Carrier Transport in Semiconductors: Understanding Diffusion Current and Drift Current, Exams of Physics of semiconductor devices

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Module 2

Carrier Transport in Semiconductors

• Current Flow Mechanisms
• Diffusion Current
• Drift Current
• Mobility of Carriers
• Current Density equation
• Continuity Equation

Diffusion of Carriers

• When excess carriers are created in a semiconductor and their concentrations vary with position, then there is a net carrier motion from regions of higher concentration to regions of lower concentration.
• This type of motion is called the diffusion , and it is an important charge transport mechanism in semiconductors.
• Diffusion and drift are the two main current transport mechanisms. Diffusion processes - Natural result of the random motion of individual electrons. - Electrons move randomly and experience collisions, on the average, after each mean free time. - Since the motion is truly random, an electron has equal probability of moving into or out of a volume through a boundary. Current Flow Mechanisms

Spreading of a pulse of electrons by diffusion

 A pulse of excess electrons injected at x = 0 at t = 0  It will spread out in time due to diffusion  Eventually n(x) becomes a constant, when no more net motion takes place. n(x)  Electron concentration in x-direction

An arbitrary electron concentration gradient in one dimension

(x-direction)

Division of n(x) into segments of length 𝒍ҧ (Mean free path) Consider any arbitrary distribution n(x)  Where x divided into 𝑙 segments (mean free path) wide  n(x) evaluated at center of each segment. Expanded view of two of the segments centered at x 0  In 𝑡 , half of the electrons in segment 1 (left of x 0 )  segment 2 (right of x 0 )   Net number of electrons moving from segment (1) to segment (2) through x 0 within a mean free time, tҧ)

(𝐧𝟏 − 𝐧𝟐) 𝒍ҧ A/2 (A is area  to x)

Similarly, holes diffuse from a region of higher concentration to a region of lower concentration with a diffusion coefficient DP Thus, Electron Flux Density Hole Flux Density Diffusion Current Density Note: electrons and holes move together in a carrier gradient, however, the resulting currents are in opposite directions because of the opposite charges of the particles.

The Haynes-Shockley Experiment

Drift and diffusion of a hole pulse in an n-type bar Sample Geometry Position and shape of the pulse for several times during its drift down the bar

• Determines the minority carrier mobility and diffusion coefficient (Counterpart of the Hall effect experiment)
• A pulse of excess holes carriers is created by a light flash at x = 0 in an n-type semiconductor bar with an electric field E. As time progresses, the holes spread out by diffusion and move due to the electric field, and their motion is monitored somewhere down the bar

• Peak values of the pulse  p decreases and the pulse spreads in  x directions with time.  Peak value of the pulse at t = td   At x =  x/2, Peak value decreases by 1/e of its Therefore, Since x cannot be measured directly, from t, the spread of the pulse seen in oscilloscope

 x =  t.vd =  t. L/td

Calculation of Dp from the shape of

the  p distribution after time td. 𝐞 −𝟏 𝛅𝐩ෝ = ෡𝛅𝐩𝐞 −(𝐱/𝟐) 𝟐 /𝟒𝐃𝐩𝐭𝐝

𝟐

Activity

1. Video on drift diffusion based simulation https://nanohub.org/resources/21156/download/11_27_10_Mehrotra_DriftDiffus ion_Demo_810x608.mp