the absolute temperature of the p–n junction, and
is the elementary charge (the magnitude of an electron's charge). The reverse saturation current is not constant for a given device, but varies with temperature; usually more significantly than , so that typically decreases as increases. Under reverse bias, the diode equation's exponential term is near 0, so the current is near the somewhat constant reverse current value (roughly a picoampere for silicon diodes or a microampere for germanium diodes, although this is obviously a function of size). For moderate forward bias voltages the exponential becomes much larger than 1, since the thermal voltage is very small in comparison. The in the diode equation is then negligible, so the forward diode current will approximate
The use of the diode equation in circuit problems is illustrated in the article on diode modeling.
где
– ток диода,
– ток насыщения обратного смещения (или масштабный ток),
– напряжение на диоде,
– тепловое напряжение, и
– фактор идеальности, также известный как фактор качества или коэффициент эмиссии. Уравнение называется идеальным уравнением диода Шокли, когда фактор идеальности равен 1, поэтому иногда опускается. Фактор идеальности обычно изменяется от 1 до 2 (хотя в некоторых случаях может быть и выше), в зависимости от технологии изготовления и материала полупроводника. Фактор идеальности был введен для учета несовершенства p–n переходов, наблюдаемых в реальных транзисторах, главным образом из-за рекомбинации носителей заряда при их прохождении через обедненную область. Тепловое напряжение приблизительно равно 25,852 мВ при Температуре. При произвольной температуре это известная постоянная:
The Shockley diode equation, or the diode law, named after transistor co inventor William Shockley of Bell Labs, models the exponential current–voltage (I–V) relationship of semiconductor diodes in moderate constant current forward bias or reverse bias:
where
is the diode current,
is the reverse bias saturation current (or scale current),
is the voltage across the diode,
is the thermal voltage, and
is the ideality factor, also known as the quality factor or emission coefficient. The equation is called the Shockley ideal diode equation when the ideality factor equals 1, thus is sometimes omitted. The ideality factor typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material. The ideality factor was added to account for imperfect junctions observed in real transistors, mainly due to carrier recombination as charge carriers cross the depletion region. The thermal voltage is approximately 25.852mV at At an arbitrary temperature, it is a known constant:
where
is the Boltzmann constant,
is the absolute temperature of the p–n junction, and
is the elementary charge (the magnitude of an electron's charge). The reverse saturation current is not constant for a given device, but varies with temperature; usually more significantly than , so that typically decreases as increases. Under reverse bias, the diode equation's exponential term is near 0, so the current is near the somewhat constant reverse current value (roughly a picoampere for silicon diodes or a microampere for germanium diodes, although this is obviously a function of size). For moderate forward bias voltages the exponential becomes much larger than 1, since the thermal voltage is very small in comparison. The in the diode equation is then negligible, so the forward diode current will approximate
The use of the diode equation in circuit problems is illustrated in the article on diode modeling.
где
– постоянная Больцмана,
– абсолютная температура p–n перехода, и
– элементарный заряд (величина заряда электрона). Обратный насыщенный ток не является постоянным для данного прибора, но изменяется с температурой; обычно более значительно, чем , поэтому обычно уменьшается с увеличением . При обратном смещении экспоненциальный член в уравнении диода близок к 0, поэтому ток близок к относительно постоянному значению обратного тока (примерно пикоампер для кремниевых диодов или микроампер для германиевых диодов, хотя это, очевидно, зависит от размера). При умеренных напряжениях прямого смещения экспонента становится намного больше 1, поскольку тепловое напряжение очень мало по сравнению с ней. в уравнении диода тогда пренебрежимо мало, поэтому прямой ток диода будет приблизительно равен
The Shockley diode equation, or the diode law, named after transistor co inventor William Shockley of Bell Labs, models the exponential current–voltage (I–V) relationship of semiconductor diodes in moderate constant current forward bias or reverse bias:
where
is the diode current,
is the reverse bias saturation current (or scale current),
is the voltage across the diode,
is the thermal voltage, and
is the ideality factor, also known as the quality factor or emission coefficient. The equation is called the Shockley ideal diode equation when the ideality factor equals 1, thus is sometimes omitted. The ideality factor typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material. The ideality factor was added to account for imperfect junctions observed in real transistors, mainly due to carrier recombination as charge carriers cross the depletion region. The thermal voltage is approximately 25.852mV at At an arbitrary temperature, it is a known constant:
where
is the Boltzmann constant,
is the absolute temperature of the p–n junction, and
is the elementary charge (the magnitude of an electron's charge). The reverse saturation current is not constant for a given device, but varies with temperature; usually more significantly than , so that typically decreases as increases. Under reverse bias, the diode equation's exponential term is near 0, so the current is near the somewhat constant reverse current value (roughly a picoampere for silicon diodes or a microampere for germanium diodes, although this is obviously a function of size). For moderate forward bias voltages the exponential becomes much larger than 1, since the thermal voltage is very small in comparison. The in the diode equation is then negligible, so the forward diode current will approximate
The use of the diode equation in circuit problems is illustrated in the article on diode modeling.
Применение уравнения диода при решении схемных задач иллюстрируется в статье о моделировании диодов.
The Shockley diode equation, or the diode law, named after transistor co inventor William Shockley of Bell Labs, models the exponential current–voltage (I–V) relationship of semiconductor diodes in moderate constant current forward bias or reverse bias:
where
is the diode current,
is the reverse bias saturation current (or scale current),
is the voltage across the diode,
is the thermal voltage, and
is the ideality factor, also known as the quality factor or emission coefficient. The equation is called the Shockley ideal diode equation when the ideality factor equals 1, thus is sometimes omitted. The ideality factor typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material. The ideality factor was added to account for imperfect junctions observed in real transistors, mainly due to carrier recombination as charge carriers cross the depletion region. The thermal voltage is approximately 25.852mV at At an arbitrary temperature, it is a known constant:
where
is the Boltzmann constant,
is the absolute temperature of the p–n junction, and
is the elementary charge (the magnitude of an electron's charge). The reverse saturation current is not constant for a given device, but varies with temperature; usually more significantly than , so that typically decreases as increases. Under reverse bias, the diode equation's exponential term is near 0, so the current is near the somewhat constant reverse current value (roughly a picoampere for silicon diodes or a microampere for germanium diodes, although this is obviously a function of size). For moderate forward bias voltages the exponential becomes much larger than 1, since the thermal voltage is very small in comparison. The in the diode equation is then negligible, so the forward diode current will approximate
The use of the diode equation in circuit problems is illustrated in the article on diode modeling.
Ограничения
Внутреннее сопротивление приводит к "выравниванию" вольт-амперной характеристики реального диода при высоком прямом смещении. Уравнение Шокли не описывает этот эффект, но его можно смоделировать, добавив последовательное сопротивление. Область обратного пробоя (особенно важная для диодов Зенера) не моделируется уравнением Шокли. Уравнение Шокли также не учитывает шум (например, тепловой шум Джонсона-Найквиста от внутреннего сопротивления или дробиновый шум). Уравнение Шокли описывает установившийся режим постоянного тока и поэтому не учитывает переходные процессы в диоде, включая влияние его внутреннего перехода и диффузионной ёмкости, а также время обратного восстановления.