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CritPt / Challenge_45_main / In goniopolar materials, the thermal power can be n-type in one direction and…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem description

# Problem setup: In goniopolar materials, the thermal power can be n-type in one direction and p-type in another direction. # Main problem: Consider a two-band 2D intrinsic semiconductor under temperature TT. The conduction band has a dispersion Ec=Δ/2+∑α=x,yℏ2kα22mc,αE_c= \Delta/2+\sum_{\alpha=x,y}\frac{\hbar^2k_{\alpha}^2}{2m_{c,\alpha}}, and the valence band has a dispersion Ev=−Δ/2−∑α=x,yℏ2kα22mv,αE_v= -\Delta/2-\sum_{\alpha=x,y}\frac{\hbar^2k_{\alpha}^2}{2m_{v,\alpha}}, where Δ\Delta is the size of band gap. We further assume that the relaxation time of the electrons and holes are the same. What condition should the effective mass mc/v,αm_{c/v,\alpha}, with α=x,y \alpha=x,y, satisfy to exhibit goniopolarity?
Plain-text mathematical notation (without MathML)

# Problem setup:
In goniopolar materials, the thermal power can be n-type in one direction and p-type in another direction.

# Main problem:
Consider a two-band 2D intrinsic semiconductor under temperature T. The conduction band has a dispersion E_(c)=Δ/2+∑_(α=x,y)(ℏ²k_(α)²)/(2m_(c,α)), and the valence band has a dispersion E_(v)=−Δ/2−∑_(α=x,y)(ℏ²k_(α)²)/(2m_(v,α)), where Δ is the size of band gap. We further assume that the relaxation time of the electrons and holes are the same. What condition should the effective mass m_(c/v,α), with α=x,y, satisfy to exhibit goniopolarity?
Original LaTeX notation

# Problem setup:
In goniopolar materials, the thermal power can be n-type in one direction and p-type in another direction.

# Main problem:
Consider a two-band 2D intrinsic semiconductor under temperature $T$. The conduction band has a dispersion $E_c= \Delta/2+\sum_{\alpha=x,y}\frac{\hbar^2k_{\alpha}^2}{2m_{c,\alpha}}$, and the valence band has a dispersion $E_v= -\Delta/2-\sum_{\alpha=x,y}\frac{\hbar^2k_{\alpha}^2}{2m_{v,\alpha}}$, where $\Delta$ is the size of band gap. We further assume that the relaxation time of the electrons and holes are the same. What condition should the effective mass $m_{c/v,\alpha}$, with $ \alpha=x,y$, satisfy to exhibit goniopolarity?

code template

Code

def answer(mc_x, mc_y, mv_x, mv_y):
    r"""
    Return the value of the goniopolarity condition.

    Inputs
    ----------
    mc_x, mc_y, mv_x, mv_y: float
        Effective masses $m_{c/v,\alpha}$ with $\alpha = x,y$, in unit of a typical carrier mass $m_0$ that is five times of the electron mass.

    Outputs
    ----------
    have_goniopolarity: bool
        True if the material exhibits goniopolarity, otherwise False.
    """

    # ------------------ FILL IN YOUR RESULTS BELOW ------------------
    have_goniopolarity = ...
    # ---------------------------------------------------------------

    return have_goniopolarity

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Source and history

upstream_id / Original problem ID
Challenge_45_main
task_id
4ae8b035-20b5-5082-af8a-c7b6e94a69ed
task_key
train--Challenge~5f45~5fmain
task_revision_id
4
config / split
/ train

Official source

initial import