Power diode I-V characteristics

Forward Biasing:

• When the anode potential is positive with respect to the cathode, the diode is forward biased and conducts.

• A conducting diode has a relatively small forward voltage drop across it, influenced by manufacturing process and junction temperature.

Reverse Biasing:

• When the cathode potential is positive with respect to the anode, the diode is reverse biased.

• Under reverse-biased conditions, a small reverse current (leakage current) flows, typically in the range of micro- or milliampere.

• The leakage current increases slowly in magnitude with reverse voltage until the avalanche or zener voltage is reached.

• For most practical purposes, a diode can be regarded as an ideal switch

• The v-i characteristics of practical diode can be expressed by an equation known as , and it is given under dc steady-state operation by \[\boxed{I_D=I_S\left(e^{V_D / n V_T}-1\right)}\] where \[\begin{aligned} I_D & = \text{current through the diode, A } \\ V_D & =\text{diode voltage with anode positive with respect to cathode,} ~ \mathrm{V} \\ I_S & = \text{leakage (or reverse saturation) current,}~ 10^{-6} - 10^{-15} \mathrm{~A} \\ n & = \text{empirical constant known as emission coefficient,}\\ & \text{ or ideality factor , value varies from 1 to 2 } \end{aligned}\]

• \(V_T\) is a constant called thermal voltage given by \[V_T=\frac{k T}{q}\] where \(q=\) electron charge: \(1.6022 \times 10^{-19}\) coulomb (C); \(T=\) absolute temperature in Kelvin \(\left(\mathrm{K}=273+{ }^{\circ} \mathrm{C}\right)\); \(k=\) Boltzmann’s constant: \(1.3806 \times 10^{-23} \mathrm{~J} / \mathrm{K}\).

• At a junction temperature of \(25^{\circ} \mathrm{C}\), \[V_T=\frac{k T}{q}=\frac{1.3806 \times 10^{-23} \times(273+25)}{1.6022 \times 10^{-19}} \approx 25.7 \mathrm{mV}\]

• At a specified temperature, the leakage current \(I_S\) is a constant for a given diode.

• The diode characteristic a can be divided into three regions:

  • Forward-biased region \(\Rightarrow V_D>0\)

  • Reverse-biased region \(\Rightarrow V_D<0\)

  • Breakdown region \(\Rightarrow V_D<-V_{B R}\)

Forward-biased region:

• In the forward-biased region, \(V_D > 0\).

• The diode current \(I_D\) is very small if the diode voltage \(V_D\) is less than a specific value \(V_{TD}\) (typically \(0.7 \mathrm{~V}\)).

• The diode conducts fully if \(V_D\) is higher than this value \(V_{TD}\), known as the threshold voltage, cut-in voltage, or turn-on voltage.

• Thus, the threshold voltage is a voltage at which the diode conducts fully.

• Let’s consider \(V_D = 0.1 \mathrm{~V}\), \(n = 1\), and \(V_T = 25.7 \mathrm{mV}\).

• The corresponding diode current \(I_D\) as: \[I_D = I_S \left(e^{V_D / n V_T} - 1\right) = I_S \left[e^{0.1 / (1 \times 0.0257)} - 1\right] = I_S(48.96 - 1) = 47.96 I_S\]

• Approximately \(I_D \approx I_S e^{V_D / n V_T} = 48.96 I_S\), with an error of \(2.1\%\).

• As \(V_D\) increases, the error decreases rapidly.

• For \(V_D > 0.1 \mathrm{~V}\), usually the case, \(I_D \gg I_S\).

• Diode current equation can be approximated within \(2.1\%\) error to: \[I_D = I_S \left(e^{V_D / n V_T} - 1\right) \approx I_S e^{V_D / n V_T}\]

Reverse-biased region:

• In the reverse-biased region, \(V_D < 0\).

• If \(V_D\) is negative and \(\left|V_D\right| \gg V_T\), which happens for \(V_D < -0.1 \mathrm{~V}\).

• The exponential term in the diode current equation becomes negligibly small compared to unity. Then, \[I_D = I_S \left(e^{-\left|V_D\right| / n V_T} - 1\right) \approx -I_S\]

• This indicates that \(I_D\) in the reverse direction is constant and equals \(I_S\).

Breakdown region:

• The reverse voltage is typically high, often exceeding 1000 V in magnitude.

• The reverse voltage may surpass a specified voltage known as the breakdown voltage \(V_{\text{BR}}\).

• A small change in reverse voltage beyond \(V_{\text{BR}}\) results in a rapid increase in reverse current.

• Operation in the breakdown region is non-destructive if the power dissipation remains within a "safe level," as specified in the manufacturer’s data sheet.

• However, it’s often necessary to limit the reverse current in the breakdown region to keep the power dissipation within a permissible value.

Reverse Recovery Characteristics:

• Diode reverse recovery refers to its behavior when transitioning from conducting to blocking state after switching from forward to reverse bias.

• During regular operation, a diode conducts in forward bias and blocks in reverse bias.

• However, there’s a brief reverse conduction period when switching abruptly from forward to reverse bias, known as reverse recovery.

• Reverse recovery is primarily determined by the time needed to remove stored charge carriers in the diode’s depletion region, called reverse recovery time (trr).

• During this time, the diode conducts in reverse direction, causing a temporary reverse current.

• Reverse recovery time includes three components:

  • trr: Time to remove stored charge carriers from the depletion region, crucial for switching speed.

  • Qrr: Total charge flowing during reverse recovery, representing stored charge from forward conduction.

  • Irr: Peak reverse current during recovery, occurring when stored charge carriers are rapidly depleted.

• Manufacturers specify these characteristics in datasheets for applications like power supplies and converters to minimize power loss and enhance efficiency.

• At time \(t_2\):

  • Current becomes negative and excess charges are removed.

  • Junction becomes reverse-biased and rapidly adopts the applied negative voltage.

  • Equilibrium charge distribution of a non-biased junction is reached.

• From \(t_2\) to \(t_3\):

  • Charge distribution approaches that of a reverse-biased junction.

• Diode behavior:

  • Begins to withstand the reverse voltage.

  • Diode current drops rapidly to zero.

  • Practical diode: Current reversal delayed due to parasitic inductance.

    • Reduction rate determined by lead inductance.

• \(t_{rr}\) (reverse recovery time):

  • Time taken for current to reverse.

  • Crucial parameter in switching applications.

• Interval between \(t_1\) and \(t_2\):

  • Sometimes termed as storage time.

• The reverse recovery time is calculated as: \[\begin{aligned} t_{rr} & = t_a+t_b \\ t_{rr} & = \sqrt{\dfrac{Q_{rr}}{(di/dt)}} \quad \text{If}~t_b << t_a \\ I_{rr} & = \sqrt{\dfrac{di}{dt}2Q_{rr}} \end{aligned}\]

Problem:

• The reverse recovery time of a diode is \(t_{rr}=3~\mathrm{\mu s}\) and the rate of fall of the diode current is \(di/dt=30~\mathrm{A/\mu s}\). Determine

  1. the storage charge \(Q_{RR}\),

  2. the peak reverse current \(I_{RR}\).

\[\begin{aligned} \text{Given data :}~t_{rr}&=3~\mu s \qquad di/dt=30~\mathrm{A/\mu s}\\ Q_{RR} &=\frac{1}{2}\frac{di}{dt}t_{rr}^{2}=0.5\times30\mathrm{A}/\mu s\times(3\times10^{-6})^{2}\\ &=135\mu\mathrm{C}\\ I_{RR}&=\sqrt{2Q_{RR}\frac{di}{dt}}=\sqrt{2\times135\times10^{-6}\times30\times10^6}\\ &=90\text{A} \end{aligned}\]