Deviations from the Ideal I-V Behavior Chapter 6 pn Junction Diodes: I-V Characteristics Deviations from the Ideal I-V Behavior Si pn-junction Diode, 300 K. Forward-bias current Reverse-bias current “Slope over” No saturation “Breakdown” Smaller slope How can we explain the deviations?

Deviations from the Ideal I-V Behavior Chapter 6 pn Junction Diodes: I-V Characteristics Deviations from the Ideal I-V Behavior Several idealized things contributed to the deviations of between ideal diode and real diode: Breakdown mechanism: Avalanching and Zener process Recombination-Generation in depletion region Effect of series resistance Effect of high-level injection

Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Voltage, VBR If the reverse bias voltage (–VA) is so large that the peak electric field exceeds a critical value ECR, then the junction will “break down” and large reverse current will flow. At breakdown, VA=–VBR Thus, the reverse bias at which breakdown occurs is

Breakdown Mechanism: Avalanching Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Mechanism: Avalanching High E-field: High energy, enabling impact ionization which causing avalanche, at doping level N < 1018 cm–3 Small E-field: ECR : critical electric field in the depletion region Low energy, causing lattice vibration and localized heating only

Breakdown Mechanism: Zener Process Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Mechanism: Zener Process Zener process is the tunneling mechanism in a reverse-biased diode. Energy barrier is higher than the kinetic energy of the particle. The particle energy remains constant during the tunneling process. Barrier must be thin  dominant breakdown mechanism when both junction sides are heavily doped. Typically, Zener process dominates when VBR < 4.5V in Si at 300 K and N > 1018 cm–3.

Empirical Observations of VBR Chapter 6 pn Junction Diodes: I-V Characteristics Empirical Observations of VBR VBR decreases with increasing N, Dominant breakdown mechanism is avalanching VBR decreases with decreasing EG. Dominant breakdown mechanism is tunneling VBR : breakdown voltage

Effect of R–G in Depletion Region Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region R–G in the depletion region contributes an additional component of diode current IR–G. The net generation rate is given by ET: trap-state energy level

Effect of R–G in Depletion Region Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region Continuing, For reverse bias, with the carrier concentrations n and p being negligible, Reverse biases with VA< – few kT/q Thermal carrier generation in the depletion layer Carriers swept by electric field and generate additional current

Effect of R–G in Depletion Region Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region Continuing, For forward bias, the carrier concentrations n and p cannot be neglected, High carrier concentrations in the depletion layer Additional carrier recombination in the region that decreases current

Effect of R–G in Depletion Region Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region Diffusion, ideal diode

Effect of Series Resistance Chapter 6 pn Junction Diodes: I-V Characteristics Effect of Series Resistance The assumption that applied voltage is dropped only across the depletion region is not fully right. Voltage drop, significant for high I

Effect of Series Resistance Chapter 6 pn Junction Diodes: I-V Characteristics Effect of Series Resistance As part of the applied voltage is wasted, a larger applied voltage is necessary to achieve the same level of current compared to the ideal. RS can be determined experimentally

Effect of High-Level Injection Chapter 6 pn Junction Diodes: I-V Characteristics Effect of High-Level Injection As VA increases and about to reach Vbi, the side of the junction which is more lightly doped will eventually reach high-level injection: (for a p+n junction) (for a pn+ junction) This means that the minority carrier concentration approaches the majority doping concentration. Then, the majority carrier concentration must increase to maintain the neutrality. This majority-carrier diffusion current reduces the diode current from the ideal.

High-Level Injection Effect Chapter 6 pn Junction Diodes: I-V Characteristics High-Level Injection Effect Significant change on both minority and majority carrier

Summary Deviations from ideal I-V Forward-bias current Chapter 6 pn Junction Diodes: I-V Characteristics Summary Deviations from ideal I-V Forward-bias current Reverse-bias current Due to high-level injection and series resistance in quasineutral regions Due to thermal generation in depletion region Due to avalanching and Zener process Due to thermal recombination in depletion region

Minority-Carrier Charge Storage Chapter 6 pn Junction Diodes: I-V Characteristics Minority-Carrier Charge Storage When VA>0, excess minority carriers are stored in the quasineutral regions of a pn junction.

Charge Control Approach Chapter 6 pn Junction Diodes: I-V Characteristics Charge Control Approach Consider a forward-biased pn junction. The total excess hole charge in the n quasineutral region is: Since the electric field E»0, Therefore (after all terms multiplied by q), The minority carrier diffusion equation is (without GL):

Charge Control Approach Chapter 6 pn Junction Diodes: I-V Characteristics Charge Control Approach Integrating over the n quasineutral region (after all terms multiplied by Adx), QP QP Furthermore, in a p+n junction, So: In steady state

Charge Control Approach Chapter 6 pn Junction Diodes: I-V Characteristics Charge Control Approach In steady state, we can calculate pn junction current in two ways: From slopes of Δnp(–xp) and Δpn(xn) From steady-state charges QN and QP stored in each “excess minority charge distribution” Therefore, Similarly,

Charge Control Approach Chapter 6 pn Junction Diodes: I-V Characteristics Charge Control Approach Moreover, in a p+n junction: In steady state

Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode Narrow-base diode: a diode where the width of the quasineutral region on the lightly doped side of the junction is on the order of or less than one diffusion length. n-side contact

Narrow-Base Diode I–V We have the following boundary conditions: Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V We have the following boundary conditions: Then, the solution is of the form: Applying the boundary conditions, we have:

Narrow-Base Diode I–V Solving for A1 and A2, and substituting back: Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V Solving for A1 and A2, and substituting back: Note that The solution can be written more compactly as

Narrow-Base Diode I–V With decrease base width, xc’0: Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V With decrease base width, xc’0: Δpn is a linear function of x due to negligible thermal R–G in region much shorter than one diffusion length  JP is constant This approximation can be derived using Taylor series approximation

Narrow-Base Diode I–V Because , then Then, for a p+n junction: Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V Because , then Then, for a p+n junction: I0’ or I0”: diode saturation current

Narrow-Base Diode I–V If xc’ << LP, Resulting Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V If xc’ << LP, Resulting Increase of reverse bias means Increase of reverse current Increase of depletion width Decrease of quasineutral region xc’=xc–xn

Back to ideal diode solution Chapter 6 pn Junction Diodes: I-V Characteristics Wide-Base Diode Rewriting the general solution for carrier excess, For the case of wide-base diode (xc’>> LP), Back to ideal diode solution

Back to ideal diode solution Chapter 6 pn Junction Diodes: I-V Characteristics Wide-Base Diode Rewriting the general solution for diffusion current, For the case of wide-base diode (xc’>> LP), Back to ideal diode solution

Chapter 6 pn Junction Diodes: I-V Characteristics Homework 7 1. (8.14) The cross-sectional area of a silicon pn junction is 10–3 cm2. The temperature of the diode is 300 K, and the doping concentrations are ND = 1016 cm–3 and NA = 8×1015 cm–3. Assume minority carrier lifetimes of τn0 = 10–6 s and τp0 = 10–7 s. Calculate the total number of excess electrons in the p region and the total number of excess holes in the n region for (a) VA = 0.3 V, (b) VA = 0.4V, and (c) VA = 0.5 V. 2. (7.2) Problem 6.11, Pierret’s “Semiconductor Device Fundamentals”. Change values of VA = 10(kT/q); NA = 1015/cm3; ND = 1018/cm3. Deadline: Monday, 7 November 2016.